Distributed weighted fusion robust white noise deconvolution estimators for multisensor systems with mixed uncertainties

This paper addresses the design of robust scalars-weighted fusion time-varying white noise deconvolution estimators (WNDEs) for uncertain multisensor systems with mixed uncertainties including uncertain-variance multiplicative noises in measurement matrix, missing measurements, and uncertain-variance linearly correlated measurement and process white noises. By introducing the fictitious noise, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case systems with the conservative upper bounds of noise variances, using the optimal fusion criterion with scalar weights, the robust scalars-weighted fusion time-varying WNDEs (filter and smoother) are presented in a unified framework. Their robustness is proved by using a combination method which consists of Lyapunov equation approach, augmented noise approach, and decomposition approach of non-negative definite matrix, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The accuracy relations between the robust local and fused time-varying WNDEs are proved. A simulation example with respect to the IS-136 multisensor communication systems shows the effectiveness and correctness of the proposed results.