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) 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

孙天翔：男，硕士生，研究领域为电磁探测、机器学习等

通讯作者:
张鹏飞　zhangpf9009@hrbeu.edu.cn

中图分类号: TN972
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- 文章访问数: 428
- HTML全文浏览量: 150
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- 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
- 刊出日期: 2026-07-10

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.
National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University, Harbin 150001, China
2.
Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China
3.
School of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China
4.
Qingdao Huangdao District Committee of the Chinese People’s Political Consultative Conference Service Support Center, Qingdao 266555, China

Funds: The 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，该文提出基于逆QR分解(IQRD)框架的改进算法，不仅有效抑制传统正则化RLS算法中舍入误差的积累，而且省去传统QR分解中权重系数回代的计算环节，从而显著提升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，首先，系统构建L1/L0约束逆QR分解架构下的L1-IQRD-RLS与L0-IQRD-RLS算法，通过理论推导得到具有普适性的权重系数递推表达式，创新性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，该文采用蒙特卡罗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 Traditional sparse-regularized Recursive Least Squares (RLS) algorithms, namely L1/L0-norm Recursive Least Squares (L1/L0-RLS), have theoretical advantages in sparse parameter-space estimation and are widely used in system identification and channel equalization. However, under limited numerical precision, iterative covariance matrix computation may cause rounding errors to accumulate. This can lead to divergence and instability in the least-squares solution. Methods To address this problem, an improved algorithm based on the Inverse QR Decomposition (IQRD) framework is proposed. The framework suppresses rounding-error accumulation in traditional regularized RLS algorithms. It also removes the back-substitution step for weight coefficients required in conventional QR decomposition. These features improve numerical robustness and system identification efficiency in finite-precision environments. Specifically, L1-IQRD-RLS and L0-IQRD-RLS algorithms are constructed under an L1/L0-constrained IQRD architecture. A general recursive expression for the weight coefficients is derived. An automatic parameter selection mechanism is also incorporated into the algorithm framework to solve the dynamic optimization problem of the sparse regularization parameter. Results and Discussions Monte Carlo simulations are conducted to evaluate the sparse constraints and robustness of the proposed algorithms. The results show that L1-IQRD-RLS and L0-IQRD-RLS maintain long-term numerical stability in an 11-decimal-place fixed-point computing environment. Compared with traditional algorithms, the proposed algorithms show clear advantages in system sparsity representation, parameter estimation variance, and covariance matrix condition number. Measured-data verification further confirms that the improved algorithms maintain numerical stability under limited-precision conditions and are more robust than traditional methods. The measured-data results also show that the regularized RLS algorithms optimized by the IQRD framework have advantages in system sparsity representation, parameter estimation, and numerical stability. Their iterative convergence success rate is higher than that of traditional methods. Conclusions This paper addresses sparse system identification in adaptive filtering. Traditional sparse-regularized RLS algorithms still face numerical stability problems under limited numerical precision. To solve this problem, an IQRD framework is constructed to reduce the numerical ill-conditioning caused by accumulated rounding errors in sparse-regularized RLS algorithms. The proposed method improves numerical robustness in low-precision environments. In addition, an automatic parameter selection mechanism is incorporated into the algorithm framework. This reduces repeated parameter tuning and supports stable performance optimization under sparse constraints. In practical electromagnetic signal processing, system identification and beamforming are limited by the finite precision of hardware implementation and often exhibit inherent system sparsity. The proposed algorithm provides a targeted solution. Its finite-word-length robustness suppresses numerical divergence during adaptive weight updates and supports stable implementation on fixed-point processors. The sparse constraints also match the physical characteristics of sparse systems and improve estimation accuracy. This study provides a practical algorithm for high-performance and high-stability sparse-constrained systems on precision-limited hardware platforms.
- Recursive least squares /
- Sparse optimization /
- Inverse QR decomposition /
- System identification

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图 1 稀疏度4:144时不同算法性能

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图 2 单次11位定点仿真

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图 3 100次蒙特卡罗11位定点仿真

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图 4 正则参数自动选择效果

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图 5 算法性能随系统稀疏度变化

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图 6 实验场景图

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图 7 滤波器系数识别结果对比

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图 8 对消结果对比

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图 9 小数16位定点运算结果

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1 CR-IQRD-RLS算法伪代码

初始化：阶数M，采样点数N，权系数w(n)，输入信号x(n)，期　望信号y(n)，
分解因子矩阵R^–T(0) = δI(δ ≥ 1)，遗忘因子λ
1：从n = 1到n = N:
2: 　${\boldsymbol{x}}^{\mathrm{T}}(n) = [x(n), x(n - 1), \cdots, x(n - M + 1)] $
3: 　$e(n \| n - 1) = d(n) - {\boldsymbol{w}}^{\mathrm{T}}({{n}} - 1){\boldsymbol{x}}({{n}}) $
4: 　$u_j^{(k)}(n) = 0, 1 \le j \le M, k \lt j $.
5: 　$b^{(0)}(n) $ = 1
6: 　从i = 1到i = M依次迭代
7: 　　$a_i(n) =\lambda^{-1/2} \displaystyle\sum\nolimits_{j = 1}^i {\boldsymbol{R}}_{ij}^{-{\mathrm{T}}}(n)(n - 1)x(n - j + 1) $
8: 　　$b^{i} (n) = \sqrt {([b^{i - 1}(n)]^2 + a_i^2(n)) }$
9: 　　$s_i(n) = a_i(n)/b^{(i)}(n) $
10: 　 $c_i(n) = b^{(i - 1)}(n)/b^{(i)}(n) $
11: 　从j = 1到j = i依次迭代
12: 　　 ${\boldsymbol{R}}_{ij}^{-{\mathrm{T}}}(n) = \lambda^{-1/2}c_i(n){\boldsymbol{R}}_{ij}^{-{\mathrm{T}}}(n - 1) $ 　　　　　 $- s_i(n)u_j^{(i - 1)}(n) $
13: 　　 $u_j^{(i)}(n) = c_i(n)u_j^{(i - 1)}(n) + \lambda^{-1/2}s_i(n)$ 　　　　　 ${\boldsymbol{R}}_{ij}^{-{\mathrm{T}}}(n - 1) $
14: 　结束第j次循环
15: 结束第i次循环
16: $w(n) = w(n - 1) + e(n \| n - 1)u(n)/b(n) $ 　　　$-\gamma(1 - \lambda)R^{(-1)}(n)[R^{(-{\mathrm{T}})}(n)\nabla^2f(w(n - 1))] $
17: 结束第n次循环

下载: 导出CSV

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