稀疏自适应系统识别算法逆QR分解优化研究

彭弋; 张鹏飞; 王晓永; 高俊奇; 李长隆; 张志远; 孙天翔

doi:10.11999/JEIT250562

稀疏自适应系统识别算法逆QR分解优化研究

doi: 10.11999/JEIT250562 cstr: 32379.14.JEIT250562

彭弋^{1, 2, 3},
张鹏飞^{1, 2, 3, ,},
王晓永⁴,
高俊奇^{1, 2, 3},
李长隆^{1, 2, 3},
张志远^{1, 2, 3},
孙天翔^{1, 2, 3}

1.
哈尔滨工程大学水声技术全国重点实验室哈尔滨 150001
2.
海洋信息获取与安全工信部重点实验室(哈尔滨工程大学) 工业和信息化部哈尔滨 150001
3.
哈尔滨工程大学水声工程学院哈尔滨 150001
4.
青岛市黄岛区政协机关服务保障中心青岛 266555

基金项目: 电波环境特性及模化技术重点实验室基金项目(JCKY2024210C61424030202)

详细信息

作者简介:
彭弋：男，硕士生，研究领域为自适应滤波技术、电磁探测、电磁对抗等

张鹏飞：男，博士，讲师，研究领域为电磁探测、电磁探测数值模拟、机器学习及深度学习的工程应用等

高俊奇：男，博士，教授，研究领域为高灵敏磁电复合型(ME)磁传感器，隧道磁电阻(TMR)磁传感器，能量收集器，弱磁目标探测等

李长隆：男，硕士生，研究领域为磁异常信号检测、深度学习等

张志远：男，硕士生，研究领域为天线设计、电路设计等

通讯作者:
张鹏飞　zhangpf9009@hrbeu.edu.cn

中图分类号: TN972
计量
- 文章访问数: 13
- HTML全文浏览量: 2
- PDF下载量: 0
- 被引次数: 0
出版历程
- 收稿日期: 2025-06-18
- 修回日期: 2026-03-12
- 录用日期: 2026-04-08
- 网络出版日期: 2026-04-25

Research on Inverse QR Decomposition Optimization for Sparse Adaptive System Identification Algorithms

PENG Yi^{1, 2, 3},
ZHANG Pengfei^{1, 2, 3
, ,},
WANG Xiaoyong⁴,
GAO Junqi^{1, 2, 3},
LI Changlong^{1, 2, 3},
ZHANG Zhiyuan^{1, 2, 3},
SUN Tianxiang^{1, 2, 3}

1.
Harbin Engineering University, National Key Laboratory of Underwater Acoustic Technology, Harbin 150001, Heilongjiang, China
2.
Key Laboratory of Marine Information Acquisition and Security, Ministry of Industry and Information Technology, Harbin Engineering University, Ministry of Industry and Information Technology, Harbin 150001, Heilongjiang, China
3.
Harbin Engineering University, School of Underwater Acoustic Engineering, Harbin 150001, Heilongjiang, China
4.
Huangdao District Political Consultative Conference Service Guarantee Center, Qingdao 266555, Shandong, China

Funds: Fundation: Key Laboratory Fund Project on Radio Wave Environment Characteristics and Modeling Technology (JCKY2024210C61424030202)

