| 刘小松,陈玥琦,单泽彪,王安妮,于艳鑫,苏成志.基于分数阶累积量的加权双曲复合函数平滑l0范数DOA估计方法[J].电子测量与仪器学报,2026,40(5):78-86 |
| 基于分数阶累积量的加权双曲复合函数平滑l0范数DOA估计方法 |
| Weighted hyperbolic composite function smoothing l0 norm DOAestimation based on fractional order cumulants |
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| DOI： |
| 中文关键词: 波达方向估计 分数阶累积量 双曲复合函数 平滑l0范数 |
| 英文关键词:DOA estimation fractional-order cumulants hyperbolic composite function smoothed l0-norm |
| 基金项目:吉林省自然科学基金面上项目（20250102050JC）资助 |
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| Author | Institution |
| Liu Xiaosong | School of Electronic and Information Engineering, Changchun University of Science and Technology, Changchun 130022, China |
| Chen Yueqi | School of Electronic and Information Engineering, Changchun University of Science and Technology, Changchun 130022, China |
| Shan Zebiao | 1.School of Electronic and Information Engineering, Changchun University of Science and Technology, Changchun 130022, China;
2.Jilin Provincial Collaborative Innovation Center for Intelligent Robots, Changchun University of Science and Technology,
Changchun 130022, China; 3.Jilin Provincial University Enterprise Joint Technological Innovation Laboratory for Intelligent
Hybrid Robots, Changchun University of Science and Technology, Changchun 130022, China |
| Wang Anni | School of Electronic and Information Engineering, Changchun University of Science and Technology, Changchun 130022, China |
| Yu Yanxin | School of Electronic and Information Engineering, Changchun University of Science and Technology, Changchun 130022, China |
| Su Chengzhi | 2.Jilin Provincial Collaborative Innovation Center for Intelligent Robots, Changchun University of Science and Technology,
Changchun 130022, China; 3.Jilin Provincial University Enterprise Joint Technological Innovation Laboratory for Intelligent
Hybrid Robots, Changchun University of Science and Technology, Changchun 130022, China |
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| 摘要点击次数: 210 |
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| 中文摘要: |
| 针对现有波达方向(direction of arrival, DOA)估计算法无法同时抑制α稳定分布噪声和高斯色噪声问题，提出了一种基于分数阶累积量和加权双曲复合函数的平滑l0范数的DOA估计算法。首先，利用分数阶累积量的半不变性以及对α稳定分布和高斯分布不敏感的特性，抑制α稳定分布和高斯色噪声。然后，将分数阶累积量矩阵进行向量化处理，并推导出基于分数阶累积量的稀疏DOA重构模型。最后，构造双曲复合函数对l0范数进行平滑逼近，并通过调节逼近因子实现平滑性与陡峭性的自适应权衡。同时，引入加权矩阵，对真实信号源对应位置进行加权增强，其余位置权值被抑制，进一步突出稀疏解的结构特征。在此基础上，采用梯度下降与投影相结合的双层迭代策略求解加权平滑l0优化问题，从而获得目标信号的DOA值。仿真实验结果表明，在α稳定分布与高斯色噪声混合且混合信噪比低至0的条件下，所提算法DOA估计的均方根误差为0.516 4°，充分验证了其在复杂噪声背景下的有效性和高精度。 |
| 英文摘要: |
| To address the limitation of existing direction-of-arrival (DOA) estimation algorithms in simultaneously suppressing alpha-stable distribution noise and Gaussian colored noise, a DOA estimation method based on fractional-order cumulants and a weighted hyperbolic composite-function smoothed l0-norm is proposed. First, by exploiting the semi-invariant property of fractional-order cumulants and their insensitivity to both alpha-stable and Gaussian distributions, the adverse effects of alpha-stable noise and Gaussian colored noise are effectively suppressed. Then, the fractional-order cumulant matrix is vectorized, and a sparse DOA reconstruction model based on fractional-order cumulants is formulated. Subsequently, a hyperbolic composite function is constructed to provide a smooth approximation of the l0-norm, where the approximation parameter is adaptively adjusted to balance smoothness and steepness. Meanwhile, a weighting matrix is introduced to enhance the coefficients corresponding to the true source locations while suppressing the remaining entries, thereby further emphasizing the sparse structure of the solution. Based on this formulation, a two-layer iterative optimization strategy combining gradient descent and projection is employed to solve the weighted smoothed l0 optimization problem, leading to accurate DOA estimation. The simulation results demonstrate that, even under conditions where the Alpha stable distribution is mixed with Gaussian colored noise and the mixed signal-to-noise ratio is as low as 0, the proposed algorithm achieves a root mean square error of 0.516 4°in DOA estimation, fully illustrating its effectiveness and high accuracy in complex noise backgrounds. |
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