A tensor model for the calibration of air-coupled ultrasonic sensor arrays in 3D imaging

TL;DR

This paper introduces a tensor-based calibration method for air-coupled ultrasonic sensor arrays in 3D imaging, improving accuracy despite manufacturing tolerances and geometric uncertainties.

Contribution

It presents a novel tensor signal model for ultrasonic transducers and formulates an optimization approach for array calibration, enhancing imaging performance.

Findings

The tensor model effectively captures ultrasonic array characteristics.

Calibration with the proposed model achieves imaging performance comparable to ideal models.

The method compensates for manufacturing and geometric deviations in sensor arrays.

Abstract

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 and solve an optimization problem based on this model to obtain the calibrated parameters of the array. Third, we assess both our model and the commonly used analytic 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 analytic array model, which requires perfect array geometry information.