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A dual parallel factor (PARAFAC)-based approach to jointly estimating the two-dimensional direction of arrival (2-D DOA) and Doppler is proposed in this paper, where an L-shaped array consisting of acoustic vector-sensor is used. First, we apply the PARAFAC decomposition to the data model formed by concatenating the outputs of multi-level delays of the observations, and we get the parameter matrix H, which accomplish the 2-D DOA estimation and pairing automatically, then the dual PARAFAC decomposition is applied to the achieved composite steering matrix from the first PARAFAC decomposition, and thus, the same permutation matrices link the estimates of steering matrices and delay matrices from X-subarray and Y-subarray, respectively. Following this, the Doppler and 2-D DOA matching information are obtained via triple matching implementation, e.g. 2-D DOA and frequency matching. Finally, Doppler is estimated by delay matrices. The proposed algorithm is computationally effective for both uniform and non-uniform L-shaped array as SNR exceeds 15dB, and its performance outperforms the joint angle and Doppler shift ESPRIT (JAD-ESPRIT) algorithm and the joint angle and Doppler shift PM (JAD-PM) algorithm. The simulation results justified the effectiveness of the proposed algorithm.

Joint 2-D DOA and Doppler Estimation for L-Shaped Array via Dual PARAFAC With Triple Matching Implementation