高斯-厄米特粒子滤波器

The Gauss-Hermite Particle Filter

针对非线性、非高斯系统状态的在线估计问题 ,本文提出一种新的基于序贯重要性抽样的粒子滤波算法 .在滤波算法中 ,我们用一簇高斯 厄米特滤波器 (GHF)来产生重要性概率密度函数 .此概率密度在系统状态的转移概率的基础上融入最新的观测数据 ,因此更接近于系统状态的后验概率 .理论分析与实验结果表明 :在观测模型具有高精度的场合或似然函数位于系统状态转移概率的尾部时 ,用GHF产生重要性概率密度函数的粒子滤波即高斯 厄米特粒子滤波 (GHPF)的性能要明显地优于标准的粒子滤波、扩展的卡尔曼滤波、GHF .

In this paper,a new particle filter based on sequential importance sampling (SIS) is proposed for the on-line estimation problem of non-Gauss nonlinear systems.In the new algorithm,a bank of Gauss-Hermite filter (GHF) is used for generating the importance density function.The density function integrates the new observations into system state transition density,so it can match the statea posteriori density well.As a result,while the likelihood function is situated on the tail of state transition density or observation model has higher precise,the theoretical analysis and experimental results show that the new particle filter outperforms obviously the standard particle filter and the other filters such as the extended Kalman filter (EKF),the GHF.