Distributed Filtering for Networked Stochastic Nonlinear Systems With Fading Measurements and Random Packet Dropouts

In practical application scenarios, the phenomena of nonlinearity and missing data are commonly present in networked multi-sensor systems. Therefore, this paper investigates distributed filtering problems for networked stochastic nonlinear systems with fading measurements and random packet dropouts. Considering the statistical characteristics of sensors' fading measurements and random losses in transmitting state estimates of their neighbor nodes, a novel distributed Kalman filter (DKF) with multiple filter gains is proposed for each sensor, where multiple filter gains include one Kalman filter gain for measurements of sensor itself and different consensus filter gains for state estimates of its different neighbor nodes. Two compensation mechanisms are used for random packet losses among sensor nodes. Based on an inequality scaling method, an upper bound of the filtering error covariance matrix (UBFECM) dependent on a set of positive scalar parameters is derived, which can avoid calculating the cross-covariance matrices among sensor nodes and the state second moment matrix. Furthermore, multiple filter gains and scalar parameters are optimized by minimizing locally an UBFECM and using nonlinear optimization methods. The exponential boundedness in mean square of filtering error of DKF is proved, and the performance of DKF is also compared with local filter. Simulation results illustrate the effectiveness of the presented DKF algorithm.