Optimal and self-tuning fusion Kalman filters for discrete-time stochastic singular systems

Abstract

Based on the optimal fusion estimation algorithm weighted by scalars in the linear minimum variance sense, a distributed optimal fusion Kalman filter weighted by scalars is presented for discrete-time stochastic singular systems with multiple sensors and correlated noises. A cross-covariance matrix of filtering errors between any two sensors is derived. When the noise statistical information is unknown, a distributed identification approach is presented based on correlation functions and the weighted average method. Further, a distributed self-tuning fusion filter is given, which includes two stage fusions where the first-stage fusion is used to identify the noise covariance and the second-stage fusion is used to obtain the fusion state filter. A simulation verifies the effectiveness of the proposed algorithm. © 2008 John Wiley & Sons, Ltd.