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Invariant extended Kalman filter

About: Invariant extended Kalman filter is a research topic. Over the lifetime, 7079 publications have been published within this topic receiving 187702 citations.


Papers
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Journal ArticleDOI
TL;DR: An SME/unscented Kalman filter pairing is shown to have improved performance versus previous approaches while possessing simpler implementation and equivalent computational complexity.
Abstract: The symmetric measurement equation approach to multiple target tracking is revisited using the unscented Kalman filter. The performance of this filter is compared to the original symmetric measurement equation implementation using an extended Kalman filter. Counterintuitive results are presented and explained for two sets of symmetric measurement equations. We find that the performance of the SME approach is dependent on the interaction of the SME equations and filter used. Furthermore, an SME/unscented Kalman filter pairing is shown to have improved performance versus previous approaches while possessing simpler implementation and equivalent computational complexity.

96 citations

01 Jan 2006
TL;DR: It is shown that the EnKF can be implemented without access to the observation matrix, and only an observation function is needed; this greatly simplifies software design.
Abstract: We present several methods for the efficient implementation of the Ensemble Kalman Filter (EnKF) of Evensen. It is shown that the EnKF can be implemented without access to the observation matrix, and only an observation function is needed; this greatly simplifies software design. New implementations of the EnKF formulas are proposed, with linear computational complexity in the number of data points. These implementations are possible when the data covariance matrix is easy to decompose, such as a diagonal or a banded matrix, or given in a factored form as sample covariance. Unlike previous methods, our method for the former case uses Choleski decomposition on a small matrix from the Sherman-Morrison-Woodbury formula instead of SVD on a large matrix, and our method in the latter case does not impose any constraints on data randomization. One version of the EnKF formulas was implemented in a distributed parallel environment, using SCALAPACK and MPI.

96 citations

Proceedings ArticleDOI
20 Sep 1999
TL;DR: Random simulation (particle filtering or Condensation) proves to provide a robust alternative algorithm for tracking that can also deal with these difficult conditions of markerless tracking.
Abstract: Some issues in markerless tracking of human body motion are addressed. Extended Kalman filters have commonly been applied to kinematic variables, to combine predictions consistent with plausible motion, with the incoming stream of visual measurements. Kalman filtering is applicable only when the underlying distribution is approximately Gaussian. Often this assumption proves remarkably robust. There are two pervasive circumstances under which the Gaussianity assumption can break down. The first is kinematic singularity and the second is at joint endstops. Failure of Kalman filtering under these circumstances is illustrated. The non-Gaussian nature of the distributions is demonstrated experimentally by means of Monte Carlo simulation. Random simulation (particle filtering or Condensation) proves to provide a robust alternative algorithm for tracking that can also deal with these difficult conditions.

96 citations

Journal ArticleDOI
TL;DR: In this article, a reduced-order Kalman filter is proposed for estimating the state of a Luenberger observer with respect to the noises in the system, where the filler is much like a Luinberger observer for the state to be estimated.
Abstract: This paper presents a method for designing an ‘optimum’ unbiased reduced-order filter. For the proposed approach to work, the order of the filter must be greater than a certain minimum determined by the number of independent observations of the system available. The filler is much like a Luenberger observer for the state to be estimated, but with parameters optimized with respect to the noises in the system. A reduced-order innovation process is proposed that has properties similar to those of the full-order innovation process when the reduced filter is optimized. The approach offers the possibility of significant reduction in real-time computational requirements compared with the full-order filter, though at the cost of some loss of performance. The algorithm for the reduced-order filter is simple to implement— quite similar to that of the Kalman filter. An example is presented to compare the performance of the proposed method with the full-order Kalman filter.

95 citations

Journal ArticleDOI
TL;DR: Empirical justification is established for the common practice of applying the Kalman filter estimator to three classes of linear quadratic problems where the model statistics are not completely known, and hence specification of the filter gains is not optimum.
Abstract: In this paper, theoretical justification is established for the common practice of applying the Kalman filter estimator to three classes of linear quadratic problems where the model statistics are not completely known, and hence specification of the filter gains is not optimum. The Kalman filter is shown to be a minimax estimator for one class of problems and to satisfy a saddlepoint condition in the other two classes of problems. Equations for the worst case covariance matrices are given which allow the specifications of the minimax Kalman filter gains and the worst case distributions for the respective classes of problems. Both time-varying and time-invariant systems are treated.

95 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202348
2022162
202120
20208
201914
201851