Design Method Of Kalman Filter Based On Additive And Multiplicative Mixed Nonlinear Systems

Filter design method and technology has always been one of the hot topics in the academic field,and has made great progress in recent years.At present,although the theory and method based on linear Kalman Filter design have formed a relatively complete architecture,the performance of existing Kalman filters designed for nonlinear systems often degrades gradually with the enhancement of nonlinearity.The Extended Kalman Filter and Strong Tracking Filter based on function approximation can not fundamentally solve the linearization error caused by discarding the high-order term of Taylor expansion.The Unscented Kalman Filter based on sampling approximation does not pay attention to the specific function form,and only samples and approximates the probability density distribution of the function,but the parameter selection problem of this "black box" processing method has not been completely solved.The above problems seriously affect its application in practice.Therefore,taking three typical strongly nonlinear systems as objects,this paper designs the corresponding high-order Kalman Filters respectively to improve the performance deficiency of the existing filters in the face of strongly nonlinear systems.(1)For a class of strongly nonlinear systems composed of linear and nonlinear terms.Firstly,the strongly nonlinear term is defined as the implicit variable of the original variable of the system;secondly,the linear dynamic model of hidden variables is established,and the extended dimension space generated by the original variables and the tensor of hidden variables is constructed;finally,the linear system model based on original variables and implicit variables is established,and the high-order extended dimension Kalman Filter of this kind of system is designed.(2)For a class of systems composed of linear terms and factorized nonlinear terms.Firstly,each nonlinear multiplier is defined as the hidden variable to be evaluated,and the dynamic correlation model of the hidden variable is established;secondly,the linear state model and linear measurement model about hidden variables,system parameters and states are established in turn;finally,a Kalman filter bank for estimating the hidden variables,parameters and states of the system is designed step by step.(3)For a class of strongly nonlinear input-output systems,a parameter identification method based on Kalman filter is established.Firstly,the multiplicative parameters and multiplicative nonlinear functions in the input-output equation are defined as different implicit variables;secondly,the dynamic models of hidden variables are established in the form of random walk,and the statistical characteristics of modeling error are set;finally,Kalman filter banks are designed to estimate the hidden variables,multiplicative parameters and parameters in the composite function.