This paper considers the localization problem of incoherently distributed near-field (IDNF) sources. It is observed that the angular and range spreads of IDNF source signals produce a useful low-rank structure, which can be used to estimate the joint angular-range distribution (JARD) for IDNF sources. Then, by analyzing the low-rank property of the JARD matrix, a rank minimization problem is formulated to directly estimate the JARD matrix, which can be solved efficiently by the truncated nuclear norm regularization with accelerated proximal gradient line search method (TNNR-APGL). Finally, for performance comparisons, off-grid estimators are applied to estimate the key parameters of the JARD. Compared with conventional algorithms, the proposed method enjoys better parameter estimation performance and faster computation, requiring no parameterized distribution model and multi-dimensional search. Numerical experiments are included to demonstrate the performance of the proposed solution.

本文考虑了非相干分布近场（IDNF）源的定位问题。据观察，IDNF 源信号的角度和范围扩展产生了一个有用的低秩结构，可用于估计 IDNF 源的联合角范围分布 (JARD)。然后，通过分析 JARD 矩阵的低秩性质，提出了一个秩最小化问题来直接估计 JARD 矩阵，该问题可以通过使用加速近端梯度线搜索方法（TNNR-APGL）的截断核范数正则化来有效解决. 最后，为了进行性能比较，应用离网估计器来估计 JARD 的关键参数。与传统算法相比，该方法具有更好的参数估计性能和更快的计算速度，不需要参数化分布模型和多维搜索。包括数值实验以证明所提出的解决方案的性能。