摘要

摘要: 传统稀疏正则化递归最小二乘算法 L1/L0 Norm Recursive Least Squares (L1/L0-RLS)在稀疏参数空间估计中展现出理论的优越性，已成为系统辨识和信道均衡领域的重要方法。但在有限数值精度条件下其协方差矩阵迭代计算过程易导致舍入误差逐次累积，诱发最小二乘解发散失稳现象。为解决该问题，本文提出基于逆QR分解(Inverse QR Decomposition, IQRD)框架的改进算法。该框架不仅有效抑制了传统正则化RLS算法中舍入误差的积累，而且省去了传统QR分解中权重系数回代的计算环节，从而显著提升了算法在有限精度环境下的数值鲁棒性与系统辨识效率。具体而言，本文首先系统构建了L1/L0约束逆QR分解架构下的L1-IQRD-RLS与L0-IQRD-RLS算法，通过理论推导得到了具有普适性的权重系数递推表达式，创新地将自动参数选择机制引入算法框架，解决了稀疏正则化参数的动态优化难题。为验证所提算法在稀疏约束与鲁棒性方面的效果，采用蒙特卡洛仿真实验对算法性能进行定量评估，结果表明L1-IQRD-RLS与L0-IQRD-RLS在系统稀疏表征、参数估计方差以及协方差矩阵条件数等关键指标上均展现出显著的性能优势。实测数据验证进一步证实，改进算法在精度受限环境下仍能保持数值稳定性，较传统方法鲁棒性显著提升。
- 递归最小二乘 /
- 稀疏优化 /
- 逆QR分解 /
- 系统识别
Abstract: Objective The traditional sparse regularization recursive least squares algorithm, L1/L0 Norm Recursive Least Squares (L1/L0-RLS), demonstrates theoretical superiority in sparse parameter space estimation and has become a significant method in system identification and channel equalization. However, under limited numerical precision conditions, its covariance matrix iterative computation process can lead to successive accumulation of rounding errors, inducing divergence and instability in the least squares solution. Methods To address this issue, this paper proposes an improved algorithm based on the Inverse QR Decomposition (IQRD) framework. This framework not only effectively suppresses the accumulation of rounding errors in traditional regularized RLS algorithms, but also eliminates the calculation step of weight coefficient replacement in traditional QR decomposition, thereby significantly improving the numerical robustness and system identification efficiency of the algorithm in finite precision environments. Specifically, this article first systematically constructs the L1-IQRD-RLS and L0-IQRD-RLS algorithms under the L1/L0 constrained inverse QR decomposition architecture. Through theoretical derivation, a universal recursive expression for weight coefficients is obtained, and an innovative automatic parameter selection mechanism is introduced into the algorithm framework to solve the dynamic optimization problem of sparse regularization parameters. Results and Discussions To verify the effectiveness of the proposed algorithm in sparse constraints and robustness, Monte Carlo simulation experiments were used to quantitatively evaluate the algorithm performance. The results showed that L1-IQRD-RLS and L0-IQRD-RLS can maintain long-term numerical stability in an 11 decimal fixed-point computing environment. Compared with traditional algorithms, they exhibit significant performance advantages in key indicators such as system sparse representation, parameter estimation variance, and covariance matrix condition number. Further verification of actual test data confirms that the improved algorithm can maintain numerical stability even in environments with limited accuracy, significantly improving its robustness compared to traditional methods. The application effect of measured data shows that the regularized RLS algorithm improved by the inverse QR framework exhibits significant advantages in key indicators such as system sparsity representation, parameter estimation, and numerical stability. Its iterative convergence success rate is significantly improved compared to traditional methods. Conclusions This paper focuses on the issue of sparse system identification in the field of adaptive filtering. Currently, traditional sparse-regularized recursive least squares (RLS) algorithms still face challenges in numerical stability under limited numerical precision. To address this problem, this study proposes constructing an inverse QR decomposition framework to overcome the numerical ill-conditioning caused by successive rounding errors in sparse-regularized RLS algorithms. This approach significantly enhances the algorithm's numerical robustness in low-precision environments. Additionally, it innovatively introduces an automatic parameter selection mechanism into the algorithm framework, effectively eliminating the need for repeated parameter tuning and ensuring stable performance optimization through sparse constraints.In practical electromagnetic signal processing, tasks such as system identification and beamforming are constrained by the finite precision of hardware implementation and often face the inherent sparsity characteristics of the system itself. This paper's algorithm provides targeted solutions: its enhanced finite word-length robustness effectively suppresses numerical divergence in adaptive weight updates, ensuring stable implementation on fixed-point processors; meanwhile, the introduced sparse constraints naturally align with the physical structure of sparse arrays, improving the accuracy of algorithm estimation results. This research offers a practical algorithmic approach for achieving high-performance, high-stability sparse-constrained systems on precision-limited hardware platforms.
- Recursive least squares /
- Sparse optimization /
- Inverse QR decomposition /
- System identification

HTML全文

图 1 稀疏度4:144时不同算法性能

下载: 全尺寸图片幻灯片

图 2 单次11位定点仿真

下载: 全尺寸图片幻灯片

图 3 一百次蒙特卡洛11位定点仿真

下载: 全尺寸图片幻灯片

图 4 正则参数自动选择效果

下载: 全尺寸图片幻灯片

图 5 算法性能随系统稀疏度变化

下载: 全尺寸图片幻灯片

图 6 实验场景图

下载: 全尺寸图片幻灯片

图 7 滤波器系数识别结果对比

下载: 全尺寸图片幻灯片

图 8 对消结果对比

下载: 全尺寸图片幻灯片

图 9 小数16位定点运算结果

下载: 全尺寸图片幻灯片

参考文献(32)

