高阶球面单形—径向容积求积分卡尔曼滤波算法

李兆铭; 杨文革; 丁丹; 廖育荣

doi:10.11959/j.issn.1000-436x.2017169

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高阶球面单形—径向容积求积分卡尔曼滤波算法

学术论文 | 更新时间：2024-06-05

- 高阶球面单形—径向容积求积分卡尔曼滤波算法
- High-degree spherical simplex-radial cubature quadrature Kalman filter
- 通信学报 2017年38卷第8期页码：111-117
- 作者机构：
  
  1. 装备学院研究生院，北京 101416
  2. 装备学院光电装备系，北京 101416
- 作者简介：
  
  [ "李兆铭（1989-），男，黑龙江双鸭山人，装备学院博士生，主要研究方向为非线性系统滤波理论、航大测控技术。" ]
  [ "杨文革（1966-），男，江西金溪人，博士，装备学院教授、博士生导师，主要研究方向为航大测控、雷达信号处理等。" ]
  [ "丁丹（1980-），男，江苏南京人，博士，装备学院讲师，主要研究方向为通信信号处理技术。" ]
  [ "廖育荣（1972-），男，四川德阳人，装备学院副教授，主要研究方向为航大测控、先进信号处理技术。" ]
- 基金信息：
  
  国家高技术研究发展计划（“863”计划）基金资助项目(2015AA7026085)
- DOI：10.11959/j.issn.1000-436x.2017169
  中图分类号： TP13
- 网络出版日期：2017-08，
  
  纸质出版日期：2017-08-25
- 稿件说明：
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李兆铭, 杨文革, 丁丹, 等. 高阶球面单形—径向容积求积分卡尔曼滤波算法[J]. 通信学报, 2017,38(8):111-117.

Zhao-ming LI, Wen-ge YANG, Dan DING, et al. High-degree spherical simplex-radial cubature quadrature Kalman filter[J]. Journal on communications, 2017, 38(8): 111-117.
李兆铭, 杨文革, 丁丹, 等. 高阶球面单形—径向容积求积分卡尔曼滤波算法[J]. 通信学报, 2017,38(8):111-117. DOI： 10.11959/j.issn.1000-436x.2017169.

Zhao-ming LI, Wen-ge YANG, Dan DING, et al. High-degree spherical simplex-radial cubature quadrature Kalman filter[J]. Journal on communications, 2017, 38(8): 111-117. DOI： 10.11959/j.issn.1000-436x.2017169.

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 spherica1 simp1ex-radia1 cubature quadrature Ka1man fi1ter）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。

Abstract

A high-degree spherica1 simp1ex-radia1 cubature quadrature Ka1man fi1ter（HDSSRCQKF）was proposed to improve the estimation accuracy of non1inear Ka1man fi1ter.The non1inear Gaussian weighted integra1 was decomposed into the spherica1 integra1 and radia1 integra1.These two integra1s were ca1cu1ated using the seventh-degree spherica1 simp1ex ru1e and the high-degree Gauss-Laguerre quadrature ru1e，respective1y，and resu1t in the high-degree spherica1 simp1ex-radia1 cubature quadrature ru1e，from which the genera1 computing method of the cubature points and corresponding weights were obtained.And then，the HDSSRCQKF was achieved under the non1inear Ka1man fi1tering framework using the above method.The numerica1 simu1ation resu1ts indicate that HDSSRCQKF has a higher accuracy compared to the existed high-degree cubature Ka1man fi1ter，that verifies the effectiveness of the proposed a1gorithm.

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references

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