Computational requirements for a discrete Kalman filter.
NASA Technical Reports Server (NTRS)
Mendel, J. M.
1971-01-01
Computational requirements - i.e., computing time per cycle (iteration) and required storage - which determine minimum sampling rates and computer memory size, were obtained as functions of the dimensions of the important system matrices for a discrete Kalman filter. Two types of measurement processing are discussed: simultaneous and sequential. It is shown that it is often better to process statistically independent measurements in more than one batch and then use sequential processing than to process them together via simultaneous processing.
Two-Dimensional Systolic Array For Kalman-Filter Computing
NASA Technical Reports Server (NTRS)
Chang, Jaw John; Yeh, Hen-Geul
1988-01-01
Two-dimensional, systolic-array, parallel data processor performs Kalman filtering in real time. Algorithm rearranged to be Faddeev algorithm for generalized signal processing. Algorithm mapped onto very-large-scale integrated-circuit (VLSI) chip in two-dimensional, regular, simple, expandable array of concurrent processing cells. Processor does matrix/vector-based algebraic computations. Applications include adaptive control of robots, remote manipulators and flexible structures and processing radar signals to track targets.
NASA Technical Reports Server (NTRS)
Skliar, M.; Ramirez, W. F.
1997-01-01
For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.
Requirements for Kalman filtering on the GE-701 whole word computer
NASA Technical Reports Server (NTRS)
Pines, S.; Schmidt, S. F.
1978-01-01
The results of a study to determine scaling, storage, and word length requirements for programming the Kalman filter on the GE-701 Whole Word Computer are reported. Simulation tests are presented which indicate that the Kalman filter, using a square root formulation with process noise added, utilizing MLS, radar altimeters, and airspeed as navigation aids, may be programmed for the GE-701 computer to successfully navigate and control the Boeing B737-100 during landing approach, landing rollout, and turnoff. The report contains flow charts, equations, computer storage, scaling, and word length recommendations for the Kalman filter on the GE-701 Whole Word computer.
Systolic VLSI for Kalman filters
NASA Technical Reports Server (NTRS)
Yeh, H.-G.; Chang, J. J.
1986-01-01
A novel two-dimensional parallel computing method for real-time Kalman filtering is presented. The mathematical formulation of a Kalman filter algorithm is rearranged to be the type of Faddeev algorithm for generalizing signal processing. The data flow mapping from the Faddeev algorithm to a two-dimensional concurrent computing structure is developed. The architecture of the resulting processor cells is regular, simple, expandable, and therefore naturally suitable for VLSI chip implementation. The computing methodology and the two-dimensional systolic arrays are useful for Kalman filter applications as well as other matrix/vector based algebraic computations.
Generic Kalman Filter Software
NASA Technical Reports Server (NTRS)
Lisano, Michael E., II; Crues, Edwin Z.
2005-01-01
The Generic Kalman Filter (GKF) software provides a standard basis for the development of application-specific Kalman-filter programs. Historically, Kalman filters have been implemented by customized programs that must be written, coded, and debugged anew for each unique application, then tested and tuned with simulated or actual measurement data. Total development times for typical Kalman-filter application programs have ranged from months to weeks. The GKF software can simplify the development process and reduce the development time by eliminating the need to re-create the fundamental implementation of the Kalman filter for each new application. The GKF software is written in the ANSI C programming language. It contains a generic Kalman-filter-development directory that, in turn, contains a code for a generic Kalman filter function; more specifically, it contains a generically designed and generically coded implementation of linear, linearized, and extended Kalman filtering algorithms, including algorithms for state- and covariance-update and -propagation functions. The mathematical theory that underlies the algorithms is well known and has been reported extensively in the open technical literature. Also contained in the directory are a header file that defines generic Kalman-filter data structures and prototype functions and template versions of application-specific subfunction and calling navigation/estimation routine code and headers. Once the user has provided a calling routine and the required application-specific subfunctions, the application-specific Kalman-filter software can be compiled and executed immediately. During execution, the generic Kalman-filter function is called from a higher-level navigation or estimation routine that preprocesses measurement data and post-processes output data. The generic Kalman-filter function uses the aforementioned data structures and five implementation- specific subfunctions, which have been developed by the user on
Multilevel ensemble Kalman filtering
Hoel, Hakon; Law, Kody J. H.; Tempone, Raul
2016-06-14
This study embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and noisy discrete-time observations. The signal dynamics is assumed to be governed by a stochastic differential equation (SDE), and a hierarchy of time grids is introduced for multilevel numerical integration of that SDE. Finally, the resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.
A cognition-based method to ease the computational load for an extended Kalman filter.
Li, Yanpeng; Li, Xiang; Deng, Bin; Wang, Hongqiang; Qin, Yuliang
2014-01-01
The extended Kalman filter (EKF) is the nonlinear model of a Kalman filter (KF). It is a useful parameter estimation method when the observation model and/or the state transition model is not a linear function. However, the computational requirements in EKF are a difficulty for the system. With the help of cognition-based designation and the Taylor expansion method, a novel algorithm is proposed to ease the computational load for EKF in azimuth predicting and localizing under a nonlinear observation model. When there are nonlinear functions and inverse calculations for matrices, this method makes use of the major components (according to current performance and the performance requirements) in the Taylor expansion. As a result, the computational load is greatly lowered and the performance is ensured. Simulation results show that the proposed measure will deliver filtering output with a similar precision compared to the regular EKF. At the same time, the computational load is substantially lowered. PMID:25479332
A Cognition-Based Method to Ease the Computational Load for an Extended Kalman Filter
Li, Yanpeng; Li, Xiang; Deng, Bin; Wang, Hongqiang; Qin, Yuliang
2014-01-01
The extended Kalman filter (EKF) is the nonlinear model of a Kalman filter (KF). It is a useful parameter estimation method when the observation model and/or the state transition model is not a linear function. However, the computational requirements in EKF are a difficulty for the system. With the help of cognition-based designation and the Taylor expansion method, a novel algorithm is proposed to ease the computational load for EKF in azimuth predicting and localizing under a nonlinear observation model. When there are nonlinear functions and inverse calculations for matrices, this method makes use of the major components (according to current performance and the performance requirements) in the Taylor expansion. As a result, the computational load is greatly lowered and the performance is ensured. Simulation results show that the proposed measure will deliver filtering output with a similar precision compared to the regular EKF. At the same time, the computational load is substantially lowered. PMID:25479332
NASA Technical Reports Server (NTRS)
Brown, R. G.
1984-01-01
The formulation of appropriate state-space models for Kalman filtering applications is studied. The so-called model is completely specified by four matrix parameters and the initial conditions of the recursive equations. Once these are determined, the die is cast, and the way in which the measurements are weighted is determined foreverafter. Thus, finding a model that fits the physical situation at hand is all important. Also, it is often the most difficult aspect of designing a Kalman filter. Formulation of discrete state models from the spectral density and ARMA random process descriptions is discussed. Finally, it is pointed out that many common processes encountered in applied work (such as band-limited white noise) simply do not lend themselves very well to Kalman filter modeling.
Application of computed order tracking, Vold-Kalman filtering and EMD in rotating machine vibration
NASA Astrophysics Data System (ADS)
Wang, K. S.; Heyns, P. S.
2011-01-01
This paper presents a study on rotating machine vibration signals by using computed order tracking, Vold-Kalman filtering and intrinsic mode functions from the empirical mode decomposition method. Through the sequential use of intrinsic mode function and order tracking methods, both speed synchronous and non-synchronous vibrations that modulate orders in rotating machine vibrations are distinguished, which is difficult when using each of the techniques in isolation alone. Simulation and experimental studies demonstrate the ability of extracting vibrations that modulate order signals through combining the techniques.
Adaptable Iterative and Recursive Kalman Filter Schemes
NASA Technical Reports Server (NTRS)
Zanetti, Renato
2014-01-01
Nonlinear filters are often very computationally expensive and usually not suitable for real-time applications. Real-time navigation algorithms are typically based on linear estimators, such as the extended Kalman filter (EKF) and, to a much lesser extent, the unscented Kalman filter. The Iterated Kalman filter (IKF) and the Recursive Update Filter (RUF) are two algorithms that reduce the consequences of the linearization assumption of the EKF by performing N updates for each new measurement, where N is the number of recursions, a tuning parameter. This paper introduces an adaptable RUF algorithm to calculate N on the go, a similar technique can be used for the IKF as well.
Robust Kriged Kalman Filtering
Baingana, Brian; Dall'Anese, Emiliano; Mateos, Gonzalo; Giannakis, Georgios B.
2015-11-11
Although the kriged Kalman filter (KKF) has well-documented merits for prediction of spatial-temporal processes, its performance degrades in the presence of outliers due to anomalous events, or measurement equipment failures. This paper proposes a robust KKF model that explicitly accounts for presence of measurement outliers. Exploiting outlier sparsity, a novel l1-regularized estimator that jointly predicts the spatial-temporal process at unmonitored locations, while identifying measurement outliers is put forth. Numerical tests are conducted on a synthetic Internet protocol (IP) network, and real transformer load data. Test results corroborate the effectiveness of the novel estimator in joint spatial prediction and outlier identification.
Reduced-order Kalman filtering with incomplete observability
NASA Technical Reports Server (NTRS)
Yonezawa, K.
1980-01-01
Kalman filtering is considered with reference to linear stochastic dynamic systems without complete observability. It is shown that the canonical decomposition theorem can be extended to the stochastic case and the matrix Riccati equation of the Kalman filter is order-reducible if some states are not observable. The inclusion of unobservable states in Kalman filtering makes the unobservable states 'asymptotically' observable in the filter if these unobservable states are dynamically connected to observable states and asymptotically stable. The reduced-order Kalman filter saves computation time when compared to the conventional Kalman filter.
NASA Astrophysics Data System (ADS)
Colburn, Christopher; Bewley, Thomas
2010-11-01
The Kalman Filter (KF) is celebrated as the optimal estimator for systems with linear dynamics and gaussian uncertainty. Although most systems of interest do not have linear dynamics and are not forced by gaussian noise, the KF is used ubiquitously within industry. Thus, we present a novel estimation algorithm, the Game-theoretic Kalman Filter (GKF), which intelligently hedges between competing sequential filters and does not require the assumption of gaussian statistics to provide a "best" estimate.
NASA Technical Reports Server (NTRS)
Thompson, E. H.; Farrell, J. L.
1976-01-01
Monte Carlo simulation of autonomous orbit determination has validated the use of an 18-bit NASA Standard Spacecraft Computer (NSSC) for the extended Kalman filter. Dimensionally consistent scales are chosen for all variables in the algorithm, such that nearly all of the onboard computation can be performed in single precision without matrix square root formulations. Allowable simplifications in algorithm implementation and practical means of ensuring convergence are verified for accuracies of a few km provided by star/vertical observations
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Geyser, L. C.
1984-01-01
AESOP is a computer program for use in designing feedback controls and state estimators for linear multivariable systems. AESOP is meant to be used in an interactive manner. Each design task that the program performs is assigned a "function" number. The user accesses these functions either (1) by inputting a list of desired function numbers or (2) by inputting a single function number. In the latter case the choice of the function will in general depend on the results obtained by the previously executed function. The most important of the AESOP functions are those that design,linear quadratic regulators and Kalman filters. The user interacts with the program when using these design functions by inputting design weighting parameters and by viewing graphic displays of designed system responses. Supporting functions are provided that obtain system transient and frequency responses, transfer functions, and covariance matrices. The program can also compute open-loop system information such as stability (eigenvalues), eigenvectors, controllability, and observability. The program is written in ANSI-66 FORTRAN for use on an IBM 3033 using TSS 370. Descriptions of all subroutines and results of two test cases are included in the appendixes.
NASA Technical Reports Server (NTRS)
Safonov, M. G.; Athans, M.
1977-01-01
Robustness properties of nonlinear extended Kalman filters with constant gains and modeling errors are presented. Sufficient conditions for the nondivergence of state estimates generated by such nonlinear estimators are given. In addition, the overall robustness and stability properties of closed-loop stochastic regulators, based upon the Linear-Quadratic-Gaussian design methodology using linearized dynamics, are presented; the sufficient conditions for closed-loop stability have 'separation-type' property.
The Kalman Filter and High Performance Computing at NASA's Data Assimilation Office (DAO)
NASA Technical Reports Server (NTRS)
Lyster, Peter M.
1999-01-01
Atmospheric data assimilation is a method of combining actual observations with model simulations to produce a more accurate description of the earth system than the observations alone provide. The output of data assimilation, sometimes called "the analysis", are accurate regular, gridded datasets of observed and unobserved variables. This is used not only for weather forecasting but is becoming increasingly important for climate research. For example, these datasets may be used to assess retrospectively energy budgets or the effects of trace gases such as ozone. This allows researchers to understand processes driving weather and climate, which have important scientific and policy implications. The primary goal of the NASA's Data Assimilation Office (DAO) is to provide datasets for climate research and to support NASA satellite and aircraft missions. This presentation will: (1) describe ongoing work on the advanced Kalman/Lagrangian filter parallel algorithm for the assimilation of trace gases in the stratosphere; and (2) discuss the Kalman filter in relation to other presentations from the DAO on Four Dimensional Data Assimilation at this meeting. Although the designation "Kalman filter" is often used to describe the overarching work, the series of talks will show that the scientific software and the kind of parallelization techniques that are being developed at the DAO are very different depending on the type of problem being considered, the extent to which the problem is mission critical, and the degree of Software Engineering that has to be applied.
A class of quaternion Kalman filters.
Jahanchahi, Cyrus; Mandic, Danilo P
2014-03-01
The existing Kalman filters for quaternion-valued signals do not operate fully in the quaternion domain, and are combined with the real Kalman filter to enable the tracking in 3-D spaces. Using the recently introduced HR-calculus, we develop the fully quaternion-valued Kalman filter (QKF) and quaternion-extended Kalman filter (QEKF), allowing for the tracking of 3-D and 4-D signals directly in the quaternion domain. To consider the second-order noncircularity of signals, we employ the recently developed augmented quaternion statistics to derive the widely linear QKF (WL-QKF) and widely linear QEKF (WL-QEKF). To reduce computational requirements of the widely linear algorithms, their efficient implementation are proposed and it is shown that the quaternion widely linear model can be simplified when processing 3-D data, further reducing the computational requirements. Simulations using both synthetic and real-world circular and noncircular signals illustrate the advantages offered by widely linear over strictly linear quaternion Kalman filters. PMID:24807449
Attitude Representations for Kalman Filtering
NASA Technical Reports Server (NTRS)
Markley, F. Landis; Bauer, Frank H. (Technical Monitor)
2001-01-01
The four-component quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation, it represents the attitude matrix as a homogeneous quadratic function, and its dynamic propagation equation is bilinear in the quaternion and the angular velocity. The quaternion is required to obey a unit norm constraint, though, so Kalman filters often employ a quaternion for the global attitude estimate and a three-component representation for small errors about the estimate. We consider these mixed attitude representations for both a first-order Extended Kalman filter and a second-order filter, as well for quaternion-norm-preserving attitude propagation.
Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering
NASA Technical Reports Server (NTRS)
Simon, Dan; Simon, Donald L.
2003-01-01
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results obtained from application to a turbofan engine model. This model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.
Optical Kalman filtering for missile guidance
NASA Technical Reports Server (NTRS)
Casasent, D.; Neuman, C. P.; Lycas, J.
1984-01-01
Optical systolic array processors constitute a powerful and general-purpose set of optical architectures with high computational rates. In this paper, Kalman filtering, a novel application for these architectures, is investigated. All required operations are detailed; their realization by optical and special-purpose analog electronics are specified; and the processing time of the system is quantified. The specific Kalman filter application chosen is for an air-to-air missile guidance controller. The architecture realized in this paper meets the design goal of a fully adaptive Kalman filter which processes a measurement every 1 msec. The vital issue of flow and pipelining of data and operations in a systolic array processor is addressed. The approach is sufficiently general and can be realized on an optical or digital systolic array processor.
The discrete-time compensated Kalman filter
NASA Technical Reports Server (NTRS)
Lee, W. H.; Athans, M.
1978-01-01
A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete time Kalman filter was derived. The resultant compensated Kalman Filter has the property that steady state bias estimation errors, resulting from modelling errors, were eliminated.
Multirate and event-driven Kalman filters for helicopter flight
NASA Technical Reports Server (NTRS)
Sridhar, Banavar; Smith, Phillip; Suorsa, Raymond E.; Hussien, Bassam
1993-01-01
A vision-based obstacle detection system that provides information about objects as a function of azimuth and elevation is discussed. The range map is computed using a sequence of images from a passive sensor, and an extended Kalman filter is used to estimate range to obstacles. The magnitude of the optical flow that provides measurements for each Kalman filter varies significantly over the image depending on the helicopter motion and object location. In a standard Kalman filter, the measurement update takes place at fixed intervals. It may be necessary to use a different measurement update rate in different parts of the image in order to maintain the same signal to noise ratio in the optical flow calculations. A range estimation scheme that accepts the measurement only under certain conditions is presented. The estimation results from the standard Kalman filter are compared with results from a multirate Kalman filter and an event-driven Kalman filter for a sequence of helicopter flight images.
Fast SIMDized Kalman filter based track fit
NASA Astrophysics Data System (ADS)
Gorbunov, S.; Kebschull, U.; Kisel, I.; Lindenstruth, V.; Müller, W. F. J.
2008-03-01
Modern high energy physics experiments have to process terabytes of input data produced in particle collisions. The core of many data reconstruction algorithms in high energy physics is the Kalman filter. Therefore, the speed of Kalman filter based algorithms is of crucial importance in on-line data processing. This is especially true for the combinatorial track finding stage where the Kalman filter based track fit is used very intensively. Therefore, developing fast reconstruction algorithms, which use maximum available power of processors, is important, in particular for the initial selection of events which carry signals of interesting physics. One of such powerful feature supported by almost all up-to-date PC processors is a SIMD instruction set, which allows packing several data items in one register and to operate on all of them, thus achieving more operations per clock cycle. The novel Cell processor extends the parallelization further by combining a general-purpose PowerPC processor core with eight streamlined coprocessing elements which greatly accelerate vector processing applications. In the investigation described here, after a significant memory optimization and a comprehensive numerical analysis, the Kalman filter based track fitting algorithm of the CBM experiment has been vectorized using inline operator overloading. Thus the algorithm continues to be flexible with respect to any CPU family used for data reconstruction. Because of all these changes the SIMDized Kalman filter based track fitting algorithm takes 1 μs per track that is 10000 times faster than the initial version. Porting the algorithm to a Cell Blade computer gives another factor of 10 of the speedup. Finally, we compare performance of the tracking algorithm running on three different CPU architectures: Intel Xeon, AMD Opteron and Cell Broadband Engine.
Identifying Optimal Measurement Subspace for the Ensemble Kalman Filter
Zhou, Ning; Huang, Zhenyu; Welch, Greg; Zhang, J.
2012-05-24
To reduce the computational load of the ensemble Kalman filter while maintaining its efficacy, an optimization algorithm based on the generalized eigenvalue decomposition method is proposed for identifying the most informative measurement subspace. When the number of measurements is large, the proposed algorithm can be used to make an effective tradeoff between computational complexity and estimation accuracy. This algorithm also can be extended to other Kalman filters for measurement subspace selection.
Mandel, Jan; Beezley, Jonathan D.; Cobb, Loren; Krishnamurthy, Ashok
2010-01-01
The FFT EnKF data assimilation method is proposed and applied to a stochastic cell simulation of an epidemic, based on the S-I-R spread model. The FFT EnKF combines spatial statistics and ensemble filtering methodologies into a localized and computationally inexpensive version of EnKF with a very small ensemble, and it is further combined with the morphing EnKF to assimilate changes in the position of the epidemic. PMID:21031155
Mandel, Jan; Beezley, Jonathan D; Cobb, Loren; Krishnamurthy, Ashok
2010-05-01
The FFT EnKF data assimilation method is proposed and applied to a stochastic cell simulation of an epidemic, based on the S-I-R spread model. The FFT EnKF combines spatial statistics and ensemble filtering methodologies into a localized and computationally inexpensive version of EnKF with a very small ensemble, and it is further combined with the morphing EnKF to assimilate changes in the position of the epidemic. PMID:21031155
Application of Kalman filters to robot calibration
NASA Technical Reports Server (NTRS)
Whitney, D. E.; Junkel, E. F.
1983-01-01
This report explores new uses of Kalman filter theory in manufacturing systems (robots in particular). The Kalman filter allows the robot to read its sensors plus external sensors and learn from its experience. In effect, the robot is given primitive intelligence. The study, which is applicable to any type of powered kinematic linkage, focuses on the calibration of a manipulator.
The History Of The Kalman Filter
NASA Technical Reports Server (NTRS)
Mcgee, Leonard A.; Schmidt, Stanley F.
1991-01-01
Paper presents historical view of adaptation of Kalman filtering techniques to aerospace applications and eventually to fields as diverse as exploration for oil and control of powerplants. Describes scientific breakthroughs and reformulations that transformed Kalman filtering techniques into fundamental tool for analyzing and solving broad class of estimation problems.
Objects tracking with adaptive correlation filters and Kalman filtering
NASA Astrophysics Data System (ADS)
Ontiveros-Gallardo, Sergio E.; Kober, Vitaly
2015-09-01
Object tracking is commonly used for applications such as video surveillance, motion based recognition, and vehicle navigation. In this work, a tracking system using adaptive correlation filters and robust Kalman prediction of target locations is proposed. Tracking is performed by means of multiple object detections in reduced frame areas. A bank of filters is designed from multiple views of a target using synthetic discriminant functions. An adaptive approach is used to improve discrimination capability of the synthesized filters adapting them to multiple types of backgrounds. With the help of computer simulation, the performance of the proposed algorithm is evaluated in terms of detection efficiency and accuracy of object tracking.
NASA Astrophysics Data System (ADS)
Bhattacharya, Kolahal; Banerjee, Sudeshna; Mondal, Naba K.
2016-07-01
In the context of track fitting problems by a Kalman filter, the appropriate functional forms of the elements of the random process noise matrix are derived for tracking through thick layers of dense materials and magnetic field. This work complements the form of the process noise matrix obtained by Mankel [1].
Kalman Filtering with Inequality Constraints for Turbofan Engine Health Estimation
NASA Technical Reports Server (NTRS)
Simon, Dan; Simon, Donald L.
2003-01-01
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops two analytic methods of incorporating state variable inequality constraints in the Kalman filter. The first method is a general technique of using hard constraints to enforce inequalities on the state variable estimates. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The second method uses soft constraints to estimate state variables that are known to vary slowly with time. (Soft constraints are constraints that are required to be approximately satisfied rather than exactly satisfied.) The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results. The use of the algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate health parameters. The turbofan engine model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.
UDU/T/ covariance factorization for Kalman filtering
NASA Technical Reports Server (NTRS)
Thornton, C. L.; Bierman, G. J.
1980-01-01
There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.
Theory and application of Kalman filtering
NASA Technical Reports Server (NTRS)
Teng, L.
1970-01-01
As a unified extension of a group of related mathematical procedures, Kalman filtering is of assistance in the design of aircraft- and ground-based guidance and navigation data reduction and display systems.
Attitude Error Representations for Kalman Filtering
NASA Technical Reports Server (NTRS)
Markley, F. Landis; Bauer, Frank H. (Technical Monitor)
2002-01-01
The quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation. The quaternion must obey a unit norm constraint, though, which has led to the development of an extended Kalman filter using a quaternion for the global attitude estimate and a three-component representation for attitude errors. We consider various attitude error representations for this Multiplicative Extended Kalman Filter and its second-order extension.
Reduced-Order Kalman Filtering for Processing Relative Measurements
NASA Technical Reports Server (NTRS)
Bayard, David S.
2008-01-01
A study in Kalman-filter theory has led to a method of processing relative measurements to estimate the current state of a physical system, using less computation than has previously been thought necessary. As used here, relative measurements signifies measurements that yield information on the relationship between a later and an earlier state of the system. An important example of relative measurements arises in computer vision: Information on relative motion is extracted by comparing images taken at two different times. Relative measurements do not directly fit into standard Kalman filter theory, in which measurements are restricted to those indicative of only the current state of the system. One approach heretofore followed in utilizing relative measurements in Kalman filtering, denoted state augmentation, involves augmenting the state of the system at the earlier of two time instants and then propagating the state to the later time instant.While state augmentation is conceptually simple, it can also be computationally prohibitive because it doubles the number of states in the Kalman filter. When processing a relative measurement, if one were to follow the state-augmentation approach as practiced heretofore, one would find it necessary to propagate the full augmented state Kalman filter from the earlier time to the later time and then select out the reduced-order components. The main result of the study reported here is proof of a property called reduced-order equivalence (ROE). The main consequence of ROE is that it is not necessary to augment with the full state, but, rather, only the portion of the state that is explicitly used in the partial relative measurement. In other words, it suffices to select the reduced-order components first and then propagate the partial augmented state Kalman filter from the earlier time to the later time; the amount of computation needed to do this can be substantially less than that needed for propagating the full augmented
NASA Astrophysics Data System (ADS)
Trigo, F. C.; Martins, F. P. R.; Fleury, A. T.; Silva, H. C.
2014-02-01
Aiming at overcoming the difficulties derived from the traditional camera calibration methods to record the underwater environment of a towing tank where experiments of scaled-model risers are carried on, a computer vision method, combining traditional image processing algorithms and a self-calibration technique was implemented. This method was used to identify the coordinates of control-points viewed on a scaled-model riser submitted to a periodic force applied to its fairlead attachment point. To study the observed motion, the riser was represented as a pseudo-rigid body model (PRBM) and the hypotheses of compliant mechanisms theory were assumed in order to cope with its elastic behavior. The derived Lagrangian equations of motion were linearized and expressed as a state-space model in which the state variables include the generalized coordinates and the unknown generalized forces. The state-vector thus assembled is estimated through a Kalman Filter. The estimation procedure allows the determination of both the generalized forces and the tension along the cable, with statistically proven convergence.
Is the hippocampus a Kalman filter?
Bousquet, O; Balakrishnan, K; Honavar, V
1998-01-01
Based on a large body of neurophysiological, neuroanatomical, and behavioral data, it has been suggested that the hippocampal formation serves as a spatial learning and localization system. This spatial representation is metric in nature and arises as a result of associations between sensory inputs and dead-reckoning information generated by the animal. However, despite the fact that these two information streams provide uncertain information (e.g., recognition errors, dead-reckoning drifts, etc.), the hippocampal computational models suggested to date have not explicitly addressed information fusion from erroneous sources. In this paper we develop a computational model of hippocampal spatial learning and relate its functioning to a probabilistic tool used for uncertain sensory fusion in robots: the Kalman filter. This parallel allows us to derive statistically optimal update expressions for the localization performed by our computational model. PMID:9697220
Kalman Filter Tracking on Parallel Architectures
NASA Astrophysics Data System (ADS)
Cerati, Giuseppe; Elmer, Peter; Lantz, Steven; McDermott, Kevin; Riley, Dan; Tadel, Matevž; Wittich, Peter; Würthwein, Frank; Yagil, Avi
2015-12-01
Power density constraints are limiting the performance improvements of modern CPUs. To address this we have seen the introduction of lower-power, multi-core processors, but the future will be even more exciting. In order to stay within the power density limits but still obtain Moore's Law performance/price gains, it will be necessary to parallelize algorithms to exploit larger numbers of lightweight cores and specialized functions like large vector units. Example technologies today include Intel's Xeon Phi and GPGPUs. Track finding and fitting is one of the most computationally challenging problems for event reconstruction in particle physics. At the High Luminosity LHC, for example, this will be by far the dominant problem. The need for greater parallelism has driven investigations of very different track finding techniques including Cellular Automata or returning to Hough Transform. The most common track finding techniques in use today are however those based on the Kalman Filter [2]. Significant experience has been accumulated with these techniques on real tracking detector systems, both in the trigger and offline. They are known to provide high physics performance, are robust and are exactly those being used today for the design of the tracking system for HL-LHC. Our previous investigations showed that, using optimized data structures, track fitting with Kalman Filter can achieve large speedup both with Intel Xeon and Xeon Phi. We report here our further progress towards an end-to-end track reconstruction algorithm fully exploiting vectorization and parallelization techniques in a realistic simulation setup.
Detection of atomic clock frequency jumps with the Kalman filter.
Galleani, Lorenzo; Tavella, Patrizia
2012-03-01
Frequency jumps are common anomalies in atomic clocks aboard navigation system satellites. These anomalous behaviors must be detected quickly and accurately to minimize the impact on user positioning. We develop a detector for frequency jumps based on the Kalman filter. Numerical simulations show that the detector is fast, with high probability of detection and low probability of false alarms. It also has a low computational cost because it takes advantage of the recursive nature of the Kalman filter. Therefore, it can be used in applications in which little computational power is available, such as aboard navigation system satellites. PMID:22481785
Reduced Kalman Filters for Clock Ensembles
NASA Technical Reports Server (NTRS)
Greenhall, Charles A.
