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

Abstract

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

CLC Number:

TN 958.97

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.

Figures/Tables 8

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References 31

1	WANG G, ZHENG R C, HO K C. Elliptic localization of a moving object by transmitter at unknown position and velocity: a semidefinite relaxation approach[J]. IEEE Trans. on Mobile Computing, 2023, 22 (5): 2675- 2692. doi: 10.1109/TMC.2021.3123330
2	PEI J, WANG G, HO K C, et al. Reducing bias for multistatic localization of a moving object by transmitter at unknown position[J]. IEEE Trans. on Aerospace and Electronic Systems, 2023, 59 (5): 5324- 5341. doi: 10.1109/TAES.2023.3257277
3	YAN L J, PALLOTTA L, GIUNTA G, et al. Robust target localization for multistatic passive radar networks[J]. IEEE Sensors Letters, 2023, 7 (7): 6003604- 4.
4	KANG X, WANG D J, SHAO Y, et al. An efficient hybrid multi-station TDOA and single-station AOA localization method[J]. IEEE Trans. on Wireless Communications, 2023, 22 (8): 5657- 5670. doi: 10.1109/TWC.2023.3235753
5	MAO Z, SU H T, SONG J K, et al. Joint target and transmitter localization with AOA and DTD using passive sensors[J]. IEEE Signal Processing Letters, 2024, 31, 1570- 1574. doi: 10.1109/LSP.2024.3408674
6	LI Q, CHEN B X, YANG M L. Improved two-step constrained total least-squares TDOA localization algorithm based on the alternating direction method of multipliers[J]. IEEE Sensors Journal, 2020, 20 (22): 13666- 13673. doi: 10.1109/JSEN.2020.3004235
7	WU W J, WANG G, HO K C. Multistatic localization by differential time delays and time differences of arrival in the absence of transmitter position[J]. IEEE Trans. on Aerospace and Electronic Systems, 2023, 59 (5): 7020- 7034. doi: 10.1109/taes.2023.3287814
8	WU L H, ZOU Y B, FAN J N. A simple and effective iterative algorithm for elliptic localization[J]. IEEE Sensors Letters, 2022, 6 (10): 7003604. doi: 10.1109/lsens.2022.3205711
9	XIAO Y D, WANG G, HO K C. Exact solution for elliptic localization with imperfect clock synchronization[C]//Proc. of the IEEE 12th Sensor Array and Multichannel Signal Processing Workshop, 2022: 96−100.
10	YANG H S, CHUN J H, CHAE D Y. Hyperbolic localization in MIMO radar systems[J]. IEEE Antennas and Wireless Propagation Letters, 2014, 14, 618- 621.
11	SHEN J Y, MOLISCH A F, SALMI J. Accurate passive location estimation using TOA measurements[J]. IEEE Trans. on Wireless Communications, 2012, 11 (6): 2182- 2192. doi: 10.1109/TWC.2012.040412.110697
12	WANG Y, MA S D, CHEN C L P. TOA-based passive localization in quasi-synchronous networks[J]. IEEE Communications Letters, 2014, 18 (4): 592- 595. doi: 10.1109/LCOMM.2014.021214.132662
13	邓杏松, 亓亮, 朱元江. 基于观测站精确距离信息的多站时差定位方法[J]. 系统工程与电子技术, 2024, 46 (8): 2592- 2599. doi: 10.12305/j.issn.1001-506X.2024.08.07
	DENG X S, QI L, ZHU Y J. Positioning method using time difference measurements from multi-station based on precise distance information of observation stations[J]. Systems Engineering and Electronics, 2024, 46 (8): 2592- 2599. doi: 10.12305/j.issn.1001-506X.2024.08.07
14	ZHANG S K, JIANG H J, YANG K H. Detection and localization for an unknown emitter using TDOA measurements and sparsity of received signals in a synchronized wireless sensor network[C]//Proc. of the IEEE International Conference on Acoustics, Speech and Signal Processing, 2013: 5146−5149.
15	PANWAR K, BABU P. Multistatic target localization in absence of transmitter position using differential time delay measurements[J]. IEEE Trans. on Radar Systems, 2024, 2, 41- 46. doi: 10.1109/TRS.2023.3346931
