Robust centralized and weighted measurement fusion steady-state Kalman estimators with uncertain linearly correlated white noises

For the multisensor systems with uncertain-variance linearly correlated white noises, according to the minimax robust estimation principle, applying the weighted least squares(WLS) and the full-rank decomposition of matrix, the robust centralized fusion and weighted measurement fusion steady-state Kalman estimators (filter, predictor and smoother) are presented in a unified framework. Their equivalence and accuracy relations are proved. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have a minimal upper bound for all admissible uncertain noise variances. A simulation example to tracking system verifies their correctness and effectiveness.