Showing papers on "Invariant extended Kalman filter published in 1979"
TL;DR: In this paper, a convergence analysis of the extended Kalman filter for nonlinear systems with unknown parameters is given, and it is shown that in general the estimates may be biased or divergent and the causes for this are displayed.
Abstract: The extended Kalman filter is an approximate filter for nonlinear systems, based on first-order linearization. Its use for the joint parameter and state estimation problem for linear systems with unknown parameters is well known and widely spread. Here a convergence analysis of this method is given. It is shown that in general, the estimates may be biased or divergent and the causes for this are displayed. Some common special cases where convergence is guaranteed are also given. The analysis gives insight into the convergence mechanisms and it is shown that with a modification of the algorithm, global convergence results can be obtained for a general case. The scheme can then be interpreted as maximization of the likelihood function for the estimation problem, or as a recursive prediction error algorithm.
1,021 citations
TL;DR: In this paper, the extended Kalman filter applied to bearings-only target tracking is theoretically analyzed, and closed-form expressions for the state vector and its associated covariance matrix are introduced, and subsequently used to demonstrate how bearing and range estimation errors can interact to cause filter instability.
Abstract: The extended Kalman filter applied to bearings-only target tracking is theoretically analyzed. Closed-form expressions for the state vector and its associated covariance matrix are introduced, and subsequently used to demonstrate how bearing and range estimation errors can interact to cause filter instability (i.e., premature covariance collapse and divergence). Further investigation reveals that conventional initialization techniques often precipitate such anomalous behavior. These results have important practical implications and are not presently being exploited to full advantage. In particular, they suggest that substantial improvements in filter stability can be realized by employing alternative initialization and relinearization procedures. Some candidate methods are proposed and discussed.
431 citations
TL;DR: A theoretical introduction to the use of Kalman filtering in analytical chemistry is based on multicomponent-analysis computations with the non-recursive least-squares estimation method as a starting point.
85 citations
TL;DR: In this paper, a new derivation of the classification of the minimal Markovian representations of the given process z is presented which is based on a certain backward filter of the innovations.
Abstract: Invariant directions of the Riccati difference equation of Kalman filtering are shown to occur in a large class of prediction problems and to be related to a certain invariant subspace of the transpose of the feedback matrix. The discrete time stochastic realization problem is studied in its deterministic as well as probabilistic aspects. In particular a new derivation of the classification of the minimal Markovian representations of the given process z is presented which is based on a certain backward filter of the innovations. For each Markovian representation which can be determined from z the space of invariant directions is decomposed into two subspaces, one on which it is possible to predict the state process without error forward in time and one on which this can be done backward in time.
52 citations
TL;DR: An approximate two-dimensional recursive filtering algorithm that parallels the one-dimensional Kalman filter is presented for a causal system considered by Habibi and a numerical result is shown.
Abstract: An approximate two-dimensional recursive filtering algorithm that parallels the one-dimensional Kalman filter is presented for a causal system considered by Habibi [1]. A numerical result is also shown.
46 citations
01 Jan 1979
TL;DR: In this paper, a new extended Kalman filtering scheme is introduced which has an improved performance relative to previous designs, compared with one based upon a linear Kalman filter, which is compared with the one based on a non-linear filter.
Abstract: Recent dynamic positioning systems have involved the use of a Kalman filter, in a state estimate feedback control scheme, based upon the separation principle of stochastic optimal control theory. Both linear and non-linear filtering schemes have been proposed for this application. A new extended Kalman filtering scheme is introduced which has an improved performance relative to previous designs. This system is compared with one based upon a linear Kalman filter.
44 citations
01 Apr 1979
TL;DR: The application of the reduced update Kalman filter in the enhancement of two-dimensional images using a composite model description of the image shows considerable improvement in the visual quality compared with linear constant coefficient Kalman filtering.
