In Europe, most train passengers use only a small portion of the railway network. In France, capillary lines make up 42% of the network but account for only 10% of the commercial offer. Despite their importance for urban development, traditional rail solutions are often uneconomical for low passenger traffic, leading to the decommissioning of thousands of kilometers of tracks. To create a sustainable solution, lighter infrastructure is essential.

A promising approach is replacing costly Train Detection Devices (TDD) located on tracks with GNSS-based on-board systems. While GNSS could reduce infrastructure costs, its use in passenger rail is hindered by safety standards and non-predictable errors like multipath and interference. To address these, recent research focuses on multi-sensor GNSS solutions to ensure safety and performance for rail applications. However, for lighter railway systems, that usually consist of single tracks, the absolute position of the trains is not the actual necessary data for collision avoidance systems but more inter distance between trains. We explore then the use of pseudorange differencing ranging. This technique is expected to be more resilient, easier to certify and a more cost-effective approach than the multi-sensor approach. However, direct ranging with pseudorange differencing in the railway industry is not usual and statistical error models are still to be determined.

Pseudorange differencing error model varies based on factors such as speed, baseline length, dilution of precision and multipath. In a previous work, we characterized the impact of those parameters on baseline errors. In this paper, we intend to use the data collected during a previous simulation campaign of over 205 hours to propose a parametric error model. This model is designed to be later integrated into an integrity monitoring algorithm for trains. Its performance will be validated on a test track in a subsequent paper.