Unified Near-Field and Far-Field Localization for AOA and Hybrid AOA-TDOA Positionings

Point positioning of a signal source is feasible if it is not far from the sensors and direction of arrival (DOA) localization is only applicable if it is distant. Point positioning and DOA localization employ different estimation models and prior knowledge about the source range is often not available to decide which model is appropriate. This paper introduces the modified polar representation to unify the localization of a source using angle of arrival (AOA) regardless if it is near or far. From the Gaussian AOA measurements, we utilize the hybrid Bhattacharyya-Barankin (HBB) bound to illustrate it is not possible to obtain the Cartesian coordinates of a distant source when applying the near-field model, and derive the DOA bias of a not so distant source when using the far-field model. An iterative maximum likelihood estimator (MLE) is next derived under the modified polar representation with a single model, where the HBB bound confirms the stable behavior of the estimator regardless it is near or far. The algorithm yields a position if the source is close and a DOA if it is distant. A preliminary solution to initialize the MLE using semidefinite relaxation is also proposed. The HBB bound, the analysis and the algorithm are extended for hybrid AOA-TDOA localization.