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应用科学学报 ›› 2012, Vol. 30 ›› Issue (2): 187-193.doi: 10.3969/j.issn.0255-8297.2012.02.013

• 论文 • 上一篇    下一篇

Cholesky 分解在协方差矩阵恢复中的使用

杜航原， 郝燕玲， 赵玉新， 陈立娟   

  1. 哈尔滨工程大学自动化学院，哈尔滨150001  
  • 收稿日期:2011-03-09 修回日期:2011-11-26 出版日期:2012-03-26 发布日期:2012-03-30
  • 通信作者: 杜航原，博士生，研究方向：导航制导与控制、同步定位与地图创建，E-mail: dhy6957901@126.com；
  • 作者简介:杜航原，博士生，研究方向：导航制导与控制、同步定位与地图创建，E-mail: dhy6957901@126.com；郝燕玲，教授，博导，研究方向：现代舰船组合导航技术，E-mail: haoyanling@hrbeu.edu.cn
  • 基金资助:

    国家自然科学基金(No.60904087, No.51109045)；中央高校基本科研业务费专项基金(No.HEUCF110419)资助

Cholesky Factorization for Covariance Matrix Recovery

DU Hang-yuan, HAO Yan-ling, ZHAO Yu-xin, CHEN Li-juan   

  1. College of Automation, Harbin Engineering University, Harbin 150001, China
  • Received:2011-03-09 Revised:2011-11-26 Online:2012-03-26 Published:2012-03-30

PDF

2371

被引次数

2

摘要：

针对基于稀疏扩展信息滤波的同步定位与地图创建(simultaneous localization and mapping, SLAM) 问题，分析并比较了最近邻数据关联、极大似然数据关联以及联合相容性检验数据关联的原理，阐述了边缘协方差矩阵恢复的必要性. 在此基础上提出一种利用Cholesky 分解由信息矩阵准确恢复协方差任意元素的方法，该方法具有较高的计算效率. 在仿真实验中将该方法与协方差边界估计法比较，并分别用于3 种数据关联算法的比较分析，表明所提出的方法适用于多种数据关联方法，能在保证定位精度的同时有效控制算法复杂度. 最后对各种数据关联算法在稀疏扩展信息滤波SLAM中的性能进行了讨论.

关键词: 信息滤波, 同步定位与地图创建, 数据关联, 协方差恢复, Cholesky 分解

Abstract:

 For simultaneous localization and mapping based on sparse extended information filter, we compare
the principles of nearest neighbor data association, maximum likelihood data association and joint compatibility
test data association, and discuss the requirements of marginal covariance matrix recovering in data
association. A computationally efficient approach based on Cholesky factorization is proposed to exactly recover
the marginal covariance from information matrix. In the simulation, we compare the proposed algorithm
with covariance bound approximation, and analyze three common data association approaches using the proposed
algorithm in SLAM based on a sparse extended information filter. The results show that the proposed
recovery algorithm is suitable for various data association approaches, leading to high localization accuracy
and reduced computational complexity. Performance of different data association approaches in SEIF-SLAM
are discussed.

Key words: information filter, simultaneous localization and mapping (SLAM), data association, covariance recovery, Cholesky factorization

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