In this paper, we investigate the problem of estimating the directions-of-arrival (DOAs) and ranges of multiple narrowband near-field sources in unknown spatially nonuniform noise (spatially inhomogeneous temporary white noise) environment, which is usually encountered in many practical applications of sensor array processing. A new subspace-based localization of near-field sources (SLONS) is proposed by exploiting the advantages of a symmetric uniform linear sensor array and using Toeplitzation of the array correlations. Firstly three Toeplitz correlation matrices are constructed by using the anti-diagonal elements of the array covariance matrix, where the nonuniform variances of additive noises are reduced to a uniform one, and then the location parameters (i.e., the DOAs and ranges) of near-field sources can be estimated by using the MUSIC-like method, while a new pair-matching scheme is developed to associate the estimated DOAs and ranges. Additionally, an alternating iterative scheme is considered to improve the estimation accuracy of the location parameters by utilizing the oblique projection operator, where the “saturation behavior” caused by finite number of snapshots is overcome effectively. Furthermore, the closed-form stochastic Cramér-Rao lower bound (CRB) is also derived explicitly for the near-field sources in the additive unknown nonuniform noises. Finally, the effectiveness of the proposed method and the theoretical analysis are substantiated through numerical examples.

中文翻译：

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未知空间非均匀噪声环境中基于子空间的近场源定位

在本文中，我们研究了在未知空间非均匀噪声（空间非均匀临时白噪声）环境中估计多个窄带近场源的到达方向（DOA）和范围的问题，这通常在许多实际应用中遇到传感器阵列处理。通过利用对称均匀线性传感器阵列的优势并使用阵列相关性的 Toeplitzation，提出了一种新的基于子空间的近场源定位 (SLONS)。首先利用阵列协方差矩阵的反对角元素构造三个托普利兹相关矩阵，其中加性噪声的非均匀方差减少到一个均匀的，然后位置参数（即，近场源的 DOA 和距离）可以通过使用类似 MUSIC 的方法来估计，同时开发了一种新的配对方案来关联估计的 DOA 和距离。此外，还考虑了一种交替迭代方案，利用斜投影算子提高位置参数的估计精度，有效克服了有限数量快照引起的“饱和行为”。此外，封闭形式的随机 Cramér-Rao 下界 (CRB) 还针对加性未知非均匀噪声中的近场源明确导出。最后，通过数值算例验证了所提方法的有效性和理论分析。考虑了交替迭代方案，利用斜投影算子提高位置参数的估计精度，有效克服有限数量快照引起的“饱和行为”。此外，封闭形式的随机 Cramér-Rao 下界 (CRB) 还针对加性未知非均匀噪声中的近场源明确导出。最后，通过数值算例验证了所提方法的有效性和理论分析。考虑了交替迭代方案，利用斜投影算子提高位置参数的估计精度，有效克服有限数量快照引起的“饱和行为”。此外，封闭形式的随机 Cramér-Rao 下界 (CRB) 还针对加性未知非均匀噪声中的近场源明确导出。最后，通过数值算例验证了所提方法的有效性和理论分析。封闭形式的随机 Cramér-Rao 下界 (CRB) 也为加性未知非均匀噪声中的近场源明确导出。最后，通过数值算例验证了所提方法的有效性和理论分析。封闭形式的随机 Cramér-Rao 下界 (CRB) 也为加性未知非均匀噪声中的近场源明确导出。最后，通过数值算例验证了所提方法的有效性和理论分析。