基于多目标空域规律约束的卫星与短波信号协同直接定位方法

doi:10.12305/j.issn.1001-506X.2026.07.03

系统工程与电子技术 ›› 2026, Vol. 48 ›› Issue (7): 2153-2163.doi: 10.12305/j.issn.1001-506X.2026.07.03

• 电子技术 • 上一篇

基于多目标空域规律约束的卫星与短波信号协同直接定位方法

余天歌¹(), 尹洁昕¹(), 王鼎¹(), 聂福全²()

1. 信息工程大学信息系统工程学院，河南郑州 450000
2. 河南科技学院，河南新乡 453000

收稿日期:2025-06-24 修回日期:2025-11-10 接受日期:2025-12-04 出版日期:2026-01-26 发布日期:2026-01-26
通讯作者: 尹洁昕 E-mail:ytg0520@163.com;Cindyin0807@163.com;wang_ding814@aliyun.com;nfq@hist.edu.cn
基金资助:
国家自然科学基金（61901526，62171469，62071029）；中国科协青年人才托举工程（2022-JCJQ-QT-028）；河南省优秀青年科学基金（242300421174）资助课题

Cooperative direct position determination method for satellite and shortwave signals based on multi-target spatial domain law constraints

Tiange YU¹(), Jiexin YIN¹(), Ding WANG¹(), Fuquan NIE²()

1. School of Information Systems Engineering，University of Information Engineering，Zhengzhou 450000，China
2. Henan Institute of Science and Technology，Xinxiang 453000，China

Received:2025-06-24 Revised:2025-11-10 Accepted:2025-12-04 Online:2026-01-26 Published:2026-01-26
Contact: Jiexin YIN E-mail:ytg0520@163.com;Cindyin0807@163.com;wang_ding814@aliyun.com;nfq@hist.edu.cn

摘要/Abstract

摘要：

针对多个能够同时发射短波信号和卫星信号的辐射源定位场景，提出一种基于多目标空域规律约束的卫星与短波信号协同直接定位方法。首先，根据短波方位角关于多个短波观测站与辐射源地理坐标之间的几何关系、卫星时差关于多颗卫星与卫星地面站及辐射源地理坐标之间的几何关系，建立联合短波和卫星观测信号的定位模型；然后，根据多个待定位辐射源之间存在的距离约束规律建立不等式方程组，构造带约束的最大似然估计优化模型；最后，利用拉格朗日乘子法将含约束的优化模型转换为无约束优化模型，并利用梯度下降法进行数值求解，用于获得多个辐射源地理坐标的估计值。仿真结果表明，该定位方法对多个远距离目标相比于短波交汇定位方法、卫星时差直接定位方法与基于定位结果的线性融合方法的定位精度更高，且在低信噪比条件下优势更为显著。

关键词: 直接定位, 短波信号, 卫星信号, 多辐射源, 距离约束规律

Abstract:

Aiming at multiple radiation sources position scenarios that can emit shortwave and satellite signals simultaneously, a cooperative direct position determination method for satellite and shortwave signals based on multi-target spatial domain law constraints is proposed. Firstly, a joint shortwave and satellite observation signal positioning model is established based on the shortwave azimuth angle with respect to the geometrical relationship between the geographical coordinates of multiple shortwave observation stations and the radiation sources, and the satellite time difference with respect to the geometrical relationship between the geographical coordinates of multiple satellites, the satellite ground station and the radiation sources. Then, an inequality equation system is established to construct a constrained maximum likelihood estimation optimization model based on the distance constraint law existing between multiple radiation sources to be positioned. Finally, The Lagrange multiplier method is used to convert the constrained optimization model into the unconstrained optimization model, and the gradient descent method is used for numerical solution, which is used to estimate the geographical coordinates of multiple radiation sources. The simulation results show that this positioning method has higher localization accuracy for multiple long-distance targets compared with the shortwave intersection positioning method, the satellite time difference direct positioning method and the linear fusion positioning method, and the advantage is more significant in the condition of low signal-to-noise ratio.

Key words: direct position, shortwave signal, satellite signal, multiple radiation source, distance constraint law

中图分类号:

TN 911.7

余天歌, 尹洁昕, 王鼎, 聂福全. 基于多目标空域规律约束的卫星与短波信号协同直接定位方法[J]. 系统工程与电子技术, 2026, 48(7): 2153-2163.

Tiange YU, Jiexin YIN, Ding WANG, Fuquan NIE. Cooperative direct position determination method for satellite and shortwave signals based on multi-target spatial domain law constraints[J]. Systems Engineering and Electronics, 2026, 48(7): 2153-2163.

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参数类型	取值
拉格朗日乘子初始值$ {{\boldsymbol{\lambda}} ^{(0)}} $	2
惩罚系数$ {\boldsymbol{\rho}} $	10
迭代步长因子$ {\boldsymbol{\mu}} $	0.9
2个目标定位场景的距离约束/km	48.41
3个目标定位场景的距离约束/km	66.46

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基于多目标空域规律约束的卫星与短波信号协同直接定位方法

Cooperative direct position determination method for satellite and shortwave signals based on multi-target spatial domain law constraints

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