基于高斯和与SCKF的非线性非高斯滤波算法

Nonlinear non-Gaussian filtering algorithm based on Gaussian sum filter and SCKF

针对均方根容积卡尔曼滤波(SCKF)对非高斯情况滤波效果差的问题,在分析SCKF和高斯和滤波基础上,提出一种高斯和均方根容积卡尔曼滤波新算法。算法采用高斯和形式来逼近非高斯后验概率密度,将SCKF作为子滤波器,对每个高斯分量进行时间和量测更新,使其有效解决非线性非高斯滤波问题。仿真结果表明,高斯和均方根容积卡尔曼滤波估计精度高于粒子滤波和高斯和扩展卡尔曼滤波算法,与容积粒子滤波精度相当,但耗时约为容积粒子滤波的15%,是一种较好平衡跟踪精度和实时性的非线性非高斯滤波算法。

To improve filtering result of square-root cubature Kalman filter（SCKF） under non-Gaussian condition, a Gaussian sum square-root cubature Kalman filter（GSSCKF） algorithm is developed based on analyzing SCKF and Gaussian sum filter（GSF）. The new algorithm uses the form of Gaussian sum to approximate the non-Gaussian posterior probability density, takes SCKF as the Gaussian sub-filter to realize time and measurement update for each Gaussian component, the algorithm can effectively deal with nonlinear non-Gaussian filtering problem. Simulation results show that the accuracy of GSSCKF is higher than particle filter（PF） and Gaussian sum extended Kalman filter（GSEKF）. Compared with cubature particle filter（CPF）, the precision is similar, but the consuming time of GSSCKF is about 15% of CPF. GSSCKF performs well in term of the balance between the tracking accuracy and the real-time.