16	黄东华, 赵勇胜, 赵拥军. 发射站/接收站位置误差下无源雷达DOA-TDOA目标定位算法[J]. 系统工程与电子技术, 2020, 42 (9): 1961- 1968. doi: 10.3969/j.issn.1001-506X.2020.09.11
	HUANG D H, ZHAO Y S, ZHAO Y J. Target localization algorithm from DOA-TDOA measurements in passive radar with transmitter and receiver position errors[J]. Systems Engineering and Electronics, 2020, 42 (9): 1961- 1968. doi: 10.3969/j.issn.1001-506X.2020.09.11
17	XIAO Y D, WANG G, HO K C. Elliptic localization with imperfect clock synchronization for known and unknown propagation speed scenarios[J]. IEEE Trans. on Aerospace and Electronic Systems, 2023, 59 (2): 1468- 1481.
18	KE X C, HO K C. Localization of a passive object in 3-D by propagation time delays to a rigid body receiver of unknown location[J]. IEEE Trans. on Signal Processing, 2024, 72, 3470- 3486. doi: 10.1109/TSP.2024.3398195
19	ZHANG Y, HO K C. Multistatic localization in partially dynamic scenario with only sensor positions available[J]. IEEE Trans. on Aerospace and Electronic Systems, 2021, 57 (5): 3416- 3432. doi: 10.1109/TAES.2021.3098164
20	MAO Z, SU H T, SHEN L, et al. Main-lobe beamwidth constrained target localization using bistatic range measurements[J]. IEEE Trans. on Signal Processing, 2024, 72, 289- 304. doi: 10.1109/TSP.2023.3344362
21	NOROOZI A, SEBT M A. Target localization from bistatic range measurements in multi-transmitter multi-receiver passive radar[J]. IEEE Signal Processing Letters, 2015, 22 (12): 2445- 2449. doi: 10.1109/LSP.2015.2491961
22	AMIRI R, BEHNIA F, ZAMANI H. Asymptotically efficient target localization from bistatic range measurements in distributed MIMO radars[J]. IEEE Signal Processing Letters, 2017, 24 (3): 299- 303. doi: 10.1109/LSP.2017.2660545
23	VARSHNEY P, BABU P, STOICA P. Outlier-robust multistatic target localization[J]. IEEE Signal Processing Letters, 2025, 32, 1161- 1165. doi: 10.1109/LSP.2025.3547859
24	ZOU Y B, XIAO Y P, ZHANG W E. A simple and efficient method for hybrid AOA and DTD localization with unknown transmitter location[J]. IEEE Signal Processing Letters, 2025, 32, 401- 405. doi: 10.1109/LSP.2024.3521317
25	LIN D Y, WANG G, WANG D. Penalized semidefinite programming method for elliptic localization[C]//Proc. of the 5th International Conference on Information Communication and Signal Processing , 2022: 108−112.
26	ZHANG Y, HO K C. Multistatic localization in the absence of transmitter position[J]. IEEE Trans. on Signal Processing, 2019, 67 (18): 4745- 4760. doi: 10.1109/TSP.2019.2929960
27	ZHANG Y, HO K C. Multistatic moving object localization by a moving transmitter of unknown location and offset[J]. IEEE Trans. on Signal Processing, 2020, 68, 4438- 4453. doi: 10.1109/TSP.2020.3008752
28	ZHAO W S, DUAN X T, TIAN D X, et al. An SDP-based TDOA localization method for wireless sensor networks[C]//Proc. of the International Conference on Control, Automation and Information Sciences, 2021: 381−386.
29	ZHENG R C, WANG G, HO K C. Accurate semidefinite relaxation method for elliptic localization with unknown transmitter position[J]. IEEE Trans. on Wireless Communications, 2021, 20 (4): 2746- 2760. doi: 10.1109/TWC.2020.3044217
30	LI Y F, WANG G. Multistatic localization with unknown transmitter position and signal propagation speed[J]. IEEE Signal Processing Letters, 2022, 29, 1427- 1431. doi: 10.1109/LSP.2022.3183499
31	袁亚湘, 孙文瑜. 最优化理论与方法[M]. 北京: 科学出版社, 1997: 94−95.
	YUAN Y X, SUN W Y. Optimization theory and methods[M]. Beijing: Science Press, 1997: 94−95.

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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TSCWLS method for multistatic passive localization with unknown transmitter position

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