Research On Particle Filtering Algorithm For Some Classes Of Nonlinear Systems

Particle filtering algorithm is the nonlinear filtering algorithm based on the sequential Monte Carlo method.It uses a set of random weighted samples,which are generated sequentially from the importance functions,to represent the filtering distribution.As particle filtering algorithm is not limited by the assumptions of linear system and Gaussian noise,it has wide applicability in theory.However,there are still some challenging problems for particle filtering algorithm to be solved in practical application:the calculation problem of likelihood function;the particle degradation phenomenon and the related importance function selection problem;the calculation complexity problem for high-dimension system.Therefore,combined with different state or measurement models of nonlinear systems,the above problems are deeply studied,major research contents of this thesis are as follows:(1)To solve the particle filtering problem for nonlinear system with multiplicative scaling factor,though giving the likelihood function expression,a novel bootstrap particle filtering algorithm is designed.This system comes from the extended target tracking and its measurement is described by the random hypersurface model.The measurement equation contains a multiplicative scaling factor and the model dimension is high.It makes the numerical calculation of likelihood function complex and unstable,while the likelihood function is a necessary condition for weight updating in bootstrap particle filtering.In order to solve this problem,the existing approximate likelihood function based on Gaussian approximation is simplified.In addition,another approximate likelihood function based on natural logarithm approximation is given.The likelihood function based on these two approximate methods are compared.Based on the obtained likelihood function,a novel bootstrap particle filtering algorithm is proposed.(2)To solve the particle filtering problem for nonlinear system with exponential family observation model,a second-order extended particle filtering algorithm is designed.For this system,in order to limit the particle degradation phenomenon effectively,a suboptimal importance function is given by approximating the theoretical optimal importance function.The approximate method is based on the second-order Taylor expansion of the natural logarithm of the theoretical optimal importance function,in order to approximate the theoretical optimal importance function to a Gaussian density function which is easy to sample.Based on the obtained suboptimal importance function,a second-order extended particle filtering algorithm is proposed.(3)To solve the particle filtering problem for nonlinear system with missing measurements,an improved Gaussian particle filtering algorithm is designed.Gaussian particle filtering is a combination of Kalman-like filtering and particle filtering.It takes the optimal filtering density function under Gaussian assumption as the importance function,in order to limit the particle degradation phenomenon.For this system,firstly,the Gaussian optimal filtering is given.Then,based on extended Kalman filter and unscented Kalman filter,two kinds of improved Gaussian particle filtering algorithms,extended particle filtering and unscented particle filtering,are proposed.Furthermore,to improve estimation accuracy and stability,through the fifth-order spherical-radial rule,an improved highorder cubature Kalman filtering algorithm is given.Based on this algorithm,a high-order cubature particle filtering algorithm is given.(4)To solve the particle filtering problem for nonlinear system with non-Gaussian exponential family priori,a novel Rao-Blackwellized particle filtering algorithm is designed.This system comes from the extended target tracking and uses the real symmetric positive definite random matrix to describe the shape extent of the target.As the priori of the random matrix is inverse Wishart distribution belonging to exponential family distribution,the existing importance functions based on Gaussian density function approximation cannot be used.In order to choose a proper importance function and limit the particle degradation phenomenon,based on the conjugation property of exponential family,an optimal importance function is derived out.As the optimal importance function cannot be computed analytically for general random matrix model,the suboptimal importance function is designed through two approximate methods.Furthermore,to improve computational efficiency,the Rao-Blackwellized particle filtering algorithm is applied for this model.For this algorithm,the extended Kalman filtering is applied for estimating the kinematic state,and the particle filtering based on the proposed suboptimal importance function is applied for estimating the extent state.