2011-01-01
This paper summarizes the author's work ontimescales based on Kalman filters that act upon the clock comparisons. The natural Kalman timescale algorithm tends to optimize long-term timescale stability at the expense of short-term stability. By subjecting each post-measurement error covariance matrix to a non-transparent reduction operation, one obtains corrected clocks with improved short-term stability and little sacrifice of long-term stability.
Kalman Filter for Spinning Spacecraft Attitude Estimation
NASA Technical Reports Server (NTRS)
Markley, F. Landis; Sedlak, Joseph E.
2008-01-01
This paper presents a Kalman filter using a seven-component attitude state vector comprising the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. The relatively slow variation of these parameters makes this parameterization advantageous for spinning spacecraft attitude estimation. The filter accounts for the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames by employing a reduced six-component error state. Four variants of the filter, defined by different choices for the reduced error state, are tested against a quaternion-based filter using simulated data for the THEMIS mission. Three of these variants choose three of the components of the error state to be the infinitesimal attitude error angles, facilitating the computation of measurement sensitivity matrices and causing the usual 3x3 attitude covariance matrix to be a submatrix of the 6x6 covariance of the error state. These variants differ in their choice for the other three components of the error state. The variant employing the infinitesimal attitude error angles and the angular momentum components in an inertial reference frame as the error state shows the best combination of robustness and efficiency in the simulations. Attitude estimation results using THEMIS flight data are also presented.
Ensemble Kalman Filtering without a Model
NASA Astrophysics Data System (ADS)
Hamilton, Franz; Berry, Tyrus; Sauer, Timothy
2016-01-01
Methods of data assimilation are established in physical sciences and engineering for the merging of observed data with dynamical models. When the model is nonlinear, methods such as the ensemble Kalman filter have been developed for this purpose. At the other end of the spectrum, when a model is not known, the delay coordinate method introduced by Takens has been used to reconstruct nonlinear dynamics. In this article, we merge these two important lines of research. A model-free filter is introduced based on the filtering equations of Kalman and the data-driven modeling of Takens. This procedure replaces the model with dynamics reconstructed from delay coordinates, while using the Kalman update formulation to reconcile new observations. We find that this combination of approaches results in comparable efficiency to parametric methods in identifying underlying dynamics, and may actually be superior in cases of model error.
Compressed state Kalman filter for large systems
NASA Astrophysics Data System (ADS)
Kitanidis, Peter K.
2015-02-01
The Kalman filter (KF) is a recursive filter that allows the assimilation of data in real time and has found numerous applications. In earth sciences, the method is applied to systems with very large state vectors obtained from the discretization of functions such as pressure, velocity, solute concentration, and voltage. With state dimension running in the millions, the implementation of the standard or textbook version of KF is very expensive and low-rank approximations have been devised such as EnKF and SEEK. Although widely applied, the error behavior of these methods is not adequately understood. This article focuses on very large linear systems and presents a complete computational method that scales roughly linearly with the dimension of the state vector. The method is suited for problems for which the effective rank of the state covariance matrix is much smaller than its dimension. This method is closest to SEEK but uses a fixed basis that should be selected in accordance with the characteristics of the problem, mainly the transition matrix and the system noise covariance. The method is matrix free, i.e., does not require computation of Jacobian matrices and uses the forward model as a black box. Computational results demonstrate the ability of the method to solve very large, say 106 , state vectors.
Concrete ensemble Kalman filters with rigorous catastrophic filter divergence
Kelly, David; Majda, Andrew J.; Tong, Xin T.
2015-01-01
The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood. One of the central mysteries is the numerical phenomenon known as catastrophic filter divergence, whereby ensemble-state estimates explode to machine infinity, despite the true state remaining in a bounded region. In this article we provide a breakthrough insight into the phenomenon, by introducing a simple and natural forecast model that transparently exhibits catastrophic filter divergence under all ensemble methods and a large set of initializations. For this model, catastrophic filter divergence is not an artifact of numerical instability, but rather a true dynamical property of the filter. The divergence is not only validated numerically but also proven rigorously. The model cleanly illustrates mechanisms that give rise to catastrophic divergence and confirms intuitive accounts of the phenomena given in past literature. PMID:26261335
Q-Method Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Zanetti, Renato; Ainscough, Thomas; Christian, John; Spanos, Pol D.
2012-01-01
A new algorithm is proposed that smoothly integrates non-linear estimation of the attitude quaternion using Davenport s q-method and estimation of non-attitude states through an extended Kalman filter. The new method is compared to a similar existing algorithm showing its similarities and differences. The validity of the proposed approach is confirmed through numerical simulations.
Discovery of the Kalman filter as a practical tool for aerospace and industry
NASA Technical Reports Server (NTRS)
Mcgee, L. A.; Schmidt, S. F.
1985-01-01
The sequence of events which led the researchers at Ames Research Center to the early discovery of the Kalman filter shortly after its introduction into the literature is recounted. The scientific breakthroughs and reformulations that were necessary to transform Kalman's work into a useful tool for a specific aerospace application are described. The resulting extended Kalman filter, as it is now known, is often still referred to simply as the Kalman filter. As the filter's use gained in popularity in the scientific community, the problems of implementation on small spaceborne and airborne computers led to a square-root formulation of the filter to overcome numerical difficulties associated with computer word length. The work that led to this new formulation is also discussed, including the first airborne computer implementation and flight test. Since then the applications of the extended and square-root formulations of the Kalman filter have grown rapidly throughout the aerospace industry.
Real-time shipboard orbit determination using Kalman filtering techniques
NASA Technical Reports Server (NTRS)
Brammer, R. F.
1974-01-01
The real-time tracking and orbit determination program used on board the NASA tracking ship, the USNS Vanguard, is described in this paper. The computer program uses a variety of filtering algorithms, including an extended Kalman filter, to derive real-time orbit determinations (position-velocity state vectors) from shipboard tracking and navigation data. Results from Apollo missions are given to show that orbital parameters can be estimated quickly and accurately using these methods.
Simplification of the Kalman filter for meteorological data assimilation
NASA Technical Reports Server (NTRS)
Dee, Dick P.
1991-01-01
The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.
NASA Astrophysics Data System (ADS)
Hut, Rolf; Amisigo, Barnabas A.; Steele-Dunne, Susan; van de Giesen, Nick
2015-12-01
Reduction of Used Memory Ensemble Kalman Filtering (RumEnKF) is introduced as a variant on the Ensemble Kalman Filter (EnKF). RumEnKF differs from EnKF in that it does not store the entire ensemble, but rather only saves the first two moments of the ensemble distribution. In this way, the number of ensemble members that can be calculated is less dependent on available memory, and mainly on available computing power (CPU). RumEnKF is developed to make optimal use of current generation super computer architecture, where the number of available floating point operations (flops) increases more rapidly than the available memory and where inter-node communication can quickly become a bottleneck. RumEnKF reduces the used memory compared to the EnKF when the number of ensemble members is greater than half the number of state variables. In this paper, three simple models are used (auto-regressive, low dimensional Lorenz and high dimensional Lorenz) to show that RumEnKF performs similarly to the EnKF. Furthermore, it is also shown that increasing the ensemble size has a similar impact on the estimation error from the three algorithms.
Kalman filtering for spacecraft attitude estimation
NASA Technical Reports Server (NTRS)
Lefferts, E. J.; Markley, F. L.; Shuster, M. D.
1982-01-01
Several schemes in current use for sequential estimation of spacecraft attitude using Kalman filters are examined. These differ according to their treatment of the attitude error, namely: using the complete four-component quaternion; using a truncated quaternion in which one of the components has been eliminated; or using a quaternion referred to approximate body-fixed axes. These schemes are examined for the case of a spacecraft carrying line-of-sight attitude sensors and three-axis gyros whose measurements are corrupted by noise on both the drift rate and the drift-rate ramp. The analysis of the covariance is carried out in detail. The historical development of Kalman filtering of attitude is reviewed.
NASA Astrophysics Data System (ADS)
Ahrens, H.; Argin, F.; Klinkenbusch, L.
2013-07-01
The non-invasive and radiation-free imaging of the electrical activity of the heart with Electrocardiography (ECG) or Magnetocardiography (MCG) can be helpful for physicians for instance in the localization of the origin of cardiac arrhythmia. In this paper we compare two Kalman Filter algorithms for the solution of a nonlinear state-space model and for the subsequent imaging of the activation/depolarization times of the heart muscle: the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF). The algorithms are compared for simulations of a (6×6) magnetometer array, a torso model with piecewise homogeneous conductivities, 946 current dipoles located in a small part of the heart (apex), and several noise levels. It is found that for all tested noise levels the convergence of the activation times is faster for the UKF.
Ijaz, Umer Zeeshan; Khambampati, Anil Kumar; Lee, Jeong Seong; Kim, Sin; Kim, Kyung Youn
2008-07-20
In this paper, an effective nonstationary phase boundary estimation scheme in electrical impedance tomography is presented based on the unscented Kalman filter. The inverse problem is treated as a stochastic nonlinear state estimation problem with the nonstationary phase boundary (state) being estimated online with the aid of unscented Kalman filter. This research targets the industrial applications, such as imaging of stirrer vessel for detection of air distribution or detecting large air bubbles in pipelines. Within the domains, there exist 'voids' having zero conductivity. The design variables for phase boundary estimation are truncated Fourier coefficients. Computer simulations and experimental results are provided to evaluate the performance of unscented Kalman filter in comparison with extended Kalman filter to show a better performance of the unscented Kalman filter approach.
A Reduced Dimension Static, Linearized Kalman Filter and Smoother
NASA Technical Reports Server (NTRS)
Fukumori, I.
1995-01-01
An approximate Kalman filter and smoother, based on approximations of the state estimation error covariance matrix, is described. Approximations include a reduction of the effective state dimension, use of a static asymptotic error limit, and a time-invariant linearization of the dynamic model for error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. Examples of use come from TOPEX/POSEIDON.
Application of Kalman filtering to spacecraft range residual prediction
NASA Technical Reports Server (NTRS)
Madrid, G. A.; Bierman, G. J.
1977-01-01
One function of the Deep Space Network is validation of the range data that they receive. In this paper we present an automated online sequential range predictor which shows promise of significantly reducing computational and manpower expenditures. The proposed algorithm, a U-D covariance factored Kalman filter, is demonstrated by processing a four-month record of Viking spacecraft data taken enroute to Mars.
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul
2016-05-03
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d
Spectral abundance fraction estimation of materials using Kalman filters
NASA Astrophysics Data System (ADS)
Wang, Su; Chang, Chein; Jensen, Janet L.; Jensen, James O.
2004-12-01
Kalman filter has been widely used in statistical signal processing for parameter estimation. Although a Kalman filter approach has been recently developed for spectral unmixing, referred to as Kalman filter-based linear unmixing (KFLU), its applicability to spectral characterization within a single pixel vector has not been explored. This paper presents a new application of Kalman filtering in spectral estimation and quantification. It develops a Kalman filter-based spectral signature esimator (KFSSE) which is different from the KFLU in the sense that the former performs a Kalman filter wavelength by wavelength across a spectral signature as opposed to the latter which implements a Kalman filter pixel vector by pixel vector in an image cube. The idea of the KFSSE is to implement the state equation to characterize the true spectral signature, while the measurement equation is being used to describe the spectral signature to be processed. Additionally, since a Kalman filter can accurately estimate spectral abundance fraction of a signature, our proposed KFSSE can further used for spectral quantification for subpixel targets and mixed pixel vectors, called Kalman filter-based spectral quantifier (KFSQ). Such spectral quantification is particularly important for chemical/biological defense which requires quantification of detected agents for damage control assessment. Several different types of hyperspectral data are used for experiments to demonstrate the ability of the KFSSE in estimation of spectral signature and the utility of the KFSQ in spectral quantification.
Constrained Kalman Filtering Via Density Function Truncation for Turbofan Engine Health Estimation
NASA Technical Reports Server (NTRS)
Simon, Dan; Simon, Donald L.
2006-01-01
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter truncates the PDF (probability density function) of the Kalman filter estimate at the known constraints and then computes the constrained filter estimate as the mean of the truncated PDF. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is demonstrated via simulation results obtained from a turbofan engine model. The turbofan engine model contains 3 state variables, 11 measurements, and 10 component health parameters. It is also shown that the truncated Kalman filter may be a more accurate way of incorporating inequality constraints than other constrained filters (e.g., the projection approach to constrained filtering).
Streamflow Data Assimilation in SWAT Model Using Extended Kalman Filter
NASA Astrophysics Data System (ADS)
Sun, L.; Nistor, I.; Seidou, O.
2014-12-01
Although Extended Kalman Filter (EKF) is regarded as the de facto method for the application of Kalman Filter in non-linear system, it's application to complex distributed hydrological models faces a lot of challenges. Ensemble Kalman Filter (EnKF) is often preferred because it avoids the calculation of the linearization Jacobian Matrix and the propagation of estimation error covariance. EnKF is however difficult to apply to large models because of the huge computation demand needed for parallel propagation of ensemble members. This paper deals with the application of EKF in stream flow prediction using the SWAT model in the watershed of Senegal River, West Africa. In the Jacobian Matrix calculation, SWAT is regarded as a black box model and the derivatives are calculated in the form of differential equations. The state vector is the combination of runoff, soil, shallow aquifer and deep aquifer water contents. As an initial attempt, only stream flow observations are assimilated. Despite the fact that EKF is a sub-optimal filter, the coupling of EKF significantly improves the estimation of daily streamflow. The results of SWAT+EKF are also compared to those of a simpler quasi linear streamflow prediction model where both state and parameters are updated with the EKF.
Spacecraft Dynamics Should be Considered in Kalman Filter Attitude Estimation
NASA Technical Reports Server (NTRS)
Yang, Yaguang; Zhou, Zhiqiang
2016-01-01
Kalman filter based spacecraft attitude estimation has been used in some high-profile missions and has been widely discussed in literature. While some models in spacecraft attitude estimation include spacecraft dynamics, most do not. To our best knowledge, there is no comparison on which model is a better choice. In this paper, we discuss the reasons why spacecraft dynamics should be considered in the Kalman filter based spacecraft attitude estimation problem. We also propose a reduced quaternion spacecraft dynamics model which admits additive noise. Geometry of the reduced quaternion model and the additive noise are discussed. This treatment is more elegant in mathematics and easier in computation. We use some simulation example to verify our claims.
Flexible Generation of Kalman Filter Code
NASA Technical Reports Server (NTRS)
Richardson, Julian; Wilson, Edward
2006-01-01
Domain-specific program synthesis can automatically generate high quality code in complex domains from succinct specifications, but the range of programs which can be generated by a given synthesis system is typically narrow. Obtaining code which falls outside this narrow scope necessitates either 1) extension of the code generator, which is usually very expensive, or 2) manual modification of the generated code, which is often difficult and which must be redone whenever changes are made to the program specification. In this paper, we describe adaptations and extensions of the AUTOFILTER Kalman filter synthesis system which greatly extend the range of programs which can be generated. Users augment the input specification with a specification of code fragments and how those fragments should interleave with or replace parts of the synthesized filter. This allows users to generate a much wider range of programs without their needing to modify the synthesis system or edit generated code. We demonstrate the usefulness of the approach by applying it to the synthesis of a complex state estimator which combines code from several Kalman filters with user-specified code. The work described in this paper allows the complex design decisions necessary for real-world applications to be reflected in the synthesized code. When executed on simulated input data, the generated state estimator was found to produce comparable estimates to those produced by a handcoded estimator
Global systems for mobile position tracking using Kalman and Lainiotis filters.
Assimakis, Nicholas; Adam, Maria
2014-01-01
We present two time invariant models for Global Systems for Mobile (GSM) position tracking, which describe the movement in x-axis and y-axis simultaneously or separately. We present the time invariant filters as well as the steady state filters: the classical Kalman filter and Lainiotis Filter and the Join Kalman Lainiotis Filter, which consists of the parallel usage of the two classical filters. Various implementations are proposed and compared with respect to their behavior and to their computational burden: all time invariant and steady state filters have the same behavior using both proposed models but have different computational burden. Finally, we propose a Finite Impulse Response (FIR) implementation of the Steady State Kalman, and Lainiotis filters, which does not require previous estimations but requires a well-defined set of previous measurements. PMID:24883349
VLBI TRF determination via Kalman filtering
NASA Astrophysics Data System (ADS)
Soja, Benedikt; Karbon, Maria; Nilsson, Tobias; Glaser, Susanne; Balidakis, Kyriakos; Heinkelmann, Robert; Schuh, Harald
2015-04-01
The determination of station positions is one of the primary tasks for space geodetic techniques. Station coordinate offsets are usually determined with respect to a linear coordinate model after removing elastic displacements caused by mass redistributions within the Earth's system. In operational VLBI analysis, the coordinate offsets are estimated in a least-squares adjustment as a constant over the duration of a 24-hour VLBI experiment. Terrestrial reference frames (TRF) are usually derived by adjusting the normal equations that contain the 24-hour constant offsets in order to estimate a linear model, possibly including breaks, for the station positions. We have created a VLBI TRF solution without the assumption of negligible subdaily motion and of linear behavior on longer time scales by applying a Kalman filter. As a preparation for the upcoming VLBI Global Observing System (VGOS), which aims for continuous observations that are available in real-time, a Kalman filter has been implemented into the VLBI software VieVS@GFZ. In addition to the real-time capability, the filter offers the possibility of stochastically modeling the parameters of interest. For station coordinates, changes in a subdaily time frame occur, for instance, from un- or mismodeled geophysical effects. The models for tidal and non-tidal ocean, atmosphere, and hydrology loading are known to have deficiencies and inconsistencies which propagate into the estimated station coordinates. The stochastic model of the Kalman filter can be adapted to take these subdaily effects into account. Comparing the resulting station coordinate time series with daily values from a least squares fit, we have investigated to what extent and in which regions the loading models currently have deficiencies. Due to the high correlation between station height and tropospheric delays, it is possible that errors in one group of parameters are partly absorbed by the other group. To detect problems with correlations and to
Software Would Largely Automate Design of Kalman Filter
NASA Technical Reports Server (NTRS)
Chuang, Jason C. H.; Negast, William J.
2005-01-01
Embedded Navigation Filter Automatic Designer (ENFAD) is a computer program being developed to automate the most difficult tasks in designing embedded software to implement a Kalman filter in a navigation system. The most difficult tasks are selection of error states of the filter and tuning of filter parameters, which are timeconsuming trial-and-error tasks that require expertise and rarely yield optimum results. An optimum selection of error states and filter parameters depends on navigation-sensor and vehicle characteristics, and on filter processing time. ENFAD would include a simulation module that would incorporate all possible error states with respect to a given set of vehicle and sensor characteristics. The first of two iterative optimization loops would vary the selection of error states until the best filter performance was achieved in Monte Carlo simulations. For a fixed selection of error states, the second loop would vary the filter parameter values until an optimal performance value was obtained. Design constraints would be satisfied in the optimization loops. Users would supply vehicle and sensor test data that would be used to refine digital models in ENFAD. Filter processing time and filter accuracy would be computed by ENFAD.
Misguided resistance using extended Kalman filter for imaging seeker
NASA Astrophysics Data System (ADS)
Li, Fugui; Bu, Kuichen; Zhao, Hong
2015-10-01
Fake targets had essential effect on target trace and guidance information extraction. Measures based on extended Kalman filter were recommended in this paper. The model of an imaging seeker was established firstly. Then the interfered model that the imaging seeker was misguided by the fake targets was introduced. The process how the fake targets misguided the imaging seeker was analyzed. An extended Kalman filter was established in the sphere coordinates, which could help to enhance the estimate level. The measurement of the seeker was transformed to the suitable information to spur the extended Kalman filter. The strategies were composed of four stages. Before the fake targets appeared, the extended Kalman filter estimated the motion information and the trend of the target quickly. When the fake targets appeared, the motion of the seeker will be controlled with the information predicted by the extended Kalman filter. The measured information of the seeker will not be used as stimulus to the extended Kalman filter until the true target was identified. After the true target was chosen, the seeker averted to the real target, and the angular information of line of sight measured by the seeker would be used to ensure the stability of the extended Kalman filter. When the transit time of the seeker from the previous direction to the target was finished, the rate of line of sight will be used to make the extended Kalman filter converged quickly. Theoretical analysis and simulation results show that the method is reasonable and efficient.
Telescope Multi-Field Wavefront Control with a Kalman Filter
NASA Technical Reports Server (NTRS)
Lou, John Z.; Redding, David; Sigrist, Norbert; Basinger, Scott
2008-01-01
An effective multi-field wavefront control (WFC) approach is demonstrated for an actuated, segmented space telescope using wavefront measurements at the exit pupil, and the optical and computational implications of this approach are discussed. The integration of a Kalman Filter as an optical state estimator into the wavefront control process to further improve the robustness of the optical alignment of the telescope will also be discussed. Through a comparison of WFC performances between on-orbit and ground-test optical system configurations, the connection (and a possible disconnection) between WFC and optical system alignment under these circumstances are analyzed. Our MACOS-based computer simulation results will be presented and discussed.
Distributed Dynamic State Estimation with Extended Kalman Filter
Du, Pengwei; Huang, Zhenyu; Sun, Yannan; Diao, Ruisheng; Kalsi, Karanjit; Anderson, Kevin K.; Li, Yulan; Lee, Barry
2011-08-04
Increasing complexity associated with large-scale renewable resources and novel smart-grid technologies necessitates real-time monitoring and control. Our previous work applied the extended Kalman filter (EKF) with the use of phasor measurement data (PMU) for dynamic state estimation. However, high computation complexity creates significant challenges for real-time applications. In this paper, the problem of distributed dynamic state estimation is investigated. One domain decomposition method is proposed to utilize decentralized computing resources. The performance of distributed dynamic state estimation is tested on a 16-machine, 68-bus test system.
Restoration of color images by multichannel Kalman filtering
NASA Technical Reports Server (NTRS)
Galatsanos, Nikolas P.; Chin, Roland T.
1991-01-01
A Kalman filter for optimal restoration of multichannel images is presented. This filter is derived using a multichannel semicausal image model that includes between-channel degradation. Both stationary and nonstationary image models are developed. This filter is implemented in the Fourier domain and computation is reduced from O(Lambda3N3M4) to O(Lambda3N3M2) for an M x M N-channel image with degradation length Lambda. Color (red, green, and blue (RGB)) images are used as examples of multichannel images, and restoration in the RGB and YIQ domains is investigated. Simulations are presented in which the effectiveness of this filter is tested for different types of degradation and different image model estimates.
Fast Kalman Filter for Random Walk Forecast model
NASA Astrophysics Data System (ADS)
Saibaba, A.; Kitanidis, P. K.
2013-12-01
Kalman filtering is a fundamental tool in statistical time series analysis to understand the dynamics of large systems for which limited, noisy observations are available. However, standard implementations of the Kalman filter are prohibitive because they require O(N^2) in memory and O(N^3) in computational cost, where N is the dimension of the state variable. In this work, we focus our attention on the Random walk forecast model which assumes the state transition matrix to be the identity matrix. This model is frequently adopted when the data is acquired at a timescale that is faster than the dynamics of the state variables and there is considerable uncertainty as to the physics governing the state evolution. We derive an efficient representation for the a priori and a posteriori estimate covariance matrices as a weighted sum of two contributions - the process noise covariance matrix and a low rank term which contains eigenvectors from a generalized eigenvalue problem, which combines information from the noise covariance matrix and the data. We describe an efficient algorithm to update the weights of the above terms and the computation of eigenmodes of the generalized eigenvalue problem (GEP). The resulting algorithm for the Kalman filter with Random walk forecast model scales as O(N) or O(N log N), both in memory and computational cost. This opens up the possibility of real-time adaptive experimental design and optimal control in systems of much larger dimension than was previously feasible. For a small number of measurements (~ 300 - 400), this procedure can be made numerically exact. However, as the number of measurements increase, for several choices of measurement operators and noise covariance matrices, the spectrum of the (GEP) decays rapidly and we are justified in only retaining the dominant eigenmodes. We discuss tradeoffs between accuracy and computational cost. The resulting algorithms are applied to an example application from ray-based travel time
A recursive solution for a fading memory filter derived from Kalman filter theory
NASA Technical Reports Server (NTRS)
Statman, J. I.
1986-01-01
A simple recursive solution for a class of fading memory tracking filters is presented. A fading memory filter provides estimates of filter states based on past measurements, similar to a traditional Kalman filter. Unlike a Kalman filter, an exponentially decaying weight is applied to older measurements, discounting their effect on present state estimates. It is shown that Kalman filters and fading memory filters are closely related solutions to a general least squares estimator problem. Closed form filter transfer functions are derived for a time invariant, steady state, fading memory filter. These can be applied in loop filter implementation of the Deep Space Network (DSN) Advanced Receiver carrier phase locked loop (PLL).
Statistical process control of a Kalman filter model.
Gamse, Sonja; Nobakht-Ersi, Fereydoun; Sharifi, Mohammad A
2014-01-01
For the evaluation of measurement data, different functional and stochastic models can be used. In the case of time series, a Kalman filtering (KF) algorithm can be implemented. In this case, a very well-known stochastic model, which includes statistical tests in the domain of measurements and in the system state domain, is used. Because the output results depend strongly on input model parameters and the normal distribution of residuals is not always fulfilled, it is very important to perform all possible tests on output results. In this contribution, we give a detailed description of the evaluation of the Kalman filter model. We describe indicators of inner confidence, such as controllability and observability, the determinant of state transition matrix and observing the properties of the a posteriori system state covariance matrix and the properties of the Kalman gain matrix. The statistical tests include the convergence of standard deviations of the system state components and normal distribution beside standard tests. Especially, computing controllability and observability matrices and controlling the normal distribution of residuals are not the standard procedures in the implementation of KF. Practical implementation is done on geodetic kinematic observations. PMID:25264959
Statistical Process Control of a Kalman Filter Model
Gamse, Sonja; Nobakht-Ersi, Fereydoun; Sharifi, Mohammad A.
2014-01-01
For the evaluation of measurement data, different functional and stochastic models can be used. In the case of time series, a Kalman filtering (KF) algorithm can be implemented. In this case, a very well-known stochastic model, which includes statistical tests in the domain of measurements and in the system state domain, is used. Because the output results depend strongly on input model parameters and the normal distribution of residuals is not always fulfilled, it is very important to perform all possible tests on output results. In this contribution, we give a detailed description of the evaluation of the Kalman filter model. We describe indicators of inner confidence, such as controllability and observability, the determinant of state transition matrix and observing the properties of the a posteriori system state covariance matrix and the properties of the Kalman gain matrix. The statistical tests include the convergence of standard deviations of the system state components and normal distribution beside standard tests. Especially, computing controllability and observability matrices and controlling the normal distribution of residuals are not the standard procedures in the implementation of KF. Practical implementation is done on geodetic kinematic observations. PMID:25264959
The discrete Kalman filtering approach for seismic signals deconvolution
Kurniadi, Rizal; Nurhandoko, Bagus Endar B.
2012-06-20
Seismic signals are a convolution of reflectivity and seismic wavelet. One of the most important stages in seismic data processing is deconvolution process; the process of deconvolution is inverse filters based on Wiener filter theory. This theory is limited by certain modelling assumptions, which may not always valid. The discrete form of the Kalman filter is then used to generate an estimate of the reflectivity function. The main advantage of Kalman filtering is capability of technique to handling continually time varying models and has high resolution capabilities. In this work, we use discrete Kalman filter that it was combined with primitive deconvolution. Filtering process works on reflectivity function, hence the work flow of filtering is started with primitive deconvolution using inverse of wavelet. The seismic signals then are obtained by convoluting of filtered reflectivity function with energy waveform which is referred to as the seismic wavelet. The higher frequency of wavelet gives smaller wave length, the graphs of these results are presented.
Longitudinal Factor Score Estimation Using the Kalman Filter.
ERIC Educational Resources Information Center
Oud, Johan H.; And Others
1990-01-01
How longitudinal factor score estimation--the estimation of the evolution of factor scores for individual examinees over time--can profit from the Kalman filter technique is described. The Kalman estimates change more cautiously over time, have lower estimation error variances, and reproduce the LISREL program latent state correlations more…
Stable Kalman filters for processing clock measurement data
NASA Technical Reports Server (NTRS)
Clements, P. A.; Gibbs, B. P.; Vandergraft, J. S.
