Linear and nonlinear filters based on statistical similarity measure for sensor network systems

Abstract

In this paper, to address the non-Gaussian noise issue in linear and nonlinear sensor network systems, one centralized and two distributed state estimation algorithms are designed by introducing a statistical similarity measure (SSM). Firstly, a modified cost function is constructed for the linear sensor network system based on SSM, and a centralized SSM Kalman filtering (CSSMKF) algorithm is derived by maximizing the lower bound of the cost function. Secondly, a distributed SSM information filtering (DSSMIF) algorithm is designed by introducing a weighted average consensus (WAC) strategy, which approximates the information form of CSSMKF in a distributed manner. Then, a distributed SSM cubature information filtering (DSSMCIF) algorithm is developed to handle the non-Gaussian noise in the nonlinear sensor network system. Furthermore, the mean squared estimation errors of DSSMIF and DSSMCIF are proved to be exponentially bounded. Finally, the simulation results confirm that the proposed algorithms outperform the existing methods by at least 10 % in position accuracy and 5 % in velocity accuracy, respectively.