Distributed state estimation for stochastic non‐linear systems with random delays and packet dropouts

Abstract

A novel distributed fusion Kalman filter is proposed for a class of stochastic non-linear systems with multi-step transmission delays and packet dropouts. The stochastic non-linearities described by statistical means enter into both state equation and measurement equation, and some Bernoulli distributed random variables are introduced to model the delayed measurements. Using the measurement reorganisation approach instead of state augmentation, the addressed system is transformed into a delay-free one. For each subsystem, the optimal local estimators are designed via the innovation analysis method. The filtering error cross-covariance matrices between any two local filters are then obtained. On this basis, a distributed fusion filter is derived by means of matrix-weighted fusion estimation criterion. The effects of stochastic non-linearities, random delays and packet dropouts on the performance of the filter are all considered in the proposed algorithms. Moreover, some sufficient conditions that guarantee the convergence of the estimation error covariance matrices are established. Finally, a numerical example is given to illustrate the effectiveness of the developed algorithms.