An Efficient Near-Field Model Gain-Phase Self-Calibration Method for Uniform Rectangular Arrays

Large uniform rectangular arrays (URAs) are widely used in 3-D underwater imaging systems to obtain high-quality images; however, the gain and phase errors of these arrays can distort the results. To restore the image quality, many calibration methods have been proposed, most of which adopt a far-field model. This model requires the calibrator source to be far away, which reduces the signal-to-noise ratio and adversely affects the calibration accuracy. An effective means of alleviating this contradiction is to adopt the near-field signal model. However, the source location estimation in the near-field model typically uses spectral peak searches, which is a significant computational burden, particularly for large URAs. A fast and efficient near-field model self-calibration method for large URAs is proposed to obtain improved calibration results. First, a convenient preprocessing and two extended three-step iterative algorithms are used instead of spectral peak searches to estimate the source location efficiently. The array is then calibrated using a spatial matched filter and maximum a posteriori approach. Numerical results proved that the proposed method almost reaches the Cramér–Rao bound. Compared with existing near-field model calibration methods using spectral peak searches, the computational complexity of the proposed method is reduced by more than three orders of magnitude when the array size reaches 60 $\times $ 60 or more. By virtue of the near-field model, the phase calibration accuracy for large URAs at a close range is more than 10 times that of far-field model calibration methods.