Abstract: In this paper, we demonstrate the application of the reduced update Kalman filter in the enhancement of two-dimensional images using a composite model description of the image. Typically, for the purpose of simulation, five models corresponding to four predominant correlation directions (at angles of 0°, 45°, 90°, 135° to the horizontal) and one isotropic model, are considered. These models are then used to synthesize a filtering algorithm that estimates the image with near minimum mean square error. The results show considerable improvement in the visual quality compared with linear constant coefficient Kalman filtering.
37 citations
TL;DR: A minimal-error entropy estimator for linear systems disturbed by Gaussian random processes is easily derived, which is identical to the Kalman filter under non-Gaussian disturbances.
32 citations
TL;DR: In this paper, a technique for obtaining low order state estimators for time-invariant, linear systems where estimates of a restricted set of state variables are required is presented, based on reducing the order of the system and then designing a Kalman filter for the reduced order system.
Abstract: A technique is presented for obtaining low order state estimators for time-invariant, linear systems where estimates of a restricted set of state variables are required. The technique is based on reducing the order of the system and then designing a Kalman filter for the reduced order system.
30 citations
TL;DR: It is shown how the refined instrumental variable (r.i.v.) method of recursive parameter estimation can be modified simply so that it functions as an optimal adaptive filter and state-estimation algorithm.
Abstract: It is shown how the refined instrumental variable (r.i.v.) method of recursive parameter estimation can be modified simply so that it functions as an optimal adaptive filter and state-estimation algorithm.
TL;DR: In this article, a failure diagnosis for a discrete-time system with parametric failure is proposed, in which the occurrence time and mode of parametric failures cannot be estimated in advance.
Abstract: This paper is concerned with the problem of a failure diagnosis for a discrete-time system with parametric failure, in which the occurrence time and mode of parametric failure cannot be estimated in advance. The failure diagnosis system which is proposed consists of three parts : (i) a normal mode filter, (ii) a detector for anomaly states, and (iii) an adaptive extended Kalman filter. The normal mode filter is called the optimal Kalman filter and transports the information of its innovation sequence to the detector. The detector which is based on the SPRT approach detects anomaly states affected by the parametric failure. The adaptive extended Kalman filter estimates simultaneously system parameters and the states under the failure mode. The adaptive procedure is directed by increasing the calculated covariance on the basis of hypothesis tests for the estimation errors of unknown parameters. Numerical results for a simple plant model illustrate the effectiveness of the proposed failure diagnosis system.
01 Dec 1979
TL;DR: In this article, a simple form of the extended Kalman filter, where the state consists only of the parameters to be estimated, is proposed, based on the inclusion of the computed residuals in the observation matrix of a state representation of the system, an idea first introduced in the extended least squares or Panuska's method.
Abstract: A well-known method for estimation of parameters in linear systems with correlated noise is the extended Kalman filter where the unknown parameters are estimated as a part of an enlarged state vector. To avoid the computational burden in determining the state estimates when only the parameter estimates are required, a new simple form of the extended Kalman filter, where the state consists only of the parameters to be estimated, is proposed. The algorithm is based on the inclusion of the computed residuals in the observation matrix of a state representation of the system, an idea first introduced in the so-called extended least squares or Panuska's method. Convergence properties of the proposed algorithm are studied and the algorithm is shown to perform a gradient-based minimization of the maximum likelihood loss function. Some special cases of the algorithm are also discussed and an extension to an estimator for randomly varying parameters is outlined.
TL;DR: In this paper, the refined instrumental variable method of parameter/state estimation for single-input single-output (s.i.s.o.) systems was extended to multi-input multi-output systems.
Abstract: It is shown how the refined instrumental variable method of parameter/state estimation for single-input single-output (s.i.s.o.) systems proposed by Young1 can be extended to multi-input multi-output (m.i.m.o.) systems. As might be expected, the extension follows directly from the s.i.s.o. analysis, but involves some difficult and interesting matrix manipulations.
TL;DR: The two-dimensional (2-D) reduced update Kalman filter was introduced as an optimal approximation to the 2-DKalman filter for scalar observations obtained from a raster scan.
