Improvement And Accuracy Analysis Of Nonlinear Kalman Filtering Algorithms

The application of target tracking is more and more popular in the modern life,from the orbit forecast tracking of the spacecraft in the national military fields to the vehicle tracking in the daily life.From the definition,the target tracking can be simply perceived as the estimation problem about the target trajectory.How to deal with these problems and track the target accurately in the real-time becomes a technical difficulty.Over the years,people have never quitted the steps of researching the target tracking theory and its application.As an important approach for the target tracking,the Bayesian filtering algorithm is always a hotspot and also a difficult point.Among them,the Kalman filtering algorithm is the most typical one.During its implementation process,the unknown parameters need to be regarded as random variables,and both the prior probability and the current observation data are utilized to calculate the posterior probability,which coordinates the application of the prior probability and the current observation data.In addition,by the condition of the minimum mean square error,the Kalman filtering algorithm can utilize the recursive computation between the prior probability and the posterior probability,thus yields the optimal estimate of the signal under the linear systems.However,in practice,the systems in the application are almost nonlinear.The application of the conventional Kalman filtering algorithm is routinely confined to the linear systems.Therefore,people pay more attention to the nonlinear Kalman filtering algorithms which are gradually proposed.In the past years,the widely used nonlinear Kalman filtering algorithms are the unscented Kalman filtering algorithm,the cubature Kalman filtering algorithm,the spherical simplex-radial cubature Kalman filtering algorithm and so on.All these filtering algorithms are proposed under the Gaussian assumption using the Bayesian filter theory and by the approximation to the probability density functions.Then,a set of sampling points and the corresponding weights are obtained through the approximated calculation based on the numerical integral theory.Considering the complicated noise and other uncertain factors in the nonlinear environment,people have to look for a nonlinear Kalman filtering algorithm which has better robustness and can adapt to the complicated nonlinear environment,to improve the estimation performance.In addition,with the development of science and technology,requirements to the algorithm are higher and higher,which means that the research on filtering algorithm can’t be restricted to the design of the novel algorithm.People must realize the importance of performance analysis in its application.The estimation accuracy about the state by different filters is an important index to measure the performance of the filters.Accordingly,based on the previous researches,this thesis mainly involves the following aspects:(1)Improvement on the sampling rule.The improvement here is achieved mainly for the cubature rule.Based on the conventional cubature Kalman filter,this paper proposes a novel cubature Kalman filter,which introduces the idea of mixed degrees in the spherical-radial cubature rule.Besides,through the comparison of the estimate accuracy and the computational complexity between the proposed algorithm and the conventional algorithm,simulations by the MATLAB verify the practical value of the novel filtering algorithm in the engineering.(2)Research about the robustness of augmented-nonlinear algorithms in the complicated environment.A class of augmented-nonlinear Kalman filtering algorithm that is based on the deterministic sampling is applied to the target tracking model in this thesis.By setting the mutation interference and complex noise,the augmented-nonlinear Kalman filtering algorithm still performs good robustness,which also proves its practicability in the real-time target tracking.(3)Accuracy analysis about the novel algorithm based on mixed degrees.Based on the conventional spherical simplex-radial cubature Kalman filtering algorithm,we apply the mixed degrees to the simplex spherical-radial cubature rule,and utilize the conventional method of accuracy analysis which is based on the Taylor expansions to analyze the mean and covariance of the novel simplex spherical-radial cubature Kalman filtering algorithm.Simulations show the novel algorithm can efficiently improve the filtering accuracy.