[1]	WIDROW B and STEARNS S D. Adaptive Signal Processing[M]. Englewood Cliffs: Prentice-Hall, 1985.
[2]	HAYKIN S. Adaptive Filter Theory[M]. 3rd ed. Upper Saddle River: Prentice-Hall, Inc. , 1996.
[3]	PALEOLOGU C, BENESTY J, and CIOCHINA S. A robust variable forgetting factor recursive least-squares algorithm for system identification[J]. IEEE Signal Processing Letters, 2008, 15: 597–600. doi: 10.1109/LSP.2008.2001559.
[4]	CHOWDHURY N M M and ULLAH M A. An efficient channel equalization scheme with multi-layer of adaptation[C]. Proceedings of 2025 International Conference on Electrical, Computer and Communication Engineering (ECCE), Chittagong, Bangladesh, 2025: 1–6. doi: 10.1109/ECCE64574.2025.11013831.
[5]	LIU Di, BALDI S, LIU Quan, et al. A recursive least squares algorithm with ℓ1 regularization for sparse representation[J]. Science China Information Sciences, 2023, 66(2): 129202. doi: 10.1007/s11432-022-3546-5.
[6]	ALEXANDER S T and GHIMIKAR A L. A method for recursive least squares filtering based upon an inverse QR decomposition[J]. IEEE Transactions on Signal Processing, 1993, 41(1): 20. doi: 10.1109/TSP.1993.193124.
[7]	GHIRNIKAR A L, ALEXANDER S T, and PLEMMONS R J. A parallel implementation of the inverse QR adaptive filter[J]. Computers & Electrical Engineering, 1992, 18(3/4): 291–300. doi: 10.1016/0045-7906(92)90021-5.
[8]	QIN Zhen, TAO Jun, XIA Yili, et al. Proportionate RLS with l₁ norm regularization: Performance analysis and fast implementation[J]. Digital Signal Processing, 2022, 122: 103366. doi: 10.1016/j.dsp.2021.103366.
[9]	WANG Yu, QIN Zhen, TAO Jun, et al. Sparse adaptive channel estimation based on l0-PRLS algorithm for underwater acoustic communications[C]. Proceedings of OCEANS 2022-Chennai, Chennai, India, 2022: 1–5. doi: 10.1109/OCEANSChennai45887.2022.9775337.
[10]	LIU Haotian, MA Lu, WANG Zhaohui, et al. Channel prediction for underwater acoustic communication: A review and performance evaluation of algorithms[J]. Remote Sensing, 2024, 16(9): 1546. doi: 10.3390/rs16091546.
[11]	YIN Jingwei, ZHU Guangjun, HAN Xiao, et al. Temporal correlation and message-passing-based sparse Bayesian learning channel estimation for underwater acoustic communications[J]. IEEE Journal of Oceanic Engineering, 2024, 49(2): 522–541. doi: 10.1109/JOE.2023.3330523.
[12]	CHAVAN S D, KANASE D B, JADHAV S P, et al. Underwater wireless communication network by magnetic field using sparse sensing[C]. Proceedings of 2024 International Conference on Intelligent Systems and Advanced Applications (ICISAA), Pune, India, 2024: 1–5. doi: 10.1109/ICISAA62385.2024.10829175.
[13]	THADIKAMALLA N R and AMARA P R. Synthesis of elliptical cylindrical antenna array using craziness particle swarm optimization for suppressing sidelobe level[J]. Journal of Electromagnetic Waves and Applications, 2024, 38(14): 1592–1604. doi: 10.1080/09205071.2024.2385502.
[14]	ZORKUN A E, SALAS-NATERA M A, and RODRÍGUEZ-OSORIO R M. An improved hybrid beamforming algorithm for fast target tracking in satellite and V2X communication[J]. Remote Sensing, 2024, 16(1): 13. doi: 10.3390/rs16010013.
[15]	HONG Jingxi, CHU Yijing, CHAN S C, et al. A robust RLS-based generalized sidelobe canceller using spatial regularization[J]. Digital Signal Processing, 2025, 164: 105273. doi: 10.1016/j.dsp.2025.105273.
[16]	曲庆, 金坚, 谷源涛. 用于稀疏系统辨识的改进l0-LMS算法[J]. 电子与信息学报, 2011, 33(3): 604–609. doi: 10.3724/SP.J.1146.2010.00417. QU Qing, JIN Jian, and GU Yuantao. An improved l0-LMS algorithm for sparse system identification[J]. Journal of Electronics & Information Technology, 2011, 33(3): 604–609. doi: 10.3724/SP.J.1146.2010.00417.
[17]	SALMAN M, YOUSSEF A A F, ELSAYED F, et al. A sparse variable step-size least-mean-square algorithm for impulsive noise in a code-division multiple access system[J]. IEEE Access, 2025, 13: 86026–86031. doi: 10.1109/ACCESS.2025.3570122.