Abstract: In the above paper, ^{1} the two-dimensional (2-D) reduced update Kalman filter was introduced as an optimal approximation to the 2-D Kalman filter for scalar observations obtained from a raster scan. The reduced update filter consists of two parts: a prediction part and a reduced update part, i.e., an update of
TL;DR: A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete-time Kalman filter is derived and has the property that steady-state bias estimation errors, resulting from modelling errors, are eliminated.
Abstract: A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete-time Kalman filter is derived. The resultant compensated Kalman filter has the property that steady-state bias estimation errors, resulting from modelling errors, are eliminated. The implementation of the compensated Kalman filter involves the use of accumulators in the residual channels in addition to the nominal dynamic model of the stochastic system.
TL;DR: In this paper, a solution is obtained in the s-domain to the finite-time optimal filtering problem where the system is constant and the noise is stationary, which enables the time-varying Kalman filter gain matrix to be calculated using transform techniques.
Abstract: A solution is obtained in the s-domain to the finite-time optimal filtering problem where the system is constant and the noise is stationary. This enables the time-varying Kalman filter gain matrix to be calculated using transform techniques. In the solution of this problem, to find the optimal time-varying linear filter, a new fixed point filtering problem is posed and solved. That is, the optimal time-invariant filter is found which will give the best state estimate after some fixed time interval T. This state estimate is the same as would be obtained from the equivalent Kalman filter at this time. It follows that this time-invariant filter can give a better state estimate than the Wiener filter, when the filtering time is finite Sub-optimal versions of both the time-invariant filter and the Kalman filter are defined from a simple approximation which can be made in the s-domain solution. This considerably simplifies the calculation of the gain matrix for the continuous-time Kalman filter. There are impo...
TL;DR: In this paper, a recursive linear estimation of a parameter vector subject to a linear equality constraint is discussed with reference to a recently proposed Kalman filter method derived using pseudo-inverses to solve an undetermined least-squares problem.
Abstract: Recursive linear estimation of a parameter vector subject to a linear equality constraint is discussed with reference to a recently proposed Kalman-filter method derived using pseudo-inverses to solve an undetermined least-squares problem. The action of the method is compared with that of an alternative which treats the constraint as an observation, and the circumstances favouring each, or neither, are considered.
TL;DR: In this paper, it was shown that the optimality of the Kalman filter prevents its application to estimate the state of deterministic; systems but that if the gain is slightly modified a deterministic filter is possible.
Abstract: It is shown that the optimality of the Kalman filter prevents its application to estimate the state of deterministic; systems but that if the gain is slightly modified a deterministic filter is possible. Such a filter is subsequently used to explain some of the difficulties encountered in Kalman filter computations, from which it transpires that much Kalman filtering is essentially an application of a deterministic filter to stochastic problems. To reduce the order of the algorithm the concept of observer robustness is incorporated into the subsequent development of the deterministic filter. Exactly equivalent discrete- and continuous-time algorithms are derived and used for a new treatment of the problem of obtaining estimates of the state variables of a stochastic system when the measurements are free of noise.
06 Aug 1979
TL;DR: In this paper, the steady state components of the covariance matrix of estimation errors after processing an observation have been analytically determined ined for a tree-dimensional Kalman tracking filter.
Abstract: The steady-state components of the covariance matrix of estimation errors after processing an observation have been analytically determined ined for a tree-dimensional Kalman tracking filter.
TL;DR: In this paper, the estimation of a least-squares parameter (or state) vector in a standard model is extended to the least square estimation of linearly constrained vector, and the required pseudo-inverses can be computed recursively.
Abstract: The estimation of a least-squares parameter (or state) vector in a standard model is extended to the least-squares estimation of a linearly constrained vector. It is shown that the required pseudoinverses can be computed recursively, and, with suitable initialisation, a standard Kalman filter will provide the same estimates. The resulting recursion is a powerful starting point in the design of adaptive communications filters and antennas.
