Millimeter accuracy depth estimation in concrete using smartphone-equipped handheld GPR and hyperbolic curve fitting with antenna distance consideration.

In the management and maintenance of structural facilities, knowing the cover thickness of rebar and the depth of buried objects is of paramount importance. Currently, Smartphone-Equipped Handheld Ground Penetrating Radars (GPR) are primarily used for detecting rebar, yet the Electromagnetic Induction (EMI) method remains the sole available technique for determining the cover thickness of rebar. This necessitates the use of two separate devices to understand the subsurface condition of rebar. In this study, we introduce a new algorithm that utilizes Hyperbolic Curve Fitting to determine depth and relative permittivity from reflection images derived from a single GPR measurement, using metal depth estimation as an exemplar. Our contributions include the automatic detection of the hyperbola's centerline before curve fitting, separation of the hyperbola into left and right for enhanced fitting accuracy by removing points near the vertex, and incorporating a rigorous theoretical model that took into account the distance between the transmitting and receiving antennas, known as the inter-antenna distance. This algorithm had enabled us to meet the performance requirements for the EMI method as stipulated by the Japanese Society for Non-Destructive Inspection (JSNDI). Notably, our method retained its accuracy even at depths exceeding the 100 mm limitation of the EMI method.