An Approximate Minimum Variance Filter for Nonlinear Systems with Randomly Delayed Observations

Abstract

In this paper, we extend our earlier results on minimum variance lter for systems with additive multiplicative noise in two di erent 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 lter 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 ltering algorithm is demonstrated through numerical exper- iments.