基于循环匹配追踪的非圆信号多径时延估计算法

doi:10.12305/j.issn.1001-506X.2026.09.03

系统工程与电子技术 ›› 2026, Vol. 48 ›› Issue (9): 2907-2916.doi: 10.12305/j.issn.1001-506X.2026.09.03

• 电子技术 • 上一篇

基于循环匹配追踪的非圆信号多径时延估计算法

王泽宇¹(), 王鼎¹^,²(), 陈晓云¹(), 张莉¹()

1. 网络空间部队信息工程大学信息系统工程学院，河南郑州 450001
2. 国家数字交换系统工程技术研究中心，河南郑州 450001

收稿日期:2025-08-28 修回日期:2025-12-10 接受日期:2026-01-26 出版日期:2026-04-24 发布日期:2026-04-24
通讯作者: 王鼎 E-mail:wwwzy181@163.com;wang_ding814@aliyun.com;450076746@qq.com;neyoul@163.com
作者简介:王泽宇（2000—），男，硕士研究生，主要研究方向为参数估计、无源定位
陈晓云（1987—），女，硕士研究生，主要研究方向为阵列信号处理、无源定位
张　莉（1975—），女，教授，博士，主要研究方向为阵列信号处理、无源定位
基金资助:
国家自然科学基金(62171469，62071029)；科技委高层次科技创新人才自主科研项目(A8124)资助课题

Multipath time delay estimation algorithm based on noncircular signal cyclic matching pursuit

Zeyu Wang¹(), Ding Wang¹^,²(), Xiaoyun Chen¹(), Li Zhang¹()

1. School of Information System Engineering，Cyberspace Force Information Engineering University，Zhengzhou 450001，China
2. National Digital Switching System Engineering and Technology Research Center，Zhengzhou 450001，China

Received:2025-08-28 Revised:2025-12-10 Accepted:2026-01-26 Online:2026-04-24 Published:2026-04-24
Contact: Ding Wang E-mail:wwwzy181@163.com;wang_ding814@aliyun.com;450076746@qq.com;neyoul@163.com

摘要/Abstract

摘要：

针对传统时延估计方法在低信噪比和小样本条件下性能受限，难以满足多径环境下的高精度估计需求, 提出一种基于循环匹配追踪的非圆信号多径时延估计算法。首先，基于辐射源信号的非圆特性，通过联合接收数据及其共轭构造扩展数据模型。然后，利用信号时延的稀疏特性构建离散化时间网格并设计非圆扩展时域字典集。在此基础上，从正交匹配追踪算法支撑集补集的角度入手，通过原子循环删增动态优化支撑集重构稀疏系数，从而得到多径时延的精确估计。此外，还推导了基于非圆信号的多径时延估计克拉美罗界，从而从理论上证明了利用非圆信息能进一步提升时延估计精度。仿真结果表明，相较于现有时延估计算法，所提算法在低信噪比、小样本条件下估计误差分别可降低27%和24%以上，验证了改进算法的优越性。

关键词: 时延估计, 多径, 非圆信号, 压缩感知, 正交匹配追踪

Abstract:

To address traditional time delay estimation methods often suffer from performance degradation in low signal-to-noise ratio and small number of samples, failing to meet high-precision estimation requirements in multipath environments, a multipath time delay estimation algorithm based on noncircular signal cyclic matching pursuit is proposed. First, the algorithm constructs an extended data model based on the noncircular characteristics of the radiation source signal, using both the received data and its conjugate. Second, the sparse characteristic of signal time delay is utilized to construct a discretized time grid and design a non-circular extended time-domain dictionary set. Based on this, starting from the perspective of complementing the support set of the orthogonal matching pursuit algorithm, the sparse coefficients are reconstructed by dynamically optimizing the support set through atomic cycle deletion and addition, thereby obtaining an accurate estimation of the multipath delay. Additionally, the Cramér-Rao Bound for multipath delay estimation with noncircular signal is derived, theoretically demonstrating that utilizing noncircular information can further enhance time delay estimation accuracy. Simulation results show that compared with existing time delay estimation methods, the proposed algorithm reduces estimation errors by over 27% and 24% in low SNR and small sample respectively, validating its superior performance.

