Single- and double-difference algorithms for position and time-delay calibration of transducer-elements in a sparse array

A method for the calibration of the position and time delay of transducer elements in a large, sparse array used for underwater, high-resolution, ultrasound imaging has been described in a previous work. This algorithm is based on the direct algorithm used in the global positioning system (GPS), but the wave propagation speed is treated as one of the to-be-calibrated parameters. In this article, the performance of two other commonly used GPS algorithms, namely the single-difference algorithm and the double-difference algorithm, is evaluated. The calibration of the propagation speed also is integrated into these two algorithms. Furthermore, a novel, least-squares method is proposed to calibrate the time delay associated with each transducer element for these two algorithms. The performances of these algorithms are theoretically analyzed and evaluated using numerical analysis and simulation study. The performance of the direct algorithm, the single-difference algorithm, and the double-difference algorithm is compared. It was found that the single-difference algorithm has the best performance among the three algorithms for the current application, and it is capable of calibrating the position and time delay of transducer elements to an accuracy of one-tenth of a wavelength.