Robust Time‐Varying Estimators Using Weighted Fusion for Multisensor Networked Systems With Missing Observations and Two‐Step Random Delays

ABSTRACT This study addresses the challenge of developing a robust, time‐varying fusion Kalman estimator for multi‐sensor networks with compound indeterminacies, including multiplicative noises, two‐step stochastic delays, missing measurements, and variations in uncertain noise. To tackle this problem, a model transformation strategy that includes the augmentation method, the de‐randomization method, and the fictional noise method is employed. This approach converts the original multi‐sensor system into an equivalent system with constant parameters and unknown noise variances, laying the foundation for subsequent estimator design. Within a unified framework, three robust fusion time‐varying Kalman estimators—predictor, filter, and smoother—are derived based on the minimax robust estimation principle and the worst‐case system with the conservative upper bounds of the noise variances. The design of this robust fusion Kalman estimator utilizes the robust fusion Kalman predictor, further derives the corresponding weighted fusion filter and smoother, and adopts three weighting rules: matrix weighting, diagonal matrix weighting and scalar weighting. The robustness of the proposed fusion estimators is verified through the augmented noise method, the non‐negative definite matrix decomposition method, and the global Lyapunov equation method, which also reveal the accuracy correlation between robust local estimates and fused time‐varying Kalman estimates. Specifically, “robustness” herein refers to ensuring that the actual estimation error variances maintain corresponding minimum upper bounds for all admissible uncertainties. Finally, simulation experiments on autoregressive (AR) signal processing and the original system demonstrate that robust fusion state estimation can solve the problem of robust fusion signal estimation and verify the effectiveness and accuracy of the proposed method.