New Bayesian Estimation Method Based on Symmetric Projection Space and Particle Flow Velocity

Aiming at the state estimation problem of nonlinear systems (NLSs), the traditional typical nonlinear filtering methods (e.g., Particle Filter, PF) have large errors in system state, resulting in low accuracy and high computational speed. To perfect the imperfections, a new Bayesian estimation method based on particle flow velocity (PFV-BEM) is proposed in this paper. Firstly, a symmetrical projection space based on the state information is selected, the basis function is determined by a set of Fourier series with symmetric properties, the state update is carried out according to the projection principle to calculate the prior information of the state, and select its particle points. Secondly, the particle flow velocity is defined, which describes the evolution process of random samples from the prior distribution to the posterior distribution. The posterior information of the state is calculated by solving the parameters related to the particle flow velocity. Finally, the estimated mean and standard deviation of the state are solved. Simulation experiments are carried out based on two instances of one-dimensional general nonlinear examples and multi-target motion tracking, The newly proposed algorithm is compared with the Particle Filter (PF), and the simulation results clearly indicate the feasibility of this novel Bayesian estimation algorithm.