In this paper, we investigate the problem of estimating the directions-of-arrival (DOAs) and ranges of multiple near-field narrowband sources impinging on a symmetric uniform linear array (ULA). By forming a Toeplitz-like correlation matrix from the anti-diagonal elements of the array covariance matrix, a convex optimization problem for the resultant Toeplitz-like matrix reconstruction is established and further a gridless sparsity-based localization for near-field sources is proposed. The DOAs can then be retrieved by using the recovered correlation matrix according to root-MUSIC or Vandermonde decomposition theorem. Additionally, the ranges are obtained through a subspace-based estimator with the corresponding estimated DOAs, while the association of the estimated DOAs and ranges are completed at the same time. Finally, the numerical examples are provided to substantiate the performance of our proposed method, and the simulation results demonstrate that the proposed method provides remarkable and satisfactory estimation performance.

Near-field; DOA estimation; source localization; Toeplitz covariance matrix; gridless method; uniform linear array