Research On Simultaneous Input And State Estimation Based On Kalman Filter

In recent years,the state estimation problem based on Kalman filter has been widespread used in the fields of navigation,signal processing and machine learning,and has got one of the research hot in the field of control engineering.However,influenced by the external environment,device failure,information flow changes during device interaction and network congestion,there are usually unknown inputs,time delays and observation packet loss in real systems,which will make the estimation problem more complex and challenging,and the traditional Kalman filter estimation is unsuitable for systems with unknown inputs.The disturbances need to be found and isolated to resolve the above issues in the system,and the minimum variance unbiased estimation is commonly used to deal with linear systems containing unknown inputs.Therefore,it is necessary to establish a connection between Kalman filter estimation and minimum variance unbiased estimation.On the one hand,for linear systems with measurement packet loss and unknown disturbances in the observation equations,the thesis investigates the unbiased minimum variance state estimation algorithm as a special limit of Kalman filtering,and the estimator design is carried out in two ways.On the other hand,for linear discrete systems with measurement time delays and unknown input,the thesis unifies the minimum variance unbiased estimation and Kalman filter estimation under certain conditions.The main research of this thesis is as follows:(1)For the linear system with observation packet loss and unknown input in the observation equation,the unbiased minimum variance state estimation algorithm is studied as the special limit of Kalman filter.Firstly,the existing unbiased minimum variance state estimators are optimized and summarized.Secondly,the unknown input model is described is a Gaussian distribution with finite mean and variance,and the state estimator is obtained by using Kalman filter theory and the properties of Gaussian distribution.Then,under the condition that the unknown input variance tends to infinity,the existing minimum variance unbiased estimation and Kalman filter algorithm are unified by using the matrix inverse lemma.Finally,the simulation results show that the estimator based on timestamp technology has better tracking effect than the estimator considering only the statistical characteristics of packet loss variables.(2)For measurement-delay systems with unknown inputs,a research scheme using unknown input and state estimation algorithm as the limit of Kalman filter is proposed.Firstly,the existing state and input recursive filters are optimized and summarized.Secondly,assuming that the unknown input is Gaussian white noise with finite variance,the recursive filter of unknown input and state is designed by using Kalman filter theory.Then,under the specific condition that the variance of unknown input tends to infinity,it is testified that the simultaneous estimation of unknown input and state is a standard Kalman filter algorithm with specific unknown input model.Finally,the simulation experiment designed by Matlab verifies the effectiveness of this method.