一种基于提议分布选择的改进边缘粒子滤波算法

An Improved Marginal Particle Filter with Proposal Distribution

在估计系统状态后验密度函数时,传统粒子滤波需估计整个状态序列再取其当前值,导致状态空间维数和粒子重要性权值方差随时间增大而必须增加重采样环节加以抑制.边缘粒子滤波保证在低维状态空间下的估计,但估计精度和粒子集重要性权值方差仍不够理想.本文首先推导出更接近状态后验密度函数的提议分布;然后将最新观测信息融入边缘粒子滤波中的单个粒子提议分布权值,提出了提议分布更为合理的改进边缘粒子滤波算法;最后设计了两组仿真实验,表明改进边缘粒子滤波的估计精度更高,粒子重要性权值方差进一步明显减小,粒子退化现象得到有效抑制.

When estimating the posterior density of system state,the traditional Particle Filtering estimates the throughout state se- quence and drop the history state values, which results in both higher dimensional state space and higher variance of the importance weights and so requires the use of resampling stages. Marginal Particle Filter can run in low-dimensional state space, but the estimation accuracy and the variance of the importance weights of particle set are still not ideal. In this paper, a better proposal distribution which is closer to posterior density is deduced, and by taking the most recent observation into account, an improved version of marginal Parti- cle Filter is proposed to enhance the performance of the particle set. The current observation is incorporated into the weight of proposal distribution of each particle, which makes the new proposal distribution is more suitable over the original marginal particle filter. Final- ly, two simulation results are presented to demonstrate the improvement of the estimation accuracy and decrease of importance weight variance. Hence,the proposed algorithm can achieve a significant reduction in weight degeneracy over the original marginal particle filter.