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On LMVDR Estimators for LDSS Models: Conditions for Existence and Further Applications

Chaumette, Eric and Vincent, François and Priot, Benoit and Pages, Gaël and Dion, Arnaud On LMVDR Estimators for LDSS Models: Conditions for Existence and Further Applications. (2019) IEEE Transactions on Automatic Control, 64 (6). 2598-2605. ISSN 0018-9286

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Official URL: https://doi.org/10.1109/TAC.2018.2868239

Abstract

For linear discrete state-space models, under certain conditions, the linear least mean squares (LLMS) filter estimate has a recursive format, a.k.a. the Kalman filter (KF). Interestingly, the linear minimum variance distortionless response (LMVDR) filter, when it exists, shares exactly the same recursion as the KF, except for the initialization. If LMVDR estimators are suboptimal in mean-squared error sense, they do not depend on the prior knowledge on the initial state. Thus, the LMVDR estimators may outperform the usual LLMS estimators in case of misspecification of the prior knowledge on the initial state. In this perspective, we establish the general conditions under which existence of the LMVDRF is guaranteed. An immediate benefit is the introduction of LMVDR fixed-point and fixed-lag smoothers (and possibly other smoothers or predictors), which has not been possible so far. Indeed, the LMVDR fixed-point smoother can be used to compute recursively the solution of a generalization of the deterministic least-squares problem.

Item Type:Article
Additional Information:Thanks to the IEEE (Institute of Electrical and Electronics Engineers). This paper is available at : https://ieeexplore.ieee.org/document/8452962 “© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
HAL Id:hal-02269674
Audience (journal):International peer-reviewed journal
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Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
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Deposited By: Arnaud Dion
Deposited On:23 Aug 2019 07:35

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