Robust measurement fusion Kalman filter for multisensor systems with multiplicative noises and uncertain noise variances

This paper addresses the design of robust measurement fusion Kalman filter for linear discrete-time multisensor systems with multiplicative noises perturbations both on state equation and measurement equations, and with uncertain noise variances. By introducing two fictitious noises, the system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case weighted fusion measurement system with the conservative upper bounds of the noise variances, the robust weighted measurement fusion (WMF) time-varying Kalman filter is presented. Its actual filtering error variance is guaranteed to have the corresponding minimal upper bound for all admissible noise variance uncertainties. The robustness of the designed filter is proved by using Lyapunov equation approach. The accuracy relations among the robust local and fused Kalman filter are proved. Simulation results show the effectiveness and correctness of the proposed results.