Unbiasedness-constrained least squares state estimation for time-varying systems with missing measurements under round-robin protocol

Abstract

In this paper, we present an unbiasedness-constrained approach to deal with the state estimation issue for a class of time-varying stochastic systems subject to missing measurements. The state estimates are generated from measurements collected by multiple sensing nodes whose information are transmitted via communication networks under scheduling of the Round-Robin protocol. The purpose of the addressed problem is to design an optimal state estimation algorithm in the sense of least mean square with an unknown initial condition in the existence of possible data missing. By resorting to the batch form technique, the optimal filter is proposed by minimising the estimation error covariance in the sense of matrix trace subject to the unbiasedness constraint. Then, a recursive computational algorithm is exploited for the optimal filter to facilitate practical realisation. Finally, simulations are carried out to demonstrate that the proposed method can be utilised to handle missing measurements in the multi-sensor systems when the initial states are unavailable, which outperforms the Kalman filter especially in the initial stage.