非线性非高斯模型的高斯和滤波算法

Gaussian sum filtering methods for nonlinear non-Gaussian models

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%。

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 cases of the deduced algorithm.The simulation results show that the proposed EKSF and GHSF can deal with the state estimation of the nonlinear non-Gaussian models effectively,and only consume about 5% and 6% of the computing time required by the Gaussian sum particle filter（GSPF）,while the consistent filtering performance is kept.