Unified optimization-based analysis of GPR hyperbolic fitting models

Ground Penetrating Radar (GPR) is a valuable tool for exploring underground spaces, particularly for detecting cylindrical objects such as pipelines and rebar, where data often forms hyperbolic pattern. The technique of hyperbola fitting is a commonly used approach for extracting information from these data. However, the existing literature has not thoroughly examined how different parameters - such as antenna separation, target radius, burial depth, and the relative permittivity of the host media - influence the performance of various hyperbola fitting, or strictly speaking, non-hyperbolic ray-path models. This study presents an extensive comparative analysis of 2 hyperbolic and 3 non-hyperbolic fitting models by formulating them as a common optimization problem mathematically. A novel cost function (C-value) is introduced to quantitatively evaluate the five models. The results demonstrate that various parameters have distinct influences on the performance of the models to the reality. Recommendations for model selection are provided, taking into account the availability of prior information and efficacy in matching the models. The findings and recommendations offer practical insights that are poised to improve the precision and reliability of hyperbola and non-hyperbolic fitting in various GPR studies.