Modeling the VLBI delay for Earth satellites

Abstract

Very-long-baseline interferometry (VLBI) observations of satellites orbiting the Earth and emitting an artificial radio signal have the potential of becoming an important technique for improving the frame ties between celestial and terrestrial reference frames. Modeling the delay of the signal reception at one station with respect to the other station of a baseline is a fundamental step for correlation and parameter estimation. The near-field VLBI delay models developed so far include numerical computation, which may become expensive in terms of computation time. This applies especially when partial derivatives are to be computed, which is the normal case for least squares adjustments. Furthermore, all the models are formulated in the barycentric celestial reference system requiring large numbers. Here we present an analytical expression for the VLBI delay for the special case of satellites orbiting the Earth, observed by ground-based radio telescopes. We analytically solve the light time equation for each signal propagation path from the source to receiver one and to receiver two under the simplification of linearizing the trajectory of the satellite. By approximating the motion of the Earth as uniform during the short signal travel times we are able to work in the geocentric celestial reference system. We investigate differences between numerical and analytical solutions by simulating VLBI observations of Earth satellites. These tests reveal that delays computed with the analytical formula are consistent with those computed with the numerical solution below the detection level of VLBI but at less computational cost.