Determination of the Regional Geoid from Simulated GPS Measurements by the Aristoteles Solid-Earth Satellite

Abstract

ARISTOTELES orbits over a geographical area extending from 5 deg W to 25 deg E and 35 deg N to 65 deg N have been simulated using a spherical harmonic expansion of the earth’s gravity field complete to degree and order 360. This area covers a great part of Western Europe. In addition, GPS orbits have been simulated for the full 18 satellite configuration, using a truncated spherical harmonic expansion for the gravity field. All orbits span a period of 30 days. From the orbits of the GPS and ARISTOTELES satellites simulated GPS-to-ARISTOTELES satellite-to-satellite (SST) range measurements have been computed. From these measurements precise ARISTOTELES accelerations in the direction of the line-of-sight to each GPS satellite in view have been recovered. These precise ARISTOTELES accelerations have been transformed into accelerations in the radial (upward), longitude (West-East) and latitude (South-North) directions. Subsequently, these accelerations, irregularly distributed over the selected area and at various altitudes along the ARISTOTELES tracks, have been transformed into a regular grid of accelerations at a mean ARISTOTELES altitude of 191 km by means of least-squares collocation.

From this regular grid of accelerations, the regional geoid has been determined through downward continuation by the method of least-squares collocation. This geoid has been compared with the geoid as computed directly from the spherical harmonic expansion used to compute the ARISTOTELES orbit. The results of the simulations indicate that it is possible to recover the greater part of the high-frequency geoid (i.e. above degree 36) from GPS SST range measurements acquired by the low altitude satellite ARISTOTELES, if space-borne GPS receivers are applied that will produce carrier phase measurements with a precision at the millimeter level and with a measurement interval of only a few seconds.