Robust weighted fusion Kalman estimators for multi-model multisensor systems with uncertain-variance multiplicative and linearly correlated additive white noises

For multi-model multisensor systems with both the uncertain-variance multiplicative and linearly correlated additive white noises, a universal fictitious noise-based Lyapunov equation approach is presented, by which the original system can be converted into one with only uncertain additive noise variances, and then the local and four weighted fused minimax robust time-varying Kalman estimators (predictor, filter and smoother) of the common state are presented in a unified framework, where the robust Kalman filter and smoother are designed based on the robust Kalman predictor. They include the three fusers weighted by matrices, scalars and diagonal matrices, and a modified Covariance Intersection(CI) fuser. Their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their accuracy relations are proved. The corresponding local and fused robust steady-state Kalman estimators also are presented. The convergence analysis is also given. Two simulation examples applied to design the robust fusers for an autoregressive (AR) signal and an uninterruptible power system (UPS) are given to show the effectiveness of the proposed results.