七阶球面单形-径向容积卡尔曼滤波方法

Seventh-Degree Spherical Simplex-Radial Cubature Kalman Filtering Method

针对传统低阶容积卡尔曼滤波非线性滤波精度较低的问题,提出一种基于七阶球面单形-径向容积准则的高阶容积卡尔曼滤波算法。将非线性函数的高斯加权积分分解为球面积分和径向积分,采用基于正则单形变换群的七阶球面单形准则计算球面积分,使用矩匹配法求积分准则计算径向积分,推导出七阶球面单形-径向容积求积分准则。将准则代入一般非线性滤波框架,得到七阶球面单形-径向容积卡尔曼滤波算法。仿真表明,算法可获得高于传统三阶、五阶CKF的估计精度。具有较好的前景与应用价值。

A high-degree cubature Kalman filter based on the seven-degree spherical simplex-radial criterion is presented to improve the nonlinear filtering accuracy of traditional lower-degree cubature Kalman filter. The Gaussian weighted integral of nonlinear function is decomposed into spherical integral and radial integral. The spherical integral is calculated by the seven-degree spherical simplex criterion based on the regular simplex transformation group,and the moment-matching method is used to the radial integral. The simulation shows that this algorithm has higher estimation accuracy than the traditional algorithm of third-degree and fifth-degree,and has better stability. This algorithm will have a good prospect and application value in the future.