1989-01-01
Kalman filters have been used for some time to process clock measurement data. Due to instabilities in the standard Kalman filter algorithms, the results have been unreliable and difficult to obtain. During the past several years, stable forms of the Kalman filter have been developed, implemented, and used in many diverse applications. These algorithms, while algebraically equivalent to the standard Kalman filter, exhibit excellent numerical properties. Two of these stable algorithms, the Upper triangular-Diagonal (UD) filter and the Square Root Information Filter (SRIF), have been implemented to replace the standard Kalman filter used to process data from the Deep Space Network (DSN) hydrogen maser clocks. The data are time offsets between the clocks in the DSN, the timescale at the National Institute of Standards and Technology (NIST), and two geographically intermediate clocks. The measurements are made by using the GPS navigation satellites in mutual view between clocks. The filter programs allow the user to easily modify the clock models, the GPS satellite dependent biases, and the random noise levels in order to compare different modeling assumptions. The results of this study show the usefulness of such software for processing clock data. The UD filter is indeed a stable, efficient, and flexible method for obtaining optimal estimates of clock offsets, offset rates, and drift rates. A brief overview of the UD filter is also given.
Kalman Filter Constraint Tuning for Turbofan Engine Health Estimation
NASA Technical Reports Server (NTRS)
Simon, Dan; Simon, Donald L.
2005-01-01
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints are often neglected because they do not fit easily into the structure of the Kalman filter. Recently published work has shown a new method for incorporating state variable inequality constraints in the Kalman filter, which has been shown to generally improve the filter s estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy as the Kalman filter is theoretically optimal. This paper proposes a way to tune the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high. When confidence in the unconstrained filter is not so high, then we use our heuristic knowledge to constrain the state estimates. The confidence measure is based on the agreement of measurement residuals with their theoretical values. The algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate engine health.
Stochastic stability of the derivative unscented Kalman filter
NASA Astrophysics Data System (ADS)
Hu, Gao-Ge; Gao, She-Sheng; Zhong, Yong-Min; Gao, Bing-Bing
2015-07-01
This is the second of two consecutive papers focusing on the filtering algorithm for a nonlinear stochastic discrete-time system with linear system state equation. The first paper established a derivative unscented Kalman filter (DUKF) to eliminate the redundant computational load of the unscented Kalman filter (UKF) due to the use of unscented transformation (UT) in the prediction process. The present paper studies the error behavior of the DUKF using the boundedness property of stochastic processes. It is proved that the estimation error of the DUKF remains bounded if the system satisfies certain conditions. Furthermore, it is shown that the design of the measurement noise covariance matrix plays an important role in improvement of the algorithm stability. The DUKF can be significantly stabilized by adding small quantities to the measurement noise covariance matrix in the presence of large initial error. Simulation results demonstrate the effectiveness of the proposed technique. Project supported by the National Natural Science Foundation of China (Grant No. 61174193) and the Doctorate Foundation of Northwestern Polytechnical University, China (Grant No. CX201409).
Initial flight results of the TRMM Kalman filter
NASA Technical Reports Server (NTRS)
Andrews, Stephen F.; Morgenstern, Wendy M.
1998-01-01
The Tropical Rainfall Measuring Mission (TRMM) spacecraft is a nadir pointing spacecraft that nominally controls attitude based on the Earth Sensor Assembly (ESA) output. After a potential single point failure in the ESA was identified, the contingency attitude determination method chosen to backup the ESA-based system was a sixth-order extended Kalman filter that uses magnetometer and digital sun sensor measurements. A brief description of the TRMM Kalman filter will be given, including some implementation issues and algorithm heritage. Operational aspects of the Kalman filter and some failure detection and correction will be described. The Kalman filter was tested in a sun pointing attitude and in a nadir pointing attitude during the in-orbit checkout period, and results from those tests will be presented. This paper will describe some lessons learned from the experience of the TRMM team.
Initial Flight Results of the TRMM Kalman Filter
NASA Technical Reports Server (NTRS)
Andrews, Stephen F.; Morgenstern, Wendy M.
1998-01-01
The Tropical Rainfall Measuring Mission (TRMM) spacecraft is a nadir pointing spacecraft that nominally controls attitude based on the Earth Sensor Assembly (ESA) output. After a potential single point failure in the ESA was identified, the contingency attitude determination method chosen to backup the ESA-based system was a sixth-order extended Kalman filter that uses magnetometer and digital sun sensor measurements. A brief description of the TRMM Kalman filter will be given, including some implementation issues and algorithm heritage. Operational aspects of the Kalman filter and some failure detection and correction will be described. The Kalman filter was tested in a sun pointing attitude and in a nadir pointing attitude during the in-orbit checkout period, and results from those tests will be presented. This paper will describe some lessons learned from the experience of the TRMM team.
Kalman filter data assimilation: Targeting observations and parameter estimation
Bellsky, Thomas Kostelich, Eric J.; Mahalov, Alex
2014-06-15
This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly located observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation.
NASA Technical Reports Server (NTRS)
Schmidt, S. F.; Flanagan, P. F.; Sorenson, J. A.
1978-01-01
A Kalman filter for aircraft terminal area and landing navigation was implemented and flight tested in the NASA Ames STOLAND avionics computer onboard a Twin Otter aircraft. This system combines navaid measurements from TACAN, MODILS, air data, radar altimeter sensors along with measurements from strap-down accelerometer and attitude angle sensors. The flight test results demonstrate that the Kalman filter provides improved estimates of the aircraft position and velocity as compared with estimates from the more standard complementary filter. The onboard computer implementation requirements to achieve this improved performance are discussed.
A Physics-Based Kalman Filter for the Ionosphere
NASA Astrophysics Data System (ADS)
Scherliess, L.; Schunk, R.; Sojka, J.; Thompson, D.
A physics-based data assimilation model of the ionosphere is under development as the central part of a DoD MURI funded program called GAIM (Global Assimilation of Ionospheric Measurements). With the significant increase in the number of ionospheric observations that will become available over the next decade, this model will provide a powerful tool towards an improved specification and forecasting of the global ionosphere, with an unprecedented accuracy and reliability. The goal of this effort will be the development of an operational ionospheric assimilation model that will provide specifications and forecasts on spatial grids that can be global, regional, or local (50 km x 50 km). The specification/forecast will be in the form of 3-dimensional electron density distributions from 90 km to geosynchronous altitudes (35,000 km). In this paper we report on the development of a Kalman filter for GAIM using a new physics-based ionosphere/plasmasphere model (IPM). The model solves the continuity and momentum equations for 5 ion species (O+ , N+ , NO+ , O+ , and H+ ) and 2 2 covers the low and mid latitudes from 90 km to about 30,000 km altitude. The Kalman filter used in GAIM is based on approximations of the state error covariance matrix, employing a reduction of the model dimension and a linearization of the physical model for the propagation of the error covariance matrix. These approximations lead to a dramatic reduction in the computational requirements. In this paper, we will give an update on the status of the Kalman filter development and present initial results from a global assimilation run.
3D hand tracking using Kalman filter in depth space
NASA Astrophysics Data System (ADS)
Park, Sangheon; Yu, Sunjin; Kim, Joongrock; Kim, Sungjin; Lee, Sangyoun
2012-12-01
Hand gestures are an important type of natural language used in many research areas such as human-computer interaction and computer vision. Hand gestures recognition requires the prior determination of the hand position through detection and tracking. One of the most efficient strategies for hand tracking is to use 2D visual information such as color and shape. However, visual-sensor-based hand tracking methods are very sensitive when tracking is performed under variable light conditions. Also, as hand movements are made in 3D space, the recognition performance of hand gestures using 2D information is inherently limited. In this article, we propose a novel real-time 3D hand tracking method in depth space using a 3D depth sensor and employing Kalman filter. We detect hand candidates using motion clusters and predefined wave motion, and track hand locations using Kalman filter. To verify the effectiveness of the proposed method, we compare the performance of the proposed method with the visual-based method. Experimental results show that the performance of the proposed method out performs visual-based method.
Subsurface characterization with localized ensemble Kalman filter employing adaptive thresholding
NASA Astrophysics Data System (ADS)
Delijani, Ebrahim Biniaz; Pishvaie, Mahmoud Reza; Boozarjomehry, Ramin Bozorgmehry
2014-07-01
Ensemble Kalman filter, EnKF, as a Monte Carlo sequential data assimilation method has emerged promisingly for subsurface media characterization during past decade. Due to high computational cost of large ensemble size, EnKF is limited to small ensemble set in practice. This results in appearance of spurious correlation in covariance structure leading to incorrect or probable divergence of updated realizations. In this paper, a universal/adaptive thresholding method is presented to remove and/or mitigate spurious correlation problem in the forecast covariance matrix. This method is, then, extended to regularize Kalman gain directly. Four different thresholding functions have been considered to threshold forecast covariance and gain matrices. These include hard, soft, lasso and Smoothly Clipped Absolute Deviation (SCAD) functions. Three benchmarks are used to evaluate the performances of these methods. These benchmarks include a small 1D linear model and two 2D water flooding (in petroleum reservoirs) cases whose levels of heterogeneity/nonlinearity are different. It should be noted that beside the adaptive thresholding, the standard distance dependant localization and bootstrap Kalman gain are also implemented for comparison purposes. We assessed each setup with different ensemble sets to investigate the sensitivity of each method on ensemble size. The results indicate that thresholding of forecast covariance yields more reliable performance than Kalman gain. Among thresholding function, SCAD is more robust for both covariance and gain estimation. Our analyses emphasize that not all assimilation cycles do require thresholding and it should be performed wisely during the early assimilation cycles. The proposed scheme of adaptive thresholding outperforms other methods for subsurface characterization of underlying benchmarks.
NASA Astrophysics Data System (ADS)
Tao, Dongwang; Li, Hui; Ma, Qiang
2016-04-01
Complete structure identification of complicate nonlinear system using extend Kalman filter (EKF) or unscented Kalman filter (UKF) may have the problems of divergence, huge computation and low estimation precision due to the large dimension of the extended state space for the system. In this article, a decentralized identification method of hysteretic system based on the joint EKF and UKF is proposed. The complete structure is divided into linear substructures and nonlinear substructures. The substructures are identified from the top to the bottom. For the linear substructure, EKF is used to identify the extended space including the displacements, velocities, stiffness and damping coefficients of the substructures, using the limited absolute accelerations and the identified interface force above the substructure. Similarly, for the nonlinear substructure, UKF is used to identify the extended space including the displacements, velocities, stiffness, damping coefficients and control parameters for the hysteretic Bouc-Wen model and the force at the interface of substructures. Finally a 10-story shear-type structure with multiple inter-story hysteresis is used for numerical simulation and is identified using the decentralized approach, and the identified results are compared with those using only EKF or UKF for the complete structure identification. The results show that the decentralized approach has the advantage of more stability, relative less computation and higher estimation precision.
Recursive least squares estimation and Kalman filtering by systolic arrays
NASA Technical Reports Server (NTRS)
Chen, M. J.; Yao, K.
1988-01-01
One of the most promising new directions for high-throughput-rate problems is that based on systolic arrays. In this paper, using the matrix-decomposition approach, a systolic Kalman filter is formulated as a modified square-root information filter consisting of a whitening filter followed by a simple least-squares operation based on the systolic QR algorithm. By proper skewing of the input data, a fully pipelined time and measurement update systolic Kalman filter can be achieved with O(n squared) processing cells, resulting in a system throughput rate of O (n).
Tractography from HARDI using an Intrinsic Unscented Kalman Filter
Cheng, Guang; Salehian, Hesamoddin; Forder, John R.; Vemuri, Baba C.
2014-01-01
A novel adaptation of the unscented Kalman filter (UKF) was recently introduced in literature for simultaneous multi-tensor estimation and fiber tractography from diffusion MRI. This technique has the advantage over other tractography methods in terms of computational efficiency, due to the fact that the UKF simultaneously estimates the diffusion tensors and propagates the most consistent direction to track along. This UKF and its variants reported later in literature however are not intrinsic to the space of diffusion tensors. Lack of this key property can possibly lead to inaccuracies in the multi-tensor estimation as well as in the tractography. In this paper, we propose a novel intrinsic unscented Kalman filter (IUKF) in the space of diffusion tensors which are symmetric positive definite matrices, that can be used for simultaneous recursive estimation of multi-tensors and propagation of directional information for use in fiber tractography from diffusion weighted MR data. In addition to being more accurate, IUKF retains all the advantages of UKF mentioned above. We demonstrate the accuracy and effectiveness of the proposed method via experiments publicly available phantom data from the fiber cup-challenge (MICCAI 2009) and diffusion weighted MR scans acquired from human brains and rat spinal cords. PMID:25203986
Tractography from HARDI using an intrinsic unscented Kalman filter.
Cheng, Guang; Salehian, Hesamoddin; Forder, John R; Vemuri, Baba C
2015-01-01
A novel adaptation of the unscented Kalman filter (UKF) was recently introduced in literature for simultaneous multitensor estimation and fiber tractography from diffusion MRI. This technique has the advantage over other tractography methods in terms of computational efficiency, due to the fact that the UKF simultaneously estimates the diffusion tensors and propagates the most consistent direction to track along. This UKF and its variants reported later in literature however are not intrinsic to the space of diffusion tensors. Lack of this key property can possibly lead to inaccuracies in the multitensor estimation as well as in the tractography. In this paper, we propose a novel intrinsic unscented Kalman filter (IUKF) in the space of diffusion tensors which are symmetric positive definite matrices, that can be used for simultaneous recursive estimation of multitensors and propagation of directional information for use in fiber tractography from diffusion weighted MR data. In addition to being more accurate, IUKF retains all the advantages of UKF mentioned above. We demonstrate the accuracy and effectiveness of the proposed method via experiments publicly available phantom data from the fiber cup-challenge (MICCAI 2009) and diffusion weighted MR scans acquired from human brains and rat spinal cords. PMID:25203986
Realizations and performances of least-squares estimation and Kalman filtering by systolic arrays
Chen, M.J.
1987-01-01
Fast least-squares (LS) estimation and Kalman-filtering algorithms utilizing systolic-array implementation are studied. Based on a generalized systolic QR algorithm, a modified LS method is proposed and shown to have superior computational and inter-cell connection complexities, and is more practical for systolic-array implementation. After whitening processing, the Kalman filter can be formulated as a SRIF data-processing problem followed by a simple LS operation. This approach simplifies the computational structure, and is more reliable when the system has singular or near singular coefficient matrix. To improve the throughput rate of the systolic Kalman filter, a topology for stripe QR processing is also proposed. By skewing the order of input matrices, a fully pipelined systolic Kalman-filtering operation can be achieved. With the number of processing units of the O(n/sup 2/), the system throughput rate becomes of the O(n). The numerical properties of the systolic LS estimation and the Kalman filtering algorithms under finite word-length effect are studied via analysis and computer simulations, and are compared with that of conventional approaches. Fault tolerance of the LS estimation algorithm is also discussed. It is shown that by using a simple bypass register, reasonable estimation performance is still possible for a transient defective processing unit.
Application of Consider Covariance to the Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Lundberg, John B.
1996-01-01
The extended Kalman filter (EKF) is the basis for many applications of filtering theory to real-time problems where estimates of the state of a dynamical system are to be computed based upon some set of observations. The form of the EKF may vary somewhat from one application to another, but the fundamental principles are typically unchanged among these various applications. As is the case in many filtering applications, models of the dynamical system (differential equations describing the state variables) and models of the relationship between the observations and the state variables are created. These models typically employ a set of constants whose values are established my means of theory or experimental procedure. Since the estimates of the state are formed assuming that the models are perfect, any modeling errors will affect the accuracy of the computed estimates. Note that the modeling errors may be errors of commission (errors in terms included in the model) or omission (errors in terms excluded from the model). Consequently, it becomes imperative when evaluating the performance of real-time filters to evaluate the effect of modeling errors on the estimates of the state.
Switching Kalman filter for failure prognostic
NASA Astrophysics Data System (ADS)
Lim, Chi Keong Reuben; Mba, David
2015-02-01
The use of condition monitoring (CM) data to predict remaining useful life have been growing with increasing use of health and usage monitoring systems on aircraft. There are many data-driven methodologies available for the prediction and popular ones include artificial intelligence and statistical based approach. The drawback of such approaches is that they require a lot of failure data for training which can be scarce in practice. In lieu of this, methods using state-space and regression-based models that extract information from the data history itself have been explored. However, such methods have their own limitations as they utilize a single time-invariant model which does not represent changing degradation path well. This causes most degradation modeling studies to focus only on segments of their CM data that behaves close to the assumed model. In this paper, a state-space based method; the Switching Kalman Filter (SKF), is adopted for model estimation and life prediction. The SKF approach however, uses multiple models from which the most probable model is inferred from the CM data using Bayesian estimation before it is applied for prediction. At the same time, the inference of the degradation model itself can provide maintainers with more information for their planning. This SKF approach is demonstrated with a case study on gearbox bearings that were found defective from the Republic of Singapore Air Force AH64D helicopter. The use of in-service CM data allows the approach to be applied in a practical scenario and results showed that the developed SKF approach is a promising tool to support maintenance decision-making.
A numerical comparison of discrete Kalman filtering algorithms: An orbit determination case study
NASA Technical Reports Server (NTRS)
Thornton, C. L.; Bierman, G. J.
1976-01-01
The numerical stability and accuracy of various Kalman filter algorithms are thoroughly studied. Numerical results and conclusions are based on a realistic planetary approach orbit determination study. The case study results of this report highlight the numerical instability of the conventional and stabilized Kalman algorithms. Numerical errors associated with these algorithms can be so large as to obscure important mismodeling effects and thus give misleading estimates of filter accuracy. The positive result of this study is that the Bierman-Thornton U-D covariance factorization algorithm is computationally efficient, with CPU costs that differ negligibly from the conventional Kalman costs. In addition, accuracy of the U-D filter using single-precision arithmetic consistently matches the double-precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity of variations in the a priori statistics.
Mobile indoor localization using Kalman filter and trilateration technique
NASA Astrophysics Data System (ADS)
Wahid, Abdul; Kim, Su Mi; Choi, Jaeho
2015-12-01
In this paper, an indoor localization method based on Kalman filtered RSSI is presented. The indoor communications environment however is rather harsh to the mobiles since there is a substantial number of objects distorting the RSSI signals; fading and interference are main sources of the distortion. In this paper, a Kalman filter is adopted to filter the RSSI signals and the trilateration method is applied to obtain the robust and accurate coordinates of the mobile station. From the indoor experiments using the WiFi stations, we have found that the proposed algorithm can provide a higher accuracy with relatively lower power consumption in comparison to a conventional method.
An optimal modification of a Kalman filter for time scales
NASA Technical Reports Server (NTRS)
Greenhall, C. A.
2003-01-01
The Kalman filter in question, which was implemented in the time scale algorithm TA(NIST), produces time scales with poor short-term stability. A simple modification of the error covariance matrix allows the filter to produce time scales with good stability at all averaging times, as verified by simulations of clock ensembles.
Feedback Robust Cubature Kalman Filter for Target Tracking Using an Angle Sensor
Wu, Hao; Chen, Shuxin; Yang, Binfeng; Chen, Kun
2016-01-01
The direction of arrival (DOA) tracking problem based on an angle sensor is an important topic in many fields. In this paper, a nonlinear filter named the feedback M-estimation based robust cubature Kalman filter (FMR-CKF) is proposed to deal with measurement outliers from the angle sensor. The filter designs a new equivalent weight function with the Mahalanobis distance to combine the cubature Kalman filter (CKF) with the M-estimation method. Moreover, by embedding a feedback strategy which consists of a splitting and merging procedure, the proper sub-filter (the standard CKF or the robust CKF) can be chosen in each time index. Hence, the probability of the outliers’ misjudgment can be reduced. Numerical experiments show that the FMR-CKF performs better than the CKF and conventional robust filters in terms of accuracy and robustness with good computational efficiency. Additionally, the filter can be extended to the nonlinear applications using other types of sensors. PMID:27171081
Feedback Robust Cubature Kalman Filter for Target Tracking Using an Angle Sensor.
Wu, Hao; Chen, Shuxin; Yang, Binfeng; Chen, Kun
2016-01-01
The direction of arrival (DOA) tracking problem based on an angle sensor is an important topic in many fields. In this paper, a nonlinear filter named the feedback M-estimation based robust cubature Kalman filter (FMR-CKF) is proposed to deal with measurement outliers from the angle sensor. The filter designs a new equivalent weight function with the Mahalanobis distance to combine the cubature Kalman filter (CKF) with the M-estimation method. Moreover, by embedding a feedback strategy which consists of a splitting and merging procedure, the proper sub-filter (the standard CKF or the robust CKF) can be chosen in each time index. Hence, the probability of the outliers' misjudgment can be reduced. Numerical experiments show that the FMR-CKF performs better than the CKF and conventional robust filters in terms of accuracy and robustness with good computational efficiency. Additionally, the filter can be extended to the nonlinear applications using other types of sensors. PMID:27171081
AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS
NASA Technical Reports Server (NTRS)
Lehtinen, B.
1994-01-01
AESOP was developed to solve a number of problems associated with the design of controls and state estimators for linear time-invariant systems. The systems considered are modeled in state-variable form by a set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are the linear quadratic regulator (LQR) design problem and the steady-state Kalman filter design problem. AESOP is designed to be used in an interactive manner. The user can solve design problems and analyze the solutions in a single interactive session. Both numerical and graphical information are available to the user during the session. The AESOP program is structured around a list of predefined functions. Each function performs a single computation associated with control, estimation, or system response determination. AESOP contains over sixty functions and permits the easy inclusion of user defined functions. The user accesses these functions either by inputting a list of desired functions in the order they are to be performed, or by specifying a single function to be performed. The latter case is used when the choice of function and function order depends on the results of previous functions. The available AESOP functions are divided into several general areas including: 1) program control, 2) matrix input and revision, 3) matrix formation, 4) open-loop system analysis, 5) frequency response, 6) transient response, 7) transient function zeros, 8) LQR and Kalman filter design, 9) eigenvalues and eigenvectors, 10) covariances, and 11) user-defined functions. The most important functions are those that design linear quadratic regulators and Kalman filters. The user interacts with AESOP when using these functions by inputting design weighting parameters and by viewing displays of designed system response. Support functions obtain system transient and frequency responses, transfer functions, and covariance matrices. AESOP can also provide the user
Kalman Filter for Calibrating a Telescope Focal Plane
NASA Technical Reports Server (NTRS)
Kang, Bryan; Bayard, David
2006-01-01
The instrument-pointing frame (IPF) Kalman filter, and an algorithm that implements this filter, have been devised for calibrating the focal plane of a telescope. As used here, calibration signifies, more specifically, a combination of measurements and calculations directed toward ensuring accuracy in aiming the telescope and determining the locations of objects imaged in various arrays of photodetectors in instruments located on the focal plane. The IPF Kalman filter was originally intended for application to a spaceborne infrared astronomical telescope, but can also be applied to other spaceborne and ground-based telescopes. In the traditional approach to calibration of a telescope, (1) one team of experts concentrates on estimating parameters (e.g., pointing alignments and gyroscope drifts) that are classified as being of primarily an engineering nature, (2) another team of experts concentrates on estimating calibration parameters (e.g., plate scales and optical distortions) that are classified as being primarily of a scientific nature, and (3) the two teams repeatedly exchange data in an iterative process in which each team refines its estimates with the help of the data provided by the other team. This iterative process is inefficient and uneconomical because it is time-consuming and entails the maintenance of two survey teams and the development of computer programs specific to the requirements of each team. Moreover, theoretical analysis reveals that the engineering/ science iterative approach is not optimal in that it does not yield the best estimates of focal-plane parameters and, depending on the application, may not even enable convergence toward a set of estimates.
NASA Astrophysics Data System (ADS)
Culp, Robert D.; Mackison, Don; Fu, Ho-Ling
This paper deals with an advanced Kalman filter application to orbit determination from satellite tracking data. Modern control theory is used to set up an optimal Kalman gain for the estimation problem and to estimate its errors out of the system outputs. The classical orbit determination techniques have been used over the years for the evaluation of data analysis. A recent study was conducted to find the initial state values by modern orbit determination with Kalman gain. An original algorithm introduced by Born et al. (1986) has been applied to the spacecraft and earth satellite orbit determination for several years. The determination of the desired process and special Kalman gain for the best estimator include three kinds of computational algorithms: Batch, Sequential, and Extended Sequential processors. The model is based on a minimum variance using estimation and prediction techniques. Moreover, the estimation and computational algorithms have been modified in the UNIX system simulating to the TOPEX satellite orbit data process.
Deconvolution Kalman filtering for force measurements of revolving wings
NASA Astrophysics Data System (ADS)
Vester, R.; Percin, M.; van Oudheusden, B.
2016-09-01
The applicability of a deconvolution Kalman filtering approach is assessed for the force measurements on a flat plate undergoing a revolving motion, as an alternative procedure to correct for test setup vibrations. The system identification process required for the correct implementation of the deconvolution Kalman filter is explained in detail. It is found that in the presence of a relatively complex forcing history, the DK filter is better suited to filter out structural test rig vibrations than conventional filtering techniques that are based on, for example, low-pass or moving-average filtering. The improvement is especially found in the characterization of the generated force peaks. Consequently, more reliable force data is obtained, which is vital to validate semi-empirical estimation models, but is also relevant to correlate identified flow phenomena to the force production.
Kriged Kalman filtering for predicting the wildfire temperature evolution
NASA Astrophysics Data System (ADS)
Phan, Connie N. K. K.
Existing wildfire evolution models have been mostly developed in a deterministic modelling framework. As a complementary alternative, this thesis presents a stochastic framework based on the Kriged Kalman filter to obtain global temperature predictions given local temperature measurements. By solving the heat transfer partial differential equation driving the wildfire evolution, it is shown that the spatio-temporal mean temperature process associated with a wildfire evolving in a finite spatial domain under certain prescribed conditions can be approximated by a Fourier series. The potential of the proposed Kriged Kalman filtering framework in predicting the wildfire temperature evolution is demonstrated in simulations on temperature data generated by a simplified physical wildfire propagation model. The performance of the Kriged Kalman filter in predicting the wildfire temperature evolution is compared to that of standard Gaussian process regression.
Tropospheric delay determination by Kalman filtering VLBI data
NASA Astrophysics Data System (ADS)
Soja, Benedikt; Nilsson, Tobias; Karbon, Maria; Zus, Florian; Dick, Galina; Deng, Zhiguo; Wickert, Jens; Heinkelmann, Robert; Schuh, Harald
2015-09-01
The troposphere is one of the most important error sources for space geodetic techniques relying on radio signals. Since it is not possible to model the wet part of the tropospheric delay with sufficient accuracy, it needs to be estimated from the observational data. In the analysis of very long baseline interferometry (VLBI) data, the parameter estimation is routinely performed using a least squares adjustment. In this paper, we investigate the application of a Kalman filter for parameter estimation, specifically focusing on the tropospheric delays. The main advantages of a Kalman filter are its real-time capability and stochastic approach. We focused on the latter and derived stochastic models for VLBI zenith wet delays, taking into account temporal and location-based differences. Compared to a static noise model, the quality of station coordinates, also estimated in the Kalman filter, increased as a result. In terms of baseline length and station coordinate repeatabilities, this improvement amounted to 2.3 %. Additionally, we compared the Kalman filter and least squares results for VLBI with zenith wet delays derived from GPS (Global Positioning System), water vapor radiometers, and ray tracing in numerical weather models. The agreement of the Kalman filter VLBI solution with respect to water vapor radiometer data was larger than that of the least squares solution by 6-15 %. Our investigations are based on selected VLBI data (CONT campaigns) that are closest to how future VLBI infrastructure is designed to operate. With the aim for continuous and near real-time parameter estimation and the promising results which we have achieved in this study, we expect Kalman filtering to grow in importance in VLBI analysis.
Iterated unscented Kalman filter for phase unwrapping of interferometric fringes.
Xie, Xianming
2016-08-22
A fresh phase unwrapping algorithm based on iterated unscented Kalman filter is proposed to estimate unambiguous unwrapped phase of interferometric fringes. This method is the result of combining an iterated unscented Kalman filter with a robust phase gradient estimator based on amended matrix pencil model, and an efficient quality-guided strategy based on heap sort. The iterated unscented Kalman filter that is one of the most robust methods under the Bayesian theorem frame in non-linear signal processing so far, is applied to perform simultaneously noise suppression and phase unwrapping of interferometric fringes for the first time, which can simplify the complexity and the difficulty of pre-filtering procedure followed by phase unwrapping procedure, and even can remove the pre-filtering procedure. The robust phase gradient estimator is used to efficiently and accurately obtain phase gradient information from interferometric fringes, which is needed for the iterated unscented Kalman filtering phase unwrapping model. The efficient quality-guided strategy is able to ensure that the proposed method fast unwraps wrapped pixels along the path from the high-quality area to the low-quality area of wrapped phase images, which can greatly improve the efficiency of phase unwrapping. Results obtained from synthetic data and real data show that the proposed method can obtain better solutions with an acceptable time consumption, with respect to some of the most used algorithms. PMID:27557170
On the equivalence of Kalman filtering and least-squares estimation
NASA Astrophysics Data System (ADS)
Mysen, E.
