Guaranteed Cost Robust Fusion Kalman Filtering For Uncertain Systems

Multi-sensor information fusion is the new mult-discipline-crossing edge subject,and its object is how to combine the local measurement or local state estimators to obtain a global fused state estimator,whose accuracy is higher than that of each local state estimator.There are two basic fusion approaches: centralized fusion and distributed fusion.Kalman filtering is a basic tool for multi-sensor information fusion,but it requires to know the model parameter and noise variance exactly.However,due to some reasons such as model reduction,modeling error,unmodeled dynamics,and stochastic disturbance,the model parameter and noise variance are uncertain in numerous applications.With the rapid development of network technology and sensor technology,the state estimation of networked system is a new research direction.But due to limited communication bandwidth,sensor failure,as well as a variety of external stochastic disturbance,there are many uncertainties in networked system,including packet loss,missing measurement,multiplicative noise,random measurement time-delay and so on.Therefore,to overcome the degradation and even divergence of filter performance caused by these uncertainties,the research on the robust fusion Kalman filtering has become a hot topic recently.In this paper,according to minimax robust estimation principle,we will design the minimum variance estimator based on the worst-case conservative systems,and study the problem of guaranteed cost robust fusion Kalman filtering.The so-called guaranteed cost robust Kalman filter is to design a filter such that for all admissible uncertainties,its accuracy deviations are guaranteed to have maximum lower bound and minimum upper bound,or remain within the prescribed range.The main contributions of this paper are as follows:Firstly,for linear discrete time-invariant multisensor systems with uncertain noise variances,based on the minimax robust estimation principle and the parameterization representation of noise variance perturbations,and applying Lyapunov equation approach,the two classes of guaranteed cost robust fusion Kalman filter and predictor are designed respectively,and they include guaranteed cost robust weighted measurement fusion predictor,guaranteed cost robust fusion filter weighted by matrices,and a unified form of guaranteed cost robust centralized fusion and weighted measurement fusion filters.One class is,for the prescribed index of accuracy deviation,to construct a maximal perturbation region of uncertain noise variances such that for all admissible perturbations in this region,the accuracy deviations are guaranteed to remain within the prescribed range.The other class is to find minimal upper bound and maximal lower bound of accuracy deviations under given bounded perturbation region of uncertain noise variances.The analytical solutions to these classes of problems are given by the Lagrange multiplier method and linear program method respectively presented in this paper.Secondly,for linear discrete time-invariant multisensor systems with uncertain noise variances and missing measurements,the original system can be converted into one only with uncertain noise variances by applying fictitious noises technology.According to the minimax robust estimation principle and the parameterization representation of noise variances perturbations,applying the Lyapunov equation approach,two classes of guaranteed cost robust fusion Kalman estimators are designed respectively,they include guaranteed cost robust weighted measurement fusion Kalman estimator(filter,predictor and smoother),and guaranteed cost robust centralized fusion Kalman predictor.Finally,for linear discrete time-invariant multisensor systems with uncertain noise variances,multiplicative noise and colored measurement noise,the original system can be converted into one only with uncertain noise variances by using augmented state method and fictitious noises technology.According to the minimax robust estimation principle and the parameterization representation of noise variances perturbations,applying the Lyapunov equation approach,two classes of guaranteed cost robust fusion Kalman predictor with matrix weights are presented respectively.Several simulation examples applied to tracking system,uninterruptible power system(UPS)with 1kVA and spring system show the correctness,effectiveness and applicability of the proposed results.