摘要
为了进一步提高非线性卡尔曼滤波算法的估计精度,提出一种高阶球面单形—径向容积求积分卡尔曼滤波(HDSSRCQKF,high-degree spherical simplex-radial cubature quadrature Kalman filter)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,使用高阶高斯—拉盖尔求积分准则计算径向积分,推导出高阶球面单形—径向容积求积分准则。从该准则中提取出容积点及其相应权值的一般计算方法,并利用该计算方法给出非线性卡尔曼滤波框架下高阶球面单形—径向容积求积分卡尔曼滤波的具体计算步骤。数值仿真实验结果表明,所提算法具有比高阶容积卡尔曼滤波更高的估计精度,在信道估计与均衡、语音增强和混沌通信等领域具有一定的应用价值。
A high-degree spherical simplex-radial cubature quadrature Kalman filter （HDSSRCQKF） was proposed to improve the estimation accuracy of nonlinear Kalman filter. The nonlinear Gaussian weighted integral was decomposed into the spherical integral and radial integral. These two integrals were calculated using the seventh-degree spherical simplex rule and the high-degree Gauss-Laguerre quadrature rule, respectively, and result in the high-degree spherical simplex-radial cubature quadrature rule, from which the general computing method of the cubature points and corres-ponding weights were obtained. And then, the HDSSRCQKF was achieved under the nonlinear Kalman filtering frame-work using the above method. The numerical simulation results indicate that HDSSRCQKF has a higher accuracy com-pared to the existed high-degree cubature Kalman filter, that verifies the effectiveness of the proposed algorithm.
出处
《通信学报》
EI
CSCD
北大核心
2017年第8期111-117,共7页
Journal on Communications
基金
国家高技术研究发展计划("863"计划)基金资助项目(No.2015AA7026085)~~
