Joint azimuth-elevation/(-range) estimation of mixed near-field and far-field sources using two-stage separated steering vectorbased algorithm

Passive source localization has wide applications in array signal processing. In the practical applications, the observations collected by an array may be "arbitrary "-field signals, i.e., which are either mixed near-field and far-field signals or multiple near-field signals or multiple far-field signals. With a cross array, a two-stage separated steering vector-based algorithm is developed to localize "arbitrary "field narrowband sources in the spherical coordinates. The key points of this paper are: i) different physical steering vectors of near-field and far-field sources are transformed into the virtual ones with the same form, thus linearizing the quadratic phases of near-field sources and allowing the same operations for near-field and far-field sources; ii) the virtual steering vector is separated into two parts and restored by introducing a special phase angle, and thus it is used to estimate the azimuth-elevation arrival-angles of "arbitrary "-field sources; and iii) special Hermitian matrices are constructed using the separated physical steering vector and their eigenvalue decomposition (EVD) are performed, thus the ranges of near-field sources are easily obtained from the eigenvector being corresponding to the smallest eigenvalue. The proposed algorithm can localize "arbitrary "-field sources without pairing parameters and multidimensional search. Simulation results are provided to validate the performance of the proposed method.