非线性非高斯模型的高斯和滤波算法

通过将模型的状态噪声和观测噪声均表示成高斯和的形式，推导出非线性非高斯状态空间模型的高斯和递推算法，进一步提出了对应的扩展卡尔曼和滤波器（extended Kalman sum filter, EKSF）和高斯厄密特和滤波器（Gauss-Hermite sum filter, GHSF）。EKSF和GHSF分别用扩展卡尔曼滤波器（extended Kalman filter, EKF）和高斯厄密特滤波器（Gauss-Hermite filter, GHF）作为高斯子滤波器。分析的结果表明，现有的高斯和滤波算法是本文算法的特例；仿真结果表明，EKSF和GHSF能有效处理非线性非高斯模型的状态滤波问题，与高斯和粒子滤波器（Gaussian sum particle filter, GSPF）相比，EKSF和GHSF在保证精度的同时，大大降低了计算量，仿真时间分别约为GSPF的5%和6%。

Gaussian sum filtering methods for nonlinear non-Gaussian models

The Gaussian sum recursive algorithms for nonlinear non-Gaussian state space models,on the assumption that the process and measurement noises are denoted by Gaussian-sums,is firstly deduced.And then the corresponding extended Kalman sum filter(EKSF) and the Gauss-Hermite sum filter(GHSF) are proposed,which use the extended Kalman filter(EKF) and Gauss-Hermite filter(GHF) as the Gaussian sub-filter respectively.The analysis shows that the existing Gaussian sum filtering algorithms are nothing but special cas...