Unified Model for Near and Far Field Localization: Subspace-Based Solution and Limitations Analysis

SUN Yi-mao; XU Yi-huai; TANG Bei-chuan; YANG Yan-bing; CHEN Liang-yin

doi:10.12263/DZXB.20230184

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Unified Model for Near and Far Field Localization: Subspace-Based Solution and Limitations Analysis

PAPERS | 更新时间：2025-12-08

- Unified Model for Near and Far Field Localization: Subspace-Based Solution and Limitations Analysis
- ACTA ELECTRONICA SINICA Vol. 51, Issue 8, Pages: 2134-2143(2023)
- 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：
- 基金信息：
  
  National Natural Science Foundation of China(62101359;62272329)
- DOI：10.12263/DZXB.20230184
  CLC： TN953.7
- Received：02 March 2023，
  
  Revised：2023-07-12，
  
  Published：25 August 2023
- 稿件说明：
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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

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