A Spatial Calibration Strategy of Multiple Airborne Ultrasonic Phased Arrays based on Acoustic Beam Steering

In application use of electronically controllable ultrasound fields, spatial calibration of multiple airborne ultrasonic phased arrays forming a synthetic aperture must be completed with subwavelength accuracy for extending workspaces. However, manually completing the calibration requires a lot of time and effort, and there has been no established automatic method for this problem. Here we propose an acoustic calibration method using spatiotemporal structured ultrasound field sequentially generated by each array and a single microphone for acoustic measurement. We form a point cloud of microphone positions by the measurement and then register them into Gaussian model in the global coordinate system common across all arrays. We apply likelihood maximization approach to estimate the positions and postures of all arrays that minimizes the discrepancy of global microphone positions retrieved from local observations. We conducted numerical experiments to find that the calibration with no error was achieved with no measurement errors in microphone position, whereas mean estimation errors of less than a quarter of the wavelength in position and one degree in posture were observed when assuming a possible magnitude of measurement errors estimated in previous works.