Passive Localization Method Using TDOA/TDOA-AOA with Unknown Transceivers

ZHANG Shuo; SUN Ting; WANG Wei; YU Zehua; DONG Yangyang; DONG Chunxi

doi:10.12263/DZXB.20260212

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Passive Localization Method Using TDOA/TDOA-AOA with Unknown Transceivers

PAPERS | 更新时间：2026-10-16

- Passive Localization Method Using TDOA/TDOA-AOA with Unknown Transceivers
- ACTA ELECTRONICA SINICA Vol. 54, Issue 6, Pages: 2776-2789(2026)
- 作者机构：
  
  1.长安大学信息工程学院，陕西西安 710064
  2.西安电子科技大学电子工程学院，陕西西安 710071
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(62501079)
- DOI：10.12263/DZXB.20260212
  CLC： TN971.5;
- Received：05 May 2026，
  
  Accepted：02 June 2026，
  
  Published：25 June 2026
- 稿件说明：
移动端阅览
张烁, 孙霆, 王威, 等. 中继收发器未知的TDOA/TDOA-AOA无源定位算法[J]. 电子学报, 2026, 54(06): 2776-2789.

ZHANG Shuo, SUN Ting, WANG Wei, et al. Passive Localization Method Using TDOA/TDOA-AOA with Unknown Transceivers[J]. Acta Electronica Sinica, 2026, 54(06): 2776-2789.
张烁, 孙霆, 王威, 等. 中继收发器未知的TDOA/TDOA-AOA无源定位算法[J]. 电子学报, 2026, 54(06): 2776-2789. DOI：10.12263/DZXB.20260212

ZHANG Shuo, SUN Ting, WANG Wei, et al. Passive Localization Method Using TDOA/TDOA-AOA with Unknown Transceivers[J]. Acta Electronica Sinica, 2026, 54(06): 2776-2789. DOI：10.12263/DZXB.20260212

摘要

远距离目标定位在无线通信、电子侦察、目标监视及智能感知等领域具有重要的应用价值。然而，随着目标与接收站距离的增加，信号传播过程中将面临严重的路径损耗、阴影衰落及非视距效应等挑战。这些因素会显著降低接收信号质量，从而削弱传统无源定位系统的性能。利用中继收发器辅助信号放大与转发，构建视距传播路径，可以在一定程度上克服上述问题。尽管如此，现有中继辅助的定位研究多聚焦于主动或合作定位场景，且需要依赖多次获取目标-中继-接收站传播时间以实现高精度定位。在电子侦察、隐蔽目标探测等无源目标定位场景中，观测系统难以与目标进行协同交互，现有中继辅助定位方法无法直接应用。针对上述问题，本文开展中继位置未知条件下的远距离无源目标定位研究，并提出一种基于时空观测信息的目标与中继联合定位算法。首先，利用目标-同一中继-不同接收站和目标-不同中继-同一接收站这两路信号传播路径，构建两组瞬时到达时间差（Time Difference Of Arrival，TDOA）观测模型，并结合参考接收站获取的目标信号到达角（Angle Of Arrival，AOA）信息，建立角度观测模型。随后，基于TDOA观测信息分别构建中继位置和目标位置的优化问题，并利用半定松弛（Semidefinite Relaxation，SdR）技术将非凸问题转化为凸优化问题，从而获得中继与目标位置的粗略估计。由于所提算法前两步未能充分利用观测信息，第三步分别基于TDOA及联合TDOA-AOA修正估计误差以提升定位精度。此外，通过理论推导给出了仅利用TDOA信息与联合TDOA-AOA信息的克拉美罗下界（Cramér-Rao Lower Bound，CRLB），并明确了实现定位所需的节点条件。理论分析证明了在适度测量噪声或误差条件下，所提联合定位算法对于目标与中继位置估计均可实现CRLB性能。数值仿真实验进一步验证了理论分析的正确性，同时表明引入单一接收站的角度信息能够显著提升目标与中继的联合定位精度。

Abstract

Far-field object localization plays an important role in wireless communications

electronic reconnaissance

object surveillance

and intelligent sensing applications. However

as the distance between the object and receiving stations increases

severe path loss

shadow fading

and Non-Line-Of-Sight (NLOS) effects significantly degrade the received signal quality

thereby deteriorating the performance of conventional passive localization systems. To address this issue

transceiver-aided localization techniques employ transceivers to amplify and forward signals

thereby establishing line-of-sight propagation paths and improving localization performance. Nevertheless

existing transceiver-aided localization studies mainly focus on active or cooperative localization scenarios and rely on multiple measurements of the object-transceiver-receiver propagation time to achieve high localization accuracy. In passive localization applications

such as electronic reconnaissance and covert object detection

the observation system cannot interact cooperatively with the object

rendering existing transceiver-aided localization methods inapplicable. To address this challenge

this paper investigates far-field passive localization with unknown transceiver positions and proposes a joint object and transceiver localization algorithm based on spatio-temporal observations. Specifically

two instantaneous time difference of arrival (TDOA) measurement models are constructed by exploiting the signal propagation paths of object-common transceiver-different receivers and object-different transceivers-common receiver

respectively. In addition

an angle of arrival (AOA) measurement model is established using the angle information obtained at a reference receiver. Subsequently

two optimization problems corresponding to transceiver localization and object localization are formulated based on the TDOA measurements. By applying semidefinite relaxation (SdR) technique

the resulting nonconvex problems are transformed into convex optimization problems

yielding coarse estimates of both transceiver and object positions. Since the first two stages do not fully exploit the available measurements

a third-stage refinement procedure is developed based on TDOA-only and joint TDOA-AOA observations to further improve localization accuracy. Furthermore

the Cramér-Rao lower bound (CRLB) corresponding to TDOA-only and joint TDOA-AOA observations is derived

and the minimum node requirements for localization feasibility are established. Theoretical analysis demonstrates that

under moderate measurement noise and error conditions

the proposed joint localization algorithm can achieve the CRLB performance for both object and transceivers position estimation. Numerical simulation results further validate the theoretical analysis and show that incorporating AOA information from a single receiver can significantly enhance the joint localization accuracy of both the object and transceivers.

关键词

Keywords

references

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