Robust centralized and weighted measurement fusion Kalman estimators for multisensor systems with multiplicative and uncertain-covariance linearly correlated white noises

Abstract

This paper addresses the design of robust centralized and weighted measurement fusion (WMF) Kalman estimators for a class of uncertain multisensor systems with linearly correlated measurement and process white noises. The uncertainties of the systems include the same multiplicative noises in state and measurement matrices, and the uncertain noise variances. By introducing the fictitious noises to compensate the multiplicative noises, the system under consideration is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of the noise variances, the robust centralized and two WMF time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Their robustness is proved by using Lyapunov equation approach, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities are analyzed and compared. Compared with the centralized fusion algorithm, the two WMF algorithms can significantly reduce the computational burden when the number of sensors is larger. The corresponding robust local and fused steady-state Kalman estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust fused Kalman estimators is proved by the dynamic error system analysis (DESA) method. A simulation example with application to signal processing to show the effectiveness and correctness of the proposed results.