复数多维标度移动定位算法

Complex Multidimensional Scaling Analysis of Mobile Localization

基于多维标度(Multidimensional scaling,MDS)的定位算法,利用移动站与多个基站两两节点间距离的相关性对移动站进行定位,其高稳健性近年来已被证实。但是其性能有限,即使在测量噪声很小的情况下MDS算法也无法达到克拉美罗下界。本文提出了一种新颖的基于到达时间(Time of arrival,TOA)定位方法的复数MDS方法。不同于经典多维标度算法,这种算法并不需要对标度生成矩阵进行奇异值分解,而是对本文定义的一个复数距离矩阵进行奇异值分解获得更多信息从而得到更好的性能。本文对该算法进行了计算机仿真,并与另外几种定位方法做出比较。

Multidimensional scaling （MDS） algorithms have been verified to be robust for the mobile localization. However, they have not attained Cramer-Rao lower bound （CRLB）, even though the measurement noise is small. A novel complex method is proposed for time-of-arrival （TOA） based mobile location. Unlike the existing MDS algorithms depending on the eigen decomposition of the scalar product matrix, the proposed method relies on the complex matrix and contains more information. A complex distance matrix using eigenvalue factorization is decomposed and better performance is obtained. Computer simulations are included to contrast the estimator performance with several kinds of position methods.