一种联合时频差与差分多普勒变化率的运动辐射源定位新方法

王鼎; 尹洁昕; 高路; 张莉

doi:10.7527/S1000-6893.2025.31873

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DOI: https://doi.org/10.7527/S1000-6893.2025.31873

一种联合时频差与差分多普勒变化率的运动辐射源定位新方法

王鼎 ,
尹洁昕 ,
高路 ,
张莉

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1. 信息工程大学信息系统工程学院
2. 战略支援部队信息工程大学
3. 北京航天长征飞行器研究所
4. 中国人民解放军战略支援部队信息工程大学信息系统工程学院

收稿日期: 2025-02-14

修回日期: 2025-05-21

网络出版日期: 2025-05-27

基金资助

国家自然科学基金;国家自然科学基金;军委科技委高层次科技创新人才自主科研项目

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A novel method for locating moving emitter by combining time-difference-of-arrival, frequency-difference-of-arrival, and differential Doppler rate measurements

WANG Ding ,
YIN Jie-Xin ,
GAO Lu ,
ZHANG Li

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Received date: 2025-02-14

Revised date: 2025-05-21

Online published: 2025-05-27

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摘要

针对运动辐射源进行高精度定位对于目标态势感知至关重要，除了时频差观测量以外，差分多普勒变化率也可用于提升对运动辐射源的定位性能。本文提出一种联合时频差与差分多普勒变化率观测量的运动辐射源定位新方法，该方法将加权多维标度分析原理与正交投影变换相结合，无需迭代运算，可有效提高大观测误差存在条件下和观测平台状态参数受到随机扰动条件下的定位精度。所提方法包含3个计算阶段：阶段1利用时频差与差分多普勒变化率观测量构造3个标量积矩阵与3个伪逆矩阵，并进而形成定位观测方程；阶段2利用正交投影变换消除阶段1定位观测方程中非线性辅助变量的影响，由此获得定位问题的中间闭式解；阶段3利用此中间闭式解抵消辅助变量，补偿正交投影变换所带来的信息损失，与此同时再次利用全部观测信息以获得最终定位结果。此外，该文还基于Kronecker积与正交投影矩阵的数学性质证明新方法的渐近统计最优性。仿真实验结果验证所提方法相比其他相关定位方法的优越性。

关键词： 无源定位; 运动辐射源; 时频差; 差分多普勒变化率; 加权多维标度分析; 正交投影矩阵; Kronecker积

本文引用格式

王鼎 , 尹洁昕 , 高路 , 张莉 . 一种联合时频差与差分多普勒变化率的运动辐射源定位新方法[J]. 航空学报, 0 : 1 -0 . DOI: 10.7527/S1000-6893.2025.31873

Abstract

High-precision localization of moving emitters is crucial for target situation awareness. In addition to conventional time-difference-of-arrival (TDOA) and frequency-difference-of-arrival (FDOA) measurements, differential Doppler rate (DDR) measurements can also be employed to enhance the positioning performance of moving emitters. In this paper, a novel non-iterative method combining TDOA, FDOA and DDR measurements is proposed to locate a moving emitter. This method integrates the principles of weighted multidimensional scaling analysis with orthogonal projection transformation. When the measurement error is large, and the observation platform’s state parameters are subject to random perturbations, the positioning accuracy can be effectively improved. The proposed method consists of three calculation stages, namely Stage 1, Stage 2, and Stage 3. Specifically, Stage 1 constructs three scalar product matrices and corresponding pseudo-inverse matrices from TDOA, FDOA, and DDR measurements to establish the positioning observation equation. Stage 2 employs orthogonal projection transformation to eliminate the influence of nonlinear auxiliary variables in the positioning observation equation in Stage 1, generating an intermediate closed-form solution for the positioning result. Stage 3 uses this intermediate closed-form solution to eliminate auxiliary variables and compensate for the information loss induced by the orthogonal projection transformation, and at the same time, uses all measurement information again to produce the final positioning result. Furthermore, based on the properties of the Kronecker product and the orthogonal projection matrix, the asymptotic efficiency of this new estimator is demonstrated through mathematical analysis. Simulation results validate the superiority of the proposed method over other related positioning methods.

Key words： passive location; moving emitter; time-difference-of-arrival (TDOA); and frequency-difference-of-arrival (FDOA); differential Doppler rate (DDR); weighted multidimensional scaling analysis; orthogonal projection matrix; Kronecker product

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