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A new unbiased minimum variance observer for stochastic LTV systems with unknown inputs

Abstract : This paper is devoted to the state and input estimation of a linear time varying system in the presence of an unknown input (UI) in both state and measurement equations, and affected by Gaussian noises. The classical rank condition used in this kind of approach is relaxed in order to be able to be used in a wider range of systems. A state observer, that is an unbiased estimator with minimum error variance, is proposed. Then a UI observer is constructed, in order to be a best linear unbiased estimator, it follows a unique construction whether the direct feedthrough matrix is null or not. In a sense the proposed approach, generalizes and unifies the existing ones. Besides, a stability result is given for linear time invariant systems, which is a novelty for unbiased minimum variance observers relaxing the classical rank condition.
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https://hal.archives-ouvertes.fr/hal-02442000
Contributor : Frédéric Davesne <>
Submitted on : Thursday, January 16, 2020 - 11:33:37 AM
Last modification on : Monday, July 6, 2020 - 10:37:48 AM

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Luc Meyer, Dalil Ichalal, Vincent Vigneron. A new unbiased minimum variance observer for stochastic LTV systems with unknown inputs. IMA Journal of Mathematical Control and Information, Oxford University Press (OUP), 2020, 37 (2), pp.471--492. ⟨10.1093/imamci/dnz009⟩. ⟨hal-02442000⟩

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