<p>To address the issue of near-field localization within the spherical wavefronts, in this paper, a cumulant matrices-based algorithm is proposed based on the exact spatial propagation model. Multiple fourth-order cumulant matrices are constructed with the changed position number of the array elements, which are then cascaded to a cumulant-based long matrix. Next, the covariance matrix of the cumulant matrix is computed, and eigen-decomposition is performed to estimate the corresponding array manifold matrix by using the ESPRIT. The subsequent step involves extracting amplitude attenuation and spatial phase from the estimated manifold matrix. The least squares method is then employed to yield unambiguous coarse estimates and ambiguity-resolving fine estimates for angle and range parameters. In addition, the asymptotic variance for the proposed estimator is theoretically derived. Simulation results demonstrate that the correctness of the proposed algorithm.</p>