近远场统一定位模型：基于子空间的方法与局限性分析
Unified Model for Near and Far Field Localization: Subspace-Based Solution and Limitations Analysis
- 电子学报 2023年51卷第8期 页码：2134-2143
- 作者机构：
1.四川大学计算机学院，四川成都 610065
2.四川大学工业互联网研究院，四川成都 610065
- 作者简介：
[ "孙奕髦 男，1990年9月出生于四川省德阳市.2019年毕业于电子科技大学信息与通信工程学院.现为四川大学计算机学院特聘副研究员、硕士生导师.从事无线传感网、目标定位、参数估计等方面的研究.中国电子学会会员：E190016838M. E-mail: yimaosun@scu.edu.cn" ]
[ "徐屹淮 男，2000年7月生于四川省阿坝藏族羌族自治州.现为四川大学计算机学院硕士研究生.主要研究方向为可见光定位、室内定位技术. E-mail: yihuaixu@stu.scu.edu.cn" ]
[ "唐北川 男，2001年3月出生于四川省南充市.现为四川大学计算机学院硕士研究生.主要研究方向为参数估计、定位技术. E-mail: tbc@stu.scu.edu.cn" ]
[ "杨彦兵 男，1987年3月出生于四川省绵阳市.2010年6月和2013年6月于电子科技大学分别获得工业工程学士和电子与通信工程硕士学位，2017年12月获新加坡南洋理工大学计算机科学与工程博士学位.现为四川大学副研究员、博士生导师，物联网工程系副主任.从事智能感知与通信、通信感知一体化、物联网、嵌入式人工智能方面的研究工作.中国电子学会会员：E190025922M. E-mail: yangyanbing@scu.edu.cn" ]
[ "陈良银 男，1968年3月出生于重庆市.2008年于四川大学计算机学院取得博士学位.现为四川大学计算机学院教授.从事物联网系统及安全、工业互联网、智能识别、大数据分析、区块链、传感网方面的研究工作. E-mail: chenliangyin@scu.edu.cn" ]
- 基金信息：国家自然科学基金(62101359;62272329)
DOI：10.12263/DZXB.20230184
中图分类号： TN953.7收稿：2023-03-02，
修回：2023-07-12，
纸质出版：2023-08-25
- 稿件说明：
移动端阅览
孙奕髦,徐屹淮,唐北川等.近远场统一定位模型：基于子空间的方法与局限性分析[J].电子学报,2023,51(08):2134-2143.
SUN Yi-mao,XU Yi-huai,TANG Bei-chuan,et al.Unified Model for Near and Far Field Localization: Subspace-Based Solution and Limitations Analysis[J].ACTA ELECTRONICA SINICA,2023,51(08):2134-2143.
孙奕髦,徐屹淮,唐北川等.近远场统一定位模型：基于子空间的方法与局限性分析[J].电子学报,2023,51(08):2134-2143. DOI： 10.12263/DZXB.20230184.
SUN Yi-mao,XU Yi-huai,TANG Bei-chuan,et al.Unified Model for Near and Far Field Localization: Subspace-Based Solution and Limitations Analysis[J].ACTA ELECTRONICA SINICA,2023,51(08):2134-2143. DOI： 10.12263/DZXB.20230184.
摘要
修正极坐标表示（Modified Polar Representation，MPR）实现了近场定位与远场测向模型的统一表达，克服了定位或测向对目标距离先验信息的依赖，巧妙地规避了传统坐标系下因远场距离模糊及距离-角度相互耦合导致的定位精度下降.然而现有MPR定位方法存在性能和稳健性不足、边界条件不清晰等问题，无法满足工程应用的实际需求.本文从子空间的角度着手以求解MPR下的时差（Time Difference Of Arrival，TDOA）定位问题，将角度和逆距离的估计分离到两个正交的空间，从而提高算法性能和稳健性.首先利用零空间投影消除逆距离以求解角度的最优估计，然后再代回原方程求解逆距离.在求解逆距离估计时，考虑角度估计误差使得矩阵出现秩亏，可通过向矩阵非零特征值对应的子空间投影解决秩亏的问题，再由加权最小二乘直接求得逆距离的最优估计.与现有研究中最优闭式解广义信赖域子问题（Generalized Trust Region Sub-problem，GTRS）相比，分析和仿真实验都证实所提算法具有更好的性能和大噪声场景下的稳健性.本文还分析了包括所提算法在内的现有基于MPR的TDOA定位算法的局限性，明确了不同算法对最小传感器数量和适用场景的的要求，为工程中算法的选择提供参考.
Abstract
The modified polar representation (MPR) achieves a unified expression of near-field localization and far-field direction-finding models
overcoming the dependency on prior information of source range for either localization or direction-finding. It cleverly avoids the loss in localization accuracy caused by the range ambiguity and the coupling between range and angle in far field. However
existing MPR localization methods suffer from insufficient performance and robustness
as well as unclear boundary conditions
making them unable to satisfy the requirements of practical engineering applications. This paper addresses the time difference of arrival (TDOA) localization problem in MPR from the perspective of subspaces
separating the estimation of angles and inverse-range into two orthogonal spaces to enhance performance and robustness. We first employ nullspace projection to eliminate inverse-range and obtain the optimal estimation of angles
and then put the result back into the original equation to solve for inverse-range. When solving the inverse range
the matrix is rank-deficient due to the consideration of angle estimation errors. This problem is resolved by projecting the equations onto the subspace corresponding to the non-zero eigenvalues
so the optimal estimation of inverse-range is obtained straightforwardly through weighted least squares. Analysis and simulation experiments demonstrate that the proposed algorithm outperforms the existing best closed-form solution
generalized trust region sub-problem (GTRS)
in terms of performance and robustness in high-noise scenarios. This article also analyzes the limitations of existing TDOA localization algorithms based on MPR
including the proposed algorithm. It clarifies the requirements of different algorithms concerning the minimum number of sensors and applicable scenarios
providing references for algorithm selection in engineering applications.
关键词
Keywords
references
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