A gridless one-step method for mixed far-field and near-field sources localization

To locate mixed far-field (FF) and near-field (NF) sources, most existing methods require two or three steps to first find the direction-of-arrival (DOA) and then retrieve the range parameters based on the DOA estimates. Hence, the range estimation performance highly relies on the DOA estimation accuracy in these methods. On the other hand, the MUSIC-like or on-grid sparse methods require discretization of the angle and range spaces which may bring in high computations and grid mismatch problem. In this paper, we propose a new method named Gridless OnE-Step (GOES) to jointly retrieve the DOA and range without requiring the pairing and discretization of the angle and range. In particular, we first construct a virtual single-snapshot signal model by the fourth-order cumulants, and then formulate a semidefinite programming (SDP) based on the atomic norm technique to simultaneously estimate the angle and range information. To reduce the computational complexity, we also propose a projected Wirtinger gradient descent algorithm Wirtinger-GOES (W-GOES) for the implementation. Because of the one-step procedure, our method not only has higher resolution than many existing methods in distinguishing both the angles and the ranges of different sources, but also can locate multiple NF or mixed FF and NF sources closely-located in angle domain or even with the same DOA. Extensive simulations are carried out to verify the superiorities of our method. (C) 2020 Elsevier Inc. All rights reserved.