Research On Unscented Transform-based Nonlinear Filtering Algorithm And Its Application

The state estimation problem of nonlinear dynamic systems has attracted wide attention in the fields of control,signal processing and information fusion.Filter algorithm is a favorable means to deal with state estimation problems,so filtering algorithm plays an important role in nonlinear dynamic systems.A posteriori probability density of nonlinear dynamic systems cannot be described by closed probability density function(PDF),so that there is no optimal analytical solution to the nonlinear state estimation problem.Therefore,the weighted integral method is used to solve the approximate solution.Based on the data information of state estimation,this paper studies the state estimation of nonlinear systems on the premise of adapting to non-ideal environment and aiming at improving the accuracy,adaptive ability and robustness of nonlinear state estimation.A series of improved state estimation methods are proposed based on a weighted integral unscented transformation(UT)method,and the effectiveness and superiority of the proposed method are verified in the target tracking and navigation system.The main work of the dissertation is as follows:1.Based on unscented Kalman filter(UKF)error source analysis of nonlinear system.Different integral rules have different accuracy and rounding error.UT is approximated by PDF,the accuracy can reach more than second order under ideal conditions.Firstly,the Gauss approximate filtering framework is given,and then UKF algorithm flow is given;Secondly,a high-order UT sampling strategy is proposed for the under-estimation of the filter's intrinsic UT method which can only match the first second-order moment information;According to the influence of the external environment,including the inaccuracy of the system model,the unknown measurement and the influence of noise on the whole system,a residual covariance(RC)method is designed as the performance index of the evaluation filter.On this basis,it is proved by theory that it is biased estimation under non-ideal conditions.2.Based on the high-order UT Gaussian approximation state estimation method.The posterior estimation accuracy of UT method is more than the second moment.To match high-order moment information,a sampling strategy based on high-order sigma points is proposed.The closed solution of high-order UT method is obtained by introducing free parameters,and the basis of selecting free parameters is verified.Finally,the nonlinear model is used to simulate and analyze it,and the conclusion is given.3.The state estimation method under uncertain system model.In order to solve the problem of imprecise model and model mutation in error analysis,an interactive multiple model(IMM)nonlinear filter based on high-order UT framework is proposed.In this method,high-order sigma points and weights are used to estimate the state random variables to improve the probability of effective model.Secondly,an adaptive high-order UKF is proposed to solve the model mutation problem in the case of large maneuvering.The adaptive factor is derived from orthogonality principle to correct the one-step prediction covariance.The high-order UT method is used to construct sigma points and weights to match the high-order moment information.The correctness and superiority of the proposed algorithm are verified by experiments under the non-ideal conditions of model uncertainty of nonlinear system and model mismatch caused by large maneuver of high-speed vehicle.4.The method of state estimation under uncertain conditions.A novel adaptive robust filtering method is proposed for unreliable sensors and unknown noise statistics characteristics.Firstly,the M-estimation method is used to improve the robustness of the algorithm.In order to further reduce the weight of the covariance in the stationary state,adjust the gain matrix and suppress the influence of state mutation,the adaptive factor is introduced into the prediction covariance matrix to improve the adaptive ability of UKF algorithm,and QR method and SVD method are used to improve the robustness of the algorithm;Secondly,a method of maximum entropy criterion combined with high order UT is used to solve the problem of interference and moment information loss of measurement model.The advantages of the proposed algorithm are fully proved by simulation of target tracking example and strong nonlinear dynamic model.5.Research on a filtering method with noise estimator.Estimating the statistical characteristics of noise has been a very difficult problem in target tracking and combined navigation systems.To solve this problem,an adaptive UKF with noise estimator is proposed in this paper.The variational inference is used to solve the approximate solution in nonlinear function domain.This method can be extended to generalized Gaussian approximation filter and applied to target tracking and integrated navigation.Simulation results show that the proposed adaptive filtering algorithm with noise estimator is better than the existing filtering algorithm good accuracy and stability.