Robust Fusion Kalman Filtering And Its Application Research In Signal Processing

Multisensor information fusion filtering is widely used in high-tech fields such as target tracking,GPS positioning,Unmanned Aerial Vehicle(UAV),image processing,navigation guidance and so on.The classical Kalman filtering method is an important methodology and basic tool for information fusion filtering(state estimation)and signal processing.But its limitation is that it requires the assumption that the model parameters and noise variances are known precisely.However,in practical applications,there are stochastic or norm-bounded uncertainties of model parameters and noise variances due to unmodeled dynamics,stochastic disturbances,model simplification,and linearization of nonlinear system and so on.Especially with the booming development of NSs,under the influence of the limited net communication capability,the sensor failures,stochastic disturbance and so on,there inevitably exist stochastic uncertainties such as multiplicative noises,missing measurements,packet loss,random measurement delay and so on.This situation makes the classical Kalman filter lose the optimality and yields the filtering performance to decline and even to diverge.Therefore,the robust filtering problems of uncertain system arises a lot of attention in the last twenty years.The so-called robust filter is concerned with a filter whose actual filtering error variances are guaranteed to have a minimal upper bound for all admissible uncertainties,or its some performance remains unchanged.The robust fusion Kalman filtering problems for system with above mixed uncertainties and its application in ARMA(Autoregressive moving average)signal processing have not been solved satisfactorily.Therefore,that are studied in this paper,and the main innovations are as follows:Firstly,for the single sensor system with uncertain noise variances,the general definition of guaranteed cost robustness and two classes of guaranteed cost robust steady state Kalman estimation problems are presented.In addition,by the Lyapunov equation method based on the minimax robust Kalman filtering and the parameterization method of the uncertain noise variances,two classes of problems are converted into the corresponding nonlinear and linear optimization problems with constraint.And their analytic solution can be solved by the Larange multiplier method and LP method,respectively.Two classes of guranteed cost minimax steady-state Kalman filters are presented.For the multisensor systems with uncertain-variance linear correlated noises,two classes of modified CI(Covariance intersection)fused guaranteed cost robust Kalman estimators are presented by the above method.For the multisensor system with uncertain noise variances and missing measurements,by introducing the measurement fictitious noises,the original system is converted into that with only uncertain noise variances,and then the two classes of modified CI fused guaranteed cost robust Kalman filters are presented by the proposed method.Their robustness and the accuracy relationship are proved,and the robust accuracy of the original CI fuser is improved.Secondly,for the multisensor systems with missing measurements and uncertain-variance multiplicative and additive noises and for ones with uncertain-variance additive noises,the state-dependent and noise-dependent multiplicative noises,by the Lyapunov equation method,the robust Kalman estimators weighted by diagonal matrices are presented in a unified framework,respectively.And their robustness and accuracy relationship are proved.Finally,for the multisensor single-channel and multi-channel ARMA signals with uncertain noise variances and missing measurements and stochastic parameters,the original ARMA signals are converted into equivalent state space model.And by the fictitious noise method and the Lyapunov equation method,the centralized and weighted measurement fusion ARMA signal estimators,the ARMA signal estimators weighted by matrices and scalars are presented,respectively.The equivalence of the centralized and weighted measurement fusion estimators is proved and the robustness and the accuracy relationship are proved.Some simulation examples applied to target tracking,UPS and ARMA signal processing are given to verify the correctness,validity and applicability of the proposed results.