Distributed Fusion Filter for Time-Varying Systems with Stochastic Nonlinearities and Fading Measurement

This paper studies the problem of optimal state fusion estimation in nonlinear distributed systems characterized with correlated process noise and measurement noise. First, a nonlinear distributed system with stochastic nonlinearities and fading measurement is introduced, and the covariance of the system is derived by using correlation lemmas and associated mathematical formulations. Second, a recursive equation with the upper bound of the local filtering error covariance is established based on the derived covariance. In order to optimize the performance, a local filter gain is designed according to the obtained minimum upper bound. Then, a distributed fusion filter is proposed by leveraging the matrix-weighted fusion criterion. Finally, the effectiveness of the proposed results is demonstrated through a simulation example involving a tracking system.