Journal ArticleDOI
The Kalman filter: A robust estimator for some classes of linear quadratic problems
TLDR
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.read more
Citations
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Journal ArticleDOI
Robust techniques for signal processing: A survey
Saleem A. Kassam,H.V. Poor +1 more
TL;DR: The minimax approach for the design of robust methods for signal processing is discussed, which has proven to be a very useful approach because it leads to constructive procedures for designing robust schemes.
Journal ArticleDOI
Maximum correntropy Kalman filter
TL;DR: In this article, the robust maximum correntropy criterion (MCC) was adopted as the optimality criterion instead of using the minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption.
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Maximum Correntropy Kalman Filter
TL;DR: In this paper, the robust maximum correntropy criterion (MCC) was adopted as the optimality criterion instead of using the minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption.
Journal ArticleDOI
Approximate Inference in State-Space Models With Heavy-Tailed Noise
TL;DR: This work proposes a novel approach to extending the applicability of state-space models to a wider range of noise distributions without losing the computational advantages of the associated algorithms.
Journal ArticleDOI
On minimax robustness: A general approach and applications
Sergio Verdu,H.V. Poor +1 more
TL;DR: It is shown that if the performance functional and the uncertainty set are convex then a certain type of regularity condition on the functional is sufficient to ensure that the optimal strategy for a least favorable element of the uncertaintySet is minimax robust.
References
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Book
Introduction to Matrix Analysis
TL;DR: In this article, the Second Edition Preface is presented, where Maximization, Minimization, and Motivation are discussed, as well as a method of Hermite and Quadratic Form Index.
Journal ArticleDOI
Error bounds of continuous Kalman filters and the application to orbit determination problems
TL;DR: In this paper, the effect of errors due to incorrect a priori information on initial states as well as on noise models in continuous Kalman-Bucy filters has been investigated, and a convenient formula for computing error bounds has been derived which will allow parametric studies of the error effect.
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