Three-Dimensional Localization of Mixed Near-Field and Far-Field Sources Based on a Unified Exact Propagation Model

In applications like speaker localization using a microphone array, the collected signals are typically a mixture of far-field (FF) and near-field (NF) sources. To find the positions of both NF and FF sources, a three-dimensional spatial-temporal localization algorithm based on a unified exact propagation geometry is developed in this paper, which avoids approximating the spatial phase difference with the first-order and second-order Taylor expansions applied to FF and NF sources, respectively. Our scheme utilizes cross-correlation to produce virtual observations for establishing a third-order parallel factor data model with the use of spatial and temporal information. The array's steering vectors can be extracted by trilinear decomposition. The amplitude and phase information of the whole array elements is jointly exploited to classify the source types and obtain the location estimates via a least squares method. Moreover, the proposed algorithm is computationally efficient since no spectral searches, high-order statistics calculations or parameter pairing procedures are required. The deterministic Cramér-Rao bound is also derived as a performance benchmark, and numerical results are provided to demonstrate the effectiveness of the developed method.