Ionospheric differential error determination using ray tracing for a short baseline

Since the United States government discontinued Selective Availability (SA) on 1 May 2000, ionospheric effects have been responsible for the largest errors in GPS systems. The standard Differential GPS (DGPS) method is incapable of completely eliminating the ionospheric error. This paper describes a new approach to determine the differential ionospheric error between geographically distributed receiver stations. The ray paths of GPS signals were simulated using a modified Jones 3D ray tracing programme that includes the effect of the geomagnetic field. A Nelder–Mead optimisation algorithm was embedded in the program to precisely determine the satellite-to-station path. A realistic ionospheric model is essential for accurate ray tracing results and for estimates of differential error that are accurate on sub-centimetre scales. Here, the ionospheric model used in the ray tracing programme was developed by fitting realistic ionosphere profiles with a number of exponential functions. Results were compared to the theoretical approach. Results show that the differential delay is about 1–5 cm at low elevation angles for a short baseline of 10 km, as reported in other literature. This delay is often neglected in DGPS application. The differential delay also shows a pattern similar to that predicted by the Klobuchar model. The method proposed here can be used to improve future GPS applications.