一种多维尺度分析到达时间差定位算法  

A Multi-dimensional Scaling-based TDOA Localization Algorithm

作　　者：王琳[1] 蒋武扬[1] 徐昌庆[1] 

机构地区：[1]上海交通大学上海市北斗导航与位置服务重点实验室,上海200240

出　　处：《导航定位学报》2014年第4期58-62,73,共6页Journal of Navigation and Positioning

基　　金：中国卫星导航系统管理办公室(北斗办)和上海市科学技术委员会的联合资助;资助课题编号为BDZX005

摘　　要：基于多维尺度分析的到达时间差定位算法是一种新型而高效的到达时间差定位算法,它通过多维尺度分析,将到达时间差定位问题建模为矩阵范数的最优化问题,然后通过子空间分析将该最优化问题转化为线性方程求解问题。指出该算法在推导过程中的一处疏漏,即在转化为线性方程求解问题过程中,并不能通过标量积矩阵的正定性得到目标线性方程,因为标量积矩阵并非正定。针对二维定位的情形给出一种严格的证明。该证明针对位置坐标矩阵列向量的线性相关性进行分类,当该矩阵的列向量线性无关时,目标线性方程成立;而当该矩阵的列向量线性相关时,通过分析该矩阵的列秩和行秩,可以得出参考点和目标点所必须满足的几何排布条件,并验证在该条件下目标线性方程仍然成立。The multi-dimensional scaling （MDS） -based TDOA algorithm is a new and efficient TDOA localization algorithm. The basic idea is to model the TDOA localization problem into a problem of optimizing the norm of a special matrix, which is then transformed into a set of linear equations by subspace analysis. In this paper, an omission in the derivation process of the original algorithm is pointed out, i.e. , during the process of transforming the matrix norm optimization problem into the linear equations, the objective linear equations should not be derived by the positive definiteness of the scalar product matrix, because the scalar product matrix is not positive definite. This paper presents a rigorous proof in the two- dimensional. In the case when the column vectors of the position coordinates matrix are linearly independent, the objective linear equations hold. In the case when the above column vectors are linearly dependent, by analyzing the column rank and the row rank of the matrix, the necessary condition on the geometric arrangement of the reference points and the target point is obtained, under which the objective linear equations still hold. By this way, the correctness of the MDS algorithm is confirmed.

关 键 词：到达时间差 多维尺度分析 二维 几何排布 

分 类 号：TN96[电子电信—信号与信息处理]