Weighted Fusion Robust Steady‐State Estimators for Multi‐Sensor Networked Systems With One‐Step Random Delay, Fading Measurements and Multiple Packet Dropouts

ABSTRACT This paper focuses on the design of the robust fusion steady‐state Kalman estimation for multi‐sensor networked systems, in which there are phenomena of one‐step random measurement delay and multiple packet dropouts under the influence of fading measurements. By applying the augmented method and the extended fictitious noise technique, the original system is equivalently transformed into a subsystem with only uncertain noise variances. Based on the principle of minimax robust estimation, three kinds of weighted fusion robust steady‐state Kalman estimators (predictors, filters, and smoothers) are proposed in a unified framework, including a robust covariance intersection (CI) fuser and two fast covariance intersection (FCI) fusers. The fast covariance intersection fusion reduces the computational burden while ensuring the accuracy. Then, by combining the Lyapunov equation approach, the augmented noise approach, and the decomposition method of non‐negative definite matrices, the robustness of the proposed estimators is rigorously proved, and the accuracy relationships between the local and fusion steady‐state estimators are analyzed. Furthermore, the accuracy relationships among the robust local and fusion steady‐state Kalman estimators are analyzed. To demonstrate the effectiveness of this study, an application simulation is conducted for autoregressive moving average (ARMA) signals with such mixed uncertainties. The simulation results verify the practicality and correctness of the design.