Kalman Filter Design For A Class Of Strongly Nonlinear Systems With Non-Gaussian Noise

With the development of science and technology,strong nonlinear systems with non-Gaussian noise are widely used in theoretical research and practical applications.Therefore,designing appropriate filters for strong nonlinear systems with non-Gaussian noise is a hot topic in the field of filter design,and is also urgently needed in practical applications.At present,the maximum correlation entropy Kalman filter(MCKF)has been developed to solve the state estimation problem of linear systems with non-Gaussian noise,and the maximum correlation entropy extended Kalman filter(MCEKF)and maximum correlation entropy unscented Kalman filter(MCUKF)have been developed to solve the estimation problem of nonlinear systems with non-Gaussian noise by combining the extended Kalman filter(EKF)and unscented Kalman filter(UKF),But it also inherits the problem of EKF and UKF,that is,the truncation error is large,so their estimation error is large in the estimation problem of strong nonlinear systems with non-Gaussian noise.Therefore,this paper aims at the problem of state estimation of strongly nonlinear systems with non-Gaussian noise,and designs different filters by transforming general nonlinear systems into polynomials,combining basic functions with polynomials and multiplying them.The main contributions of this paper are as follows:(1)Design of high order extended Kalman filter with maximum correlation entropy based on polynomial representation.Firstly,the system is transformed from a general nonlinear system model to a higher-order polynomial form through a multidimensional Taylor network;Secondly,by introducing the concept of hidden variables,the higher-order terms in the system are treated as hidden variables,thus simplifying the system into pseudolinear form.Then,the dynamic relationship between hidden variables is established,so as to convert the system from pseudo-linear model to linear model.Finally,according to the converted linear model of the system,a high-order extended Kalman filter based on maximum correlation entropy is established.(2)The design of adaptive kernel maximum correlation entropy high order extended Kalman filter based on the combination of basic functions and polynomials.Firstly,a multi-dimensional Taylor network model with basic functions as nodes is established,and the system is approximated using the step-by-step approximation method based on Kalman filter;Secondly,by introducing the concept of hidden variables and establishing the dynamic relationship between the hidden variables and other variables of the system,the system is transformed from the pseudo-linearized form to the linearized model.Finally,according to the converted linearized model,the maximum correlation entropy high-order extended Kalman filter with adaptive kernel is established.(3)The design of high order extended Kalman filter based on multiplicative decomposition and stepwise linearization of maximum correlation entropy.Firstly,the general nonlinear system is decomposed into the form of first order polynomial,multiple basic functions and the multiplication of the constructed nonlinear functions;Secondly,the basic functions in the system are regarded as hidden variables of the system,and the dynamic model of all hidden variables is established;Thirdly,the estimated variables in the measurement model after multiplicative decomposition are described as linear models with other variables as conditions,and the corresponding Kalman filter is designed based on the established linear dynamic model of hidden variables.Realize the gradual linearization estimation of state variables.