Modeling and estimation of relativistic and atmospheric effects on time delay for satellite applications

The focus of this study is on the main physical sources of time delay and their consequences on position error estimation in geolocation algorithms performed with a passive receiver on a satellite. The toy model scenario of reference considers an emitter of electromagnetic waves placed on the surface of the Earth and a receiver mounted on a satellite which is able to perform AoA (Angle of Arrival) measurements. In particular, the main physical origin of the time delay is due the finite speed of propagation of the electromagnetic waves, and starting from the Newtonian mathematical description, its corrections due to relativistic effects and the presence of the atmosphere are described and derived. After a mathematical description of the contributions on time delay, a quantitative analysis through simulations is performed to show the main dependencies with respect to orbital parameters and clock synchronization. Possible civil applications of interest are scenarios of geolocation for search and rescue, spectrum monitoring of jamming of E1/L1 GNSS signals used by in civil aviation, and satellite-based wireless communication and synchronization.