基于QR分解的正则化回溯匹配追踪算法DOA估计

张宁宁, 张骄

PDF(2669 KB)
中国高校科技期刊信息汇聚平台
PDF(2669 KB)
山西大学学报(自然科学版) ›› 2025, Vol. 48 ›› Issue (3) : 565-577. DOI: 10.13451/j.sxu.ns.2024034
物理

基于QR分解的正则化回溯匹配追踪算法DOA估计

作者信息 +

DOA Estimation of Regularization Backtracking Algorithms Based on QR Decomposition

Author information +
History +

摘要

针对传统算法在低信噪比、小快拍、信源相干等情况下，波达方向 （Directional of Arrival，DOA）估计精度低的问题，提出了一种基于正交三角分解（Orthogonal Triangular Decomposition，QR）的正则化回溯匹配追踪算法（QR-Regularized Backtracking Matching Pursuit，QR-RBMP）。该算法首先对感知矩阵进行QR分解，以增大感知矩阵的独立性；再利用正则化思想和回溯机制优化匹配追踪算法，来提高信号重构精度；正则化思想对匹配追踪算法初次选择的原子进行二次筛选，选出最相关且能量最大的相关原子，回溯思想对正则化选择得到的原子进行再次筛选，删除不正确的原子，提高所选择原子的正确性，进而提高了匹配追踪算法的重构精度。最后得到重构的信号，信号非零元素所对应的位置即为DOA估计的结果。通过一系列仿真实验，并与多重信号分类算法（Multiple Signal Classification，MUSIC）、正则化正交匹配追踪算法（Regularized Orthogonal Matching Pursuit，ROMP）、基于子空间追踪算法（Subspace Tracking Algorithm，SP）、无平方根方法的SP算法（ISP）以及能量排序的回溯正则化匹配追踪算法（Backtracking Regularization Matching Pursuit for Energy Sorting，ESBRMP）估计方法基于均方根误差（Root Mean Square Error，RMSE）、分辨概率（Probability of Resolution，POR）进行对比分析。结果表明该算法在相同条件下均方根误差比现有最优方法降低了约42%，成功分辨率提高了8%。

Abstract

A matching pursuit algorithm for regularization backtracking based on QR decomposition (QR-RBMP) is proposed in this paper to solve the problems of low precision of directional of arrival (DOA) estimation in the cases of low signal noise ratio (SNR), small snapshot and coherent signals. Firstly, the algorithm is performed on sensing matrix by QR decomposition to increase the independence of the sensing matrix. Then, the regularization idea and backtracking mechanism are used to optimize matching pursuit algorithm to improve the signal reconstruction precision. The regularization idea carries out secondary screening on the atoms initially selected by the matching tracking algorithm, and selects the most relevant atoms with the largest energy. The backtracking idea carries out secondary screening on the atoms selected by the regularization, deletes the incorrect atoms, improves the correctness of the selected atoms, and thus improves the reconstruction accuracy of the matching tracking algorithm. Finally, we obtain the reconstructed signal. The position of the non-zero element of the signal is the result of DOA estimation. Through a series of simulation experiments, the proposed algorithm is compared with MUSIC algorithm, regularized orthogonal matching pursuit algorithm (ROMP), subspace tracking algorithm, SP algorithm without Square Root (ISP) and energy sorting based backtracking regularized matching pursuit algorithm (ESBRMP) based on RMSE and POR. The results show that the proposed algorithm reduces the RMSE by 42% and improves the POR by 8% compared with the existing optimal methods under the same conditions.

关键词

波达方向估计 / 嵌套阵列 / 矩阵分解 / 正则化思想 / 回溯机制 / 压缩感知

Key words

DOA estimation / nested array / matrix decomposition / regularization idea / backtracking mechanism / compressed sensing

中图分类号

TN911.7

引用本文

EndNote

Ris (Procite)

Bibtex

导出引用
张宁宁 , 张骄. 基于QR分解的正则化回溯匹配追踪算法DOA估计. 山西大学学报(自然科学版). 2025, 48(3): 565-577 https://doi.org/10.13451/j.sxu.ns.2024034
ZHANG Ningning, ZHANG Jiao. DOA Estimation of Regularization Backtracking Algorithms Based on QR Decomposition[J]. Journal of Shanxi University(Natural Science Edition). 2025, 48(3): 565-577 https://doi.org/10.13451/j.sxu.ns.2024034

