Subspace-Based localization of near-field signals in unknown nonuniform noise

In this paper, we consider the problem of estimating the directions-of-arrival (DOAs) and ranges of multiple nearfield narrowband signals impinging on a symmetric uniform linear array (ULA) in nonuniform noise in practical applications. By forming a Toeplitz-like correlation matrix from the anti-diagonal elements of the array covariance matrix to convert the nonuniform noise to a uniform one, a new subspace-based localization method is proposed, where the null space is obtained through eigendecomposition of the resultant Toeplitz-like matrix, and the MUSIC method is used to estimate the location parameters, while a new pairing scheme is presented as well. Additionally, an oblique projector based alternating iteration is presented to improve the estimation accuracy of the location parameters, where the 'saturation behavior'encountered in most of localization methods is solved effectively. Furthermore, the Cramér-Rao lower bound (CRB) for the near-field signals in unknown nonuniform noise is also derived explicitly. Finally, the effectiveness of the proposed method is verified through numerical examples.