Key words: time delay estimation, multipath, noncircular signal, compressed sensing, orthogonal matching pursuit (OMP)

中图分类号:

TN 911.7

王泽宇, 王鼎, 陈晓云, 张莉. 基于循环匹配追踪的非圆信号多径时延估计算法[J]. 系统工程与电子技术, 2026, 48(9): 2907-2916.

Zeyu Wang, Ding Wang, Xiaoyun Chen, Li Zhang. Multipath time delay estimation algorithm based on noncircular signal cyclic matching pursuit[J]. Systems Engineering and Electronics, 2026, 48(9): 2907-2916.

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参考文献 25

1	Liao Y P, Wang Y P. Source localization using TDOA based on improved snake optimizer[J]. Circuits, Systems, and Signal Processing, 2024, 43 (8): 5237. doi: 10.1007/s00034-024-02703-4
2	李俊霞, 王欣, 黄高见, 等. 无源定位技术发展及其展望[J]. 无线电工程, 2024, 54 (8): 1825. doi: 10.3969/j.issn.1003-3106.2024.08.001
3	Pallotta L, Giunta G. Accurate delay estimation for multisensor passive locating systems exploiting the cross-correlation between signals cross-correlations[J]. IEEE Trans. on Aerospace and Electronic Systems, 2022, 58 (3): 2568. doi: 10.1109/TAES.2021.3116927
4	Abdelkhalek M, Amor S B, Affes S. Data-aided maximum likelihood joint angle and delay estimator over orthogonal frequency division multiplex single-input multiple-output channels based on new gray wolf optimization embedding importance sampling[J]. Sensors, 2024, 24 (17): 5821. doi: 10.3390/s24175821
5	Ma J T, Zhang J C, Yang Z Y, et al. Super-resolution time delay estimation using exponential kernel correlation in impulsive noise and multipath environments[J]. Digital Signal Processing, 2023, 133, 103882. doi: 10.1016/j.dsp.2022.103882
6	Wang S H, Xiang Y, Gao Y Y, et al. The time difference of arrival estimation method utilizing an inexact reconstruction within the framework of compressed sensing[J]. Remote Sensing, 2024, 16 (21): 4039. doi: 10.3390/rs16214039
7	Ji X Y, Cheng L, Zhao H F. Multipath time-delay estimation with impulsive noise via Bayesian compressive sensing[J]. IEEE Signal Processing Letters, 2023, 30, 937. doi: 10.1109/LSP.2023.3295750
8	Fereidoony F, Chamaani S, Mirtahari S A, et al. Continuous basis compressive time-delay estimation in overlapped echoes[J]. IET Signal Processing, 2017, 11 (5): 566. doi: 10.1049/iet-spr.2016.0496
9	Ahmed I, Khalil A, Ahmed I, et al. Sparse signal representation, sampling, and recovery in compressive sensing frameworks[J]. IEEE Access, 2022, 10, 85002. doi: 10.1109/ACCESS.2022.3197594
10	Wang F Q, Zhang X F. Joint estimation of TOA and DOA in IR-UWB system using sparse representation framework[J]. ETRI Journal, 2014, 36 (3): 460. doi: 10.4218/etrij.14.0113.0555
11	Sun M, Pan J J, Wang Y D, et al. Time-delay estimation by enhanced orthogonal matching pursuit method for thin asphalt pavement with similar permittivity[J]. IEEE Trans. on Intelligent Transportation Systems, 2022, 23 (7): 8940. doi: 10.1109/TITS.2021.3088312
