GPR uncertainty modelling and analysis of object depth based on constrained least squares

The development of ground penetrating radar (GPR) in recent decades has promoted the role of this popular near-surface geophysical detection method. A step further involves its transition from use as a prospecting tool aimed at estimating the approximate location of buried objects to its application as an accurate piece of survey equipment [1], which then requires an understanding of measurement errors/uncertainties. This paper firstly discusses the sources of uncertainty affecting an object’s depth measurement with respect to host material, instrumentation, data collection method and signal processing. These error sources were modelled by formulating computation sets based on the application of a constrained least squares algorithm to hyperbolic re-flections produced by buried objects. Based on the computation, uncertainty analysis was performed (1) through identification of errors on measurements of hyperbolic reflections and (2) by conducting error propagation to evaluate the combined uncertainty of the surveyed depth. At a geophysical test site at IFSTTAR, Nantes, France, sets of controlled experiments were conducted to validate the proposed uncertainty analysis method and to investigate the correlation between the evaluated uncertainty and the factors of host material, antenna centre frequency, target depth and the horizontal and vertical resolution in the radargram. Based on the experiments, it was possible to draw two main conclusions. Firstly, a centimetre-order of uncertainty can be achieved in the survey results for depth estimation of objects at several metres deep with a 95% confidence level at ±2 standard deviations. Secondly, errors of time zero location at different GPR centre frequencies dominate the evaluation of uncertainty, whereas the resolution of radargrams and scattering noise do not explicitly affect the evaluated uncertainty.