Cholesky分解在协方差矩阵恢复中的使用

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.

Cholesky Factorization for Covariance Matrix Recovery

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.