New Results on LMVDR Estimators for LDSS Models

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.
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Eric Chaumette, François Vincent, Benoit Priot, Gaël Pages, Arnaud Dion. New Results on LMVDR Estimators for LDSS Models. 26th European Signal Processing Conference (EUSIPCO), Sep 2018, Rome, Italy. pp.1332-1336, ⟨10.23919/EUSIPCO.2018.8553365⟩. ⟨hal-02269388⟩

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