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The least squares-virtual ESPRIT algorithm (LS-VESPA) is extended to jointly estimate the direction-of-arrival (DOA) and ranges of multiple near-field sources impinging on an array of crossed dipoles. The algorithm utilizes fourth-order cumulants for direct estimation of the arrival angle and range parameters via the eigenvalues of certain constructed matrices. Compared with several existing algorithms, the loss of array aperture is effectively avoided. As a result, the proposed method can estimate DOAs and ranges of (N - 1) polarized near-field sources using N dual-polarization sensors. Simulation results show that the proposed method outperforms a fourth-order statistics based ESPRIT-like method.