Array calibration of angularly dependent gain and phase uncertainties with carry-on instrumental sensors

Array calibration with angularly dependent gain and phase uncertainties has long been a difficult problem. Although many array calibration methods have been reported extensively in the literature, they almost all assumed an angularly independent model for array uncertainties. Few calibration methods have been developed for the angularly dependent array uncertainties. A novel and efficient auto-calibration method for angularly dependent gain and phase uncertainties is proposed in this paper, which is called ISM (Instrumental Sensors Method). With the help of a few well-calibrated instrumental sensors, the ISM is able to achieve favorable and unambiguous direction-of-arrivals (DOAs) estimate and the corresponding angularly dependent gain and phase estimate simultaneously, even in the case of multiple non-disjoint sources. Since the mutual coupling and sensor position errors can all be described as angularly dependent gain/phase uncertainties, the ISM proposed still works in the presence of a combination of all these array perturbations. The ISM can be applied to arbitrary array geometries including linear arrays. The ISM is computationally efficient and requires only one-dimensional search, with no high-dimensional nonlinear search and convergence burden involved. Besides, no small error assumption is made, which is always an essential prerequisite for many existing array calibration techniques. The estimation performance of the ISM is analyzed theoretically and simulation results are provided to demonstrate the effectiveness and behavior of the proposed ISM.