发射站位置未知下多基外辐射源TSCWLS定位算法

doi:10.12305/j.issn.1001-506X.2026.04.04

摘要/Abstract

摘要：

针对发射站位置未知的多基外辐射源定位问题，提出一种两步约束加权最小二乘（two-stage constrained weighted least squares, TSCWLS）算法，实现发射站位置和目标位置的解耦估计。在第一步，仅利用直接距离（direct range, DR）量测与发射站位置的二次等式约束，建立一个约束加权最小二乘（constrained weighted least squares，CWLS）模型估计发射站的位置。第二步，将DR定位方程的代数特征引入至双基地距离量测，联合构建关于目标的CWLS新模型，并采用牛顿法对目标位置进行迭代求解。最后推导了算法的理论误差。仿真结果表明，该定位算法对于两步加权最小二乘方法和半定规划方法的定位精度更高，且适用于较少数目的观测站场景。

关键词: 多基外辐射源定位, 发射站位置未知, 约束加权最小二乘, 双基地距离, 牛顿法

Abstract:

This article addresses the multistatic passive localization problem when the transmitter position is unknown. A two-stage constrained weighted least squares （TSCWLS） algorithm is proposed to achieve decoupled estimation of the target and transmitter positions. In the first stage, a constrained weighted least squares （CWLS） minimization problem with quadratic equality constraints is formulated to estimate the transmitter position using the direct range （DR） measurements between the transmitter and the receivers. In the second stage, the algebraic characteristics of the DR equation is introduced into the bistatic range measurements. Which are jointly used to construct a new CWLS problem to estimate the target. It is solved iteratively using the Newton Method. The simulation results show that the proposed algorithm has higher localization accuracy compared with the two-step weighted least squares and the semi-definite program method. It is suitable for the scenarios with fewer receivers.

Key words: multistatic passive localization, unknown transmitter position, constrained weighted least squares （CWLS）, bistatic range, Newton method

中图分类号:

TN 958.97

林庆宝, 左燕, 彭冬亮. 发射站位置未知下多基外辐射源TSCWLS定位算法[J]. 系统工程与电子技术, 2026, 48(4): 1137-1144.

Qingbao LIN, Yan ZUO, Dongliang PENG. TSCWLS method for multistatic passive localization with unknown transmitter position[J]. Systems Engineering and Electronics, 2026, 48(4): 1137-1144.

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运算单元	复杂度
$ {\boldsymbol{A}}_{1} $	$ 4M $
$ {\boldsymbol{b}}_{1} $	$ M $
$ {\boldsymbol{W}}_{1} $	$ 4M+15{M}^{3} $
$ \boldsymbol{H}_{1}^{-1}{\boldsymbol{g}}_{1} $	$ 24M+3{M}^{2} $
$ {\boldsymbol{t}}_{0} $	$ 36M $
$ {\boldsymbol{A}}_{2} $	$ 4M $
$ {\boldsymbol{b}}_{2} $	$ 2M $
$ {\boldsymbol{W}}_{2} $	$ 32M+48{M}^{2}+54{M}^{3} $
$ \boldsymbol{H}_{2}^{-1}{\boldsymbol{g}}_{2} $	$ 48M+12{M}^{2} $
$ {\boldsymbol{u}}_{0} $	$ 72M $

算法	复杂度
所提TSCWLS算法	$ O(335M+126{M}^{2}+138{M}^{3}) $
文[26]TSWLS算法	$ O(712M+144{M}^{2}+108{M}^{3}) $
文[29]SDP算法	$ O(22\;072\cdot \ln (1/\delta )+468M+96{M}^{2}+108{M}^{3}) $

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