Extension of minimum variance estimation for systems with unknown inputs

Mohamed Darouach (1) , Michel Zasadzinski (1) , Mohamed Boutayeb (2)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection

In this paper, we address the problem of minimum variance estimation for discrete-time time-varying stochastic systems with unknown inputs. The objective is to construct an optimal filter in the general case where the unknown inputs affect both the stochastic model and the outputs. It extends the results of Darouach and Zasadzinski (Automatica, 1997) where the unknown inputs are only present in the model. The main difficulty in treating this problem lies in the fact that the estimation error is correlated with the systems noises, this fact leads generally to suboptimal filters. Necessary and sufficient conditions for the unbiasedness of this filter are established. Then conditions under which the estimation error and the system noises are uncorrelated are presented, and an optimal estimator and a predictor filters are derived. Sufficient conditions for the existence of these filters are given and sufficient conditions for their stability are obtained for the time-invariant case. A numerical example is given in order to illustrate the proposed method.

Mots clés: Minimum variance filter; Unknown inputs; Stability; Convergence; Linear time-varying systems

Domaines: Automatique / Robotique

Mohamed Darouach, Michel Zasadzinski, Mohamed Boutayeb. Extension of minimum variance estimation for systems with unknown inputs. Automatica, 2003, 39 (5), pp.867-876. ⟨10.1016/S0005-1098(03)00006-2⟩. ⟨hal-00098113⟩