Robust weighted fusion Kalman predictor for multisensor systems with multiplicative noises and uncertain noise variances

This paper addresses the design of robust weighted fusion Kalman predictor for a class of linear discrete-time multisensor systems with multiplicative noises in the state and measurement matrices, and with the uncertain noise variances. By introducing two fictitious noises, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of the noise variances, using the optimal fusion criterion with scalar weights, the robust scalars-weighted fusion time-varying Kalman predictor is presented. By use of the Lyapunov equation approach, its robustness is proved such that its actual prediction error variance is guaranteed to have the corresponding minimal upper bound for all admissible noise variance uncertainties. The accuracy relations between the robust local and fused time-varying Kalman predictors are proved. Simulation results show the effectiveness and correctness of the proposed results.