2016-07-01
The Kalman filter is derived directly from the least-squares estimator, and generalized to accommodate stochastic processes with time variable memory. To complete the link between least-squares estimation and Kalman filtering of first-order Markov processes, a recursive algorithm is presented for the computation of the off-diagonal elements of the a posteriori least-squares error covariance. As a result of the algebraic equivalence of the two estimators, both approaches can fully benefit from the advantages implied by their individual perspectives. In particular, it is shown how Kalman filter solutions can be integrated into the normal equation formalism that is used for intra- and inter-technique combination of space geodetic data.
Extended Kalman filter sensor failure detection method for pressurizer monitoring
Filho, E.O.A.; Nakata, H. )
1992-01-01
This work presents the development of the sensor failure detection and isolation system (FDIS) methodology, which is suitable for implementation in nuclear plant control systems. The methodology is based on the extended Kalman filter applied to a pressurized water reactor pressurizer. The utilization of the Kalman filter follows the standard procedure: First, an estimate of the state variables and the corresponding covariances are obtained; then, based on the state equations, the estimated state variables are propagated until the next measurements for the new estimate.
NASA Technical Reports Server (NTRS)
Park, K. C.; Belvin, W. Keith
1990-01-01
A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.
2014-01-01
total computational time needed for the Kalman filters is under 25% of the total signal length rendering it possible to perform the filtering in real-time. Conclusions It is possible to measure in real-time heart and breathing rates using an adaptive Kalman filter approach. Adapting the Kalman filter matrices improves the estimation results and makes the filter universally deployable when measuring cardiorespiratory signals. PMID:24886253
Fuzzy Adaptive Cubature Kalman Filter for Integrated Navigation Systems.
Tseng, Chien-Hao; Lin, Sheng-Fuu; Jwo, Dah-Jing
2016-01-01
This paper presents a sensor fusion method based on the combination of cubature Kalman filter (CKF) and fuzzy logic adaptive system (FLAS) for the integrated navigation systems, such as the GPS/INS (Global Positioning System/inertial navigation system) integration. The third-degree spherical-radial cubature rule applied in the CKF has been employed to avoid the numerically instability in the system model. In processing navigation integration, the performance of nonlinear filter based estimation of the position and velocity states may severely degrade caused by modeling errors due to dynamics uncertainties of the vehicle. In order to resolve the shortcoming for selecting the process noise covariance through personal experience or numerical simulation, a scheme called the fuzzy adaptive cubature Kalman filter (FACKF) is presented by introducing the FLAS to adjust the weighting factor of the process noise covariance matrix. The FLAS is incorporated into the CKF framework as a mechanism for timely implementing the tuning of process noise covariance matrix based on the information of degree of divergence (DOD) parameter. The proposed FACKF algorithm shows promising accuracy improvement as compared to the extended Kalman filter (EKF), unscented Kalman filter (UKF), and CKF approaches. PMID:27472336
Lall, Pradeep; Wei, Junchao; Davis, J Lynn
2014-06-24
Abstract— Solid-state lighting (SSL) luminaires containing light emitting diodes (LEDs) have the potential of seeing excessive temperatures when being transported across country or being stored in non-climate controlled warehouses. They are also being used in outdoor applications in desert environments that see little or no humidity but will experience extremely high temperatures during the day. This makes it important to increase our understanding of what effects high temperature exposure for a prolonged period of time will have on the usability and survivability of these devices. Traditional light sources “burn out” at end-of-life. For an incandescent bulb, the lamp life is defined by B50 life. However, the LEDs have no filament to “burn”. The LEDs continually degrade and the light output decreases eventually below useful levels causing failure. Presently, the TM-21 test standard is used to predict the L70 life of LEDs from LM-80 test data. Several failure mechanisms may be active in a LED at a single time causing lumen depreciation. The underlying TM-21 Model may not capture the failure physics in presence of multiple failure mechanisms. Correlation of lumen maintenance with underlying physics of degradation at system-level is needed. In this paper, Kalman Filter (KF) and Extended Kalman Filters (EKF) have been used to develop a 70-percent Lumen Maintenance Life Prediction Model for LEDs used in SSL luminaires. Ten-thousand hour LM-80 test data for various LEDs have been used for model development. System state at each future time has been computed based on the state space at preceding time step, system dynamics matrix, control vector, control matrix, measurement matrix, measured vector, process noise and measurement noise. The future state of the lumen depreciation has been estimated based on a second order Kalman Filter model and a Bayesian Framework. Life prediction of L70 life for the LEDs used in SSL luminaires from KF and EKF based models have
State estimation Kalman filter using optical processings Noise statistics known
NASA Technical Reports Server (NTRS)
Jackson, J.; Casasent, D.
1984-01-01
Reference is made to a study by Casasent et al. (1983), which gave a description of a frequency-multiplexed acoustooptic processor and showed how it was capable of performing all the individual operations required in Kalman filtering. The data flow and organization of all required operations however, were not detailed in that study. Consideration is given here to a simpler Kalman filter state estimation problem. Equally spaced time-sampled intervals (k times T sub s, with k the iterative time index) are assumed. It is further assumed that the system noise vector w and the measurement noise vector v are uncorrelated and Gaussian distributed and that the noise statistics (Q and R) and the system model (Phi, Gamma, H) are known. The error covariance matrix P and the extrapolated error covariance matrix M can thus be precomputed and the Kalman gain matrix K sub k can be precomputed and stored for each input time sample.
Parallelized unscented Kalman filters for carrier recovery in coherent optical communication.
Jignesh, Jokhakar; Corcoran, Bill; Lowery, Arthur
2016-07-15
We show that unscented Kalman filters can be used to mitigate local oscillator phase noise and to compensate carrier frequency offset in coherent single-carrier optical communication systems. A parallel processing architecture implementing the unscented Kalman filter is proposed, improving upon a previous parallelized linear Kalman filter (LKF) implementation. PMID:27420508
Application of Kalman filtering in VLBI data analysis
NASA Astrophysics Data System (ADS)
Nilsson, Tobias; Soja, Benedikt; Karbon, Maria; Heinkelmann, Robert; Schuh, Harald
2015-08-01
In this paper, we demonstrate the advantage of applying a Kalman filter for the parameter estimation in very-long-baseline interferometry (VLBI) data analysis. We present the implementation of a Kalman filter in the VLBI software VieVS@GFZ. The performance is then investigated by looking at the accuracy obtained for various parameters, like baseline lengths, Earth Orientation Parameters, radio source coordinates, and tropospheric delays. The results are compared to those obtained when the classical least squares method (LSM) is applied for the parameter estimation, where clocks and zenith wet delays are estimated with 30-min intervals and gradients with 120-min intervals. We show that the accuracy generally is better for the Kalman filter solution, for example, the baseline length repeatabilities are on average about 10 % better compared to the LSM solution. We also discuss the possibilities to use the Kalman filter to estimate sub-diurnal station position variations and show that the variations caused by solid Earth tides can be retrieved with an accuracy of about 2 cm.
Performance enhancement for GPS positioning using constrained Kalman filtering
NASA Astrophysics Data System (ADS)
Guo, Fei; Zhang, Xiaohong; Wang, Fuhong
2015-08-01
Over the past decades Kalman filtering (KF) algorithms have been extensively investigated and applied in the area of kinematic positioning. In the application of KF in kinematic precise point positioning (PPP), it is often the case where some known functional or theoretical relations exist among the unknown state parameters, which can be and should be made use of to enhance the performance of kinematic PPP, especially in an urban and forest environment. The central task of this paper is to effectively blend the commonly used GNSS data and internal/external additional constrained information to generate an optimal PPP solution. This paper first investigates the basic algorithm of constrained Kalman filtering. Then two types of PPP model with speed constraints and trajectory constraints, respectively, are proposed. Further validation tests based on a variety of situations show that the positioning performances (positioning accuracy, reliability and continuity) from the constrained Kalman filter are significantly superior to those from the conventional Kalman filter, particularly under extremely poor observation conditions.
Combining Earth Orientation Measurements Using a Kalman Filter
NASA Technical Reports Server (NTRS)
Gross, R.
2000-01-01
A Kalman filter has many properties that make it an attractive choice as a technique for combining Earth orientation measurements. It allows the full accuracy of the measurements to be used, whether the measurements are degenerate or are of full rank, are irregularly or regularly spaced in time, or are corrupted by systematic or other errors that can be described by stochastic models.
Identification of observer/Kalman filter Markov parameters: Theory and experiments
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Phan, Minh; Horta, Lucas G.; Longman, Richard W.
1991-01-01
An algorithm to compute Markov parameters of an observer or Kalman filter from experimental input and output data is discussed. The Markov parameters can then be used for identification of a state space representation, with associated Kalman gain or observer gain, for the purpose of controller design. The algorithm is a non-recursive matrix version of two recursive algorithms developed in previous works for different purposes. The relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and gives bounds on the proper choice of observer order. It is shown that if one uses data containing noise, and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. Results are demonstrated in numerical studies and in experiments on an ten-bay truss structure.
Adaptive distributed Kalman filtering with wind estimation for astronomical adaptive optics.
Massioni, Paolo; Gilles, Luc; Ellerbroek, Brent
2015-12-01
In the framework of adaptive optics (AO) for astronomy, it is a common assumption to consider the atmospheric turbulent layers as "frozen flows" sliding according to the wind velocity profile. For this reason, having knowledge of such a velocity profile is beneficial in terms of AO control system performance. In this paper we show that it is possible to exploit the phase estimate from a Kalman filter running on an AO system in order to estimate wind velocity. This allows the update of the Kalman filter itself with such knowledge, making it adaptive. We have implemented such an adaptive controller based on the distributed version of the Kalman filter, for a realistic simulation of a multi-conjugate AO system with laser guide stars on a 30 m telescope. Simulation results show that this approach is effective and promising and the additional computational cost with respect to the distributed filter is negligible. Comparisons with a previously published slope detection and ranging wind profiler are made and the impact of turbulence profile quantization is assessed. One of the main findings of the paper is that all flavors of the adaptive distributed Kalman filter are impacted more significantly by turbulence profile quantization than the static minimum mean square estimator which does not incorporate wind profile information. PMID:26831389
Adaptive error covariances estimation methods for ensemble Kalman filters
Zhen, Yicun; Harlim, John
2015-08-01
This paper presents a computationally fast algorithm for estimating, both, the system and observation noise covariances of nonlinear dynamics, that can be used in an ensemble Kalman filtering framework. The new method is a modification of Belanger's recursive method, to avoid an expensive computational cost in inverting error covariance matrices of product of innovation processes of different lags when the number of observations becomes large. When we use only product of innovation processes up to one-lag, the computational cost is indeed comparable to a recently proposed method by Berry–Sauer's. However, our method is more flexible since it allows for using information from product of innovation processes of more than one-lag. Extensive numerical comparisons between the proposed method and both the original Belanger's and Berry–Sauer's schemes are shown in various examples, ranging from low-dimensional linear and nonlinear systems of SDEs and 40-dimensional stochastically forced Lorenz-96 model. Our numerical results suggest that the proposed scheme is as accurate as the original Belanger's scheme on low-dimensional problems and has a wider range of more accurate estimates compared to Berry–Sauer's method on L-96 example.
Implementation of a Parallel Kalman Filter for Stratospheric Chemical Tracer Assimilation
NASA Technical Reports Server (NTRS)
Chang, Lang-Ping; Lyster, Peter M.; Menard, R.; Cohn, S. E.
1998-01-01
A Kalman filter for the assimilation of long-lived atmospheric chemical constituents has been developed for two-dimensional transport models on isentropic surfaces over the globe. An important attribute of the Kalman filter is that it calculates error covariances of the constituent fields using the tracer dynamics. Consequently, the current Kalman-filter assimilation is a five-dimensional problem (coordinates of two points and time), and it can only be handled on computers with large memory and high floating point speed. In this paper, an implementation of the Kalman filter for distributed-memory, message-passing parallel computers is discussed. Two approaches were studied: an operator decomposition and a covariance decomposition. The latter was found to be more scalable than the former, and it possesses the property that the dynamical model does not need to be parallelized, which is of considerable practical advantage. This code is currently used to assimilate constituent data retrieved by limb sounders on the Upper Atmosphere Research Satellite. Tests of the code examined the variance transport and observability properties. Aspects of the parallel implementation, some timing results, and a brief discussion of the physical results will be presented.
Star spot location estimation using Kalman filter for star tracker.
Liu, Hai-bo; Yang, Jian-kun; Wang, Jiong-qi; Tan, Ji-chun; Li, Xiu-jian
2011-04-20
Star pattern recognition and attitude determination accuracy is highly dependent on star spot location accuracy for the star tracker. A star spot location estimation approach with the Kalman filter for a star tracker has been proposed, which consists of three steps. In the proposed approach, the approximate locations of the star spots in successive frames are predicted first; then the measurement star spot locations are achieved by defining a series of small windows around each predictive star spot location. Finally, the star spot locations are updated by the designed Kalman filter. To confirm the proposed star spot location estimation approach, the simulations based on the orbit data of the CHAMP satellite and the real guide star catalog are performed. The simulation results indicate that the proposed approach can filter out noises from the measurements remarkably if the sampling frequency is sufficient. PMID:21509065
Estimating short-period dynamics using an extended Kalman filter
NASA Technical Reports Server (NTRS)
Bauer, Jeffrey E.; Andrisani, Dominick
1990-01-01
An extended Kalman filter (EKF) is used to estimate the parameters of a low-order model from aircraft transient response data. The low-order model is a state space model derived from the short-period approximation of the longitudinal aircraft dynamics. The model corresponds to the pitch rate to stick force transfer function currently used in flying qualities analysis. Because of the model chosen, handling qualities information is also obtained. The parameters are estimated from flight data as well as from a six-degree-of-freedom, nonlinear simulation of the aircraft. These two estimates are then compared and the discrepancies noted. The low-order model is able to satisfactorily match both flight data and simulation data from a high-order computer simulation. The parameters obtained from the EKF analysis of flight data are compared to those obtained using frequency response analysis of the flight data. Time delays and damping ratios are compared and are in agreement. This technique demonstrates the potential to determine, in near real time, the extent of differences between computer models and the actual aircraft. Precise knowledge of these differences can help to determine the flying qualities of a test aircraft and lead to more efficient envelope expansion.
Spitzer Instrument Pointing Frame (IPF) Kalman Filter Algorithm
NASA Technical Reports Server (NTRS)
Bayard, David S.; Kang, Bryan H.
2004-01-01
This paper discusses the Spitzer Instrument Pointing Frame (IPF) Kalman Filter algorithm. The IPF Kalman filter is a high-order square-root iterated linearized Kalman filter, which is parametrized for calibrating the Spitzer Space Telescope focal plane and aligning the science instrument arrays with respect to the telescope boresight. The most stringent calibration requirement specifies knowledge of certain instrument pointing frames to an accuracy of 0.1 arcseconds, per-axis, 1-sigma relative to the Telescope Pointing Frame. In order to achieve this level of accuracy, the filter carries 37 states to estimate desired parameters while also correcting for expected systematic errors due to: (1) optical distortions, (2) scanning mirror scale-factor and misalignment, (3) frame alignment variations due to thermomechanical distortion, and (4) gyro bias and bias-drift in all axes. The resulting estimated pointing frames and calibration parameters are essential for supporting on-board precision pointing capability, in addition to end-to-end 'pixels on the sky' ground pointing reconstruction efforts.
An Adaptive Kalman Filter using a Simple Residual Tuning Method
NASA Technical Reports Server (NTRS)
Harman, Richard R.
1999-01-01
One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.
An Adaptive Kalman Filter Using a Simple Residual Tuning Method
NASA Technical Reports Server (NTRS)
Harman, Richard R.
1999-01-01
One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. A. H. Jazwinski developed a specialized version of this technique for estimation of process noise. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.
Nonlinear Kalman Filtering for acoustic emission source localization in anisotropic panels.
Dehghan Niri, E; Farhidzadeh, A; Salamone, S
2014-02-01
Nonlinear Kalman Filtering is an established field in applied probability and control systems, which plays an important role in many practical applications from target tracking to weather and climate prediction. However, its application for acoustic emission (AE) source localization has been very limited. In this paper, two well-known nonlinear Kalman Filtering algorithms are presented to estimate the location of AE sources in anisotropic panels: the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). These algorithms are applied to two cases: velocity profile known (CASE I) and velocity profile unknown (CASE II). The algorithms are compared with a more traditional nonlinear least squares method. Experimental tests are carried out on a carbon-fiber reinforced polymer (CFRP) composite panel instrumented with a sparse array of piezoelectric transducers to validate the proposed approaches. AE sources are simulated using an instrumented miniature impulse hammer. In order to evaluate the performance of the algorithms, two metrics are used: (1) accuracy of the AE source localization and (2) computational cost. Furthermore, it is shown that both EKF and UKF can provide a confidence interval of the estimated AE source location and can account for uncertainty in time of flight measurements. PMID:23972569
Upper Atmosphere Research Satellite (UARS) onboard attitude determination using a Kalman filter
NASA Technical Reports Server (NTRS)
Garrick, Joseph
1993-01-01
The Upper Atmospheric Research Satellite (UARS) requires a highly accurate knowledge of its attitude to accomplish its mission. Propagation of the attitude state using gyro measurements is not sufficient to meet the accuracy requirements, and must be supplemented by a observer/compensation process to correct for dynamics and observation anomalies. The process of amending the attitude state utilizes a well known method, the discrete Kalman Filter. This study is a sensitivity analysis of the discrete Kalman Filter as implemented in the UARS Onboard Computer (OBC). The stability of the Kalman Filter used in the normal on-orbit control mode within the OBC, is investigated for the effects of corrupted observations and nonlinear errors. Also, a statistical analysis on the residuals of the Kalman Filter is performed. These analysis is based on simulations using the UARS Dynamics Simulator (UARSDSIM) and compared against attitude requirements as defined by General Electric (GE). An independent verification of expected accuracies is performed using the Attitude Determination Error Analysis System (ADEAS).
Model-Based Engine Control Architecture with an Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Csank, Jeffrey T.; Connolly, Joseph W.
2016-01-01
This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The non-linear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.
Model-Based Engine Control Architecture with an Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Csank, Jeffrey T.; Connolly, Joseph W.
2016-01-01
This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The nonlinear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.
Real time estimation of ship motions using Kalman filtering techniques
NASA Technical Reports Server (NTRS)
Triantafyllou, M. S.; Bodson, M.; Athans, M.
1983-01-01
The estimation of the heave, pitch, roll, sway, and yaw motions of a DD-963 destroyer is studied, using Kalman filtering techniques, for application in VTOL aircraft landing. The governing equations are obtained from hydrodynamic considerations in the form of linear differential equations with frequency dependent coefficients. In addition, nonminimum phase characteristics are obtained due to the spatial integration of the water wave forces. The resulting transfer matrix function is irrational and nonminimum phase. The conditions for a finite-dimensional approximation are considered and the impact of the various parameters is assessed. A detailed numerical application for a DD-963 destroyer is presented and simulations of the estimations obtained from Kalman filters are discussed.
Robust tracking with spatio-velocity snakes: Kalman filtering approach
Peterfreund, N.
1997-06-01
Using results from robust Kalman filtering, the author presents a new Kalman filter-based snake model for tracking of nonrigid objects in combined spatio-velocity space. The proposed model is the stochastic version of the velocity snake, an active contour model for combined tracking of position and velocity of nonrigid boundaries. The proposed model uses image gradient and optical flow measurements along the contour as system measurements. An optical-flow based measurement error is used to detect and reject image measurements which correspond to image clutter or to other objects. The method was applied to object tracking of both rigid and nonrigid objects, resulting in good tracking results and robustness to image clutter, occlusions and numerical noise.
Robust tracking with spatio-velocity snakes: Kalman filtering approach
Peterfreund, N.
1998-12-31
Using results from robust Kalman filtering, we present a new Kalman filter-based snake model for tracking of nonrigid objects in combined spatio-velocity space. The proposed model is the stochastic version of the velocity snake, an active contour model for combined tracking of position and velocity of nonrigid boundaries. The proposed model uses image gradient and optical flow measurements along the contour as system measurements. An optical-flow based measurement error is used to detect and reject image measurements which correspond to image clutter or to other objects. The method was applied to object tracking of both rigid and nonrigid objects, resulting in good tracking results and robustness to image clutter, occlusions and numerical noise. 19 refs., 3 figs.
Recent Flight Results of the TRMM Kalman Filter
NASA Technical Reports Server (NTRS)
Andrews, Stephen F.; Bilanow, Stephen; Bauer, Frank (Technical Monitor)
2002-01-01
The Tropical Rainfall Measuring Mission (TRMM) spacecraft is a nadir pointing spacecraft that nominally controls the roll and pitch attitude based on the Earth Sensor Assembly (ESA) output. TRMM's nominal orbit altitude was 350 km, until raised to 402 km to prolong mission life. During the boost, the ESA experienced a decreasing signal to noise ratio, until sun interference at 393 km altitude made the ESA data unreliable for attitude determination. At that point, the backup attitude determination algorithm, an extended Kalman filter, was enabled. After the boost finished, TRMM reacquired its nadir-pointing attitude, and continued its mission. This paper will briefly discuss the boost and the decision to turn on the backup attitude determination algorithm. A description of the extended Kalman filter algorithm will be given. In addition, flight results from analyzing attitude data and the results of software changes made onboard TRMM will be discussed. Some lessons learned are presented.
Estimating Power System Dynamic States Using Extended Kalman Filter
Huang, Zhenyu; Schneider, Kevin P.; Nieplocha, Jaroslaw; Zhou, Ning
2014-10-31
Abstract—The state estimation tools which are currently deployed in power system control rooms are based on a steady state assumption. As a result, the suite of operational tools that rely on state estimation results as inputs do not have dynamic information available and their accuracy is compromised. This paper investigates the application of Extended Kalman Filtering techniques for estimating dynamic states in the state estimation process. The new formulated “dynamic state estimation” includes true system dynamics reflected in differential equations, not like previously proposed “dynamic state estimation” which only considers the time-variant snapshots based on steady state modeling. This new dynamic state estimation using Extended Kalman Filter has been successfully tested on a multi-machine system. Sensitivity studies with respect to noise levels, sampling rates, model errors, and parameter errors are presented as well to illustrate the robust performance of the developed dynamic state estimation process.
Design of Linear Quadratic Regulators and Kalman Filters
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Geyser, L.
1986-01-01
AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.
A comparison of EAKF and particle filter: towards a ensemble adjustment Kalman particle filter
NASA Astrophysics Data System (ADS)
Zhang, Xiangming; Shen, Zheqi; Tang, Youmin
2016-04-01
Bayesian estimation theory provides a general approach for the state estimate. In this study, we first explore two Bayesian-based methods: ensemble adjustment Kalman filter (EAKF) and sequential importance resampling particle filter (SIR-PF), using a well-known nonlinear and non-Gaussian model (Lorenz '63 model). The EAKF can be regarded as a deterministic scheme of the ensemble Kalman filter (EnKF), which performs better than the classical (stochastic) EnKF in a general framework. Comparison between the SIR-PF and the EAKF reveals that the former outperforms the latter if ensemble size is very large that can avoid the filter degeneracy, and vice versa. On the basis of comparisons between the SIR-PF and the EAKF, a mixture filter, called ensemble adjustment Kalman particle filter (EAKPF), is proposed to combine their both merits. Similar to the ensemble Kalman particle filter, which combines the stochastic EnKF and SIR-PF analysis schemes with a tuning parameter, the new mixture filter essentially provides a continuous interpolation between the EAKF and SIR-PF. The same Lorenz '63 model is used as a testbed, showing that the EAKPF is able to overcome filter degeneracy while maintaining the non-Gaussian nature, and performs better than the EAKF given limited ensemble size.
Traditional Tracking with Kalman Filter on Parallel Architectures
NASA Astrophysics Data System (ADS)
Cerati, Giuseppe; Elmer, Peter; Lantz, Steven; MacNeill, Ian; McDermott, Kevin; Riley, Dan; Tadel, Matevž; Wittich, Peter; Würthwein, Frank; Yagil, Avi
2015-05-01
Power density constraints are limiting the performance improvements of modern CPUs. To address this, we have seen the introduction of lower-power, multi-core processors, but the future will be even more exciting. In order to stay within the power density limits but still obtain Moore's Law performance/price gains, it will be necessary to parallelize algorithms to exploit larger numbers of lightweight cores and specialized functions like large vector units. Example technologies today include Intel's Xeon Phi and GPGPUs. Track finding and fitting is one of the most computationally challenging problems for event reconstruction in particle physics. At the High Luminosity LHC, for example, this will be by far the dominant problem. The most common track finding techniques in use today are however those based on the Kalman Filter. Significant experience has been accumulated with these techniques on real tracking detector systems, both in the trigger and offline. We report the results of our investigations into the potential and limitations of these algorithms on the new parallel hardware.
An ensemble adjustment Kalman filter study for Argo data
NASA Astrophysics Data System (ADS)
Yin, Xunqiang; Qiao, Fangli; Yang, Yongzeng; Xia, Changshui
2010-05-01
An ensemble adjustment Kalman filter system is developed to assimilate Argo profiles into the Northwest Pacific MASNUM wave-circulation coupled model, which is based on the Princeton Ocean Model (POM). This model was recoded in FORTRAN-90 style, and some new data types were defined to improve the efficiency of system design and execution. This system is arranged for parallel computing by using UNIX shell scripts: it is easier with single models running separately with the required information exchanged through input/output files. Tests are carried out to check the performance of the system: one for checking the ensemble spread and another for the performance of assimilation of the Argo data in 2005. The first experiment shows that the assimilation system performs well. The comparison with the Satellite derived sea surface temperature (SST) shows that modeled SST errors are reduced after assimilation; at the same time, the spatial correlation between the simulated SST anomalies and the satellite data is improved because of Argo assimilation. Furthermore, the temporal evolution/trend of SST becomes much better than those results without data assimilation. The comparison against GTSPP profiles shows that the improvement is not only in the upper layers of ocean, but also in the deeper layers. All these results suggest that this system is potentially capable of reconstructing oceanic data sets that are of high quality and are temporally and spatially continuous.
Flood Nowcasting With Linear Catchment Models, Radar and Kalman Filters
NASA Astrophysics Data System (ADS)
Pegram, Geoff; Sinclair, Scott
A pilot study using real time rainfall data as input to a parsimonious linear distributed flood forecasting model is presented. The aim of the study is to deliver an operational system capable of producing flood forecasts, in real time, for the Mgeni and Mlazi catchments near the city of Durban in South Africa. The forecasts can be made at time steps which are of the order of a fraction of the catchment response time. To this end, the model is formulated in Finite Difference form in an equation similar to an Auto Regressive Moving Average (ARMA) model; it is this formulation which provides the required computational efficiency. The ARMA equation is a discretely coincident form of the State-Space equations that govern the response of an arrangement of linear reservoirs. This results in a functional relationship between the reservoir response con- stants and the ARMA coefficients, which guarantees stationarity of the ARMA model. Input to the model is a combined "Best Estimate" spatial rainfall field, derived from a combination of weather RADAR and Satellite rainfield estimates with point rain- fall given by a network of telemetering raingauges. Several strategies are employed to overcome the uncertainties associated with forecasting. Principle among these are the use of optimal (double Kalman) filtering techniques to update the model states and parameters in response to current streamflow observations and the application of short term forecasting techniques to provide future estimates of the rainfield as input to the model.
The Navstar GPS master control station's Kalman filter experience
NASA Technical Reports Server (NTRS)
Scardera, Michael P.
1990-01-01
The Navstar Global Positioning System (GPS) is a highly accurate space based navigation system providing all weather, 24 hour a day service to both military and civilian users. The system provides a Gaussian position solution with four satellites, each providing its ephemeris and clock offset with respect to GPS time. The GPS Master Clock Station (MCS) is charged with tracking each Navstar spacecraft and precisely defining the ephemeris and clock parameters for upload into the vehicle's navigation message. Briefly described here are the Navstar system and the Kalman filter estimation process used by MCS to determine, predict, and ensure quality control for each of the satellite's ephemeris and clock states. Routine performance is shown. Kalman filter reaction and response is discussed for anomalous clock behavior and trajectory perturbations. Particular attention is given to MCS efforts to improve orbital adjust modeling. The satellite out of service time due to orbital maneuvering has been reduced in the past year from four days to under twelve hours. The planning, reference trajectory model, and Kalman filter management improvements are explained.
