Unknown input and state estimation for linear discrete-time systems with missing measurements and correlated noises

Abstract

This paper is concerned with the problem of simultaneous input and state estimation for a class of linear discrete-time systems with missing measurements and correlated noises. The missing measurements occur in a random way and are governed by a series of mutually independent random variables obeying a certain Bernoulli distribution. The process and measurement noises under consideration are correlated at the same time instant. Our attention is focused on the design of recursive estimators for both input and state such that, for all missing measurements and correlated noises, the estimators are unbiased and the estimation error covariances are minimized. This objective is achieved using direct algebraic operation and the design algorithm for the desired estimators is given. Finally, an illustrative example is presented to demonstrate the effectiveness of the proposed design scheme.