TDOA Positioning Irrespective of Source Range

TDOA localization requires the knowledge if the source is in the near-field or far-field, for the purpose to decide using the curved wavefront model that enables point positioning or the linear wavefront model that provides only the DOA. Such prior knowledge is often not available in practice. The far-field model can cause a considerable amount of DOA bias if the source is not sufficiently distant from the sensor array. This paper proposes a unified model to locate a source irrespective of whether it is in the near field, the far field or in between. The proposed model represents the source location by the direction and the inverse-range. It yields the unique coordinate if the source is near or the DOA if it is distant. We developed the Maximumm Likelihood Estimator for the proposed model through the Gauss–Newton iteration and semidefinite relaxation. We analyze the proposed model using the Hybrid Bhattacharyya–Barankin bound and show that the proposed model does not have the thresholding effect as the source range increases, validating that there is no need to resort to the far-field model even if the source range is large. We also perform bias analysis and elaborate a benefit of the proposed approach in reducing the DOA bias as compared to the far-field model.