A direct approach of designing weighted fusion robust steady-state Kalman filters with uncertain noise variances is presented. Based on the steady-state Kalman filtering theory, using the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) optimal estimation rule, the six robust weighted fusion steady-state Kalman filters are designed based on the worst-case conservative system with the conservative upper bounds of noise variances. The actual filtering error variances of each fuser are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. A Lyapunov equation method for robustness analysis is proposed. Their robust accuracy relations are proved. A simulation example verifies their robustness and accuracy relations.
"Weighted Fusion Robust Steady-State Kalman Filters for Multisensor System with Uncertain Noise Variances." J. Appl. Math. 2014 1 - 11, 2014. https://doi.org/10.1155/2014/369252