Ionospheric effects on GPS range finding using 3D ray-tracing and Nelder-Mead optimisation algorithm

Abstract

The Earth's ionosphere plays a crucial role in Global Positioning System (GPS) accuracy because his layer represents the largest source of positioning error for the users of the GPS after the turn-off of Selective Availability (SA). This paper studies the ionospheric effect on transionospheric signal propagation for the Earth-satellite path using 3D Jones Ray-Tracing utilizing Nelder-Mead optimisation algorithm. The ionospheric delay or advance is obtained from the difference between the distance of the ray path from the satellite to the receiver determined from the ray-tracing and the distance for propagation over the line of sight (LOS) at the velocity of light in vacuum. The difference between the standard dual-frequency models corrected range and LOS, known as Residual Range Error (RRE) is calculated. Results show that the RRE of group delay value is different from RRE of phase advance. On the other hand, the group and phase path is longer when considering the geomagnetic field effect on both GPS frequencies L1 and L2. The higher order term in total electron content (TEC) calculation that relates to the refractive index is normally neglected due to its small value, but it is clearly shown that it does have some effects in ray-tracing. This analysis needs to be considered for more accurate GPS range finding.