Implementing a VLBI Time Delay Model for Earth-orbiting Satellites: Partial derivatives and Verification

This document describes the partial derivatives for commonly estimated parameters including antenna positions, satellite position, and satellite velocity from a near-field VLBI delay model for Earth-orbiting satellites. This model was presented in the Journal of Geodesy by Jaron & Nothnagel (2019). In this context, we present a streamlined version of the near-field VLBI delay. From this simplified model, we deduce a delay rate expression and calculate partial derivatives, maintaining only the terms with significant impact on the computed derivatives’ magnitude. To verify the accuracy of the simplified model and the partial derivatives computed from it, we have created a simple simulation in Matlab of an Earth-orbiting satellite at the altitude of a typical Global Navigation Satellite Systems (GNSS) satellite. From this simulation, we compare the simplified and original delays, and we verify the magnitude and direction of the partial derivatives against the numerically computed derivatives from the original delay model. The partial derivatives and simplified VLBI delay model detailed here are implemented in Fortran in the open-source library VTD.