2019
DOI: 10.1109/tac.2018.2868239
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On LMVDR Estimators for LDSS Models: Conditions for Existence and Further Applications

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 outperf… Show more

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Cited by 15 publications
(8 citation statements)
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“…Within the KF framework the latter can be solved with distortionless constraints 18,19 . If the state dynamics representation is unknown, a possible solution is to use several filters running in parallel with different process models via the so‐called interacting multiple model filter 20 .…”
Section: Introductionmentioning
confidence: 99%
“…Within the KF framework the latter can be solved with distortionless constraints 18,19 . If the state dynamics representation is unknown, a possible solution is to use several filters running in parallel with different process models via the so‐called interacting multiple model filter 20 .…”
Section: Introductionmentioning
confidence: 99%
“…In general, for the linear minimum MSE (MMSE) estimation problem, considering LDSS dynamic systems, a fundamental question is if the KF exists in the case where the measurement noise covariance matrix is non-invertible. This is the main concern of this article, where we generalize the results in Chaumette et al [9] and Chaumette et al [11] as follows:…”
Section: Introductionmentioning
confidence: 58%
“…These conditions have long been regarded as leading to the general form of the KF including correlated process and measurement noise. This set of minimum uncorrelation conditions has been recently generalized in Chaumette et al [9,11] , leading to…”
Section: Introductionmentioning
confidence: 99%
“…In contrast, few contributions explored how to counteract a mismatch on system matrices/functions or the filter initialisation. Within the KF framework, the latter can be solved by either the information filter form of the KF ([ 3 ] §6.2) or the so-called Fisher initialisation [ 16 ], which can be generalised by imposing initial distortionless constraints [ 17 ], i.e., the so-called minimum variance distortionless response (MVDR) estimators. In order to further generalise these MVDR results, how to incorporate non-stationary constraints within the KF has been recently proposed by Villà-Valls et al [ 18 ], leading to a general linearly constrained KF (LCKF) formulation, which has also been shown concerning linear systems to generalise the results proposed by Teixeira et al [ 19 ].…”
Section: Introductionmentioning
confidence: 99%
“…Consider a linear discrete state–space model, where the state vector must be estimated from the available measurements (for , with and are known system model matrices, and are the process and measurement noise with zero mean and known covariance. If a minimum set of uncorrelation conditions holds [ 17 ], the recursive linear estimator of , which minimises the MSE (for ) is the KF (the superscript stands for the best solution in the MSE sense), where the optimal gain is the one that minimises the MSE, …”
Section: Introductionmentioning
confidence: 99%