Mixed Near-Field and Far-Field Localization and Array Calibration With Partly Calibrated Arrays

The problem of passive localization of mixed near-field (NF) and far-field (FF) source signals in the presence of array gain-phase uncertainties is addressed. A new algorithm is aimed to use partly calibrated nonuniform linear arrays (NLAs), in which only three sensors have been fully-calibrated. Most of the existing algorithms deal with this problem by exploiting uniform linear arrays (ULAs). Moreover, they assume a simplified source-array model, in which the propagation magnitude scaling is completely neglected and the spatial phase difference is approximated by Taylor's polynomial. As an opposite, the proposed algorithm is employed to accommodate a more general situation: the exact spatial geometries and nonuniform linear arrays. In the proposed algorithm, three cumulant matrices are firstly defined to construct two matrix pencils. Unambiguous range and angle parameter estimates of the NF sources are then obtained from the generalized eigenvalues of the two defined matrix pencils. After that, these estimates are utilized to calibrate array gain-phase errors. Finally, a spectrum-MUSIC like approach is applied to accomplish the angle estimation for the FF sources. The new algorithm is shown to be readily simple and effective and will be verified both mathematically and numerically.

Automated summary

This study addresses the problem of passive localization of mixed near-field and far-field source signals in the presence of array gain-phase uncertainties. A new algorithm using partly calibrated nonuniform linear arrays is proposed to accommodate a more general situation. The proposed algorithm defines cumulant matrices and constructs matrix pencils to obtain unambiguous range and angle estimates of the near-field sources, and then calibrates array gain-phase errors using these estimates. A spectrum-MUSIC like approach is applied to estimate the angles of the far-field sources.