Robust weighted fusion Kalman estimators for systems with multiplicative noises, missing measurements and uncertain-variance linearly correlated white noises

For linear discrete time-varying and time-invariant multisensor uncertain systems with multiplicative noises, missing measurements and uncertain-variance linearly correlated white noises, by introducing the fictitious noises to compensate the stochastic uncertainties, the system under consideration can be converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with conservative upper bounds of uncertain noise variances, the four robust weighted state fusion time-varying and steady-state Kalman estimators (predictor, filter, smoother) are presented respectively. They include the three fusers weighted respectively by matrices, scalar and diagonal matrices and a new modified covariance intersection (CI) fuser. They are designed in a unified framework, such that the filters and smoothers are designed based on the predictors. By the Lyapunov equation approach, their robustness is proved in the sense that for all admissible uncertainties, their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. The convergence in a realization between the robust fused time-varying and steady-state Kalman estimators for the time-varying and time-invariant systems are proved by the dynamic error system analysis (DESA) method. Their accuracy relations are also proved. A simulation example applied to uninterruptible power system (UPS) shows the effectiveness of the proposed results.