12	Needell D, Tropp J A. CoSaMP: iterative signal recovery from incomplete and inaccurate samples[J]. Applied and Computational Harmonic Analysis, 2009, 26 (3): 301. doi: 10.1016/j.acha.2008.07.002
13	Leng X D, Ba B, Lu Z Y, et al. Sparse reconstruction time delay estimation algorithm based on backtracking filter[J]. Acta Physica Sinica, 2016, 65 (21): 210701. doi: 10.7498/aps.65.210701
14	Jiang X L, Tang Z Y, Qu S S. Detection algorithm of compressed sensing signal in generalized spatial modulation system[J]. Mobile Networks and Applications, 2020, 28 (2): 551. doi: 10.1007/s11036-020-01602-7
15	Xiang J H, Li H Y, Qi L G. Sparse signal and image reconstruction algorithm for adaptive dual thresholds matching pursuit based on variable-step backtracking strategy[J]. Circuits, Systems, and Signal Processing, 2023, 42 (4): 2132. doi: 10.1007/s00034-022-02177-2
16	Hu X R, Zhang L Y, Wu D, et al. Underwater acoustic channel estimation via an orthogonal matching pursuit algorithm based on the modified phase-transform-weighted function[J]. Journal of Marine Science and Engineering, 2023, 11 (7): 1397. doi: 10.3390/jmse11071397
17	Wang Z S, Yang Y, Yang Q H. Time-difference-of-arrival estimation algorithms by employing cyclostationary property of LFM signals[J]. IEEE Sensors Letters, 2020, 4 (5): 7001804. doi: 10.1109/lsens.2020.2990408
18	Liu Y P, Gao H Y, Du Y N, et al. Noncircularity-based DOA estimation for incoherently distributed sources with gain-phase uncertainties[J]. IEEE Sensors Journal, 2024, 24 (16): 26022. doi: 10.1109/JSEN.2024.3420104
19	Cao J K, Zhang X F, Hao H H, et al. Noncircular signal tracking with distributed passive arrays: combining data fusion and extended Kalman filter[J]. IEEE Sensors Journal, 2024, 24 (1): 757. doi: 10.1109/JSEN.2023.3333863
20	文飞. 非圆信号参数估计方法研究[D]. 成都: 电子科技大学, 2014.
21	尹洁昕. 基于阵列信号的目标直接定位方法研究[D]. 郑州: 战略支援部队信息工程大学, 2018.
22	冯欣. 压缩采样时差估计方法研究[D]. 成都: 电子科技大学, 2022.
23	Candes E J, Tao T. Near-optimal signal recovery from random projections: universal encoding strategies?[J]. IEEE Trans. on Information Theory, 2006, 52 (12): 5406. doi: 10.1109/TIT.2006.885507
24	Candes E J. The restricted isometry property and its implications for compressed sensing[J]. Comptes Rendus Mathematique, 2008, 346 (9/10): 589. doi: 10.1016/j.crma.2008.03.014
25	王松桂, 吴密霞, 贾忠贞. 矩阵不等式[M]. 2版. 北京: 科学出版社, 2006.

算法	复杂度	参考值
OMP	$ O(NLD+{D}^{2}{N}^{2}) $	7.0×10⁴
Enhanced-OMP	$ O(N{N}_{x}k+NLD+2{D}^{2}{N}^{2}) $	4.1×10⁵
M-PHAT-OMP	$ O(NLD(\mathrm{\lg }N+W)+{D}^{2}{N}^{2}) $	1.6×10⁶
NC-CMP	$ O(4NLD+8{D}^{2}{N}^{2}) $	4.4×10⁵

算法	平均运行时间/s
OMP	0.006 0
Enhanced-OMP	0.008 8
M-PHAT-OMP	0.011 0
NC-CMP	0.009 1

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基于循环匹配追踪的非圆信号多径时延估计算法

Multipath time delay estimation algorithm based on noncircular signal cyclic matching pursuit

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