Robust weighted fusion Kalman estimators for systems with uncertain noise variances, multiplicative noises, missing measurements, packets dropouts and two‐step random measurement delays

Abstract

For multisensor networked systems with uncertain noise variances, multiplicative noises and multiple networked‐induced uncertainties including missing measurements, packets dropouts and two‐step random measurement delays, the robust weighted fusion estimation problem is addressed in this article. More precisely, the system noise variances are assumed to be uncertain but bounded, the other four uncertainties are compensated into fictitious white noise by the proposed model transformation method, which includes the augmented method and extended fictitious noise technique. Then local multi‐model system is obtained, for which robust local Kalman estimator is obtained based on the minimax robust estimation principle and unified estimation method. Based on this, the six robust weighted fusion time‐varying Kalman estimators are presented in a unified form, which include robust weighted fusers weighted by matrices, diagonal, scalars, and a robust covariance intersection (CI) fuser and two fast CI (FCI) fusers. The robustness proving method, including the extended Lyapunov equation approach with two kinds of generalized Lyapunov equations, non‐negative matrix factorization and elementary transformation of matrix, is presented to prove that the actual estimation error variances are guaranteed to have minimal upper bounds for all admissible uncertainties. The accuracy relations are proved. Further, the robust local and fused steady‐state Kalman estimators are presented. Finally, a simulation example applied to Internet‐based three tank water system is given to demonstrate effectiveness of the proposed results.