Kalman filtering is widely used in numerous engineering practices and signal processing. The classical Kalman filtering is only suitable to handle the state estimation problems for systems that the model parameters and noise variances are precisely known. However, in many control and engineering applications, the uncertainties of model parameters and noise variances are widely found. In the presence of uncertainties, the filter performance is degraded and the uncertainties may yield the filter divergence. In order to solve the filtering problems for uncertain systems, in recent years, several research results about robust Kalman filtering have been derived. The so-called robust Kalman filter is to design a filter to guarantee a minimal upper bound of the corresponding actual filtering error variances for all admissible uncertainties.So far, there are two basic approaches to solve this problem for systems with uncertain model parameters, one is the Riccati equation approach and the other is the linear matrix inequality(LMI) approach. The disadvantage of these two approaches is that they are mainly suitable for systems with the uncertainties of model parameters, where the noise variances are assumed to be exactly known. In most of references, the design of the multisensor information fusion robust Kalman filters is seldom considered and the robustness of the fused robust filters was not solved completely. Therefore, information fusion robust Kalman filtering problems are studied in the thesis for multisensor systems with uncertain noise variances.For multisensor systems with uncertain noise variances, the main content of the thesis can be briefly described as follows:According to the minimax robust estimation principle, A new approach of designing the robust local and fused Kalman filters has been presented. Based on the worst-case conservative system with the conservative upper bounds of noise variances, under unbiased linear minimum variance(ULMV) optimal estimation rule, the conservative optimal local and fused Kalman filters with conservative measurements can be obtained. Replacing the conservative measurements by the actual measurements of sensors for the true system, the robust local and fused Kalman filters and the minimal upper bound of the actual filtering error variance are obtained. The Lyapunov equation approach for robustness analysis is proposed, which converts the robustness problem into the decision problem on positive semi-definiteness of the solution of a Lyapunov equation, the robustness of the proposed local and fused robust Kalman estimators is proved rigorously. This new approach is completely different from the existing Riccati equation and the LMI approaches. The concept of the robust and the actual accuracy and the robust accuracy analysis approach are presented and the robust accuracy relations of the proposed robust Kalman estimators are rigorously proved.The five robust weighted fusion time-varying Kalman estimators(filter, predictor and smoother) have been presented, which contain the three weighted state fusion robust Kalman estimators(weighted by matrix, scalar and diagonal matrix), a modified robust CI fusion Kalman estimator and a robust weighted measurement fusion Kalman estimator. Based on the augmented state method, the robust weighted fusion Kalman smoothers are obtained, and the modified CI fuser is considered the conservative cross-covariance information among the local estimators, compared with the original CI fuser without the cross-covariance information, it improves the robust accuracy, and is the minimal upper bound of the actual estimation error variances.Based on the indirect method, by taking the limits of local and fused robust time-varying Kalman estimators, the corresponding local and fused robust steady-state Kalman estimators are presented, and the convergence in a realization between the local and fused time-varying and steady-state robust Kalman estimators is proved by the dynamic error system analysis(DESA) method and the dynamic variance error system analysis(DVESA) method. Based on the steady-state Kalman filtering theory, a simple direct design method is presented for obtaining the local and fusion robust steady-state Kalman estimators.According to the minimax robust estimation principle, the two-level robust sequential covariance intersection(SCI) fusion Kalman estimators(filters and predictors) are presented for the time-delayed and without time-delayed sensor network systems with uncertain noise variances. They can avoid computing cross-covariance, and the computation burden can be significantly reduced. They can also reduce the communication burden and save the energy sources based on the clustering sensor networks divided by the nearest neighbor rule.Several simulation examples show the correctness and effectiveness of the proposed algorithms throughout this thesis. |