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A novel algorithm is developed to estimate the two-dimensional direction-of-arrival (DOA) of the coherent sources based on a sparsely-distributed acoustic vector-sensor array. Only one-dimensional spatial-smoothing (SS) is used to restore the rank of the covariance matrix, and the algorithm can offer closed-form DOA estimation of the coherent sources. The proposed approach 1) avoids the iterative search in the "particle-velocity-field smoothing" (PVFS) algorithm, and 2) compensates the array aperture decreasing in the traditional SS algorithm. The inter-sensor spacing phase-factors are used to improve the DOA estimation accuracy. Simulation results verify the efficacy of the proposed algorithm.