高斯粒子滤波器及其在非线性估计中的应用

Gaussian Particle Filter and Its Application to Nonlinear System Estimation

为了解决非线性、非高斯系统估计问题,讨论了一种新的滤波方法——高斯粒子滤波算法。通过基于重要性采样和蒙特卡罗模拟方法得到一高斯分布来近似未知状态变量的后验分布。在符合高斯假设和一定的粒子数的情况下,谈算法可以获得近似最优解。与粒子滤波算法相比,其优点是不需要重采样步骤和不存在粒子退化现象。在滤波精度、运算时间等方面与扩展卡尔曼滤波、Unscented滤波、高斯厄米特滤波及一般的粒子滤波进行了比较分析,仿真结果表明该算法性能优于其他算法。

A new Gaussian particle filter（GPF） is discussed to solve estimation problems in nonlinear non-Gaussian systems. A single Gaussian distribution is obtained to approximate the posterior distribution of state parameters based on sequential importance sampling and Monte Carlo methods. GPF is asymptotically optimal with the Gaussianity assumption and a certain number of particles. Compared with the particle filter （PF）, it avoids the resampling step and the particle degeneracy phenomenon. It is compared with the extended Kalman filter （EKF）,the Unscented （Kalman） filter（UF or UKF）, the Gauss-Hermite filter （GHF） and the generic particle filter（PF） in accuracy, computational load, and other aspects. The simulation result shows that the performance of GPF is superior to that of the other filters.