Relationship between Allan variances and Kalman Filter parameters
NASA Technical Reports Server (NTRS)
Vandierendonck, A. J.; Mcgraw, J. B.; Brown, R. G.
1984-01-01
A relationship was constructed between the Allan variance parameters (H sub z, H sub 1, H sub 0, H sub -1 and H sub -2) and a Kalman Filter model that would be used to estimate and predict clock phase, frequency and frequency drift. To start with the meaning of those Allan Variance parameters and how they are arrived at for a given frequency source is reviewed. Although a subset of these parameters is arrived at by measuring phase as a function of time rather than as a spectral density, they all represent phase noise spectral density coefficients, though not necessarily that of a rational spectral density. The phase noise spectral density is then transformed into a time domain covariance model which can then be used to derive the Kalman Filter model parameters. Simulation results of that covariance model are presented and compared to clock uncertainties predicted by Allan variance parameters. A two state Kalman Filter model is then derived and the significance of each state is explained.
Three-axis attitude determination via Kalman filtering of magnetometer data
NASA Technical Reports Server (NTRS)
Martel, Francois; Pal, Parimal K.; Psiaki, Mark L.
1988-01-01
A three-axis Magnetometer/Kalman Filter attitude determination system for a spacecraft in low-altitude Earth orbit is developed, analyzed, and simulation tested. The motivation for developing this system is to achieve light weight and low cost for an attitude determination system. The extended Kalman filter estimates the attitude, attitude rates, and constant disturbance torques. Accuracy near that of the International Geomagnetic Reference Field model is achieved. Covariance computation and simulation testing demonstrate the filter's accuracy. One test case, a gravity-gradient stabilized spacecraft with a pitch momentum wheel and a magnetically-anchored damper, is a real satellite on which this attitude determination system will be used. The application to a nadir pointing satellite and the estimation of disturbance torques represent the significant extensions contributed by this paper. Beyond its usefulness purely for attitude determination, this system could be used as part of a low-cost three-axis attitude stabilization system.
Ensemble Kalman filtering with residual nudging: some recent progress
NASA Astrophysics Data System (ADS)
Luo, Xiaodong; Hoteit, Ibrahim
2014-05-01
The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies (Luo and Hoteit, 2012, 2013b,a), the authors proposed an observation-space based strategy, called residual nudging, in order to improve the stability of the EnKF when dealing with linear observation operators. The main idea behind residual nudging is to monitor, and if necessary, adjust the distances (misfits) between the real observations and the simulated ones of the state estimates, in the hope that by doing so one may be able to obtain better estimation accuracy. In a more present study (Luo and Hoteit, 2014), residual nudging is extended and modified in order to handle nonlinear observation operators. Such extension and modification result in an iterative filtering framework that is able to achieve the objective of residual nudging in the presence of nonlinear observation operators, under suitable conditions. The 40 dimensional Lorenz 96 model is used to illustrate the performance of the iterative filter. Numerical results show that, while a normal EnKF may diverge in the presence of nonlinear observation operators, the proposed iterative filter performs very stably and leads to reasonable estimation accuracies under various experiment settings. REFERENCES Luo, X. and H. Hoteit, 2014: Ensemble kalman filtering with residual nudging: an extension to the state estimation problems with nonlinear observation operators. Submitted. Luo, X. and I. Hoteit, 2012: Ensemble Kalman filtering with residual nudging. Tellus A, 64, 17130, open access, doi:10.3402/tellusa.v64i0.17130. Luo, X. and I. Hoteit, 2013a: Covariance inflation in the ensemble Kalman filter: a residual nudging perspective and some implications. Mon. Wea. Rev., 141, 3360-3368, doi:10.1175/MWR-D-13-00067.1. Luo, X. and I. Hoteit, 2013b: Efficient particle filtering through residual nudging. Quart. J. Roy. Meteor
Temperature profile retrievals with extended Kalman-Bucy filters
NASA Technical Reports Server (NTRS)
Ledsham, W. H.; Staelin, D. H.
1979-01-01
The Extended Kalman-Bucy Filter is a powerful technique for estimating non-stationary random parameters in situations where the received signal is a noisy non-linear function of those parameters. A practical causal filter for retrieving atmospheric temperature profiles from radiances observed at a single scan angle by the Scanning Microwave Spectrometer (SCAMS) carried on the Nimbus 6 satellite typically shows approximately a 10-30% reduction in rms error about the mean at almost all levels below 70 mb when compared with a regression inversion.
Multi-channel Kalman filters for active noise control.
van Ophem, S; Berkhoff, A P
2013-04-01
By formulating the feed-forward broadband active noise control problem as a state estimation problem it is possible to achieve a faster rate of convergence than the filtered reference least mean squares algorithm and possibly also a better tracking performance. A multiple input/multiple output Kalman algorithm is derived to perform this state estimation. To make the algorithm more suitable for real-time applications, the Kalman filter is written in a fast array form and the secondary path state matrices are implemented in output normal form. The resulting filter implementation is tested in simulations and in real-time experiments. It was found that for a constant primary path the filter has a fast rate of convergence and is able to track changes in the frequency spectrum. For a forgetting factor equal to unity the system is robust but the filter is unable to track rapid changes in the primary path. A forgetting factor lower than 1 gives a significantly improved tracking performance but leads to a numerical instability for the fast array form of the algorithm. PMID:23556580
VLBI real-time analysis by Kalman Filtering
NASA Astrophysics Data System (ADS)
Karbon, Maria; Soja, Benedikt; Nilson, Tobias; Heinkelmann, Robert; Liu, Li; Lu, Ciuxian; Xu, Minghui; Raposo-Pulido, Virginia; Mora-Diaz, Julian; Schuh, Harald
2014-05-01
Geodetic Very Long Baseline Interferometry (VLBI) is one of the primary space geodetic techniques. It provides the full set of Earth Orientation Parameter (EOP) and is unique for observing long term Universal Time (UT1) and precession/nutation. Currently the VLBI products are delivered with a delay of about two weeks from the moment of the observation. However, the need for near-real time estimates of the parameters is increasing, e.g. for satellite based navigation and positioning or for enabling precise tracking of interplanetary spacecraft. The goal is thus to reduce the time span between observation and the final result to less than one day. This can be archived by replacing the classical least squares method with an adaptive Kalman filter. We have developed a Kalman filter for VLBI data analysis. This method has the advantage that it is simultaneously possible to estimate stationary parameters, e.g. station positions, and to model the highly variable stochastic behavior of non-stationary parameters like clocks or atmospheric parameters. The filter is able to perform without any human interaction, making it a completely autonomous tool. In this work we describe the filter and discuss its application for EOP determination and prediction. We discuss the implementation of the stochastic models to statistically account for unpredictable changes in EOP. Furthermore, additional data like results from other techniques can be included to improve the performance. For example, atmospheric angular momentum calculated from numerical weather models can be introduced to supplement the short-term prediction of UT1 and polar motion. This Kalman filter will be extended and embedded in the newly developed Vienna VLBI Software (VieVS) as a completely autonomous tool enabling the VLBI analysis in near real-time and providing all the parameters of interest with the highest possible accuracy.
Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms
NASA Technical Reports Server (NTRS)
Janjic, Tijana; Mclaughlin, Dennis; Cohn, Stephen E.; Verlaan, Martin
2014-01-01
This paper considers the incorporation of constraints to enforce physically based conservation laws in the ensemble Kalman filter. In particular, constraints are used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In certain situations filtering algorithms such as the ensemble Kalman filter (EnKF) and ensemble transform Kalman filter (ETKF) yield updated ensembles that conserve mass but are negative, even though the actual states must be nonnegative. In such situations if negative values are set to zero, or a log transform is introduced, the total mass will not be conserved. In this study, mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate non-negativity constraints. Simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. In two examples, an update that includes a non-negativity constraint is able to properly describe the transport of a sharp feature (e.g., a triangle or cone). A number of implementation questions still need to be addressed, particularly the need to develop a computationally efficient quadratic programming update for large ensemble.
Tropospheric delays derived from Kalman-filtered VLBI observations
NASA Astrophysics Data System (ADS)
Soja, Benedikt; Nilsson, Tobias; Karbon, Maria; Balidakis, Kyriakos; Lu, Cuixian; Anderson, James; Glaser, Susanne; Liu, Li; Mora-Diaz, Julian A.; Raposo-Pulido, Virginia; Xu, Minghui; Heinkelmann, Robert; Schuh, Harald
2015-04-01
One of the most important error sources in the products of space geodetic techniques is the troposphere. Currently, it is not possible to model the rapid variations in the path delay caused by water vapor with sufficient accuracy, thus it is necessary to estimate these delays in the data analysis. Very long baseline interferometry (VLBI) is well suited to determine wet delays with high accuracy and precision. Compared to GNSS, the analysis does not need to deal with effects related to code biases, multipath, satellite orbit mismodeling, or antenna phase center variations that are inherent in GNSS processing. VLBI data are usually analyzed by estimating geodetic parameters in a least squares adjustment. However, once the VLBI Global Observing System (VGOS) will have become operational, algorithms providing real-time capability, for instance a Kalman filter, should be preferable for data analysis. Even today, certain advantages of such a filter, for example, allowing stochastic modeling of geodetic parameters, warrant its application. The estimation of tropospheric wet delays, in particular, greatly benefits from the stochastic approach of the filter. In this work we have investigated the benefits of applying a Kalman filter in the VLBI data analysis for the determination of tropospheric parameters. The VLBI datasets considered are the CONT campaigns, which demonstrate state-of-the-art capabilities of the VLBI system. They are unique in following a continuous observation schedule over 15 days and in having data recorded at higher bandwidth than usual. The large amount of observations leads to a very high quality of geodetic products. CONT campaigns are held every three years; we have analyzed all CONT campaigns between 2002 and 2014 for this study. In our implementation of a Kalman filter in the VLBI software VieVS@GFZ, the zenith wet delays (ZWD) are modeled as random walk processes. We have compared the resulting time series to corresponding ones obtained from
Probability fields revisited in the context of ensemble Kalman filtering
NASA Astrophysics Data System (ADS)
Xu, Teng; Gómez-Hernández, J. Jaime
2015-12-01
Hu et al. (2013) proposed an approach to update complex geological facies models generated by multiple-point geostatistical simulation while keeping geological and statistical consistency. Their approach is based on mapping the facies realization onto the spatially uncorrelated uniform random numbers used by the sequential multiple-point simulation to generate the facies realization itself. The ensemble Kalman filter was then used to update the uniform random number realizations, which were then used to generate a new facies realization by multiple-point simulation. This approach has not a good performance that we attribute to the fact that, being the probabilities random and spatially uncorrelated, their correlation with the state variable (piezometric heads) is very weak, and the Kalman gain is always small. The approach is reminiscent of the probability field simulation, which also maps the conductivity realizations onto a field of uniform random numbers; although the mapping now is done using the local conditional distribution functions built based on a prior statistical model and the conditioning data. Contrary to Hu et al. (2013) approach, this field of uniform random numbers, termed a probability field, displays spatial patterns related to the conductivity spatial patterns, and, therefore, the correlation between probabilities and state variable is as strong as the correlation between conductivities and state variable could be. Similarly to Hu et al. (2013), we propose to use the ensemble Kalman filter to update the probability fields, and show that the existence of this correlation between probability values and state variables provides better results.
Improved understanding of the loss-of-symmetry phenomenon in the conventional Kalman filter
NASA Technical Reports Server (NTRS)
Verhaegen, M. H.
1987-01-01
This paper corrects an unclear treatment of the conventional Kalman filter implementation as presented by M. H. Verhaegen and P. van Dooren in Numerical aspects of different Kalman filter implementations, IEEE Trans. Automat. Contr., v. AC-31, no. 10, pp. 907-917, 1986. It is shown that habitual, incorrect implementation of the Kalman filter has been the major cause of its sensitivity to the so-called loss-of-symmetry phenomenon.
Improved understanding of the loss-of-symmetry phenomenon in the conventional Kalman filter
NASA Technical Reports Server (NTRS)
Verhaegen, M. H.
1989-01-01
This paper corrects an unclear statement of the conventional Kalman filter implementation as presented by M. H. Verhaegen and P. van Dooren in Numerical aspects of different Kalman filter implementations, IEEE Trans. Automat. Contr., v. AC-31, no. 10, pp. 907-917, 1986. It is shown that the habitual, incorrect implementation of the Kalman filter has been the major cause of its insensitivity to the so-called loss-of-symmetry phenomenon.
NASA Astrophysics Data System (ADS)
Ghorbanidehno, H.; Kokkinaki, A.; Darve, E. F.; Kitanidis, P. K.
2014-12-01
The Kalman Filter has been widely used for dynamic monitoring in reservoir engineering, and has recently gained popularity in hydrogeologic applications. A common characteristic of such applications is that the physical processes of interest are greatly affected by preferential flow (e.g., contaminant spreading, CO2 leakage), which can only be delineated if the problem is finely discretized into a large number of unknowns. However, for problems with large numbers of unknowns (e.g., larger than 10,000), the Kalman Filter has prohibitively expensive computation and storage costs. The EnKF, which is typically used to reduce the cost of computing the covariance in such cases converges slowly to the best estimate, and for a reasonable number of realizations, the estimate may not be accurate, especially for strongly heterogeneous systems. We present the Spectral Kalman Filter, a new Kalman Filter implementation that has a dramatically reduced computational cost compared to the full Kalman Filter, with comparable or higher accuracy than the EnKF for the same computational cost. Our algorithm's computational efficiency is achieved by a recurrence that updates small cross-covariance matrices instead of large covariance matrices, in combination with a low-rank approximation of the noise covariance matrix. In addition, instead of computing the expensive Jacobian matrix, a matrix-free method is used to obtain sensitivities. Finally, the error of our method can be explicitly controlled by reducing the time between matrix updates. The frequency of these updates is controlled independently from the data assimilation steps. We demonstrate the performance of the Spectral Kalman Filter for the joint estimation of domain properties and state evolution by assimilation of quasi-continuous data during a hypothetical CO2 injection in a heterogeneous domain.
Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics
NASA Technical Reports Server (NTRS)
Rodriguez, G.
1986-01-01
The inverse and forward dynamics problems for multi-link serial manipulators are solved by using recursive techniques from linear filtering and smoothing theory. The pivotal step is to cast the system dynamics and kinematics as a two-point boundary-value problem. Solution of this problem leads to filtering and smoothing techniques identical to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The solutions prescribe an inward filtering recursion to compute a sequence of constraint moments and forces followed by an outward recursion to determine a corresponding sequence of angular and linear accelerations. In addition to providing techniques to compute joint accelerations from applied joint moments (and vice versa), the report provides an approach to evaluate recursively the composite multi-link system inertia matrix and its inverse. The report lays the foundation for the potential use of filtering and smoothing techniques in robot inverse and forward dynamics and in robot control design.
Enhancement of Spanish Oesophageal Speech vowels using coherent subband modulator Kalman filtering.
Ishaq, Rizwan; Zapirain, Begoña García
2016-01-01
This paper proposes an Oesophageal Speech (OES) enhancement method, based on Kalman filtering. The Kalman filter is applied to modulators of OES frequency subbands instead of the fullband signal. The OES frequency subbands are decomposed into modulators and carriers components using coherent demodulation. In comparison with fullband Kalman filtering and pole stabilization, the proposed technique shows better results. The system performance is evaluated objectively and subjectively using the Harmonic to Noise Ratio (HNR) and Mean Opinion Score (MOS) respectively. Results have shown that Kalman filter in subband modulators processing is robust and efficient, improving the HNR by 4 to 5 dB for all Spanish vowels. PMID:26835722
A generalized polynomial chaos based ensemble Kalman filter with high accuracy
Li Jia; Xiu Dongbin
2009-08-20
As one of the most adopted sequential data assimilation methods in many areas, especially those involving complex nonlinear dynamics, the ensemble Kalman filter (EnKF) has been under extensive investigation regarding its properties and efficiency. Compared to other variants of the Kalman filter (KF), EnKF is straightforward to implement, as it employs random ensembles to represent solution states. This, however, introduces sampling errors that affect the accuracy of EnKF in a negative manner. Though sampling errors can be easily reduced by using a large number of samples, in practice this is undesirable as each ensemble member is a solution of the system of state equations and can be time consuming to compute for large-scale problems. In this paper we present an efficient EnKF implementation via generalized polynomial chaos (gPC) expansion. The key ingredients of the proposed approach involve (1) solving the system of stochastic state equations via the gPC methodology to gain efficiency; and (2) sampling the gPC approximation of the stochastic solution with an arbitrarily large number of samples, at virtually no additional computational cost, to drastically reduce the sampling errors. The resulting algorithm thus achieves a high accuracy at reduced computational cost, compared to the classical implementations of EnKF. Numerical examples are provided to verify the convergence property and accuracy improvement of the new algorithm. We also prove that for linear systems with Gaussian noise, the first-order gPC Kalman filter method is equivalent to the exact Kalman filter.
NASA Astrophysics Data System (ADS)
Li, Judith Yue; Kokkinaki, Amalia; Ghorbanidehno, Hojat; Darve, Eric F.; Kitanidis, Peter K.
2015-12-01
Reservoir monitoring aims to provide snapshots of reservoir conditions and their uncertainties to assist operation management and risk analysis. These snapshots may contain millions of state variables, e.g., pressures and saturations, which can be estimated by assimilating data in real time using the Kalman filter (KF). However, the KF has a computational cost that scales quadratically with the number of unknowns, m, due to the cost of computing and storing the covariance and Jacobian matrices, along with their products. The compressed state Kalman filter (CSKF) adapts the KF for solving large-scale monitoring problems. The CSKF uses N preselected orthogonal bases to compute an accurate rank-N approximation of the covariance that is close to the optimal spectral approximation given by SVD. The CSKF has a computational cost that scales linearly in m and uses an efficient matrix-free approach that propagates uncertainties using N + 1 forward model evaluations, where N≪m. Here we present a generalized CSKF algorithm for nonlinear state estimation problems such as CO2 monitoring. For simultaneous estimation of multiple types of state variables, the algorithm allows selecting bases that represent the variability of each state type. Through synthetic numerical experiments of CO2 monitoring, we show that the CSKF can reproduce the Kalman gain accurately even for large compression ratios (m/N). For a given computational cost, the CSKF uses a robust and flexible compression scheme that gives more reliable uncertainty estimates than the ensemble Kalman filter, which may display loss of ensemble variability leading to suboptimal uncertainty estimates.
Nonlinear Kalman filters for calibration in radio interferometry
NASA Astrophysics Data System (ADS)
Tasse, C.
2014-06-01
The data produced by the new generation of interferometers are affected by a wide variety of partially unknown complex effects such as pointing errors, phased array beams, ionosphere, troposphere, Faraday rotation, or clock drifts. Most algorithms addressing direction-dependent calibration solve for the effective Jones matrices, and cannot constrain the underlying physical quantities of the radio interferometry measurement equation (RIME). A related difficulty is that they lack robustness in the presence of low signal-to-noise ratios, and when solving for moderate to large numbers of parameters they can be subject to ill-conditioning. These effects can have dramatic consequences in the image plane such as source or even thermal noise suppression. The advantage of solvers directly estimating the physical terms appearing in the RIME is that they can potentially reduce the number of free parameters by orders of magnitudes while dramatically increasing the size of usable data, thereby improving conditioning. We present here a new calibration scheme based on a nonlinear version of the Kalman filter that aims at estimating the physical terms appearing in the RIME. We enrich the filter's structure with a tunable data representation model, together with an augmented measurement model for regularization. Using simulations we show that it can properly estimate the physical effects appearing in the RIME. We found that this approach is particularly useful in the most extreme cases such as when ionospheric and clock effects are simultaneously present. Combined with the ability to provide prior knowledge on the expected structure of the physical instrumental effects (expected physical state and dynamics), we obtain a fairly computationally cheap algorithm that we believe to be robust, especially in low signal-to-noise regimes. Potentially, the use of filters and other similar methods can represent an improvement for calibration in radio interferometry, under the condition that
Ensemble Kalman filters for dynamical systems with unresolved turbulence
Grooms, Ian; Lee, Yoonsang; Majda, Andrew J.
2014-09-15
Ensemble Kalman filters are developed for turbulent dynamical systems where the forecast model does not resolve all the active scales of motion. Coarse-resolution models are intended to predict the large-scale part of the true dynamics, but observations invariably include contributions from both the resolved large scales and the unresolved small scales. The error due to the contribution of unresolved scales to the observations, called ‘representation’ or ‘representativeness’ error, is often included as part of the observation error, in addition to the raw measurement error, when estimating the large-scale part of the system. It is here shown how stochastic superparameterization (a multiscale method for subgridscale parameterization) can be used to provide estimates of the statistics of the unresolved scales. In addition, a new framework is developed wherein small-scale statistics can be used to estimate both the resolved and unresolved components of the solution. The one-dimensional test problem from dispersive wave turbulence used here is computationally tractable yet is particularly difficult for filtering because of the non-Gaussian extreme event statistics and substantial small scale turbulence: a shallow energy spectrum proportional to k{sup −5/6} (where k is the wavenumber) results in two-thirds of the climatological variance being carried by the unresolved small scales. Because the unresolved scales contain so much energy, filters that ignore the representation error fail utterly to provide meaningful estimates of the system state. Inclusion of a time-independent climatological estimate of the representation error in a standard framework leads to inaccurate estimates of the large-scale part of the signal; accurate estimates of the large scales are only achieved by using stochastic superparameterization to provide evolving, large-scale dependent predictions of the small-scale statistics. Again, because the unresolved scales contain so much energy
Applying Kalman filtering to investigate tropospheric effects in VLBI
NASA Astrophysics Data System (ADS)
Soja, Benedikt; Nilsson, Tobias; Karbon, Maria; Heinkelmann, Robert; Liu, Li; Lu, Cuixian; Andres Mora-Diaz, Julian; Raposo-Pulido, Virginia; Xu, Minghui; Schuh, Harald
2014-05-01
Very Long Baseline Interferometry (VLBI) currently provides results, e.g., estimates of the tropospheric delays, with a delay of more than two weeks. In the future, with the coming VLBI2010 Global Observing System (VGOS) and increased usage of electronic data transfer, it is planned that the time between observations and results is decreased. This may, for instance, allow the integration of VLBI-derived tropospheric delays into numerical weather prediction models. Therefore, future VLBI analysis software packages need to be able to process the observational data autonomously in near real-time. For this purpose, we have extended the Vienna VLBI Software (VieVS) by a Kalman filter module. This presentation describes the filter and discusses its application for tropospheric studies. Instead of estimating zenith wet delays as piece-wise linear functions in a least-squares adjustment, the Kalman filter allows for more sophisticated stochastic modeling. We start with a random walk process to model the time-dependent behavior of the zenith wet delays. Other possible approaches include the stochastic model described by turbulence theory, e.g. the model by Treuhaft and Lanyi (1987). Different variance-covariance matrices of the prediction error, depending on the time of the year and the geographic latitude, have been tested. In winter and closer to the poles, lower variances and covariances are appropriate. The horizontal variations in tropospheric delays have been investigated by comparing three different strategies: assumption of a horizontally stratified troposphere, using north and south gradients modeled, e.g., as Gauss-Markov processes, and applying a turbulence model assuming correlations between observations in different azimuths. By conducting Monte-Carlo simulations of current standard VLBI networks and of future VGOS networks, the different tropospheric modeling strategies are investigated. For this purpose, we use the simulator module of VieVS which takes into
Kalman Filter Estimation of Spinning Spacecraft Attitude using Markley Variables
NASA Technical Reports Server (NTRS)
Sedlak, Joseph E.; Harman, Richard
2004-01-01
There are several different ways to represent spacecraft attitude and its time rate of change. For spinning or momentum-biased spacecraft, one particular representation has been put forward as a superior parameterization for numerical integration. Markley has demonstrated that these new variables have fewer rapidly varying elements for spinning spacecraft than other commonly used representations and provide advantages when integrating the equations of motion. The current work demonstrates how a Kalman filter can be devised to estimate the attitude using these new variables. The seven Markley variables are subject to one constraint condition, making the error covariance matrix singular. The filter design presented here explicitly accounts for this constraint by using a six-component error state in the filter update step. The reduced dimension error state is unconstrained and its covariance matrix is nonsingular.
Kalman filtering to suppress spurious signals in Adaptive Optics control
Poyneer, L; Veran, J P
2010-03-29
In many scenarios, an Adaptive Optics (AO) control system operates in the presence of temporally non-white noise. We use a Kalman filter with a state space formulation that allows suppression of this colored noise, hence improving residual error over the case where the noise is assumed to be white. We demonstrate the effectiveness of this new filter in the case of the estimated Gemini Planet Imager tip-tilt environment, where there are both common-path and non-common path vibrations. We discuss how this same framework can also be used to suppress spatial aliasing during predictive wavefront control assuming frozen flow in a low-order AO system without a spatially filtered wavefront sensor, and present experimental measurements from Altair that clearly reveal these aliased components.
Robust Kalman filter design for active flutter suppression systems
NASA Technical Reports Server (NTRS)
Garrard, W. L.; Mahesh, J. K.; Stone, C. R.; Dunn, H. J.
1982-01-01
Additional insight is provided into the use of the Doyle-Stein (1979, 1981) technique in aeroelastic control problems by examining the application of the method to a flutter control problem. The system to be controlled consists of a full-size wind tunnel model of a wing, plus an aileron, an actuator, and an accelerometer used to sense the motion of the wing. A full-state feedback controller was designed using linear optimal control theory, and a Kalman filter was used in the feedback loop for state estimation. The filter design procedure is explained along with that to improve closed-loop properties of the system. The locus of the poles of the filter is examined as a scalar design parameter is varied. The Doyle-Stein design procedure is shown to substantially improve the stability properties of an active flutter controller designed using the linear quadratic Gaussian control theory.
Analysis of dynamic deformation processes with adaptive KALMAN-filtering
NASA Astrophysics Data System (ADS)
Eichhorn, Andreas
2007-05-01
In this paper the approach of a full system analysis is shown quantifying a dynamic structural ("white-box"-) model for the calculation of thermal deformations of bar-shaped machine elements. The task was motivated from mechanical engineering searching new methods for the precise prediction and computational compensation of thermal influences in the heating and cooling phases of machine tools (i.e. robot arms, etc.). The quantification of thermal deformations under variable dynamic loads requires the modelling of the non-stationary spatial temperature distribution inside the object. Based upon FOURIERS law of heat flow the high-grade non-linear temperature gradient is represented by a system of partial differential equations within the framework of a dynamic Finite Element topology. It is shown that adaptive KALMAN-filtering is suitable to quantify relevant disturbance influences and to identify thermal parameters (i.e. thermal diffusivity) with a deviation of only 0,2%. As result an identified (and verified) parametric model for the realistic prediction respectively simulation of dynamic temperature processes is presented. Classifying the thermal bend as the main deformation quantity of bar-shaped machine tools, the temperature model is extended to a temperature deformation model. In lab tests thermal load steps are applied to an aluminum column. Independent control measurements show that the identified model can be used to predict the columns bend with a mean deviation (
NASA Astrophysics Data System (ADS)
Wetterer, C.; Hunt, B.; Kervin, P.; Jah, M.
2014-09-01
Forward modeling will never be perfect. The shape model will never be able to account for every wrinkle in the MLI coating, and similarly, the surface model as represented by the bidirectional reflectance distribution function (BRDF) will never be identical to that found on actual space objects due to space weathering and inherent differences in the same material from lot to lot. The key to making estimation filters work is thus to continually improve the shape and surface models of the space object, and to intelligently and completely account for all remaining error sources in the models and how these manifest in the observations. This paper uses a multiple hypothesis filtering scheme to determine the attitude of a model geosynchronous satellite with possible surface modeling errors to compare the estimates made when each hypothesis is either propagated by an unscented Kalman filter (UKF) or an unscented Schmidt Kalman filter (USKF). It is shown that the USKF, which incorporates the influence of the known modeling errors in so-called consider terms, provides a better estimate and a more realistic uncertainty on the final attitude estimate.
A Self-Tuning Kalman Filter for Autonomous Spacecraft Navigation
NASA Technical Reports Server (NTRS)
Truong, Son H.
