Research Of Particle Filtering Based On Variational Bayesian Learning

Particle filtering is one of the most important methods in the field of nonlinear filtering.It is a combination of Monte Carlo method and Bayesian theory.It implements recursive Bayesian filtering from the time domain perspective by nonparametric Monte Carlo simulation.The particle filter method can be applied to the system described in the state space model,and has good accuracy.Based on the existing theory,this paper focuses on the Gaussian mixture model modeling of observed noise in particle filter and the process of parameter estimation using Variational Bayesian.In the state space model of particle filtering,the observed noise kv is usually assumed to be a zero mean Gaussian white noise signal.However,in many practical applications,the absolute linear Gaussian system does not exist.The performance of the signal processing method based on the Gaussian noise model in the non-Gaussian noise environment will be greatly reduced or even impossible.If the statistical characteristics of non-Gaussian noise can be identified and utilized,the signal processing performance can be greatly improved.In this paper,the Gaussian mixture is used to model the observed noise,and then the variational Bayesian learning method is used to estimate the unknown parameters of the mixed distribution and applied to the observation of the observed noise,the main contributions are as follows:(1)the Gaussian mixture model is used to model the observed noise of non-Gaussian.The Variational Bayesian learning method is used to estimate the unknown parameters of the model.The Variational Bayesian method uses easily distributed distribution to approximate the true posterior probability distribution of a parameter.The marginalization of the likelihood function for each parameter of the joint probability density: The joint probability density distribution of the multi-parameter multivariate is decomposed into the product of the edge probability density distribution of each parameter variable.The parameter estimation of multiple variables is transformed into an iterative estimate of the edge probability density distribution for a single variable.Theoretical analysis and numerical analysis show that the Variational Bayesian algorithm can estimate the unknown parameters of the mixed model accurately and effectively.(2)we propose a marginalized particle filter method based on variational Bayesian learning parameter estimation.Firstly,the recursive model of Bayesian filtering is constructed,and then the Variational Bayesian learning method is applied to the particle filter in the Gaussian mixture model.At the same time,in order to improve the accuracy of the algorithm,the heuristic model of the super-parameter of the measurement noise is constructed to ensure that the functional form of the Gaussian mixture model can be maintained after the prediction.In this paper,we have designed a large number of contrast experiments with the algorithm of the known noise,and the theoretical analysis and simulation experiments show that this algorithm can estimate the noise of the observation noise accurately and effectively,and improve the performance of particle filter.