[18]	EKŞIOĞLU E M. RLS adaptive filtering with sparsity regularization[C]. Proceedings of the 10th International Conference on Information Science, Signal Processing and their Applications (ISSPA 2010), Kuala Lumpur, Malaysia, 2010: 550–553. doi: 10.1109/ISSPA.2010.5605592.
[19]	EKSIOGLU E M and TANC A K. RLS algorithm with convex regularization[J]. IEEE Signal Processing Letters, 2011, 18(8): 470–473. doi: 10.1109/LSP.2011.2159373.
[20]	GILL P E, GOLUB G H, MURRAY W, et al. Methods for modifying matrix factorizations[J]. Mathematics of Computation, 1974, 28(126): 505–535. doi: 10.1090/S0025-5718-1974-0343558-6.
[21]	CHU Y J and MAK C M. A new QR decomposition-based RLS algorithm using the split Bregman method for L1-regularized problems[J]. Signal Processing, 2016, 128: 303–308. doi: 10.1016/j.sigpro.2016.04.013.
[22]	CHEN Badong, ZHENG Nanning, and PRINCIPE J C. Sparse kernel recursive least squares using L1 regularization and a fixed-point sub-iteration[C]. Proceedings of 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Florence, Italy, 2014: 5257–5261. doi: 10.1109/ICASSP.2014.6854606.
[23]	STANCIU C L, ANGHEL C, and ELISEI-ILIESCU C. Regularized RLS adaptive algorithm with conjugate gradient method[C]. Proceedings of 2023 International Conference on Speech Technology and Human-Computer Dialogue (SpeD), Bucharest, Romania, 2023: 18–23. doi: 10.1109/SpeD59241.2023.10314893.
[24]	HUANG Yanjie, WANG Weijiang, XUE Chengbo, et al. Scalable hardware architecture for high-throughput implementation of ESPRIT algorithm[J]. IEEE Sensors Journal, 2025, 25(13): 24812–24828. doi: 10.1109/JSEN.2025.3568483.
[25]	LIU Quan, LIU Di, and BALDI S. A new recursive approach to sparse representation[C]. Proceedings of 2023 IEEE International Conference on Development and Learning (ICDL), Macau, China, 2023: 461–466. doi: 10.1109/ICDL55364.2023.10364401.
[26]	XING Jinling, GE Songhu, HE Fangmin, et al. RF cancellation system based on inverse QRD_RLS weight extraction[C]. Proceedings of 2023 IEEE 6th International Conference on Electronic Information and Communication Technology (ICEICT), Qingdao, China, 2023: 154–158. doi: 10.1109/ICEICT57916.2023.10245523.
[27]	DJIGAN V and KURGANOV V. Antenna arrays calibration using recursive least squares adaptive filtering algorithms based on inverse QR decomposition[C]. Proceedings of 2020 IEEE East-West Design & Test Symposium (EWDTS), Varna, Bulgaria, 2020: 1–5. doi: 10.1109/EWDTS50664.2020.9224860.
[28]	NEOH H S, DUHAMEL P, and PYE W. MVDR adaptive beamforming using oneAPI SYCL HLS targeting direct RF FPGA[C]. Proceedings of 2024 IEEE International Symposium on Phased Array Systems and Technology (ARRAY), Boston, USA, 2024: 1–5. doi: 10.1109/ARRAY58370.2024.10880432.
[29]	DJIGAN V. Adaptive arrays based on real-valued arithmetic linearly-constrained IQRD RLS adaptive filtering algorithms[C]. Proceedings of 2021 IEEE 3rd Ukraine Conference on Electrical and Computer Engineering (UKRCON), Lviv, Ukraine, 2021: 196–201. doi: 10.1109/UKRCON53503.2021.9575646.
[30]	刘金荣, 冷相文, 姬庆, 等. 水声通信信道估计技术的研究进展[J]. 电讯技术, 2024, 64(12): 2081–2090. doi: 10.20079/j.issn.1001-893x.240823003. LIU Jinrong, LENG Xiangwen, JI Qing, et al. Advances in channel estimation for underwater acoustic communications[J]. Telecommunication Engineering, 2024, 64(12): 2081–2090. doi: 10.20079/j.issn.1001-893x.240823003.
[31]	谭思炜, 赵军, 张萌, 等. 一种宽带电磁引信直接耦合干扰的快速补偿方法[J]. 水下无人系统学报, 2019, 27(4): 420–427. doi: 10.11993/j.issn.2096-3920.2019.04.009. TAN Siwei, ZHAO Jun, ZHANG Meng, et al. A method for fast compensating direct coupling interference of wideband electromagnetic fuze[J]. Journal of Unmanned Undersea Systems, 2019, 27(4): 420–427. doi: 10.11993/j.issn.2096-3920.2019.04.009.
[32]	鲁伟俊, 李斌. 主动磁探测叠加信号的自适应对消技术研究[J]. 中国仪器仪表, 2019(6): 55–59. doi: 10.3969/j.issn.1005-2852.2019.06.018. LU Weijun and LI Bin. Study of the active magnetic detection based on adaptive cancelltion for superposed signal[J]. China Instrumentation, 2019(6): 55–59. doi: 10.3969/j.issn.1005-2852.2019.06.018.