1998-01-01
Most navigation systems currently operated by NASA are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman Filter and Global Positioning System (GPS) data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for NASA spacecraft navigation. Current techniques of Kalman filtering, however, still rely on manual tuning from analysts, and cannot help in optimizing autonomy without compromising accuracy and performance. This paper presents an approach to produce a high accuracy autonomous navigation system fully integrated with the flight system. The resulting system performs real-time state estimation by using an Extended Kalman Filter (EKF) implemented with high-fidelity state dynamics model, as does the GPS Enhanced Orbit Determination Experiment (GEODE) system developed by the NASA Goddard Space Flight Center. Augmented to the EKF is a sophisticated neural-fuzzy system, which combines the explicit knowledge representation of fuzzy logic with the learning power of neural networks. The fuzzy-neural system performs most of the self-tuning capability and helps the navigation system recover from estimation errors. The core requirement is a method of state estimation that handles uncertainties robustly, capable of identifying estimation problems, flexible enough to make decisions and adjustments to recover from these problems, and compact enough to run on flight hardware. The resulting system can be extended to support geosynchronous spacecraft and high-eccentricity orbits. Mathematical methodology, systems and operations concepts, and implementation of a system prototype are presented in this paper. Results from the use of the prototype to evaluate optimal control algorithms implemented are discussed. Test data and major control issues (e.g., how to define specific roles for fuzzy logic to support the self-learning capability) are also
NASA Astrophysics Data System (ADS)
Man, Jun; Li, Weixuan; Zeng, Lingzao; Wu, Laosheng
2016-06-01
The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a sufficiently large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the polynomial chaos expansion (PCE) to represent and propagate the uncertainties in parameters and states. However, PCKF suffers from the so-called "curse of dimensionality". Its computational cost increases drastically with the increasing number of parameters and system nonlinearity. Furthermore, PCKF may fail to provide accurate estimations due to the joint updating scheme for strongly nonlinear models. Motivated by recent developments in uncertainty quantification and EnKF, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problems. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected at each assimilation step; the "restart" scheme is utilized to eliminate the inconsistency between updated model parameters and states variables. The performance of RAPCKF is systematically tested with numerical cases of unsaturated flow models. It is shown that the adaptive approach and restart scheme can significantly improve the performance of PCKF. Moreover, RAPCKF has been demonstrated to be more efficient than EnKF with the same computational cost.
Nonlinear stability and ergodicity of ensemble based Kalman filters
NASA Astrophysics Data System (ADS)
Tong, Xin T.; Majda, Andrew J.; Kelly, David
2016-02-01
The ensemble Kalman filter (EnKF) and ensemble square root filter (ESRF) are data assimilation methods used to combine high dimensional, nonlinear dynamical models with observed data. Despite their widespread usage in climate science and oil reservoir simulation, very little is known about the long-time behavior of these methods and why they are effective when applied with modest ensemble sizes in large dimensional turbulent dynamical systems. By following the basic principles of energy dissipation and controllability of filters, this paper establishes a simple, systematic and rigorous framework for the nonlinear analysis of EnKF and ESRF with arbitrary ensemble size, focusing on the dynamical properties of boundedness and geometric ergodicity. The time uniform boundedness guarantees that the filter estimate will not diverge to machine infinity in finite time, which is a potential threat for EnKF and ESQF known as the catastrophic filter divergence. Geometric ergodicity ensures in addition that the filter has a unique invariant measure and that initialization errors will dissipate exponentially in time. We establish these results by introducing a natural notion of observable energy dissipation. The time uniform bound is achieved through a simple Lyapunov function argument, this result applies to systems with complete observations and strong kinetic energy dissipation, but also to concrete examples with incomplete observations. With the Lyapunov function argument established, the geometric ergodicity is obtained by verifying the controllability of the filter processes; in particular, such analysis for ESQF relies on a careful multivariate perturbation analysis of the covariance eigen-structure.
Weighted Average Consensus-Based Unscented Kalman Filtering.
Li, Wangyan; Wei, Guoliang; Han, Fei; Liu, Yurong
2016-02-01
In this paper, we are devoted to investigate the consensus-based distributed state estimation problems for a class of sensor networks within the unscented Kalman filter (UKF) framework. The communication status among sensors is represented by a connected undirected graph. Moreover, a weighted average consensus-based UKF algorithm is developed for the purpose of estimating the true state of interest, and its estimation error is bounded in mean square which has been proven in the following section. Finally, the effectiveness of the proposed consensus-based UKF algorithm is validated through a simulation example. PMID:26168453
Automatic Certification of Kalman Filters for Reliable Code Generation
NASA Technical Reports Server (NTRS)
Denney, Ewen; Fischer, Bernd; Schumann, Johann; Richardson, Julian
2005-01-01
AUTOFILTER is a tool for automatically deriving Kalman filter code from high-level declarative specifications of state estimation problems. It can generate code with a range of algorithmic characteristics and for several target platforms. The tool has been designed with reliability of the generated code in mind and is able to automatically certify that the code it generates is free from various error classes. Since documentation is an important part of software assurance, AUTOFILTER can also automatically generate various human-readable documents, containing both design and safety related information. We discuss how these features address software assurance standards such as DO-178B.
Comparison of Sigma-Point and Extended Kalman Filters on a Realistic Orbit Determination Scenario
NASA Technical Reports Server (NTRS)
Gaebler, John; Hur-Diaz. Sun; Carpenter, Russell
2010-01-01
Sigma-point filters have received a lot of attention in recent years as a better alternative to extended Kalman filters for highly nonlinear problems. In this paper, we compare the performance of the additive divided difference sigma-point filter to the extended Kalman filter when applied to orbit determination of a realistic operational scenario based on the Interstellar Boundary Explorer mission. For the scenario studied, both filters provided equivalent results. The performance of each is discussed in detail.
NASA Technical Reports Server (NTRS)
Klein, V.; Schiess, J. R.
1977-01-01
An extended Kalman filter smoother and a fixed point smoother were used for estimation of the state variables in the six degree of freedom kinematic equations relating measured aircraft responses and for estimation of unknown constant bias and scale factor errors in measured data. The computing algorithm includes an analysis of residuals which can improve the filter performance and provide estimates of measurement noise characteristics for some aircraft output variables. The technique developed was demonstrated using simulated and real flight test data. Improved accuracy of measured data was obtained when the data were corrected for estimated bias errors.
Several recursive techniques for observer/Kalman filter system identification from data
NASA Technical Reports Server (NTRS)
Chen, Chung-Wen; Lee, Gordon; Juang, Jer-Nan
1992-01-01
This paper derives algorithms for identifying autoregressive models, with external input, of multi-input multi-output systems from data using a fast transversal filter or a least-squares lattice filter. The autoregressive models including external inputs are used to identify state-space models and the corresponding observer/Kalman filter gains of the system. The derivation is an extension of scalar autoregressive model approaches, modified to cope with multivariables, external inputs and an extra direct-influence term. Comparisons between the fast transversal filter, the least-squares lattice filter and the classical least-squares method are made in terms of complexity, computational cost and practical applications issues. A numerical example is included to illustrate the approach.
Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu
2015-01-01
Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted "useful" data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency. PMID:26569247
Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu
2015-01-01
Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted “useful” data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency. PMID:26569247
NASA Astrophysics Data System (ADS)
Rigatos, Gerasimos
2016-07-01
The Derivative-free nonlinear Kalman Filter is used for developing a communication system that is based on a chaotic modulator such as the Duffing system. In the transmitter's side, the source of information undergoes modulation (encryption) in which a chaotic signal generated by the Duffing system is the carrier. The modulated signal is transmitted through a communication channel and at the receiver's side demodulation takes place, after exploiting the estimation provided about the state vector of the chaotic oscillator by the Derivative-free nonlinear Kalman Filter. Evaluation tests confirm that the proposed filtering method has improved performance over the Extended Kalman Filter and reduces significantly the rate of transmission errors. Moreover, it is shown that the proposed Derivative-free nonlinear Kalman Filter can work within a dual Kalman Filtering scheme, for performing simultaneously transmitter-receiver synchronisation and estimation of unknown coefficients of the communication channel.
Optimal Tuner Selection for Kalman-Filter-Based Aircraft Engine Performance Estimation
NASA Technical Reports Server (NTRS)
Simon, Donald L.; Garg, Sanjay
2011-01-01
applications such as model-based diagnostic, controls, and life usage calculations. The advantage of the innovation is the significant reduction in estimation errors that it can provide relative to the conventional approach of selecting a subset of health parameters to serve as the model tuning parameter vector. Because this technique needs only to be performed during the system design process, it places no additional computation burden on the onboard Kalman filter implementation. The technique has been developed for aircraft engine onboard estimation applications, as this application typically presents an under-determined estimation problem. However, this generic technique could be applied to other industries using gas turbine engine technology.
Ensemble Kalman filter data assimilation for the MPAS system
NASA Astrophysics Data System (ADS)
Ha, Soyoung; Snyder, Chris
2015-04-01
The Model for Prediction Across Scales (MPAS; http://mpas-dev.github.io/) is a global non-hydrostatic numerical atmospheric model based on unstructured centroidal Voronoi meshes that allow both uniform and variable resolutions. The variable resolution allows locally high-resolution meshes that transition smoothly to coarser resolution over the rest of the globe, avoiding the need to drive a limited-area model with lateral boundary conditions from a separate global model. The nonhydrostatic MPAS solver (for both atmospheric and oceanic components) is now coupled to the Data Assimilation Research Testbed (DART; http://www.image.ucar.edu/ DAReS/DART) system with a full capability of ensemble Kalman filter data assimilation. The analysis/forecast cycling experiments using MPAS/DART is successfully tested with real observations for different retrospective cases. Assimilated observations are all conventional data as well as satellite winds and GPS radio occultation refractivity data. Testing on different grid mesh, we examine issues specific to the MPAS grid, such as smoothing in the interpolation and the update of horizontal wind fields, and show their impact on the Ensemble Kalman Filter (EnKF) analysis and the following short-range forecast. Up to 5-day forecasts for a month-long cycle period are verified against observations and compared to the NCEP GFS (Global Forecast System) forecasts.
Reconstruction of spacecraft rotational motion using a Kalman filter
NASA Astrophysics Data System (ADS)
Pankratov, V. A.; Sazonov, V. V.
2016-05-01
Quasi-static microaccelerations of four satellites of the Foton series (nos. 11, 12, M-2, M-3) were monitored as follows. First, according to measurements of onboard sensors obtained in a certain time interval, spacecraft rotational motion was reconstructed in this interval. Then, along the found motion, microacceleration at a given onboard point was calculated according to the known formula as a function of time. The motion was reconstructed by the least squares method using the solutions to the equations of satellite rotational motion. The time intervals in which these equations make reconstruction possible were from one to five orbital revolutions. This length is increased with the modulus of the satellite angular velocity. To get an idea on microaccelerations and satellite motion during an entire flight, the motion was reconstructed in several tens of such intervals. This paper proposes a method for motion reconstruction suitable for an interval of arbitrary length. The method is based on the Kalman filter. We preliminary describe a new version of the method for reconstructing uncontrolled satellite rotational motion from magnetic measurements using the least squares method, which is essentially used to construct the Kalman filter. The results of comparison of both methods are presented using the data obtained on a flight of the Foton M-3.
Skew redundant MEMS IMU calibration using a Kalman filter
NASA Astrophysics Data System (ADS)
Jafari, M.; Sahebjameyan, M.; Moshiri, B.; Najafabadi, T. A.
2015-10-01
In this paper, a novel calibration procedure for skew redundant inertial measurement units (SRIMUs) based on micro-electro mechanical systems (MEMS) is proposed. A general model of the SRIMU measurements is derived which contains the effects of bias, scale factor error and misalignments. For more accuracy, the effect of lever arms of the accelerometers to the center of the table are modeled and compensated in the calibration procedure. Two separate Kalman filters (KFs) are proposed to perform the estimation of error parameters for gyroscopes and accelerometers. The predictive error minimization (PEM) stochastic modeling method is used to simultaneously model the effect of bias instability and random walk noise on the calibration Kalman filters to diminish the biased estimations. The proposed procedure is simulated numerically and has expected experimental results. The calibration maneuvers are applied using a two-axis angle turntable in a way that the persistency of excitation (PE) condition for parameter estimation is met. For this purpose, a trapezoidal calibration profile is utilized to excite different deterministic error parameters of the accelerometers and a pulse profile is used for the gyroscopes. Furthermore, to evaluate the performance of the proposed KF calibration method, a conventional least squares (LS) calibration procedure is derived for the SRIMUs and the simulation and experimental results compare the functionality of the two proposed methods with each other.
Kalman Filtering USNO's GPS Observations for Improved Time Transfer Predictions
NASA Technical Reports Server (NTRS)
Hutsell, Steven T.
1996-01-01
The Global Positioning System (GPS) Master Control Station (MCS) performs the Coordinated Universal Time (UTC) time transfer mission by uploading and broadcasting predictions of the GPS-UTC offset in subframe 4 of the GS navigation message. These predictions are based on only two successive daily data points obtained from the US Naval Observatory (USNO). USNO produces these daily smoothed data points by performing a least-squares fit on roughly 38 hours worth of data from roughly 160 successive 13-minute tracks of GPS satellites. Though sufficient for helping to maintain a time transfer error specification of 28 ns (1 Sigma), the MCS's prediction algorithm does not make the best use of the available data from from USNO, and produces data that can degrade quickly over extended prediction spans. This paper investigates how, by applying Kalman filtering to the same available tracking data, the MCS could improve its estimate of GPS-UTC, and in particular, the GPS-UTC A(sub 1) term. By refining the A(sub 1) (frequency) estimate for GPS-UTC predictions, error in GPS time transfer could drop significantly. Additional, the risk of future spikes in GPS's time transfer error could similarly be minimized, by employing robust Kalman filtering for GPS-UTC predictions.
Low-dimensional recurrent neural network-based Kalman filter for speech enhancement.
Xia, Youshen; Wang, Jun
2015-07-01
This paper proposes a new recurrent neural network-based Kalman filter for speech enhancement, based on a noise-constrained least squares estimate. The parameters of speech signal modeled as autoregressive process are first estimated by using the proposed recurrent neural network and the speech signal is then recovered from Kalman filtering. The proposed recurrent neural network is globally asymptomatically stable to the noise-constrained estimate. Because the noise-constrained estimate has a robust performance against non-Gaussian noise, the proposed recurrent neural network-based speech enhancement algorithm can minimize the estimation error of Kalman filter parameters in non-Gaussian noise. Furthermore, having a low-dimensional model feature, the proposed neural network-based speech enhancement algorithm has a much faster speed than two existing recurrent neural networks-based speech enhancement algorithms. Simulation results show that the proposed recurrent neural network-based speech enhancement algorithm can produce a good performance with fast computation and noise reduction. PMID:25913233
NASA Astrophysics Data System (ADS)
Shen, Zheqi; Tang, Youmin
2016-04-01
The ensemble Kalman particle filter (EnKPF) is a combination of two Bayesian-based algorithms, namely, the ensemble Kalman filter (EnKF) and the sequential importance resampling particle filter(SIR-PF). It was recently introduced to address non-Gaussian features in data assimilation for highly nonlinear systems, by providing a continuous interpolation between the EnKF and SIR-PF analysis schemes. In this paper, we first extend the EnKPF algorithm by modifying the formula for the computation of the covariancematrix, making it suitable for nonlinear measurement functions (we will call this extended algorithm nEnKPF). Further, a general form of the Kalman gain is introduced to the EnKPF to improve the performance of the nEnKPF when the measurement function is highly nonlinear (this improved algorithm is called mEnKPF). The Lorenz '63 model and Lorenz '96 model are used to test the two modified EnKPF algorithms. The experiments show that the mEnKPF and nEnKPF, given an affordable ensemble size, can perform better than the EnKF for the nonlinear systems with nonlinear observations. These results suggest a promising opportunity to develop a non-Gaussian scheme for realistic numerical models.
Kalman filter based range estimation for autonomous navigation using imaging sensors
NASA Technical Reports Server (NTRS)
Sridhar, Banavar
1990-01-01
Rotorcraft operating in high-threat environments fly close to the surface of the earth to utilize surrounding terrain, vegetation, or man-made objects to minimize the risk of being detected by the enemy. Two basic requirements for obstacle avoidance are detection and range estimation of the object from the current rotorcraft position. There are many approaches to the estimation of range using a sequence of images. The approach used in this analysis differes from previous methods in two significant ways: an attempt is not made to estimate the rotorcraft's motion from the images; and the interest lies in recursive algorithms. The rotorcraft parameters are assumed to be computed using an onboard inertial navigation system. Given a sequence of images, using image-object differential equations, a Kalman filter (Sridhar and Phatak, 1988) can be used to estimate both the relative coordinates and the earth coordinates of the objects on the ground. The Kalman filter can also be used in a predictive mode to track features in the images, leading to a significant reduction of search effort in the feature extraction step of the algorithm. The purpose is to summarize early results obtained in extending the Kalman filter for use with actual image sequences. The experience gained from the application of this algorithm to real images is very valuable and is a necessary step before proceeding to the estimation of range during low-altitude curvilinear flight. A simple recursive method is presented to estimate range to objects using a sequence of images. The method produces good range estimates using real images in a laboratory set up and needs to be evaluated further using several different image sequences to test its robustness. The feature generation part of the algorithm requires further refinement on the strategies to limit the number of features (Sridhar and Phatak, 1989). The extension of the work reported here to curvilinear flight may require the use of the extended Kalman
NASA Technical Reports Server (NTRS)
Lam, Quang; Chipman, Richard; Sunkel, John
1991-01-01
Two algorithms, extended Kalman filter and neuro-filter, are formulated to perform mass property identification for the Space Station Freedom. Control moment gyros that are part of the Station's basic momentum management system are chosen to provide input excitation in the form of applied torques. These torques together with the measured angular body rate responses are supplied to the filters. From these data, both algorithms are shown to accurately identify the station mass properties when excitation levels are high and balanced between axes. The neuro-filter, however, is shown to be more robust and to perform well even with weakly persistent, unbalanced signals contaminated with noise.
Improved Kalman Filter Method for Measurement Noise Reduction in Multi Sensor RFID Systems
Eom, Ki Hwan; Lee, Seung Joon; Kyung, Yeo Sun; Lee, Chang Won; Kim, Min Chul; Jung, Kyung Kwon
2011-01-01
Recently, the range of available Radio Frequency Identification (RFID) tags has been widened to include smart RFID tags which can monitor their varying surroundings. One of the most important factors for better performance of smart RFID system is accurate measurement from various sensors. In the multi-sensing environment, some noisy signals are obtained because of the changing surroundings. We propose in this paper an improved Kalman filter method to reduce noise and obtain correct data. Performance of Kalman filter is determined by a measurement and system noise covariance which are usually called the R and Q variables in the Kalman filter algorithm. Choosing a correct R and Q variable is one of the most important design factors for better performance of the Kalman filter. For this reason, we proposed an improved Kalman filter to advance an ability of noise reduction of the Kalman filter. The measurement noise covariance was only considered because the system architecture is simple and can be adjusted by the neural network. With this method, more accurate data can be obtained with smart RFID tags. In a simulation the proposed improved Kalman filter has 40.1%, 60.4% and 87.5% less Mean Squared Error (MSE) than the conventional Kalman filter method for a temperature sensor, humidity sensor and oxygen sensor, respectively. The performance of the proposed method was also verified with some experiments. PMID:22346641
Some interesting observations regarding the initialization of unscented and extended Kalman filters
NASA Astrophysics Data System (ADS)
Noushin, A. J.; Daum, F. E.
2008-04-01
Contrary to assertions in the literature, we show that the Extended Kalman Filter (EKF) is superior to the Unscented Kalman Filter (UKF) for certain nonlinear estimation problems. In particular, for nonlinearities that are odd functions of the state vector (e.g., x 3) the Unscented Kalman Filter usually performs well, whereas for even nonlinearities (e.g., x2), the Extended Kalman Filter is sometimes much better than the Unscented Kalman Filter. This is contrary to the usual engineering folklore, and therefore we have checked our results very thoroughly. In particular, the Unscented Kalman Filter correctly approximates the conditional mean using a 4th order Gauss-Hermite quadrature, in contrast to the Extended Kalman Filter which uses a simple 0th order approximation, but the conditional mean is not the desired estimate in practical applications for strongly bimodal conditional probability densities, which are induced by even nonlinearities, owing to a sign ambiguity. On the other hand, even nonlinearities do not always induce multimodal densities that persist for a significant amount of time, and thus the Unscented Kalman Filter sometimes performs well for such problems. We study the effects of initial uncertainty of the state vector and nonlinearity in measurements.
Application of Kalman Filtering Techniques for Microseismic Event Detection
NASA Astrophysics Data System (ADS)
Baziw, E.; Weir-Jones, I.
- Microseismic monitoring systems are generally installed in areas of induced seismicity caused by human activity. Induced seismicity results from changes in the state of stress which may occur as a result of excavation within the rock mass in mining (i.e., rockbursts), and changes in hydrostatic pressures and rock temperatures (e.g., during fluid injection or extraction) in oil exploitation, dam construction or fluid disposal. Microseismic monitoring systems determine event locations and important source parameters such as attenuation, seismic moment, source radius, static stress drop, peak particle velocity and seismic energy. An essential part of the operation of a microseismic monitoring system is the reliable detection of microseismic events. In the absence of reliable, automated picking techniques, operators rely upon manual picking. This is time-consuming, costly and, in the presence of background noise, very prone to error. The techniques described in this paper not only permit the reliable identification of events in cluttered signal environments they have also enabled the authors to develop reliable automated event picking procedures. This opens the way to use microseismic monitoring as a cost-effective production/operations procedure. It has been the experience of the authors that in certain noisy environments, the seismic monitoring system may trigger on and subsequently acquire substantial quantities of erroneous data, due to the high energy content of the ambient noise. Digital filtering techniques need to be applied on the microseismic data so that the ambient noise is removed and event detection simplified. The monitoring of seismic acoustic emissions is a continuous, real-time process and it is desirable to implement digital filters which can also be designed in the time domain and in real-time such as the Kalman Filter. This paper presents a real-time Kalman Filter which removes the statistically describable background noise from the recorded
Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Miller, Bard A.; Howard, Samuel A.
2008-01-01
An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.
Identifying Bearing Rotodynamic Coefficients Using an Extended Kalman Filter
NASA Technical Reports Server (NTRS)
Miller, Brad A.; Howard, Samuel A.
2008-01-01
An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.
An extended Kalman filter for spinning spacecraft attitude estimation
NASA Technical Reports Server (NTRS)
Baker, David F.
1991-01-01
An extended Kalman filter for real-time ground attitude estimation of a gyro-less spinning spacecraft was developed and tested. The filter state vector includes the angular momentum direction, phase angle, inertial nutation angle, and inertial and body nutation rates. The filter solves for the nutating three-axis attitude and accounts for effects due to principle axes offset from the body axes. The attitude is propagated using the kinematics of a rigid body symmetric about the principle spin axis; disturbance torques are assumed to be small. Filter updates consist only of the measured angles between celestial objects (Sun, Earth, etc.) and the nominal spin axis, and the times these angles were measured. Both simulated data and real data from the Dynamics Explorer -A (DE-A) spacecraft were used to test the filter; the results are presented. Convergence was achieved rapidly from a wide range of a priori state estimates, and sub-degree accuracy was attained. Systematic errors affecting the solution accuracy are discussed, as are the results of an attempt to solve for sensor measurement angle biases in the state vector.
NASA Technical Reports Server (NTRS)
Snow, Frank; Harman, Richard; Garrick, Joseph
1988-01-01
The Gamma Ray Observatory (GRO) spacecraft needs a highly accurate attitude knowledge to achieve its mission objectives. Utilizing the fixed-head star trackers (FHSTs) for observations and gyroscopes for attitude propagation, the discrete Kalman Filter processes the attitude data to obtain an onboard accuracy of 86 arc seconds (3 sigma). A combination of linear analysis and simulations using the GRO Software Simulator (GROSS) are employed to investigate the Kalman filter for stability and the effects of corrupted observations (misalignment, noise), incomplete dynamic modeling, and nonlinear errors on Kalman filter. In the simulations, on-board attitude is compared with true attitude, the sensitivity of attitude error to model errors is graphed, and a statistical analysis is performed on the residuals of the Kalman Filter. In this paper, the modeling and sensor errors that degrade the Kalman filter solution beyond mission requirements are studied, and methods are offered to identify the source of these errors.
[Application of kalman filtering based on wavelet transform in ICP-AES].
Qin, Xia; Shen, Lan-sun
2002-12-01
Kalman filtering is a recursive algorithm, which has been proposed as an attractive alternative to correct overlapping interferences in ICP-AES. However, the noise in ICP-AES contaminates the signal arising from the analyte and hence limits the accuracy of kalman filtering. Wavelet transform is a powerful technique in signal denoising due to its multi-resolution characteristics. In this paper, first, the effect of noise on kalman filtering is discussed. Then we apply the wavelet-transform-based soft-thresholding as the pre-processing of kalman filtering. The simulation results show that the kalman filtering based on wavelet transform can effectively reduce the noise and increase the accuracy of the analysis. PMID:12914186
VLBI real-time analysis by Kalman Filtering
NASA Astrophysics Data System (ADS)
Karbon, M.; Nilsson, T.; Soja, B.; Heinkelmann, R.; Raposo-Pulido, V.; Schuh, H.
2013-12-01
Geodetic Very Long Baseline Interferometry (VLBI) is one of the primary space geodetic techniques providing the full set of Earth Orientation Parameter (EOP) and is unique for observing long term Universal Time (UT1) and precession/nutation. Accurate and continuous EOP obtained in near real-time are essential for satellite based navigation and positioning and for enabling the precise tracking of interplanetary spacecrafts. To meet this necessity the International VLBI Service for Geodesy and Astrometry (IVS) increased its efforts to reduce the time span between the VLBI observations and the availability of the final results. Currently the timeliness is about two weeks, but the goal is to reduce it to less than one day with the future VGOS (VLBI2010 Global Observing System) network. The FWF project VLBI-ART contributes to this new generation VLBI system by considerably accelerating the VLBI analysis procedure through the implementation of an elaborate Kalman filter. This true real-time Kalman filter will be embedded in the Vienna VLBI Software (VieVS) as a completely automated tool with no need of human interaction. This filter also allows the prediction and combination of EOP from various space geodetic techniques by implementing stochastic models to statistically account for unpredictable changes in EOP. Additionally, atmospheric angular momenta calculated from numerical weather prediction models are introduced to support the short-term EOP prediction. To optimize the performance of the new software various investigations with real as well as simulated data are foreseen. The results are compared to the ones obtained by conventional VLBI parameter estimation methods (e.g. least squares method) and to corresponding parameter series from other techniques, such as from the Global Navigation Satellite Systems (GNSS).
Using Kalman filters to reduce noise from RFID location system.
Abreu, Pedro Henriques; Xavier, José; Silva, Daniel Castro; Reis, Luís Paulo; Petry, Marcelo
2014-01-01
Nowadays, there are many technologies that support location systems involving intrusive and nonintrusive equipment and also varying in terms of precision, range, and cost. However, the developers some time neglect the noise introduced by these systems, which prevents these systems from reaching their full potential. Focused on this problem, in this research work a comparison study between three different filters was performed in order to reduce the noise introduced by a location system based on RFID UWB technology with an associated error of approximately 18 cm. To achieve this goal, a set of experiments was devised and executed using a miniature train moving at constant velocity in a scenario with two distinct shapes-linear and oval. Also, this train was equipped with a varying number of active tags. The obtained results proved that the Kalman Filter achieved better results when compared to the other two filters. Also, this filter increases the performance of the location system by 15% and 12% for the linear and oval paths respectively, when using one tag. For a multiple tags and oval shape similar results were obtained (11-13% of improvement). PMID:24592186
Using Kalman Filters to Reduce Noise from RFID Location System
Xavier, José; Reis, Luís Paulo; Petry, Marcelo
2014-01-01
Nowadays, there are many technologies that support location systems involving intrusive and nonintrusive equipment and also varying in terms of precision, range, and cost. However, the developers some time neglect the noise introduced by these systems, which prevents these systems from reaching their full potential. Focused on this problem, in this research work a comparison study between three different filters was performed in order to reduce the noise introduced by a location system based on RFID UWB technology with an associated error of approximately 18 cm. To achieve this goal, a set of experiments was devised and executed using a miniature train moving at constant velocity in a scenario with two distinct shapes—linear and oval. Also, this train was equipped with a varying number of active tags. The obtained results proved that the Kalman Filter achieved better results when compared to the other two filters. Also, this filter increases the performance of the location system by 15% and 12% for the linear and oval paths respectively, when using one tag. For a multiple tags and oval shape similar results were obtained (11–13% of improvement). PMID:24592186
Estimating ice-affected streamflow by extended Kalman filtering
Holtschlag, D.J.; Grewal, M.S.
