校正源存在下抑制部分同步时钟偏差和传感器位置误差的时差定位闭式解

doi:10.7527/S1000-6893.2022.28057

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校正源存在下抑制部分同步时钟偏差和传感器位置误差的时差定位闭式解

王鼎¹,高卫港¹,聂福全²,吴志东³

1. 战略支援部队信息工程大学信息系统工程学院
2. 卫华集团有限公司
3. 解放军信息工程大学信息系统工程学院

收稿日期:2022-09-27 修回日期:2023-01-13 出版日期:2023-01-18 发布日期:2023-01-18
通讯作者: 高卫港
基金资助:
国家自然科学基金;国家自然科学基金

A closed-form solution for TDOA source localization with calibration emitter in the presence of partial synchronization clock biases and sensor location uncertainties

Received:2022-09-27 Revised:2023-01-13 Online:2023-01-18 Published:2023-01-18

摘要/Abstract

摘要： 同步时钟偏差和传感器位置先验观测误差是影响时差（TDOA—Time Difference of Arrival）定位精度重要因素。本文针对部分同步模型，提出一种协同校正源观测信息的TDOA定位新方法，旨在显著抑制两类模型误差影响。针对TDOA观测模型的强非线性特征，文中提出一种两阶段（称为阶段A和阶段B）闭式定位方法，可实现对各类参数解耦合估计，并且避免迭代运算。具体而言，阶段A仅利用校正源观测，其基于线性消元思想，利用贝叶斯（Bayesian）估计和加权最小二乘（WLS—Weighted Least Squares）估计，分步获得传感器位置和同步时钟偏差闭式解。阶段B则联合目标源观测与阶段A估计结果，推导新的伪线性观测方程，并利用WLS估计和拉格朗日乘子法获得目标源位置闭式解，随后基于Bayesian估计得到更精确的同步时钟偏差和传感器位置联合闭式解。此外，该文还推导相关克拉美罗界（CRB—Cramér–Rao Bound），并通过数学分析证明新方法具有渐近统计最优性。仿真实验验证文中理论分析有效性和新方法优越性。

关键词: 目标源定位, 时差（TDOA）, 同步时钟偏差, 传感器位置误差, 校正源, 闭式解, 理论性能分析

Abstract: It is known that the synchronization clock biases and sensor location uncertainties can significantly degrade the target localization accuracy based on time difference of arrival (TDOA) measurements. In order to effectively restrain the influence of the two model errors, this paper proposes a new TDOA target localization method using calibration emitter for the partially synchronous model. Aiming at the highly nonlinear characteristic of the TDOA measurement model, a closed-form positioning method based on two stages (called stage-A and stage-B) is proposed, which can achieve the decoupling estimation of the unknowns and avoid iterative operation. Specifically, stage-A only uses the TDOA measurements from the calibration emitter and exploits the idea of linear elimination. The closed-form solutions for the sensor position and synchronization clock bias are obtained sequentially by utilizing the linear Bayesian estimator and weighted least squares (WLS) estimator, respectively. In stage-B, the TDOA measurements from the target are combined with the estimation results obtained in stage-A, and a set of new pseudo-linear observation equations is derived. Afterwards, the closed-form solution for the target location is produced by using the WLS estimator and Lagrange multiplier method. Finally, a more accurate joint closed-form solution for sensor position and synchronization clock bias is given based on the linear Bayesian estimator. Additionally, the relevant Cramér-Rao bound (CRB) is derived, and the asymptotic optimality of the proposed estimator is proved by mathematical analysis. Simulation results corroborate the validity of the theoretical development and illustrate the superiority of the new method.

Key words: target localization, time difference of arrival (TDOA), synchronization clock bias, sensor location error, calibration emitter, closed-form solution, theoretical performance analysis

王鼎高卫港聂福全吴志东. 校正源存在下抑制部分同步时钟偏差和传感器位置误差的时差定位闭式解[J]. 航空学报, doi: 10.7527/S1000-6893.2022.28057.

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E-mail：hkxb@buaa.edu.cn

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校正源存在下抑制部分同步时钟偏差和传感器位置误差的时差定位闭式解

A closed-form solution for TDOA source localization with calibration emitter in the presence of partial synchronization clock biases and sensor location uncertainties

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