Joint estimation of linear state-space models under non-Gaussian noises

Abstract

Joint estimation of states and time-varying parameters of linear state space models is of practical importance for fault diagnosis and fault tolerant control. Previous works on this topic haven’t considered joint estimation of linear systems in presence of outliers. They can significantly make worse the properties of linearly recursive algorithms which are designed to work in the presence of Gaussian noises. This paper proposes two kinds of strategies of joint parameter-state robust estimation of linear state space models in presence of non-Gaussian noises. Both possible cases are considered, joint robust estimation algorithm in case of parameter-independent matrices as well as in case of parameter-dependent matrices. Because of their good features in robust filtering, the modified and extended Masreliez-Martin filters represent a cornerstone for realization of the robust algorithms for joint state-parameter estimation of linear time-varying stochastic systems in presence of non-Gaussian noises. The good features of the proposed robust algorithms for joint estimation of linear time-varying stochastic systems are illustrated by simulations.