Distributed State Estimation for Multi-Agent Systems With Random Transmission Delays

Abstract

This paper investigates the distributed state estimation problem of a class of multi-agent systems with random transmission delay. The random transmission delay phenomenon is described by a random variable that obeys a Bernoulli distribution. Under the linear minimum variance criterion, a Kalman-like recursive optimal distributed filter is designed. This filter design requires the computation of cross-covariance matrices between agent nodes. To reduce the computational burden, a suboptimal distributed filter is designed by using matrix inequalities. This filter minimizes the trace of the upper bound of the estimation error covariance matrix, thereby eliminating the need to compute cross-covariance matrices between agent nodes. In the suboptimal distributed filtering algorithm, an optimal parameter selection scheme is proposed for the scalar parameters introduced by the matrix inequality. The optimal filtering gain is obtained by minimizing the upper bound of the estimation error covariance matrix with these optimal parameters. Furthermore, a sufficient condition for the stability of the filtering error covariance matrix is derived. The effectiveness of the proposed algorithm is verified through simulations.