Recursive Filter Design For Nonlinear Systems And Applied Research

Filtering technology is playing an increasingly important role in various applications.It can be used to estimate things which are interesting but difficult to observe or only partially observable.For a long time,in various engineering practices such as target tracking,robot navigation and positioning,and fault diagnosis,designing suitable filters to improve the estimation accuracy and robustness of the system has been a significant research topic with high application value.For the problems existing in the current nonlinear system filter design methods,this thesis uses the fixed-point theory,the maximum correntropy(MC)criterion as tools to research the design and application of recursive filters for nonlinear systems on the basis of learning existing nonlinear system filtering methods.(1)A novel extended Kalman filter based on fixed point iteration is designed to improve the filtering performance of nonlinear systems with Gaussian noise.Firstly,based on the extended Kalman filter algorithm,the fixed-point theory is introduced to update the estimated system state obtained by EKF.Aiming at the problem that both the state estimation of the fixed-point function and the filter gain are unknown,a nested iterative method is proposed to solve the fixed-point function and obtain the fixed-point filter.Then,the convergence and existence of the fixed-point filter are discussed,and a Steffensen's iterative method for solving the fixed-point iteration function is proposed.Finally,the effectiveness and flexibility of the proposed method are verified by simulation.(2)In order to solve the problem of non-Gaussian noise filtering for nonlinear systems,an iterative updating nonlinear filter design method based on Stirling's interpolation theory and fixed-point theory is proposed under the maximum correlation entropy criterion.The core is to construct a fixed-point function about the state of the system based on the pseudo-inverse mechanism.First,based on Stirling's interpolation theory,a sampling point approximation method for predicting the state of the system is given.Then,the nonlinear filtering method designed under the maximum correntropy criterion is used to correct the prediction with the non-Gaussian measurement value to obtain the system state estimation value.In the framework of this filter design,the expression formula of the maximum correntropy nonlinear filter gain matrix is derived,and the matrix pseudo-inverse operation is used to solve it.Then,an iterative update method of fixed-point is proposed to optimize the state estimation,and the convergence conditions of the iterative calculation are analyzed.Finally,simulation experiments show the effectiveness of the proposed maximum correntropy filtering algorithm and iterative update method for non-Gaussian nonlinear filtering problems.(3)Aiming at the problem of information space filtering for non-Gaussian noise nonlinear systems,two information space filtering methods based on maximum correntropy criterion are proposed.Method 1: Based on the MC criterion,a new information filter called maximum correntropy extended Information Filter(MCEIF)is proposed for nonlinear nonGaussian systems under the information filter framework.Similar to the classical extended information filter(EIF)under the MMSE criterion,first,the prior state estimation and prediction information matrix are calculated.Then,the MC criterion is used to reconstruct the estimated information matrix and the filter gain information matrix.Then,iteratively update the posterior state estimation and filtering information matrix.Finally,the effectiveness of the proposed algorithm is verified by numerical simulation.Method 2: First,obtain the prediction information vector through the traditional square root cubature information filtering algorithm,and then,use the contribution information vector obtained from the non-Gaussian measurement to correct the prediction information vector under the maximum correntropy criterion.Use the state information entropy matrix and the measurement information entropy matrix to obtain the information filtering gain,where the state prediction is used as the state value.In order to improve the filtering accuracy of the above-mentioned nonlinear non-Gaussian information filter,the fixed-point theory is used to further develop an iterative calculation method for updating the estimated information vector and state estimation value.Finally,the proposed algorithm is applied to the industrial component attrition system and radar target tracking system,and the effectiveness and flexibility of the proposed algorithm are verified by simulation.(4)Under the MC criterion,a novel Maximum Correntropy Cubature Kalman Filter(MCCKF)algorithm is proposed.The algorithm first uses the traditional CKF time update process to obtain the state prediction value and prediction error covariance matrix of the system.Then,based on the pseudo-inverse idea,under the MC criterion,a new filter gain matrix is obtained by reconstructing the state prediction error covariance and the observed noise variance of the system,and then the state estimation value and estimated error covariance of the system are obtained.The proposed algorithm shows strong robustness when the system measurement value is polluted by some heavy-tailed non-Gaussian noise.In order to verify the effectiveness of the proposed algorithm,we apply the proposed algorithm to the SINS/GPS integrated navigation system.Firstly,we present the nonlinear error model of SINS system,further,deduced the nonlinear error model of SINS/GPS integrated navigation system,and on this basis,we conducted the experiment simulation.The simulation results effectively prove the feasibility and effectiveness of the proposed algorithm.