参考文献

列表( 原文顺序 | 文献年度倒序 | 文中引用次数倒序 ) 可视化分析
1
HU N, YE Z F, XU X, et al. DOA Estimation for Sparse Array via Sparse Signal Reconstruction[J]. IEEE Trans Aerosp Electron Syst, 2013, 49(2): 760-773. DOI: 10.1109/TAES.2013.6494379 .
本文引用 [1]
2
KRIM H, VIBERG M. Two Decades of Array Signal Processing Research: The Parametric Approach[J]. IEEE Signal Process Mag, 1996, 13(4): 67-94. DOI: 10.1109/79.526899 .
本文引用 [1]
3
SCHMIDT R. Multiple Emitter Location and Signal Parameter Estimation[J]. IEEE Trans Anntenas Propag, 1986, 34(3): 276-280. DOI: 10.1109/TAP.1986.1143830 .
本文引用 [1]
4
ROY R, KAILATH T. ESPRIT-estimation of Signal Parameters via Rotational Invariance Techniques[J]. IEEE Trans Acoust Speech Signal Process, 1989, 37(7): 984-995. DOI: 10.1109/29.32276 .
本文引用 [1]
5
STOICA P, NEHORAI A. Performance Study of Conditional and Unconditional Direction-of-arrival Estimation[J]. IEEE Trans Acoust Speech Signal Process, 1990, 38(10): 1783-1795. DOI: 10.1109/29.60109 .
本文引用 [1]
6
TSAKALIDES P, NIKIAS C L. Maximum Likelihood Localization of Sources in Noise Modeled as a Stable Process[J]. IEEE Trans Signal Process, 1995, 43(11): 2700-2713. DOI: 10.1109/78.482119 .
7
OTTERSTEN B, VIBERG M, STOICA P, et al. Exact and Large Sample Maximum Likelihood Techniques for Parameter Estimation and Detection in Array Processing[M]//HAYKIN S, LITVA J, SHEPHERD T J. Radar Array Processing. Berlin, Heidelberg: Springer, 1993: 99-151. DOI: 10.1007/978-3-642-77347-1_4 .
本文引用 [1]
8
HAMZA R, BUCKLEY K. Second-order Statistical Analysis of Totally Weighted Subspace Fitting Methods[J]. IEEE Trans Signal Process, 1994, 42(9): 2520-2524. DOI: 10.1109/78.317877 .
本文引用 [1]
9
ÇALıK S K. UAV Path Planning with Multiagent Ant Colony System Approach[C]//2016 24th Signal Processing and Communication Application Conference (SIU). Zonguldak, Turkey: IEEE, 2016: 1409-1412. DOI: 10.1109/SIU.2016.7496013 .
本文引用 [1]
10
WAGNER M, PARK Y, GERSTOFT P. Gridless DOA Estimation and Root-MUSIC for Non-uniform Linear Arrays[J]. IEEE Trans Signal Process, 2021, 69: 2144-2157. DOI: 10.1109/TSP.2021.3068353 .
本文引用 [1]
11
TOTA R, HOSSAIN M S. Multiple Near-field Sources Localization by Optimal Beamformer Using Minimum Norm Method[C]//2021 International Conference on Electronics, Communications and Information Technology (ICECIT). Khulna, Bangladesh: IEEE, 2021: 1-4. DOI: 10.1109/ICECIT54077.2021.9641373 .
本文引用 [1]
12
QI B B, LI W. An Improved Multiple-toeplitz Matrices Reconstruction Algorithm for DOA Estimation of Coherent Signals[J]. Radioengineering, 2021, 30(3): 532-539. DOI: 10.13164/re.2021.0532 .
本文引用 [1]
13
DONOHO D L. Compressed Sensing[J]. IEEE Trans Inf Theory, 2006, 52(4): 1289-1306. DOI: 10.1109/TIT.2006.871582 .
本文引用 [2]
14
WANG H B. Compressed Sensing: Theory and Applications[J]. J Phys: Conf Ser, 2023, 2419(1): 012042. DOI: 10.1088/1742-6596/2419/1/012042 .
本文引用 [1]
15
MALLOY M L, NOWAK R D. Near-optimal Adaptive Compressed Sensing[J]. IEEE Trans Inf Theory, 2014, 60(7): 4001-4012. DOI: 10.1109/TIT.2014.2321552 .
本文引用 [1]
16
陈健, 庄耀宇, 杨丹, 等. 基于FPGA的改进的排序QR分解实现[J]. 湖南大学学报(自然科学版), 2022, 49(10): 8-16. DOI: 10.16339/j.cnki.hdxbzkb.2022351 .
CHEN J, ZHUANG Y Y, YANG D, et al. Implementation of Improved Sorted QR Decomposition on FPGA[J]. J Hunan Univ Nat Sci, 2022, 49(10): 8-16. DOI: 10.16339/j.cnki.hdxbzkb.2022351 .
