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.

中文翻译：

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基于统一优化的探地雷达双曲线拟合模型分析

探地雷达 (GPR) 是探索地下空间的宝贵工具，特别是用于检测管道和钢筋等圆柱形物体，其中数据通常形成双曲线模式。双曲线拟合技术是从这些数据中提取信息的常用方法。然而，现有文献还没有彻底研究不同的参数——例如天线间距、目标半径、埋藏深度和宿主介质的相对介电常数——如何影响各种双曲线拟合的性能，或者严格来说，非双曲线拟合的性能。路径模型。本研究通过将 2 个双曲型和 3 个非双曲型拟合模型表述为常见的数学优化问题，对它们进行了广泛的比较分析。引入一种新颖的成本函数（C 值）来定量评估这五个模型。结果表明，各种参数对模型的实际性能有不同的影响。考虑到先验信息的可用性和模型匹配的有效性，提供了模型选择的建议。研究结果和建议提供了实用的见解，有望提高各种探地雷达研究中双曲线和非双曲线拟合的精度和可靠性。