1998-01-01
An extended Kalman filter was developed to automate the real-time estimation of ice-affected streamflow on the basis of routine measurements of stream stage and air temperature and on the relation between stage and streamflow during open-water (ice-free) conditions. The filter accommodates three dynamic modes of ice effects: sudden formation/ablation, stable ice conditions, and eventual elimination. The utility of the filter was evaluated by applying it to historical data from two long-term streamflow-gauging stations, St. John River at Dickey, Maine and Platte River at North Bend, Nebr. Results indicate that the filter was stable and that parameters converged for both stations, producing streamflow estimates that are highly correlated with published values. For the Maine station, logarithms of estimated streamflows are within 8% of the logarithms of published values 87.2% of the time during periods of ice effects and within 15% 96.6% of the time. Similarly, for the Nebraska station, logarithms of estimated streamflows are within 8% of the logarithms of published values 90.7% of the time and within 15% 97.7% of the time. In addition, the correlation between temporal updates and published streamflows on days of direct measurements at the Maine station was 0.777 and 0.998 for ice-affected and open-water periods, respectively; for the Nebraska station, corresponding correlations were 0.864 and 0.997.
Parameter estimation for stiff deterministic dynamical systems via ensemble Kalman filter
NASA Astrophysics Data System (ADS)
Arnold, Andrea; Calvetti, Daniela; Somersalo, Erkki
2014-10-01
A commonly encountered problem in numerous areas of applications is to estimate the unknown coefficients of a dynamical system from direct or indirect observations at discrete times of some of the components of the state vector. A related problem is to estimate unobserved components of the state. An egregious example of such a problem is provided by metabolic models, in which the numerous model parameters and the concentrations of the metabolites in tissue are to be estimated from concentration data in the blood. A popular method for addressing similar questions in stochastic and turbulent dynamics is the ensemble Kalman filter (EnKF), a particle-based filtering method that generalizes classical Kalman filtering. In this work, we adapt the EnKF algorithm for deterministic systems in which the numerical approximation error is interpreted as a stochastic drift with variance based on classical error estimates of numerical integrators. This approach, which is particularly suitable for stiff systems where the stiffness may depend on the parameters, allows us to effectively exploit the parallel nature of particle methods. Moreover, we demonstrate how spatial prior information about the state vector, which helps the stability of the computed solution, can be incorporated into the filter. The viability of the approach is shown by computed examples, including a metabolic system modeling an ischemic episode in skeletal muscle, with a high number of unknown parameters.
Effects of measurement unobservability on neural extended Kalman filter tracking
NASA Astrophysics Data System (ADS)
Stubberud, Stephen C.; Kramer, Kathleen A.
2009-05-01
An important component of tracking fusion systems is the ability to fuse various sensors into a coherent picture of the scene. When multiple sensor systems are being used in an operational setting, the types of data vary. A significant but often overlooked concern of multiple sensors is the incorporation of measurements that are unobservable. An unobservable measurement is one that may provide information about the state, but cannot recreate a full target state. A line of bearing measurement, for example, cannot provide complete position information. Often, such measurements come from passive sensors such as a passive sonar array or an electronic surveillance measure (ESM) system. Unobservable measurements will, over time, result in the measurement uncertainty to grow without bound. While some tracking implementations have triggers to protect against the detrimental effects, many maneuver tracking algorithms avoid discussing this implementation issue. One maneuver tracking technique is the neural extended Kalman filter (NEKF). The NEKF is an adaptive estimation algorithm that estimates the target track as it trains a neural network on line to reduce the error between the a priori target motion model and the actual target dynamics. The weights of neural network are trained in a similar method to the state estimation/parameter estimation Kalman filter techniques. The NEKF has been shown to improve target tracking accuracy through maneuvers and has been use to predict target behavior using the new model that consists of the a priori model and the neural network. The key to the on-line adaptation of the NEKF is the fact that the neural network is trained using the same residuals as the Kalman filter for the tracker. The neural network weights are treated as augmented states to the target track. Through the state-coupling function, the weights are coupled to the target states. Thus, if the measurements cause the states of the target track to be unobservable, then the
Constraining the Ensemble Kalman Filter for improved streamflow forecasting
NASA Astrophysics Data System (ADS)
Maxwell, Deborah; Jackson, Bethanna; McGregor, James
2016-04-01
Data assimilation techniques such as the Kalman Filter and its variants are often applied to hydrological models with minimal state volume/capacity constraints. Flux constraints are rarely, if ever, applied. Consequently, model states can be adjusted beyond physically reasonable limits, compromising the integrity of model output. In this presentation, we investigate the effect of constraining the Ensemble Kalman Filter (EnKF) on forecast performance. An EnKF implementation with no constraints is compared to model output with no assimilation, followed by a 'typical' hydrological implementation (in which mass constraints are enforced to ensure non-negativity and capacity thresholds of model states are not exceeded), and then a more tightly constrained implementation where flux as well as mass constraints are imposed to limit the rate of water movement within a state. A three year period (2008-2010) with no significant data gaps and representative of the range of flows observed over the fuller 1976-2010 record was selected for analysis. Over this period, the standard implementation of the EnKF (no constraints) contained eight hydrological events where (multiple) physically inconsistent state adjustments were made. All were selected for analysis. Overall, neither the unconstrained nor the "typically" mass-constrained forecasts were significantly better than the non-filtered forecasts; in fact several were significantly degraded. Flux constraints (in conjunction with mass constraints) significantly improved the forecast performance of six events relative to all other implementations, while the remaining two events showed no significant difference in performance. We conclude that placing flux as well as mass constraints on the data assimilation framework encourages physically consistent state updating and results in more accurate and reliable forward predictions of streamflow for robust decision-making. We also experiment with the observation error, and find that this
Robust car tracking using Kalman filtering and Bayesian templates
NASA Astrophysics Data System (ADS)
Dellaert, Frank; Thorpe, Chuck E.
1998-01-01
We present a real-time model-based vision approach for detecting and tracking vehicles from a moving platform. It was developed in the context of the CMU Navlab project and is intended to provide the Navlabs with situational awareness in mixed traffic. Tracking is done by combining a simple image processing techniques with a 3D extended Kalman filter and a measurement equation that projects from the 3D model to image space. No ground plane assumption is made. The resulting system runs at frame rate or higher, and produces excellent estimates of road curvature, distance to and relative speed of a tracked vehicle. We have complemented the tracker with a novel machine learning based algorithm for car detection, the CANSS algorithm, which serves to initialize tracking.
4D-Var or Ensemble Kalman Filter
NASA Astrophysics Data System (ADS)
Kalnay, E.; Li, H.; Yang, S.; Miyoshi, T.; Ballabrera, J.
2007-05-01
We consider the relative advantages of two advanced data assimilation systems, 4D-Var and ensemble Kalman filter (EnKF), currently in use or considered for operational implementation. We explore the impact of tuning assimilation parameters such as the assimilation window length and background error covariance in 4D-Var, the variance inflation in EnKF, and the effect of model errors and reduced observation coverage in both systems. For short assimilation windows EnKF gives more accurate analyses. Both systems reach similar levels of accuracy if long windows are used for 4D-Var, and for infrequent observations, when ensemble perturbations grow nonlinearly and become non-Gaussian, 4D-Var attains lower errors than EnKF. Results obtained with variations of EnKF using operational models and both simulated and real observations are reviewed. A table summarizes the pros and cons of the two methods.
Kalman Filter for Mass Property and Thrust Identification (MMS)
NASA Technical Reports Server (NTRS)
Queen, Steven
2015-01-01
The Magnetospheric Multiscale (MMS) mission consists of four identically instrumented, spin-stabilized observatories, elliptically orbiting the Earth in a tetrahedron formation. For the operational success of the mission, on-board systems must be able to deliver high-precision orbital adjustment maneuvers. On MMS, this is accomplished using feedback from on-board star sensors in tandem with accelerometers whose measurements are dynamically corrected for errors associated with a spinning platform. In order to determine the required corrections to the measured acceleration, precise estimates of attitude, rate, and mass-properties is necessary. To this end, both an on-board and ground-based Multiplicative Extended Kalman Filter (MEKF) were formulated and implemented in order to estimate the dynamic and quasi-static properties of the spacecraft.
The development of a Kalman filter clock predictor
NASA Technical Reports Server (NTRS)
Davis, John A.; Greenhall, Charles A.; Boudjemaa, Redoane
2005-01-01
A Kalman filter based clock predictor is developed, and its performance evaluated using both simulated and real data. The clock predictor is shown to possess a neat to optimal Prediction Error Variance (PEV) when the underlying noise consists of one of the power law noise processes commonly encountered in time and frequency measurements. The predictor's performance is the presence of multiple noise processes is also examined. The relationship between the PEV obtained in the presence of multiple noise processes and those obtained for the individual component noise processes is examined. Comparisons are made with a simple linear clock predictor. The clock predictor is used to predict future values of the time offset between pairs of NPL's active hydrogen masers.
Model Calibration of Exciter and PSS Using Extended Kalman Filter
Kalsi, Karanjit; Du, Pengwei; Huang, Zhenyu
2012-07-26
Power system modeling and controls continue to become more complex with the advent of smart grid technologies and large-scale deployment of renewable energy resources. As demonstrated in recent studies, inaccurate system models could lead to large-scale blackouts, thereby motivating the need for model calibration. Current methods of model calibration rely on manual tuning based on engineering experience, are time consuming and could yield inaccurate parameter estimates. In this paper, the Extended Kalman Filter (EKF) is used as a tool to calibrate exciter and Power System Stabilizer (PSS) models of a particular type of machine in the Western Electricity Coordinating Council (WECC). The EKF-based parameter estimation is a recursive prediction-correction process which uses the mismatch between simulation and measurement to adjust the model parameters at every time step. Numerical simulations using actual field test data demonstrate the effectiveness of the proposed approach in calibrating the parameters.
NASA Astrophysics Data System (ADS)
Kokkinaki, A.; Li, J. Y.; Zhou, Q.; Birkholzer, J. T.; Kitanidis, P. K.
2014-12-01
Carbon dioxide (CO2) storage in deep geologic formations is gaining ground as a potential measure for climate change mitigation. Such storage projects typically operate at large scales (~km), but their performance is often governed by smaller-scale (~m) heterogeneities. The large domain sizes prohibit detailed site characterization and dense monitoring networks, leading to predictions of CO2 migration and trapping based on rough geologic models that cannot capture preferential flow. Kalman Filtering can be used to improve these prior models by assimilating available monitoring data, thereby tracking system performance and reducing prediction uncertainty. However, for large systems with fine discretization, the number of unknowns is in the order of tens of thousands or more, in which case the textbook version of the Kalman Filter has prohibitively expensive computation and storage costs. We present the Compressed State Kalman Filter (CSKF) that can be effectively used for systems with a large number of unknowns to estimate the underlying heterogeneity and to predict the state of interest (e.g., pressure and CO2 saturation). The algorithm's computational efficiency is achieved by using a low-rank approximation of the covariance matrix, as well as a Jacobian-free approach. We demonstrate the estimation and computational performance of our method in a typical CO2 storage scenario with a spatially sparse monitoring network, but with multiple datasets obtained before and during CO2 injection. Our data assimilation framework provides an efficient and practical way to characterize geological formations intended for CO2 injection and storage using monitoring data commonly collected in field applications, as well as to quantify the reduction in uncertainty brought by different types of monitoring data.
NASA Astrophysics Data System (ADS)
Wu, Xiaoping; Abbondanza, Claudio; Altamimi, Zuheir; Chin, T. Mike; Collilieux, Xavier; Gross, Richard S.; Heflin, Michael B.; Jiang, Yan; Parker, Jay W.
2015-05-01
The current International Terrestrial Reference Frame is based on a piecewise linear site motion model and realized by reference epoch coordinates and velocities for a global set of stations. Although linear motions due to tectonic plates and glacial isostatic adjustment dominate geodetic signals, at today's millimeter precisions, nonlinear motions due to earthquakes, volcanic activities, ice mass losses, sea level rise, hydrological changes, and other processes become significant. Monitoring these (sometimes rapid) changes desires consistent and precise realization of the terrestrial reference frame (TRF) quasi-instantaneously. Here, we use a Kalman filter and smoother approach to combine time series from four space geodetic techniques to realize an experimental TRF through weekly time series of geocentric coordinates. In addition to secular, periodic, and stochastic components for station coordinates, the Kalman filter state variables also include daily Earth orientation parameters and transformation parameters from input data frames to the combined TRF. Local tie measurements among colocated stations are used at their known or nominal epochs of observation, with comotion constraints applied to almost all colocated stations. The filter/smoother approach unifies different geodetic time series in a single geocentric frame. Fragmented and multitechnique tracking records at colocation sites are bridged together to form longer and coherent motion time series. While the time series approach to TRF reflects the reality of a changing Earth more closely than the linear approximation model, the filter/smoother is computationally powerful and flexible to facilitate incorporation of other data types and more advanced characterization of stochastic behavior of geodetic time series.
NASA Astrophysics Data System (ADS)
Ohkubo, Jun
2015-10-01
An alternative application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, here I employ numerical solutions of the dual processes and investigate the usefulness. As a demonstration, estimation problems of hidden variables in stochastic differential equations are discussed. Employing algebraic probability theory, a little complicated birth-death process is derived from the stochastic differential equations, and an estimation method based on the ensemble Kalman filter is proposed. As a result, the possibility for making faster computational algorithms based on the duality concepts is shown.
Ohkubo, Jun
2015-10-01
An alternative application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, here I employ numerical solutions of the dual processes and investigate the usefulness. As a demonstration, estimation problems of hidden variables in stochastic differential equations are discussed. Employing algebraic probability theory, a little complicated birth-death process is derived from the stochastic differential equations, and an estimation method based on the ensemble Kalman filter is proposed. As a result, the possibility for making faster computational algorithms based on the duality concepts is shown. PMID:26565359
Second-order discrete Kalman filtering equations for control-structure interaction simulations
NASA Technical Reports Server (NTRS)
Park, K. C.; Belvin, W. Keith; Alvin, Kenneth F.
1991-01-01
A general form for the first-order representation of the continuous, second-order linear structural dynamics equations is introduced in order to derive a corresponding form of first-order Kalman filtering equations (KFE). Time integration of the resulting first-order KFE is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete KFE involving only symmetric, N x N solution matrix.
Convergence of discrete-time Kalman filter estimate to continuous time estimate
NASA Astrophysics Data System (ADS)
Aalto, Atte
2016-04-01
This article is concerned with the convergence of the state estimate obtained from the discrete-time Kalman filter to the continuous time estimate as the temporal discretisation is refined. The convergence follows from Martingale convergence theorem as demonstrated below; however, surprisingly, no results exist on the rate of convergence. We derive convergence rate estimates for the discrete-time Kalman filter estimate for finite and infinite dimensional systems. The proofs are based on applying the discrete-time Kalman filter on a dense numerable subset of a certain time interval [0, T].
Zero Gyro Kalman Filtering in the presence of a Reaction Wheel Failure
NASA Technical Reports Server (NTRS)
Hur-Diaz, Sun; Wirzburger, John; Smith, Dan; Myslinski, Mike
2007-01-01
Typical implementation of Kalman filters for spacecraft attitude estimation involves the use of gyros for three-axis rate measurements. When there are less than three axes of information available, the accuracy of the Kalman filter depends highly on the accuracy of the dynamics model. This is particularly significant during the transient period when a reaction wheel with a high momentum fails, is taken off-line, and spins down. This paper looks at how a reaction wheel failure can affect the zero-gyro Kalman filter performance for the Hubble Space Telescope and what steps are taken to minimize its impact.
Zero Gyro Kalman Filtering in the Presence of a Reaction Wheel Failure
NASA Technical Reports Server (NTRS)
Hur-Diaz, Sun; Wirzburger, John; Smith, Dan; Myslinski, Mike
2007-01-01
Typical implementation of Kalman filters for spacecraft attitude estimation involves the use of gyros for three-axis rate measurements. When there are less than three axes of information available, the accuracy of the Kalman filter depends highly on the accuracy of the dynamics model. This is particularly significant during the transient period when a reaction wheel with a high momentum fails, is taken off-line, and spins down. This paper looks at how a reaction wheel failure can affect the zero-gyro Kalman filter performance for the Hubble Space Telescope and what steps are taken to minimize its impact.
An effective automatic tracking algorithm based on Camshift and Kalman filter
NASA Astrophysics Data System (ADS)
Liang, Juan; Hou, Jianhua; Xiang, Jun; Da, Bangyou; Chen, Shaobo
2011-11-01
An automatic tracking algorithm based on Camshift and Kalman filter is proposed in this paper to deal with the problems in traditional Camshift algorithm, such as artificial orientation and increasing possibility of tracking failure under occlusion. The inter-frame difference and canny edge detection are combined to segment perfect moving object region accurately, and the center point of the region is obtained as the initial position of the object. With regard to tracking under occlusion, Kalman filter is used to predict the position and velocity of the target. Specifically, the initial iterative position of Camshift algorithm is obtained by Kalman filter in every frame, and then Camshift algorithm is utilized to track the target position. Finally, the parameters of adaptive Kalman filter are updated by the optimal position. However, when severe occlusion appears, the optimal position calculated by Camshift algorithm is inaccurate, and the Kalman filter fails to estimate the coming state effectively. In this situation, the Kalman filter is updated by the Kalman predictive value instead of the value calculated by the Camshift algorithm. The experiment results demonstrate that the proposed algorithm can detect and track the target object accurately and has better robustness to occlusion.
Zhu, Wei; Wang, Wei; Yuan, Gannan
2016-01-01
In order to improve the tracking accuracy, model estimation accuracy and quick response of multiple model maneuvering target tracking, the interacting multiple models five degree cubature Kalman filter (IMM5CKF) is proposed in this paper. In the proposed algorithm, the interacting multiple models (IMM) algorithm processes all the models through a Markov Chain to simultaneously enhance the model tracking accuracy of target tracking. Then a five degree cubature Kalman filter (5CKF) evaluates the surface integral by a higher but deterministic odd ordered spherical cubature rule to improve the tracking accuracy and the model switch sensitivity of the IMM algorithm. Finally, the simulation results demonstrate that the proposed algorithm exhibits quick and smooth switching when disposing different maneuver models, and it also performs better than the interacting multiple models cubature Kalman filter (IMMCKF), interacting multiple models unscented Kalman filter (IMMUKF), 5CKF and the optimal mode transition matrix IMM (OMTM-IMM). PMID:27258285
Zhu, Wei; Wang, Wei; Yuan, Gannan
2016-01-01
In order to improve the tracking accuracy, model estimation accuracy and quick response of multiple model maneuvering target tracking, the interacting multiple models five degree cubature Kalman filter (IMM5CKF) is proposed in this paper. In the proposed algorithm, the interacting multiple models (IMM) algorithm processes all the models through a Markov Chain to simultaneously enhance the model tracking accuracy of target tracking. Then a five degree cubature Kalman filter (5CKF) evaluates the surface integral by a higher but deterministic odd ordered spherical cubature rule to improve the tracking accuracy and the model switch sensitivity of the IMM algorithm. Finally, the simulation results demonstrate that the proposed algorithm exhibits quick and smooth switching when disposing different maneuver models, and it also performs better than the interacting multiple models cubature Kalman filter (IMMCKF), interacting multiple models unscented Kalman filter (IMMUKF), 5CKF and the optimal mode transition matrix IMM (OMTM-IMM). PMID:27258285
Sadaghzadeh N, Nargess; Poshtan, Javad; Wagner, Achim; Nordheimer, Eugen; Badreddin, Essameddin
2014-03-01
Based on a cascaded Kalman-Particle Filtering, gyroscope drift and robot attitude estimation method is proposed in this paper. Due to noisy and erroneous measurements of MEMS gyroscope, it is combined with Photogrammetry based vision navigation scenario. Quaternions kinematics and robot angular velocity dynamics with augmented drift dynamics of gyroscope are employed as system state space model. Nonlinear attitude kinematics, drift and robot angular movement dynamics each in 3 dimensions result in a nonlinear high dimensional system. To reduce the complexity, we propose a decomposition of system to cascaded subsystems and then design separate cascaded observers. This design leads to an easier tuning and more precise debugging from the perspective of programming and such a setting is well suited for a cooperative modular system with noticeably reduced computation time. Kalman Filtering (KF) is employed for the linear and Gaussian subsystem consisting of angular velocity and drift dynamics together with gyroscope measurement. The estimated angular velocity is utilized as input of the second Particle Filtering (PF) based observer in two scenarios of stochastic and deterministic inputs. Simulation results are provided to show the efficiency of the proposed method. Moreover, the experimental results based on data from a 3D MEMS IMU and a 3D camera system are used to demonstrate the efficiency of the method. PMID:24342270
Adaptive Kalman filter implementation by a neural network scheme for tracking maneuvering targets
NASA Astrophysics Data System (ADS)
Amoozegar, Farid; Sundareshan, Malur K.
1995-07-01
Conventional target tracking algorithms based on linear estimation techniques perform quite efficiently when the target motion does not involve maneuvers. Target maneuvers involving short term accelerations, however, cause a bias (e.g. jump) in the measurement sequence, which unless compensated, results in divergence of the Kalman filter that provides estimates of target position and velocity, in turn leading to a loss of track. Accurate compensation for the bias requires processing more samples of the input signals which adds to the computational complexity. The waiting time for more samples can also result in a total loss of track since the target can begin a new maneuver and if the target begins a new maneuver before the first one is compensated for, the filter would never converge. Most of the proposed algorithms in the current literature hence have the disadvantage of losing the target in short term accelerations, i.e., when the duration of acceleration is comparable to the time period between the measurements. The time lag for maneuver modelings, which have been based on Bayesian probability calculations and linear estimation shall propose a neural network scheme for the modeling of target maneuvers. The primary motivation for employing compensation. The parallel processing capability of a properly trained neural network can permit fast processing of features to yield correct acceleration estimates and hence can take the burden off the primary Kalman filter which still provides the target position and velocity estimates.
Ghumare, Eshwar; Schrooten, Maarten; Vandenberghe, Rik; Dupont, Patrick
2015-08-01
Kalman filter approaches are widely applied to derive time varying effective connectivity from electroencephalographic (EEG) data. For multi-trial data, a classical Kalman filter (CKF) designed for the estimation of single trial data, can be implemented by trial-averaging the data or by averaging single trial estimates. A general linear Kalman filter (GLKF) provides an extension for multi-trial data. In this work, we studied the performance of the different Kalman filtering approaches for different values of signal-to-noise ratio (SNR), number of trials and number of EEG channels. We used a simulated model from which we calculated scalp recordings. From these recordings, we estimated cortical sources. Multivariate autoregressive model parameters and partial directed coherence was calculated for these estimated sources and compared with the ground-truth. The results showed an overall superior performance of GLKF except for low levels of SNR and number of trials. PMID:26736727
NASA Technical Reports Server (NTRS)
Kelly, D. A.; Fermelia, A.; Lee, G. K. F.
1990-01-01
An adaptive Kalman filter design that utilizes recursive maximum likelihood parameter identification is discussed. At the center of this design is the Kalman filter itself, which has the responsibility for attitude determination. At the same time, the identification algorithm is continually identifying the system parameters. The approach is applicable to nonlinear, as well as linear systems. This adaptive Kalman filter design has much potential for real time implementation, especially considering the fast clock speeds, cache memory and internal RAM available today. The recursive maximum likelihood algorithm is discussed in detail, with special attention directed towards its unique matrix formulation. The procedure for using the algorithm is described along with comments on how this algorithm interacts with the Kalman filter.
Analysis of Video-Based Microscopic Particle Trajectories Using Kalman Filtering
Wu, Pei-Hsun; Agarwal, Ashutosh; Hess, Henry; Khargonekar, Pramod P.; Tseng, Yiider
2010-01-01
Abstract The fidelity of the trajectories obtained from video-based particle tracking determines the success of a variety of biophysical techniques, including in situ single cell particle tracking and in vitro motility assays. However, the image acquisition process is complicated by system noise, which causes positioning error in the trajectories derived from image analysis. Here, we explore the possibility of reducing the positioning error by the application of a Kalman filter, a powerful algorithm to estimate the state of a linear dynamic system from noisy measurements. We show that the optimal Kalman filter parameters can be determined in an appropriate experimental setting, and that the Kalman filter can markedly reduce the positioning error while retaining the intrinsic fluctuations of the dynamic process. We believe the Kalman filter can potentially serve as a powerful tool to infer a trajectory of ultra-high fidelity from noisy images, revealing the details of dynamic cellular processes. PMID:20550894
NASA Astrophysics Data System (ADS)
Borodachev, S. M.
2016-06-01
The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.
Extended Kalman filtering applied to a two-axis robotic arm with flexible links
Lertpiriyasuwat, V.; Berg, M.C.; Buffinton, K.W.
2000-03-01
An industrial robot today uses measurements of its joint positions and models of its kinematics and dynamics to estimate and control its end-effector position. Substantially better end-effector position estimation and control performance would be obtainable if direct measurements of its end-effector position were also used. The subject of this paper is extended Kalman filtering for precise estimation of the position of the end-effector of a robot using, in addition to the usual measurements of the joint positions, direct measurements of the end-effector position. The estimation performances of extended Kalman filters are compared in applications to a planar two-axis robotic arm with very flexible links. The comparisons shed new light on the dependence of extended Kalman filter estimation performance on the quality of the model of the arm dynamics that the extended Kalman filter operates with.
NASA Technical Reports Server (NTRS)
Ledsham, W. H.; Staelin, D. H.
1978-01-01
An extended Kalman-Bucy filter has been implemented for atmospheric temperature profile retrievals from observations made using the Scanned Microwave Spectrometer (SCAMS) instrument carried on the Nimbus 6 satellite. This filter has the advantage that it requires neither stationary statistics in the underlying processes nor linear production of the observed variables from the variables to be estimated. This extended Kalman-Bucy filter has yielded significant performance improvement relative to multiple regression retrieval methods. A multi-spot extended Kalman-Bucy filter has also been developed in which the temperature profiles at a number of scan angles in a scanning instrument are retrieved simultaneously. These multi-spot retrievals are shown to outperform the single-spot Kalman retrievals.
Real-time data assimilation for large-scale systems: The spectral Kalman filter
NASA Astrophysics Data System (ADS)
Ghorbanidehno, Hojat; Kokkinaki, Amalia; Li, Judith Yue; Darve, Eric; Kitanidis, Peter K.
2015-12-01
The Kalman Filter (KF) is a data assimilation method that has been widely used for estimating spatially varying unknown states evolving in time. Recently, KF methods have shown potential for tracking CO2 plumes injected in deep geologic formations. Such real-time estimation would serve as an early warning system for leakage incidents. However, for the large number of unknowns of such large systems, KF methods are impractical, because updating the huge state covariance matrix is computationally expensive. Low rank approximation methods have been devised to overcome this problem; these methods assume a low rank of the covariance matrix, which they approximate by smaller matrices. The approximation error is small for smooth functions, but may be larger for more complex physical problems, potentially leading to filter divergence and inaccurate state estimates. We present the Spectral Kalman Filter (SpecKF), a new algorithm that utilizes the exact covariance matrix. Thus it avoids the approximation error and does so in a computationally efficient way, which is specially important for systems with large numbers of unknowns. The computational speed-up of the SpecKF is achieved by updating cross-covariance matrices instead of the larger covariance matrices. The benefit can be considerable, especially in large systems, because the computational complexity of the SpecKF scales with the number of measurements, as opposed to the effective rank of the covariance matrix in low-rank KFs or the number of ensemble members in ensemble methods. We investigate the accuracy and performance of the SpecKF for a diffusion problem with random perturbations, and for a more complex case of CO2 injection in a homogeneous two-dimensional domain. Our results show that the SpecKF reduces greatly the computational cost compared to the original KF algorithm, and that it can provide higher accuracy than the Ensemble Kalman Filter (EnKF) with the same or even smaller computational cost. Finally, we
A Physics-Based Kalman Filter for the Ionosphere in GAIM
NASA Astrophysics Data System (ADS)
Scherliess, L.; Schunk, R. W.; Sojka, J. J.; Thompson, D. C.
2002-12-01
A physics-based data assimilation model of the ionosphere is under development as the central part of a DoD MURI funded program called GAIM (Global Assimilation of Ionospheric Measurements). With the significant increase in the number of ionospheric observations that will become available over the next decade, this model will provide a powerful tool towards an improved specification and forecasting of the global ionosphere, with an unprecedented accuracy and reliability. The goal of this effort will be the development of an operational ionospheric assimilation model that will provide specifications and forecasts on spatial grids that can be global, regional, or local (50 km x 50 km). The specification/forecast will be in the form of 3-dimensional electron density distributions from 90 km to geosynchronous altitudes (35,000 km). In GAIM, the data assimilation is performed by a Kalman filter using a new physics-based ionosphere/plasmasphere model (IPM). This model includes 6 ion species (O2+, N2+, NO+, O+, H+, and He+) and currently covers the low and mid-latitudes from 90 km to about 20,000 km altitude. As a practical implementation the Kalman filter in GAIM is based on approximations of the state error covariance matrix, employing a reduction of the model dimension and a linearization of the physical model for the propagation of the error covariance matrix. These approximations lead to a dramatic reduction in the computational requirements. In this paper, we will give an update on the status of the Kalman filter development and present results from a global assimilation run. In this test three different data types were considered, including bottomside electron density profiles obtained from several digisondes, slant TEC from a network of ground-based GPS receivers, and in situ electron density measurements from DMSP satellites.
