A new tensorial model is herein established for a special multidimensional array of vector sensors composed of a pressure part and orthogonal velocity parts, under which a multi-linear algebra based source number estimation algorithm is proposed. The estimation projects the covariance tensor into the signal subspace. Owing to the orthogonality between the newly defined tensor signal subspace and tensor noise subspace, it is easy to differentiate the contribution of the signal and noise by using the decision value in a compact tensorial fashion, which is the magnitude of projections from twofold mode signal subspaces. To reduce computer burden, meanwhile, the real-valued preprocessing method is applied to the covariance tensor for simplicity. Simulation and experiment results exhibit the superiority of the proposed algorithm over the conventional ones based on the matrix method.

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