Near-Field Passive Localization and Gain–Phase Compensation With Partly Calibrated Arrays

Abstract

The localization of near-field sources is one of the important applications of array signal processing. Most of the existing approaches to handle this problem utilize uniform linear arrays with ideal sensors. Moreover, they assume a simplified source-sensor spatial model, where propagation loss among sensors is neglected and the spatial phase difference is approximated by a Taylor polynomial. The present work considers a more general case: the exact spatial geometry and partly calibrated irregular linear arrays. We exploit a partly calibrated array with several calibrated sensors, two of which are used as reference sensors to define two cumulant matrices for the construction of a matrix pencil. Source range–angle parameters are then derived in closed form from the generalized eigenvalues of this matrix pencil. In case that the separation of the two reference sensors is larger than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda /2$</tex-math></inline-formula> , the source location parameter estimation would, thus, be ambiguous, with each individual estimation giving its own estimate of array gain–phase error vector. The entries of this vector that correspond to the calibrated sensors are finally applied to resolve the ambiguities in the source location parameter estimation. The proposed approach is simple and effective, as will be validated via numerical examples.