Robust Kalman estimators for systems with mixed uncertainties
Wenqiang Liu, Xuemei Wang, Zili Deng · Optimal Control Applications and Methods · 2017
Summary This paper addresses the problem of designing robust Kalman estimators for uncertain systems with mixed uncertainties including the same uncertain‐variance multiplicative noise in state and measurement matrices, missing measurements, and uncertain‐variance linearly correlated measurement and process white noise. By introducing fictitious noise to compensate for multiplicative noise, the system under consideration is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, on the basis of the worst‐case system with known conservative upper bounds of uncertain variances, the minimax robust time‐varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Their robustness is proved by using a Lyapunov equation approach, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The corresponding robust steady‐state Kalman estimators are also presented, and 3 modes of convergence in a realization among the time‐varying and steady‐state robust Kalman estimators for the time‐varying and time‐invariant systems are presented and proved by the dynamic error system analysis method. A simulation example with application to autoregressive signal processing is also given to show the effectiveness and correctness of the proposed results.