An approximate minimum variance filter for nonlinear systems with randomly delayed observations

Abstract

Abstract-In this paper, we extend our earlier results on minimum variance filter for systems with additive multiplicative noise in two different ways. Firstly, we propose a novel characterization of the linearization error in terms of multiplicative noise. Secondly, we also allow for random delay of up to one time step in the measurement. The delay is modelled by Bernoulli random variables. We derive a closed-form expression for the minimum variance filter for the resulting system with a linearized state transition equation, accounting for both the linearization error as well as the random delay. The utility of the proposed filtering algorithm is demonstrated through numerical experiments.