An Extended Ensemble Kalman Filter Method For State Estimation Of A Class Of Nonlinear Non-Gaussian Systems

Kalman filtering methods are widely used in radar positioning,autopilot,navigation and guidance,and fault diagnosis.Kalman filter(KF),Extended Kalman filter(EKF)and Unscented Kalman filter(UKF)are suitable for Gaussian systems,and Particle filter(PF)can be used for non-Gaussian systems.For strongly nonlinear models,all of the above filtering methods suffer from problems such as divergence and degradation of filtering accuracy due to the lack of approximation capability for nonlinear models.To this end,this thesis conducts a study on the extended Ensemble Kalman filter method(EnKF)for state estimation of nonlinear non-Gaussian systems with the help of particle filter sampling technique,and the main research contents and results obtained are as follows:(1)An extended EnKF design combining UKF sigma sampling and weight optimization.Firstly,based on the estimated value of the current state and the covariance matrix,a UKF statistically constrained sigma sampling of the state is performed,and then random sampling is performed around each sigma sampling point to obtain a data ensemble that can better characterize the distribution of the state variables of the system to be estimated.Finally,an extended EnKF design method combining UKF sigma sampling and weight optimization is proposed.(2)Extended EnKF design for state estimation of nonlinear non-Gaussian systems.First,the non-normal distributions of the state and process noise in the current moment and the measurement noise in the future moment in the system are decomposed into a finite number of normal distribution superpositions and forms,so as to decompose the nonlinear non-Gaussian system into multiple groups of nonlinear Gaussian systems;second,the corresponding extended EnKF is established for each nonlinear Gaussian system,and the system state is weighted and fused based on multiple EnKF estimates to obtain the estimates and density distribution functions of the future moment states of the nonlinear non-Gaussian system;finally,the distribution functions of the future moment states obtained after multiple superposition are approximately simplified,and the mean and weight of each normal distribution after the simplification are optimized to avoid the combinatorial explosion of the superposition and of the density functions of the states in the filtering design process.(3)A multi-dimensional Taylor network extended EnKF design for non-Gaussian system state estimation.First,based on the obtained EnKF estimation results of the system state,an EnKF model of the multi-dimensional Taylor network is built,and the parameters of this model are trained using a BP algorithm with a driving factor;second,the subsequent state prediction estimates obtained based on the EnKF and the gain information used to correct them are input to the multi-dimensional Taylor network EnKF model to predict the obtained estimates of the current state of the system.Finally,based on the valuable state estimates obtained online,the parameters of the multi-dimensional Taylor network EnKF model are adaptively updated to achieve online recursive estimation of the system state.