Optimal And Robust State Estimation Of Generalized Systems With Random One-step Lags

The descriptor system is also called as singular system,which can describe the actual physical process more accurately.The research of descriptor system is based on the theory of normal system.Due to the special structure of uncertain descriptor system,the research on state estimation of uncertain descriptor system is not perfect,which has aroused the interest and discussion of scholars.Kalman filtering method is widely used because of its good recursive structure and small data storage.The state estimation method of descriptor system requires that the model parameters and noise statistics are completely known.However,in practical systems,the performance of classical filters deteriorates or the filters diverge due to the existence of system uncertainties such as random delay,packet loss and observation loss.To solve the problem,the state estimation algorithm of descriptor system with random one-step delay and uncertain noise variance is presented in this paper.The paper is organized as following:Firstly,the networked system with random one-step measurement delay and uncertain noise variance is considered.The SVD method and fictitious noise method are considered in this part to figure out the problem.The robustness is proved by robustness analysis.Secondly,the obtained theoretical basis is extended to descriptor system.The SVD method,augmented state method and derandomization method are used to estimate the state of descriptor system with random one-step delay and obtain the optimal time-varying filter.Finally,for the descriptor system with random one-step measurement delay and uncertain noises variance,the SVD method,augmented state method and various noise method are used to transform the descriptor system with random one-step delay and uncerntain noise variance into a standard system with only uncerntain noise variance white noise.Applying minimax robust estimation principle and Kalman filtering theory,the robust Kalman estimator of the augmented and the original system are presented.The robustness is proved by robustness analysis.