基于改进最小二乘算法的TDOA/AOA定位方法  

Improved least-squares algorithm for TDOA/AOA-based localization

作　　者：闫雷兵[1,2] 陆音[1] 张业荣[1] 

机构地区：[1]南京邮电大学电子科学与工程学院,南京210003 [2]河南科技学院,新乡453003

出　　处：《电波科学学报》2016年第2期394-400,共7页Chinese Journal of Radio Science

基　　金：国家自然科学基金(No.61271236)

摘　　要：针对现有的两步加权最小二乘(Two-stage Weighted Least Squares,TSWLS)和约束加权最小二乘(Constrained Weighted Least Squares,CWLS)在TDOA/AOA混合定位中可能产生测量矩阵奇异的情况,提出了一种改进的CWLS算法来消除奇异矩阵求逆运算.其主要思想是在约束条件下,用含有移动台位置坐标的价值函数对移动台坐标和附加变量分别取偏微分,分离出引入的附加变量,使移动台位置坐标与附加变量分别位于线性方程的两边,求解关于附加变量的一元二次方程,因此避免了对奇异矩阵求逆的运算.在零均值的高斯白噪声环境下,且移动台位于或接近监测基站阵列中心时,通过MATLAB仿真验证了改进的CWLS算法比TSWLS和CWLS算法均能取得更高的定位精度,可以达到克拉美-罗下界(CramérRao Lower Bound,CRLB).The two-stage weighted least squares （TSWLS） and constrained weighted least squares （CWLS） are used to locate mobile station with TDOA/AOA hybrid model, and they both have the same measurement matrix that become ill-conditioned when base-station present circular array distribution and Mobile-Station is close to the array center. An improved constrained weighted least square algorithm is proposed to circumvent this problem. The main strategy is to separate the mobile station coordinates and the additional variable to different sides of the linear equations, the additional variable is first solved via a quadratic equation in order to avoid the inverse operation of ill-conditioned matrix. Under the zero mean Gaussian white noise environment and the mobile station is located in or near the array center, the simula- tion results evaluate its localization accuracy by comparing with the existing TSWLS and CWLS algorithms as well as the Cram4r-Rao lower bound.

关 键 词：加权最小二乘 约束优化 到达时间差 到达角 

分 类 号：TN929.53[电子电信—通信与信息系统]