Array auto-calibration using a generalized least-squares method

Abstract

This paper introduces a new class of auto-calibration algorithms, based on a generalized least-squares (GLS) cost function. This class supports both gain-phase calibration and mutual coupling calibration and it is independent of array shape. The GLS cost function is minimized cyclically with respect to the direction of arrivals (DOA) and calibration parameters. These two minimization steps are repeated until convergence. In the DOA estimation step, minimization leads to the SPICE (SParse Iterative Covariance-based Estimation) DOA estimation algorithm. In fact, the innovation of this paper mainly lies in the calibration step. In the DOA estimation step, a generalized form of the SPICE algorithm should be used in the coherent sources case. Consequently, the proposed auto-calibration algorithm is able to support coherent source cases. Moreover, the proposed algorithm does not need multi-dimensional search. The necessary condition for the existence of a solution is studied as well. Using simulations, the performance of the proposed algorithm is compared with several other auto-calibration algorithms. Simulation results show that the proposed algorithm is more robust than the other algorithms and usually has better performance.