On the Limitations of Hyperbola Fitting for Estimating the Radius of Cylindrical Targets in Non-Destructive Testing and Utility Detection

Hyperbola fitting is a mainstream interpretation technique used in ground-penetrating radar (GPR) due to its simplicity and relatively low computational requirements. Conventional hyperbola fitting is based on the assumption that the investigated medium is a homogeneous half-space, and that the target is an ideal reflector with zero radius. However, the zero-radius assumption can be easily removed by formulating the problem in a more generalized way that considers targets with arbitrary size. Such approaches were recently investigated in the literature, suggesting that hyperbola fitting can be used not only for estimating the velocity of the medium, but also for estimating the radius of subsurface cylinders, a very challenging problem with no conclusive solution to this day. In this letter, through a series of synthetic and laboratory experiments, we demonstrate that for practical GPR survey, hyperbola fitting is not suitable for simultaneously estimating both the velocity of the medium and the size of the target, due to its inherent nonuniqueness, making the results unreliable and sensitive to noise.