A Bayesian Approach to Modeling GPS Errors for Comparing Forensic Evidence

This paper introduces a Bayesian approach to modeling GPS er-rors for comparing forensic evidence, addressing the challenge of determining the most likely source of a single GPS localization given two proposed locations. We develop a probabilistic model that transforms GPS coordinates into polar coordinates, capturing distance and directional errors. Our method employs Markov chain Monte Carlo (MCMC) sampling to estimate the data-generating processes of GPS measurements, enabling robust comparison of potential device locations while quantifying uncertainty. We apply this approach to three datasets: one from existing literature and two newly collected datasets from Ljubljana and Novo mesto. The result is a posterior distribution of log-likelihood ratios directly compar-ing the two propositions, which can be transformed into likelihood ratios to comply with current standards in forensic science.