Robust Weighted Fusion Kalman Estimators for Systems with Uncertain-Variance Multiplicative and Additive Noises and Missing Measurements

This paper investigates the robust weighted fusion estimation problem of multi-sensor systems with mixed uncertainties, including stochastic parameter uncertainties, missing measurements and uncertain noise variances. The stochastic parameter uncertainties are described by multiplicative noise. Especially, the variances of both the multiplicative and additive noises are uncertain. By introducing two fictitious noises, the original system is converted into that with deterministic parameters and uncertain noise variances. Based on the mini-max robust estimation principle, the robust local and fused Kalman estimators weighted by diagonal matrices are designed in a unified framework, where the filter and smoother are designed based on the predictor. By the Lyapunov equation method, their robustness is proved. Their accuracy relations are also proved. A simulation example applied to the UPS systems is given to verify the correctness and effectiveness of the proposed results.