本文引用 [1]
17
CANDES E J, ROMBERG J, TAO T. Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information[J]. IEEE Trans Inf Theory, 2006, 52(2): 489-509. DOI: 10.1109/TIT.2005.862083 .
本文引用 [1]
18
LI Y Q, WANG J. Time-frequency Analysis of Seismic Data Based on Basis Pursuit[C]//2014 12th International Conference on Signal Processing (ICSP). Hangzhou, China: IEEE, 2014: 175-179. DOI: 10.1109/ICOSP.2014.7014992 .
本文引用 [1]
19
TROPP J A, GILBERT A C. Signal Recovery from Random Measurements via Orthogonal Matching Pursuit[J]. IEEE Trans Inf Theory, 2007, 53(12): 4655-4666. DOI: 10.1109/TIT.2007.909108 .
本文引用 [1]
20
NEEDELL D, VERSHYNIN R. Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit[J]. Found Comput Math, 2009, 9(3): 317-334. DOI: 10.1007/s10208-008-9031-3 .
本文引用 [1]
21
DAI W, MILENKOVIC O. Subspace Pursuit for Compressive Sensing Signal Reconstruction[J]. IEEE Trans Inf Theory, 2009, 55(5): 2230-2249. DOI: 10.1109/TIT.2009.2016006 .
本文引用 [1]
22
DO T T, GAN L, NGUYEN N, et al. Sparsity Adaptive Matching Pursuit Algorithm for Practical Compressed Sensing[C]//2008 42nd Asilomar Conference on Signals, Systems and Computers. Pacific Grove, CA, USA: IEEE, 2008: 581-587. DOI: 10.1109/ACSSC.2008.5074472 .
本文引用 [1]
23
NEEDELL D, TROPP J A. CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Samples[J]. Appl Comput Harmon Anal, 2009, 26(3): 301-321. DOI: 10.1016/j.acha.2008.07.002 .
本文引用 [1]
24
ZHAO J, BAI X. An Improved Orthogonal Matching Pursuit Based on Randomly Enhanced Adaptive Subspace Pursuit[C]//2017 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC). Kuala Lumpur, Malaysia: IEEE, 2017: 437-441. DOI: 10.1109/APSIPA.2017.8282071 .
本文引用 [1]
25
ZHANG C J. An Orthogonal Matching Pursuit Algorithm Based on Singular Value Decomposition[J]. Circuits Syst Signal Process, 2020, 39(1): 492-501. DOI: 10.1007/s00034-019-01182-2 .
本文引用 [1]
26
LIU Y Z, SONG T, ZHUANG Y Q. A High-throughput Subspace Pursuit Processor for ECG Recovery in Compressed Sensing Using Square-root-free MGS QR Decomposition[J]. IEEE Trans Very Large Scale Integr VLSI Syst, 2020, 28(1): 174-187. DOI: 10.1109/TVLSI.2019.2936867 .
本文引用 [2]
27
LI L X, XU D F, PENG H P, et al. Reconstruction of Complex Network Based on the Noise via QR Decomposition and Compressed Sensing[J]. Sci Rep, 2017, 7(1): 15036. DOI: 10.1038/s41598-017-15181-3 .
本文引用 [1]
28
ZHANG H F, XIAO S G, ZHOU P. A Matching Pursuit Algorithm for Backtracking Regularization Based on Energy Sorting[J]. Symmetry, 2020, 12(2): 231. DOI: 10.3390/sym12020231 .
本文引用 [2]
29
ZHENG Z, YANG C L, WANG W Q, et al. Robust DOA Estimation Against Mutual Coupling with Nested Array[J]. IEEE Signal Process Lett, 2020, 27: 1360-1364. DOI: 10.1109/LSP.2020.3011314 .
本文引用 [1]
30
JIANG G J, YANG Y L. Synthetic Sparse Nested Array with Extended Aperture and Reduced Mutual Coupling for DOA Estimation[J]. Signal Process, 2023, 204: 108849. DOI: 10.1016/j.sigpro.2022.108849 .
本文引用 [1]
31
CANDÈS E, ROMBERG J. Sparsity and Incoherence in Compressive Sampling[J]. Inverse Probl Int J Inverse Probl Inverse Meth Comput Inversion Data, 2007, 23(3): 969-985. DOI:10.1088/0266-5611/23/3/008 .
本文引用 [1]

基金

广东省光纤传感与通信技术重点实验室开放基金资助(01110122120181)

评论

PDF(2669 KB)

Accesses

Citation

Detail
段落导航
相关文章
Copyright 中国高校科技期刊信息汇聚平台 2024-2025
技术支持：北京玛格泰克科技发展有限公司
京ICP备05021913号-19

/

〈 〉