Summary The robust fusion steady‐state filtering problem is investigated for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, one‐step random delay, missing measurements, and uncertain noise variances, the phenomena of one‐step random delay and missing measurements occur in a random way, and are described by two Bernoulli distributed random variables with known conditional probabilities. Using a model transformation approach, which consists of augmented approach, derandomization approach, and fictitious noise approach, the original multisensor system under study is converted into a multimodel multisensor system with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady‐state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the optimal fusion algorithm weighted by matrices, the robust distributed weighted state fusion steady‐state Kalman estimators are derived for the considered system. In addition, by using the proposed model transformation approach, the centralized fusion system is obtained, furthermore the robust centralized fusion steady‐state Kalman estimators are proposed. The robustness of the proposed estimators is proved by using a combination method consisting of augmented noise approach, decomposition approach of nonnegative definite matrix, matrix representation approach of quadratic form, and Lyapunov equation approach, such that for all admissible uncertainties, the actual steady‐state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fused steady‐state Kalman estimators are proved. An example with application to autoregressive signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.

For the multisensor systems with unknown noise variances, by the correlation method, the information fusion noise variance estimators are presented by taking the average of the local noise variance estimators under the least squares fusion rule. They have the average accuracy and have consistency. A self-tuning Riccati equation with the fused noise variance estimators is presented, and then a self-tuning decoupled fusion Kalman predictor is presented based on the optimal fusion rule weighted by scalars for state component predictors. In order to prove their convergence, the dynamic variance error system analysis (DVESA) method is presented, which transforms the convergence problem of the selftuning Riccati equation into a stability problem of a dynamic variance error system described by the Lyapunov equation. A stability decision criterion of the Lyapunov equation is presented. By the DVESA method, the convergence of the self-tuning Riccati equation is proved, and then it is proved that the self-tuning decoupled fusion Kalman predictor converges to the optimal decoupled fusion Kalman predictor in a realization, so it has asymptotic optimality. A simulation example for a tracking system with 3-sensor shows the effectiveness, and verifies the convergence.Index Terms-Convergence, dynamic variance error system analysis (DVESA) method, information fusion noise variance estimation, multisensor information fusion, self-tuning Riccati equation, self-tuning weighted fusion Kalman predictor.

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