A tensor model for calibration and imaging with air-coupled ultrasonic sensor arrays

Arrays of ultrasonic sensors are capable of 3D imaging in air and an affordable supplement to other sensing modalities, such as radar, lidar, and camera, i.e. in heterogeneous sensing systems. However, manufacturing tolerances of air-coupled ultrasonic sensors may lead to amplitude and phase deviations. Together with artifacts from imperfect knowledge of the array geometry, there are numerous factors that can impair the imaging performance of an array. We propose a reference-based calibration method to overcome possible limitations. First, we introduce a novel tensor signal model to capture the characteristics of piezoelectric ultrasonic transducers (PUTs) and the underlying multidimensional nature of a multiple-input multiple-output (MIMO) sensor array. Second, we formulate an optimization problem based on the proposed tensor model to obtain the calibrated parameters of the array and solve the problem using a modified block coordinate descent (BCD) method. Third, we assess both our model and the commonly used analytical model using real data from a 3D imaging experiment. The experiment reveals that our array response model we learned with calibration data yields an imaging performance similar to that of the analytical array model, which requires perfect array geometry information.