Robust weighted fusion Kalman filter with multiplicative noises, uncertain noise variances, and missing measurements

In this work, the robust weighted state fusion Kalman filter is studied for multisensor systems with multiplicative noises, uncertain noise variances and missing measurements. 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 conservative system with the upper bound variances, using the optimal fusion criterion with matrix weights, the robust weighted fusion time-varying Kalman filter is presented. By use of the Lyapunov equation approach, its robustness is proved such that its actual filtering error variances are guaranteed to have the minimal upper bound for all admissible noise variance uncertainties. The accuracy relations among the robust local and fused time-varying Kalman filters are proved. Simulation results show the effectiveness and correctness of the proposed results.