TL;DR: In this paper, an electric-arc-furnace electrode-controller model, whose parameters are known approximately a priori, is tuned by applying the extended Kalman filter to measurements of pseudorandom binary-sequency system-input disturbance and response.
Abstract: The Kalman-filter parameter estimator is extended to the case of estimation of the parameters of a linearised model of a nonlinear system. To illustrate the technique, an electric-arc-furnace electrode-controller model, whose parameters are known approximately a priori, is tuned by applying the extended Kalman filter to measurements of pseudorandom binary-sequency system-input disturbance and response.
Journal Article•
TL;DR: An adaptive Extended Kalman Filter algorithm is designed to track a distributed (elliptical) source target in a closed loop tracking problem, using outputs from a forward looking infrared (FLIR) sensor as measurements.
Abstract: : An adaptive Extended Kalman Filter algorithm is designed to track a distributed (elliptical) source target in a closed loop tracking problem, using outputs from a forward looking infrared (FLIR) sensor as measurements. The filter adaptively estimates image intensity, target size and shape, dynamic driving noise, and translational position changes due to two effects: actual target motion, and atmospheric jitter. Atmospheric backgrounds are studied for the effect of temporal and spatial correlations on filter performance. A Monte Carlo analysis is conducted to determine filter performance for two target scenarios: approximately straight approach and cross range constant velocity. Good performance is obtained for the first two trajectories. For the second trajectory, a one sigma tracking error of .2 pixel (4 microrad) with a signal to noise ratio of 12.5. The filter adapts well to changes in image intensity, size, and shape. (Author)
TL;DR: A suboptimal analog or hybrid Kalman filter implementation is described, stressing reliability, robustness, and speed requirements.
Abstract: A suboptimal analog or hybrid Kalman filter implementation is described, stressing reliability, robustness, and speed requirements. The filter is assumed to have mismatched dynamics, noise, and drift, but also computational errors. The state estimation error propagation is studied, and time-dependent bounds established to determine the reinitialization rate. Three alternate filter architectures are studied, and their reliability computed; the device itself applies triple-modular filter redundancy, with failure detection and localization logics.
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01 Jan 1979
TL;DR: In this paper, a simple extension of the extended Kalman filter, where the state consists only of the para-meters to be estimated, is proposed, based on the inclusion of the computed residuals in the observation matrix of a state representation.
Abstract: A well-known method for estimation of para- meters in linear systems with correlated noise is the extended Kalman filter where the unknown parameters To avoid the computational burden in determining the are estimated as a part of an enlarged state vector. state estimates when only the parameter estimates are required, a new simple fom of the extended Kalman filter, where the state consists only of the para- meters to be estimated, is proposed. The algorithm is based on the inclusion of the computed residuals in the observation matrix of a state representation of the system, an idea first introduced in the so- called extended least squares or Panuska's method. Convergence properties of the proposed a1 gori thm are studied and the algorithm is shown to perform a grad- ient-based minimization of the maximum likelihood loss function. Some special cases of the algorithm are also discussed and an extension to an estimator for randomly varying parameters is outlined.
TL;DR: In this article, a suboptimal Kalman filter is constructed in order to replace the sequentially correlated measurement noise by the appropriate white measurement noise, and the covariance of the estimation error due to the replacement of the measurement noise is derived in the form of the differential equation.
Abstract: There are many occasions when approximate design of the Kalman filter is inevitable in the identification. This paper proposes the algorithms for two kinds of suboptimal Kalman filters based on the error analysis of the filter. It is rare that each noise added to the dynamical equation, or the measurement equation may be regarded as sequentially correlated in the practical situation. The suboptimal Kalman filter is constructed in order to replace the sequentially correlated measurement noise by the appropriate white measurement noise. The concept of the design for the proposed filter is delineated. The covariance of the estimation error due to the replacement of the measurement noise, called the actual covariance, is derived in the form of the differential equation. This is the known result of the error analysis of the Kalman filter. Secondly, the stationary condition is assumed on the actual covariance in place of the usual optimal covariance of the estimation error. One suboptimal Kalman filter with the...