尺度不变范数比正则的稀疏DOA估计

Scale Invariant Norm Ratio Regularized Sparse DOA Estimation

波达方向估计(Direction Of Arrival,DOA)通过使用传感器阵列来识别声源方位,而传统的DOA估计方法忽略了声源在空间分布的稀疏性,目前的凸稀疏DOA估计方法和非凸稀疏DOA估计方法所使用的惩罚函数未考虑稀疏度量l0范数的重要特性——尺度不变性,因此无法精确描述声源的空域稀疏结构,难以获得较高的DOA估计精度.为此,本文首先使用具有尺度不变性的范数比函数来逼近l0范数,刻画声源空域稀疏结构;接着,针对范数比函数的非凸特性,采用光滑化的思想,构建了平滑的近似函数;然后,构建了基于光滑lp比lq范数的稀疏DOA估计模型,开发了基于光滑lp比lq范数的稀疏DOA估计算法(Smoothed lp-Over-lqregularized Sparse DOA Estimation algorithm,SPOQ-SDOA).大量仿真分析表明,与流行的多快拍DOA估计算法相比,本文提出的算法在不同信噪比和快拍数下有更高的DOA估计精度和更好的性能表现.SWell Ex-96海试实验中的S5事件分析结果验证了所提算法的有效性.

Direction of arrival(DOA)estimation uses sensor arrays to identify the direction of sound sources,while traditional DOA estimation methods ignore the sparsity of sound sources in spatial distribution.The penalty function used by current convex sparse DOA estimation methods and non-convex sparse DOA estimation methods do not consider the im⁃portant scale invariance feature of sparseℓ0 norm,which cannot accurately describe the spatial sparse structure of the sound source,and it is difficult to obtain high DOA estimation accuracy.For this reason,firstly,the scale-invariance norm ratio function is used to approximate theℓ0 norm and characterize the spatial sparse structure of the sound source in this paper;Secondly,aiming at the non-convex property of the norm ratio function,a smooth approximation function is constructed by using the idea of smoothing;Then,the scale-invariantℓp-over-ℓq regularized sparse DOA estimation model is constructed,and meanwhile an optimization algorithm is developed for it.A lot of simulation analysis demonstrate that the proposed al⁃gorithm has higher DOA estimation accuracy and better performance under different SNR and snapshot numbers than the popular multi-snapshot DOA estimation algorithm.The analysis results of S5 events in SWellEx-96 sea trial experiment verified the effectiveness of the proposed algorithm.