Mirror-assisted calibration of a multi-modal sensing array with a ground penetrating radar and a camera

To develop a multi-modal in-traffic bridge deck scanning device, we need to estimate the relative pose between a ground penetrating radar (GPR) and a camera. Unlike camera images, GPR output is in a non-Euclidean coordinate system because it only detects underground objects relative to road surface. When road surface is non-planar, its output cannot be trivially mapped to a 3D Cartesian system which is necessary for sensor fusion. Since there is no joint coverage between two sensors due to mounting requirements, we design an artificial planar bridge assisted by a planar mirror as the calibration rig. We combine the pinhole camera model with mirror reflection transformation and model the GPR imaging process. We estimate the camera and mirror poses and extract readings from hyperbolas generated from metal balls. We employ the maximum likelihood estimator to estimate the rigid body transformation between the two sensors and provide the closed form error analysis. We have conducted physical experiments to validate our calibration process and shown the average error of 6.67 mm for our calibration model. The result is satisfying considering the GPR signal wave length is 18.75 cm.