Robust Fusion Kalman Filtering And Deconvolution For Uncertain Systems

The Kalman filtering method is a basic tool to handle the state estimate problems.The classical Kalman filtering method requires that the model parameters and noise variances of the considered system are exactly known.However,in practical applications,the uncertainties always exist in the system models due to a number of reasons such as unmodeled dynamics and stochastic perturbations,including the model parameter uncertainties and noise variance uncertainties.The former include norm-bounded parameter uncertainties and random parameter uncertainties(multiplicative noises).In addition,the phenomenon of missing measurements is also common due to the accidental sensor failures.When uncertainties exist in the system model,the performance of classical Kalman filter deteriorates and the uncertainties may lead to the filter divergence.This has motivated many studies on robust Kalman filter design.The so-called robust Kalman filter is concerned with the design of a fixed filter for a family of system models formed by uncertainties,such that its actual filtering error variances are guaranteed to have minimal upper bound for all admissible uncertainties.There are two basic approaches to design the robust Kalman estimators for systems with uncertain model parameters but known noise variances,one is the Riccati equation approach and the other is the linear matrix inequality(LMI)approach.The Lyapunov equation approach is applied to design the robust Kalman estimators for systems with uncertain noise variances but known model parameters.So far,there are few researches on information fusion robust Kalman filtering and white noise deconvolution for the systems with mixed uncertainties including uncertain model parameters,uncertain noise variances and missing measurements.Therefore,information fusion robust Kalman filtering and white noise deconvolution problems are studied in the thesis for systems with mixed uncertainties.For multisensor systems with mixed uncertainties,the main contents of this thesis are as follows:First,a minimax robust Kalman filtering method based on fictitious noises and Lyapunov equations is proposed,which can solve the robust fusion estimation problem for mixed uncertain multisensor systems.We have also proposed an approach to design the robust Kalman estimators,whose principle is to design robust Kalman filter and smoother based on the robust Kalman predictor,and the augmented noise approach and non-negative matrix decomposition approach are also proposed,which are applied to prove the robustness.Secondly,applying the above-mentioned minimax robust Kalman filtering method,the local and six information fusion robust time-varying and steady-state Kalman state estimators(predictor,filter and smoother)are proposed for uncertain multisensor systems with multiplicative noises,uncertain noise variances,and the measurement noise is linearly correlated with the process noise,where the fused estimators contain the three weighted state fusion robust Kalman estimators with matrix weights,scalar weights and diagonal matrix weights,a modified covariance intersection(CI)fusion robust Kalman estimator,as well as the centralized and weighted measurement fusion robust Kalman estimators.The local,centralized and weighted measurement fusion robust time-varying and steady-state Kalman state estimators as well as a robust weighted least square filter are proposed for the mixed uncertain multisensor systems with multiplicative noise,missing measurements,uncertain noise variances,and the measurement noise is uncorrelated with the process noise or is linearly correlated with the process noise.For the proposed robust local and fused estimators,we have proved their robustness,analyzed the accuracy relations among the robust estimators,and analyzed the numerical equivalence and the computation complexity.Compared with the robust centralized fuser,the robust weighted measurement fuser can significantly reduce the computational burden when the number of sensors is larger.The three modes of convergence in a realization among the time-varying and steady-state robust Kalman estimators are proved by the convergence of self-tuning Riccati equation and the dynamic error system analysis(DESA)method.Thirdly,applying the above-mentioned minimax robust Kalman filtering method,the local and six information fusion robust steady-state white noise deconvolution smoothers are proposed for multisensor systems only with uncertain noise variances and the measurement noise is uncorrelated with the process noise.For the multisensor systems with multiplicative noise,missing measurements,uncertain noise variances,and the measurement noise is linearly correlated with the process noise,the centralized and weighted measurement fusion robust time-varying and steady-state white noise deconvolution estimators(filter and smoother)are proposed.We have proved the robustness,the equivalence,and the accuracy relations of the proposed white noise estimators,and proved the convergence in a realization between the time-varying and steady-state estimators,and analyzed their computation complexity.Several simulation examples include the application to autoregressive(AR)signal,spring-mass-damper system,uninterruptible power system,continuous stirred tank reactor system,as well as IS-136 mobile communication system verify the correctness,effectiveness and applicability of the proposed theoretical results.