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New Results on LMVDR Estimators for LDSS Models

Chaumette, Eric and Vincent, François and Priot, Benoit and Pages, Gaël and Dion, Arnaud New Results on LMVDR Estimators for LDSS Models. (2018) In: 26th European Signal Processing Conference (EUSIPCO), 3 September 2018 - 7 September 2018 (Rome, Italy).

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Official URL: https://doi.org/10.23919/EUSIPCO.2018.8553365

Abstract

In the context of linear discrete state-space (LDSS) models, we generalize a result lately introduced in the restricted case of invertible state matrices, namely that the linear minimum variance distortionless response (LMVDR) filter shares exactly the same recursion as the linear least mean squares (LLMS) filter, aka the Kalman filter (KF), except for the initialization. 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. This result is particularly noteworthy given the fact that, although LMVDR estimators are sub-optimal in mean-squared error sense, they are infinite impulse response distortionless estimators which do not depend on the prior knowledge on the mean and covariance matrix of 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. Seen from this perspective, we also show that the LMVDR filter can be regarded as a generalization of the information filter form of the KF. On another note, LMVDR estimators may also allow to derive unexpected results, as highlighted with the LMVDR fixed-point smoother.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to the IEEE (Institute of Electrical and Electronics Engineers). This paper is available at : https://ieeexplore.ieee.org/document/8553365 “© 2018 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-02269388
Audience (conference):International conference proceedings
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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:22 Aug 2019 15:14

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