Spatial–Temporal-Based 3-D Parameters Estimation Method for Near-Field Sources Using Parallel Factor Model

In this paper, a novel algorithm is presented for estimating three-dimensional (3-D) parameters of near-field (NF) sources with a centro-symmetric cross array, where the sub-array x and the sub-array y are uniform linear arrays equipped with the same number of array elements. By exploiting the time-delay-based spatial correlation of the received signal, the proper array elements are selected, respectively, from the two sub-arrays to define two sets of variables, and then two time-delay-based vectors are constructed. Further, a series of delay lags are uniformly sampled to form pseudo snapshots so as to obtain two corresponding time delay matrices, which facilitates the formation of the parallel factor (PARAFAC) model in time domain. Finally, trilinear alternating least squares decomposition is utilized to jointly estimate the two-dimensional (2-D) direction-of arrival and range parameters of NF sources from the PARAFAC model. In the case of low signal-to-noise ratio and small snapshots conditions, the estimation performance in the 3-D parameters of the proposed algorithm is superior to that of the subspace-based algorithm. In addition, the proposed algorithm only involves simple parameter pairing, which requires no eigenvalue decomposition and spectral peak searching.