Subspace-Based Near-Field Source Localization in Unknown Spatially Nonuniform Noise Environment

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.