Multisource self-calibration for sensor arrays

Abstract—Calibration of a sensor array is more involved if the antennas have direction dependent gains and multiple calibrator sources are simultaneously present. We study this case for a sensor array with arbitrary geometry but identical elements, i.e., elements with the same direction dependent gain pattern. A weighted alter-nating least squares (WALS) algorithm is derived that iteratively solves for the direction independent complex gains of the array ele-ments, their noise powers and their gains in the direction of the cal-ibrator sources. An extension of the problem is the case where the apparent calibrator source locations are unknown, e.g., due to re-fractive propagation paths. For this case, the WALS method is sup-plemented with weighted subspace fitting (WSF) direction finding techniques. Using Monte Carlo simulations we demonstrate that both methods are asymptotically statistically efficient and converge within two iterations even in cases of low SNR. Index Terms—Array signal processing, radio astronomy, self-calibration. I