Rigatos, Gerasimos
2014-12-01
A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of two coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie derivatives. For such a model it becomes possible to design a state feedback controller that assures the synchronization of the membrane's voltage variations for the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments. PMID:26396646
NASA Astrophysics Data System (ADS)
Raitoharju, Matti; Nurminen, Henri; Piché, Robert
2015-12-01
Indoor positioning based on wireless local area network (WLAN) signals is often enhanced using pedestrian dead reckoning (PDR) based on an inertial measurement unit. The state evolution model in PDR is usually nonlinear. We present a new linear state evolution model for PDR. In simulated-data and real-data tests of tightly coupled WLAN-PDR positioning, the positioning accuracy with this linear model is better than with the traditional models when the initial heading is not known, which is a common situation. The proposed method is computationally light and is also suitable for smoothing. Furthermore, we present modifications to WLAN positioning based on Gaussian coverage areas and show how a Kalman filter using the proposed model can be used for integrity monitoring and (re)initialization of a particle filter.
Hybrid Kalman Filter: A New Approach for Aircraft Engine In-Flight Diagnostics
NASA Technical Reports Server (NTRS)
Kobayashi, Takahisa; Simon, Donald L.
2006-01-01
In this paper, a uniquely structured Kalman filter is developed for its application to in-flight diagnostics of aircraft gas turbine engines. The Kalman filter is a hybrid of a nonlinear on-board engine model (OBEM) and piecewise linear models. The utilization of the nonlinear OBEM allows the reference health baseline of the in-flight diagnostic system to be updated to the degraded health condition of the engines through a relatively simple process. Through this health baseline update, the effectiveness of the in-flight diagnostic algorithm can be maintained as the health of the engine degrades over time. Another significant aspect of the hybrid Kalman filter methodology is its capability to take advantage of conventional linear and nonlinear Kalman filter approaches. Based on the hybrid Kalman filter, an in-flight fault detection system is developed, and its diagnostic capability is evaluated in a simulation environment. Through the evaluation, the suitability of the hybrid Kalman filter technique for aircraft engine in-flight diagnostics is demonstrated.
A numerical comparison of discrete Kalman filtering algorithms - An orbit determination case study
NASA Technical Reports Server (NTRS)
Thornton, C. L.; Bierman, G. J.
1976-01-01
An improved Kalman filter algorithm based on a modified Givens matrix triangularization technique is proposed for solving a nonstationary discrete-time linear filtering problem. The proposed U-D covariance factorization filter uses orthogonal transformation technique; measurement and time updating of the U-D factors involve separate application of Gentleman's fast square-root-free Givens rotations. Numerical stability and accuracy of the algorithm are compared with those of the conventional and stabilized Kalman filters and the Potter-Schmidt square-root filter, by applying these techniques to a realistic planetary navigation problem (orbit determination for the Saturn approach phase of the Mariner Jupiter-Saturn Mission, 1977). The new algorithm is shown to combine the numerical precision of square root filtering with the efficiency of the original Kalman algorithm.
Relating the Hadamard Variance to MCS Kalman Filter Clock Estimation
NASA Technical Reports Server (NTRS)
Hutsell, Steven T.
1996-01-01
The Global Positioning System (GPS) Master Control Station (MCS) currently makes significant use of the Allan Variance. This two-sample variance equation has proven excellent as a handy, understandable tool, both for time domain analysis of GPS cesium frequency standards, and for fine tuning the MCS's state estimation of these atomic clocks. The Allan Variance does not explicitly converge for the nose types of alpha less than or equal to minus 3 and can be greatly affected by frequency drift. Because GPS rubidium frequency standards exhibit non-trivial aging and aging noise characteristics, the basic Allan Variance analysis must be augmented in order to (a) compensate for a dynamic frequency drift, and (b) characterize two additional noise types, specifically alpha = minus 3, and alpha = minus 4. As the GPS program progresses, we will utilize a larger percentage of rubidium frequency standards than ever before. Hence, GPS rubidium clock characterization will require more attention than ever before. The three sample variance, commonly referred to as a renormalized Hadamard Variance, is unaffected by linear frequency drift, converges for alpha is greater than minus 5, and thus has utility for modeling noise in GPS rubidium frequency standards. This paper demonstrates the potential of Hadamard Variance analysis in GPS operations, and presents an equation that relates the Hadamard Variance to the MCS's Kalman filter process noises.
A multimodel data assimilation framework via the ensemble Kalman filter
NASA Astrophysics Data System (ADS)
Xue, Liang; Zhang, Dongxiao
2014-05-01
The ensemble Kalman filter (EnKF) is a widely used data assimilation method that has the capacity to sequentially update system parameters and states as new observations become available. One noticeable feature of the EnKF is that it not only can provide real-time updates of model parameters and state variables, but also can give the uncertainty associated with them in each assimilation step. The natural system is open and complex, rendering it prone to multiple interpretations and mathematical descriptions. In this paper, a multimodel data assimilation method is proposed by embedding the EnKF into the Bayesian model averaging framework to account for the uncertainty stemming from the model itself. An illustrative example, considering both hydrogeological and groundwater flow uncertainties, is employed to demonstrate the proposed multimodel data assimilation approach via the EnKF. Results show that statistical bias and uncertainty underestimation can occur when the data assimilation process relies on a single postulated model. The posterior model weight can adjust itself dynamically in time according to its consistency with observations. The performances of log conductivity estimation and head prediction are compared to the standard EnKF method based on the postulated single model and the proposed multimodel EnKF method. Comparisons show that the multimodel EnKF performs better in terms of statistical measures, such as log score and coverage, when sufficient observations have been assimilated in this case.
Updating multipoint simulations using the ensemble Kalman filter
NASA Astrophysics Data System (ADS)
Hu, L. Y.; Zhao, Y.; Liu, Y.; Scheepens, C.; Bouchard, A.
2013-02-01
In the last two decades, the multipoint simulation (MPS) method has been developed and increasingly used for building complex geological facies models that are conditioned to geological and geophysical data. In the meantime, the ensemble Kalman filter (EnKF) approach has been developed and recognized as a promising way for assimilating dynamic production data into reservoir models. So far, the EnKF approach is proven efficient for updating continuous model parameters that have a linear statistical relation with the flow responses. It remains challenging to extend the EnKF approach to updating complex geological facies models generated by MPS, while preserving their geological and statistical consistency. In this paper, we introduce a new method for parameterizing geostatistical reservoir models generated by MPS. It is mathematically proven that updating these parameters during a history matching process does not compromise the hard data conditioning and the geological and statistical consistency of the reservoir model defined by the training image and other information including global facies proportions, trend maps etc. This method is an alternative to the gradual deformation method but has an enlarged search space for covering possible solutions. Based on the above parameterization, we present two algorithms of using EnKF approach to update multipoint simulations to dynamic data. We also present results of using the above methodology to condition a sector model of a fluvial reservoir to dynamic data.
Streamflow data assimilation in SWAT model using Extended Kalman Filter
NASA Astrophysics Data System (ADS)
Sun, Leqiang; Nistor, Ioan; Seidou, Ousmane
2015-12-01
The Extended Kalman Filter (EKF) is coupled with the Soil and Water Assessment Tools (SWAT) model in the streamflow assimilation of the upstream Senegal River in West Africa. Given the large number of distributed variables in SWAT, only the average watershed scale variables are included in the state vector and the Hydrological Response Unit (HRU) scale variables are updated with the a posteriori/a priori ratio of their watershed scale counterparts. The Jacobian matrix is calculated numerically by perturbing the state variables. Both the soil moisture and CN2 are significantly updated in the wet season, yet they have opposite update patterns. A case study for a large flood forecast shows that for up to seven days, the streamflow forecast is moderately improved using the EKF-subsequent open loop scheme but significantly improved with a newly designed quasi-error update scheme. The former has better performances in the flood rising period while the latter has better performances in the recession period. For both schemes, the streamflow forecast is improved more significantly when the lead time is shorter.
Extended Kalman filter for multiwavelength differential absorption lidar
NASA Astrophysics Data System (ADS)
Warren, Russell E.; Vanderbeek, Richard G.
2001-08-01
Our earlier study described an approach for estimating the path-integrated concentration, CL, of a set of vapor materials using time series data from topographic backscatter lidar with frequency-agile lasers. That methodology assumed the availability of background data samples collected before the release of the vapors of interest to estimate statistical parameters such as the mean topographic backscatter return and the transmitter energy mean and variance as a function of wavelength. The background data were then used in an extended Kalman filter approach for estimating the CL components as a function of time. That approach worked well for data that showed negligible drift in the mean parameters over the data collection time. In practice, however, the transmitter energy and background return can drift, producing substantial bias in the estimates. In this paper we generalize the approach to a more complete state model that includes the mean transmitter energy and background return in addition to the CL vapor set. This generalization allows the algorithm to track slow drift in those parameters and provides generally improved estimates. Results of the new algorithm are compared with those of a two-wavelength classical DIAL estimator on synthetic and field test data.
4-D-Var or ensemble Kalman filter?
NASA Astrophysics Data System (ADS)
Kalnay, Eugenia; Li, Hong; Miyoshi, Takemasa; Yang, Shu-Chih; Ballabrera-Poy, Joaquim
2007-10-01
We consider the relative advantages of two advanced data assimilation systems, 4-D-Var and ensemble Kalman filter (EnKF), currently in use or under consideration for operational implementation. With the Lorenz model, we explore the impact of tuning assimilation parameters such as the assimilation window length and background error covariance in 4-D-Var, variance inflation in EnKF, and the effect of model errors and reduced observation coverage. For short assimilation windows EnKF gives more accurate analyses. Both systems reach similar levels of accuracy if long windows are used for 4-D-Var. For infrequent observations, when ensemble perturbations grow non-linearly and become non-Gaussian, 4-D-Var attains lower errors than EnKF. If the model is imperfect, the 4-D-Var with long windows requires weak constraint. Similar results are obtained with a quasi-geostrophic channel model. EnKF experiments made with the primitive equations SPEEDY model provide comparisons with 3-D-Var and guidance on model error and `observation localization'. Results obtained using operational models and both simulated and real observations indicate that currently EnKF is becoming competitive with 4-D-Var, and that the experience acquired with each of these methods can be used to improve the other. A table summarizes the pros and cons of the two methods.
Fuzzy Logic Based Autonomous Parallel Parking System with Kalman Filtering
NASA Astrophysics Data System (ADS)
Panomruttanarug, Benjamas; Higuchi, Kohji
This paper presents an emulation of fuzzy logic control schemes for an autonomous parallel parking system in a backward maneuver. There are four infrared sensors sending the distance data to a microcontroller for generating an obstacle-free parking path. Two of them mounted on the front and rear wheels on the parking side are used as the inputs to the fuzzy rules to calculate a proper steering angle while backing. The other two attached to the front and rear ends serve for avoiding collision with other cars along the parking space. At the end of parking processes, the vehicle will be in line with other parked cars and positioned in the middle of the free space. Fuzzy rules are designed based upon a wall following process. Performance of the infrared sensors is improved using Kalman filtering. The design method needs extra information from ultrasonic sensors. Starting from modeling the ultrasonic sensor in 1-D state space forms, one makes use of the infrared sensor as a measurement to update the predicted values. Experimental results demonstrate the effectiveness of sensor improvement.
Discrete Kalman Filter based Sensor Fusion for Robust Accessibility Interfaces
NASA Astrophysics Data System (ADS)
Ghersi, I.; Mariño, M.; Miralles, M. T.
2016-04-01
Human-machine interfaces have evolved, benefiting from the growing access to devices with superior, embedded signal-processing capabilities, as well as through new sensors that allow the estimation of movements and gestures, resulting in increasingly intuitive interfaces. In this context, sensor fusion for the estimation of the spatial orientation of body segments allows to achieve more robust solutions, overcoming specific disadvantages derived from the use of isolated sensors, such as the sensitivity of magnetic-field sensors to external influences, when used in uncontrolled environments. In this work, a method for the combination of image-processing data and angular-velocity registers from a 3D MEMS gyroscope, through a Discrete-time Kalman Filter, is proposed and deployed as an alternate user interface for mobile devices, in which an on-screen pointer is controlled with head movements. Results concerning general performance of the method are presented, as well as a comparative analysis, under a dedicated test application, with results from a previous version of this system, in which the relative-orientation information was acquired directly from MEMS sensors (3D magnetometer-accelerometer). These results show an improved response for this new version of the pointer, both in terms of precision and response time, while keeping many of the benefits that were highlighted for its predecessor, giving place to a complementary method for signal acquisition that can be used as an alternative-input device, as well as for accessibility solutions.
Kalman Filter Based Railway Tracking from Mobile LIDAR Data
NASA Astrophysics Data System (ADS)
Jwa, Y.; Sonh, G.
2015-08-01
This study introduces a new method to reconstruct 3D model of railway tracks from a railway corridor scene captured by mobile LiDAR data. The proposed approach starts to approximate the orientation of railway track trajectory from LiDAR point clouds and extract a strip, which direction is orthogonal to the trajectory of railway track. Within the strip, a track region and its track points are detected based on the Bayesian decision process. Once the main track region is localized, rail head points are segmented based on the region growing approach from the detected track points and then initial track models are reconstructed using a third-degree polynomial function. Based on the initial modelling result, a potential track region with varying lengths is dynamically predicted and the model parameters are updated in the Kalman Filter framework. The key aspect is that the proposed approach is able to enhance the efficiency of the railway tracking process by reducing the complexity for detecting track points and reconstructing track models based on the use of the track model previously reconstructed. An evaluation of the proposed method is performed over an urban railway corridor area containing multiple railway track pairs.
Ensemble Kalman Filter Data Assimilation for the Martian Atmosphere
NASA Astrophysics Data System (ADS)
Hoffman, Matthew J.; Greybush, S.; Wilson, R. J.; Gyarmati, G.; Ide, K.; Miyoshi, T.; Szunyogh, I.; Kalnay, E.
2009-09-01
A data assimilation system provides a means of optimally combining information from sparse observations and an atmospheric model to provide an accurate depiction of the state of a planetary atmosphere. Here a Mars General Circulation Model (MGCM) is coupled with the local ensemble transform Kalman filter (LETKF) as the basis of an advanced data assimilation system for Mars. Identical twin experiments, in which observations are generated synthetically from a nature run of the MGCM to approximate the spatial distribution of PDS TES profiles, explore the potential of ensemble data assimilation for the Martian atmosphere. The experiments find that the LETKF is able to correct errors in the Martian atmospheric model and improve the state estimates of the temperature and wind fields, even in the absence of wind observations. The error in the state estimate quickly reduces to below the observation error, and both the forecast and subsequent analysis errors remain low for the duration of a 60 day simulation. Large-scale baroclinic waves along the Northern (winter) Hemisphere temperature front and instabilities in the upper atmosphere zonal wind jet are two predominant sources of error in the MGCM-LETKF system. This study forms the first step toward creating the MGCM-LETKF Martian Atmosphere Reanalysis, which will be incorporating real observations obtained from the MGS TES instrument.
A steady-state Kalman filter for assimilating data from a single polar orbiting satellite
NASA Technical Reports Server (NTRS)
Banfield, Don; Ingersoll, Andrew P.; Keppenne, Christian L.
1995-01-01
A steady-state scheme for data assimilation in the context of a single, short period (relative to a day), sun-synchronous, polar-orbiting satellite is examined. If the satellite takes observations continuously, the gains, which are the weights for blending observations and predictions together, are steady in time. For a linear system forced by random noise, the optimal steady-state gains (Wiener gains) are equivalent to those of a Kalman filter. Computing the Kalman gains increases the computational cost of the model by a large factor, but computing the Wiener gains does not. The latter are computed by iteration using prior estimates of the gains to assimilate simulated observations of one run of the model, termed 'truth' into another run termed 'prediction'. At each stage, the prediction errors form the basis for the next estimate of the gains. Steady state is achieved after three or four iterations. Further simplification is achieved by making the gains depend on longitudinal distance from the observation point, not on absolute longitude. For a single-layer primitive equation model, the scheme works well even if only the mass field is observed but not the velocity field. Although the scheme was developed for Mars Observer, it should be applicable to data retrieved from Earth atmosphere satellites, for example, UARS.
Ensemble Kalman filter implementations based on shrinkage covariance matrix estimation
NASA Astrophysics Data System (ADS)
Nino-Ruiz, Elias D.; Sandu, Adrian
2015-11-01
This paper develops efficient ensemble Kalman filter (EnKF) implementations based on shrinkage covariance estimation. The forecast ensemble members at each step are used to estimate the background error covariance matrix via the Rao-Blackwell Ledoit and Wolf estimator, which has been specifically developed to approximate high-dimensional covariance matrices using a small number of samples. Two implementations are considered: in the EnKF full-space (EnKF-FS) approach, the assimilation process is performed in the model space, while the EnKF reduce-space (EnKF-RS) formulation performs the analysis in the subspace spanned by the ensemble members. In the context of EnKF-RS, additional samples are taken from the normal distribution described by the background ensemble mean and the estimated background covariance matrix, in order to increase the size of the ensemble and reduce the sampling error of the filter. This increase in the size of the ensemble is obtained without running the forward model. After the assimilation step, the additional samples are discarded and only the model-based ensemble members are propagated further. Methodologies to reduce the impact of spurious correlations and under-estimation of sample variances in the context of the EnKF-FS and EnKF-RS implementations are discussed. An adjoint-free four-dimensional extension of EnKF-RS is also discussed. Numerical experiments carried out with the Lorenz-96 model and a quasi-geostrophic model show that the use of shrinkage covariance matrix estimation can mitigate the impact of spurious correlations during the assimilation process.
Durantin, Gautier; Scannella, Sébastien; Gateau, Thibault; Delorme, Arnaud; Dehais, Frédéric
2016-01-01
Working memory (WM) is a key executive function for operating aircraft, especially when pilots have to recall series of air traffic control instructions. There is a need to implement tools to monitor WM as its limitation may jeopardize flight safety. An innovative way to address this issue is to adopt a Neuroergonomics approach that merges knowledge and methods from Human Factors, System Engineering, and Neuroscience. A challenge of great importance for Neuroergonomics is to implement efficient brain imaging techniques to measure the brain at work and to design Brain Computer Interfaces (BCI). We used functional near infrared spectroscopy as it has been already successfully tested to measure WM capacity in complex environment with air traffic controllers (ATC), pilots, or unmanned vehicle operators. However, the extraction of relevant features from the raw signal in ecological environment is still a critical issue due to the complexity of implementing real-time signal processing techniques without a priori knowledge. We proposed to implement the Kalman filtering approach, a signal processing technique that is efficient when the dynamics of the signal can be modeled. We based our approach on the Boynton model of hemodynamic response. We conducted a first experiment with nine participants involving a basic WM task to estimate the noise covariances of the Kalman filter. We then conducted a more ecological experiment in our flight simulator with 18 pilots who interacted with ATC instructions (two levels of difficulty). The data was processed with the same Kalman filter settings implemented in the first experiment. This filter was benchmarked with a classical pass-band IIR filter and a Moving Average Convergence Divergence (MACD) filter. Statistical analysis revealed that the Kalman filter was the most efficient to separate the two levels of load, by increasing the observed effect size in prefrontal areas involved in WM. In addition, the use of a Kalman filter increased
Durantin, Gautier; Scannella, Sébastien; Gateau, Thibault; Delorme, Arnaud; Dehais, Frédéric
2015-01-01
Working memory (WM) is a key executive function for operating aircraft, especially when pilots have to recall series of air traffic control instructions. There is a need to implement tools to monitor WM as its limitation may jeopardize flight safety. An innovative way to address this issue is to adopt a Neuroergonomics approach that merges knowledge and methods from Human Factors, System Engineering, and Neuroscience. A challenge of great importance for Neuroergonomics is to implement efficient brain imaging techniques to measure the brain at work and to design Brain Computer Interfaces (BCI). We used functional near infrared spectroscopy as it has been already successfully tested to measure WM capacity in complex environment with air traffic controllers (ATC), pilots, or unmanned vehicle operators. However, the extraction of relevant features from the raw signal in ecological environment is still a critical issue due to the complexity of implementing real-time signal processing techniques without a priori knowledge. We proposed to implement the Kalman filtering approach, a signal processing technique that is efficient when the dynamics of the signal can be modeled. We based our approach on the Boynton model of hemodynamic response. We conducted a first experiment with nine participants involving a basic WM task to estimate the noise covariances of the Kalman filter. We then conducted a more ecological experiment in our flight simulator with 18 pilots who interacted with ATC instructions (two levels of difficulty). The data was processed with the same Kalman filter settings implemented in the first experiment. This filter was benchmarked with a classical pass-band IIR filter and a Moving Average Convergence Divergence (MACD) filter. Statistical analysis revealed that the Kalman filter was the most efficient to separate the two levels of load, by increasing the observed effect size in prefrontal areas involved in WM. In addition, the use of a Kalman filter increased
Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering.
Fraanje, Rufus; Rice, Justin; Verhaegen, Michel; Doelman, Niek
2010-11-01
Efficient and optimal prediction of frozen flow turbulence using the complete observation history of the wavefront sensor is an important issue in adaptive optics for large ground-based telescopes. At least for the sake of error budgeting and algorithm performance, the evaluation of an accurate estimate of the optimal performance of a particular adaptive optics configuration is important. However, due to the large number of grid points, high sampling rates, and the non-rationality of the turbulence power spectral density, the computational complexity of the optimal predictor is huge. This paper shows how a structure in the frozen flow propagation can be exploited to obtain a state-space innovation model with a particular sparsity structure. This sparsity structure enables one to efficiently compute a structured Kalman filter. By simulation it is shown that the performance can be improved and the computational complexity can be reduced in comparison with auto-regressive predictors of low order. PMID:21045884
NASA Astrophysics Data System (ADS)
Hirpa, F. A.; Gebremichael, M.; Hopson, T. M.; Wojick, R.
2011-12-01
We present results of data assimilation of ground discharge observation and remotely sensed soil moisture observations into Sacramento Soil Moisture Accounting (SACSMA) model in a small watershed (1593 km2) in Minnesota, the Unites States. Specifically, we perform assimilation experiments with Ensemble Kalman Filter (EnKF) and Particle Filter (PF) in order to improve streamflow forecast accuracy at six hourly time step. The EnKF updates the soil moisture states in the SACSMA from the relative errors of the model and observations, while the PF adjust the weights of the state ensemble members based on the likelihood of the forecast. Results of the improvements of each filter over the reference model (without data assimilation) will be presented. Finally, the EnKF and PF are coupled together to further improve the streamflow forecast accuracy.
NASA Astrophysics Data System (ADS)
Gray, Morgan; Petit, Cyril; Rodionov, Sergey; Bertino, Laurent; Bocquet, Marc; Fusco, Thierry
2013-12-01
We propose a new algorithm for an AO control law which allows to reduce the computation burden in the case of an Extremely Large Telescope and to deal with a non stationary behavior of the atmospheric turbulence. This approach uses Ensemble Transform Kalman Filter (ETKF) and localizations by domains decomposition: the assimilation is split into local domains on the pupil of the telescope and each of the update data assimilation for each domain is performed independently. This kind of assimilation enables parallel computation of much less data during the update stage. This is a Kalman Filter adaptation for large scale systems with a non stationary turbulence when the explicit storage and manipulation of extremely large covariance matrices are impossible. This distributed parallel environment implementation is highlighted and studied in the context of an ELT application. First simulation results are proposed to assess our theoretical analysis and to demonstrate the potentiality of this new approach for an AO control law on ELTs.
Extended Kalman filter based structural damage detection for MR damper controlled structures
NASA Astrophysics Data System (ADS)
Jin, Chenhao; Jang, Shinae; Sun, Xiaorong; Jiang, Zhaoshuo; Christenson, Richard
2016-04-01
The Magneto-rheological (MR) dampers have been widely used in many building and bridge structures against earthquake and wind loadings due to its advantages including mechanical simplicity, high dynamic range, low power requirements, large force capacity, and robustness. However, research about structural damage detection methods for MR damper controlled structures is limited. This paper aims to develop a real-time structural damage detection method for MR damper controlled structures. A novel state space model of MR damper controlled structure is first built by combining the structure's equation of motion and MR damper's hyperbolic tangent model. In this way, the state parameters of both the structure and MR damper are added in the state vector of the state space model. Extended Kalman filter is then used to provide prediction for state variables from measurement data. The two techniques are synergistically combined to identify parameters and track the changes of both structure and MR damper in real time. The proposed method is tested using response data of a three-floor MR damper controlled linear building structure under earthquake excitation. The testing results show that the adaptive extended Kalman filter based approach is capable to estimate not only structural parameters such as stiffness and damping of each floor, but also the parameters of MR damper, so that more insights and understanding of the damage can be obtained. The developed method also demonstrates high damage detection accuracy and light computation, as well as the potential to implement in a structural health monitoring system.
Gyro Drift Correction for An Indirect Kalman Filter Based Sensor Fusion Driver
Lee, Chan-Gun; Dao, Nhu-Ngoc; Jang, Seonmin; Kim, Deokhwan; Kim, Yonghun; Cho, Sungrae
2016-01-01
Sensor fusion techniques have made a significant contribution to the success of the recently emerging mobile applications era because a variety of mobile applications operate based on multi-sensing information from the surrounding environment, such as navigation systems, fitness trackers, interactive virtual reality games, etc. For these applications, the accuracy of sensing information plays an important role to improve the user experience (UX) quality, especially with gyroscopes and accelerometers. Therefore, in this paper, we proposed a novel mechanism to resolve the gyro drift problem, which negatively affects the accuracy of orientation computations in the indirect Kalman filter based sensor fusion. Our mechanism focuses on addressing the issues of external feedback loops and non-gyro error elements contained in the state vectors of an indirect Kalman filter. Moreover, the mechanism is implemented in the device-driver layer, providing lower process latency and transparency capabilities for the upper applications. These advances are relevant to millions of legacy applications since utilizing our mechanism does not require the existing applications to be re-programmed. The experimental results show that the root mean square errors (RMSE) before and after applying our mechanism are significantly reduced from 6.3×10-1 to 5.3×10-7, respectively. PMID:27294941
Data assimilation with the ensemble Kalman filter in a numerical model of the North Sea
NASA Astrophysics Data System (ADS)
Ponsar, Stéphanie; Luyten, Patrick; Dulière, Valérie
2016-07-01
Coastal management and maritime safety strongly rely on accurate representations of the sea state. Both dynamical models and observations provide abundant pieces of information. However, none of them provides the complete picture. The assimilation of observations into models is one way to improve our knowledge of the ocean state. Its application in coastal models remains challenging because of the wide range of temporal and spatial variabilities of the processes involved. This study investigates the assimilation of temperature profiles with the ensemble Kalman filter in 3-D North Sea simulations. The model error is represented by the standard deviation of an ensemble of model states. Parameters' values for the ensemble generation are first computed from the misfit between the data and the model results without assimilation. Then, two square root algorithms are applied to assimilate the data. The impact of data assimilation on the simulated temperature is assessed. Results show that the ensemble Kalman filter is adequate for improving temperature forecasts in coastal areas, under adequate model error specification.
Data assimilation with the ensemble Kalman filter in a numerical model of the North Sea
NASA Astrophysics Data System (ADS)
Ponsar, Stéphanie; Luyten, Patrick; Dulière, Valérie
2016-08-01
Coastal management and maritime safety strongly rely on accurate representations of the sea state. Both dynamical models and observations provide abundant pieces of information. However, none of them provides the complete picture. The assimilation of observations into models is one way to improve our knowledge of the ocean state. Its application in coastal models remains challenging because of the wide range of temporal and spatial variabilities of the processes involved. This study investigates the assimilation of temperature profiles with the ensemble Kalman filter in 3-D North Sea simulations. The model error is represented by the standard deviation of an ensemble of model states. Parameters' values for the ensemble generation are first computed from the misfit between the data and the model results without assimilation. Then, two square root algorithms are applied to assimilate the data. The impact of data assimilation on the simulated temperature is assessed. Results show that the ensemble Kalman filter is adequate for improving temperature forecasts in coastal areas, under adequate model error specification.