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快速非负稀疏贝叶斯反卷积方位估计方法

Fast nonnegative sparse Bayesian deconvolution method for direction-of-arrival estimation

  • 摘要: 稀疏反卷积波束形成技术通过挖掘常规波束形成结果中波束和声源之间的卷积关系,设计声源在空间中的稀疏分布正则,通过解卷积有效消除了波束主瓣带来的模糊现象,显著提升了水下目标的方位估计精度。然而,稀疏反卷积波束形成采用凸或非凸正则描述声源稀疏模式,缺少针对稀疏表征的数据自适应机制,加之反卷积模型中的平移不变波束字典维数较高,导致其定位精度和计算效率严重不足。为此,文章提出了快速非负稀疏贝叶斯反卷积方位估计方法。该方法利用阵列波束构建点扩散函数反卷积字典,通过贝叶斯建模和非负约束自动描述声源的稀疏分布结构。同时采用动态活跃集机制,仅对具有较高相关性或较大能量的候选角度进行后验估计,降低密集角度网格字典的计算复杂度,提升了求解效率。在此基础上,采用期望最大化算法完成超参数更新、噪声功率自适应估计以及低能量候选剪枝,实现目标方位的自适应筛选与稀疏空间谱重构。最后,通过不同信噪比条件下的双声源仿真实验,并结合浅海拖曳阵数据,验证了所提方法在谱峰锐化、相邻目标分辨能力以及连续方位跟踪方面的有效性。

     

    Abstract: Sparse deconvolution beamforming exploits the convolutional relationship between the beam pattern and the source distribution embedded in conventional beamforming outputs, and introduces sparsity-promoting regularization to characterize the spatial distribution of acoustic sources. By deconvolving the beamforming results, the spatial blurring induced by the main lobe of the array’s beam pattern can be effectively suppressed, thereby significantly improving the direction-of-arrival (DOA) estimation accuracy for underwater targets. However, existing sparse deconvolution beamforming methods generally employ deterministic convex or nonconvex regularization to enforce source sparsity, lacking a data-adaptive mechanism for sparse representation. Moreover, the shift-invariant beam dictionary involved in the deconvolution model is typically high-dimensional, imposing substantial limitations on both localization accuracy and computational efficiency. To address these issues, this paper proposes a fast nonnegative sparse Bayesian deconvolution method for DOA estimation. The proposed method constructs a point-spread-function (PSF)-based deconvolution dictionary from the array’s beam pattern and employs Bayesian modeling—combined with nonnegativity constraints—to adaptively characterize the sparse spatial distribution of acoustic sources. Meanwhile, a dynamic active-set mechanism is introduced, wherein posterior inference is performed only for candidate directions exhibiting relatively high correlation with the observed data or significant energy. This strategy substantially reduces the computational burden associated with densely discretized angular dictionaries and improves overall inference efficiency. Moreover, an expectation-maximization (EM) algorithm is developed to derive iterative updates for the model hyperparameters, enable adaptive estimation of the noise power, and prune low-energy candidate directions. Finally, extensive two-source simulations under various signal-to-noise ratio (SNR) conditions—as well as experimental data collected using a shallow-water towed array—are employed to validate the proposed method. The results demonstrate its effectiveness in sharpening spatial-spectrum peaks, resolving closely spaced targets, and enabling continuous DOA tracking.

     

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