Modeling the VLBI delay for Earth satellites
- 160 Downloads
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.
KeywordsGeodetic VLBI VLBI near-field models VLBI satellite tracking
The authors thank Armin Corbin for carefully reading the manuscript. This research is supported by the Deutsche Forschungsgemeinschaft, DFG, Project Number NO 318/14-1.
- Bar-Sever Y, Haines B, Wu S (2009) The geodetic reference antenna in space (GRASP) mission concept. EGU Gen Assembl Conf Abstr 11:1645Google Scholar
- Biancale R, Pollet A, Coulot D, & Mandea M (2016) E-GRASP/Eratosthenes: a mission proposal for millimetric TRF realization. In: EGU general assembly geophysical research abstracts, Vol. 19, EGU2017-8752, 2017Google Scholar
- Haas R, Halsig S, Han S, Iddink A, Jaron F, La Porta L, Lovell J, Neidhardt A, Nothnagel A, Plötz C, Tang G, Zhang Z (2017) Observing the Chang’E-3 Lander with VLBI (OCEL). In: Proceedings of the first international workshop on VLBI observations of near-field targets, October 5–6, 2016, A. Nothnagel and F. Jaron (eds.), Schriftenreihe des Inst. f. Geodäsie u. Geoinformation, Vol. 54, ISSN 1864-1113, Bonn, 41-64Google Scholar
- Kaplan GH (2005) The IAU resolutions on astronomical reference systems, time scales, and earth rotation models: explanation and implementation. USNO Circular 179Google Scholar
- Klioner SA (1991) General relativistic model of VLBI observables. In: Geodetic VLBI: monitoring global change. Proceedings of the AGU chapman conference held April 22–26, 1991, in Washington, D. C., USA. NOAA Technical Report NOS 137 NGS49. William E. Carter from the Laboratory for Geosciences, Convenor. Published by the U. S. Department of Commerce and the National Oceanic and Atmospheric Administration, National Ocean Service, 1991, p.188Google Scholar
- Moyer TD (2000) Formulation for observed and computed values of deep space 4 network data types for navigation. JPL Monograph 2 (JPL Publication 00-7). This is published from JPL deep space communications and navigation series, Wiley, Hoboken, ISBN 0-471-44535-5Google Scholar
- Nothnagel A, Jaron F (2017) In: Proceedings of the first international workshop on VLBI observations of near-field targets, October 5–6, 2016, A. Nothnagel and F. Jaron (eds.), Schriftenreihe des Inst. f. Geodäsie u. Geoinformation, Vol. 54, ISSN 1864-1113, BonnGoogle Scholar
- Petit G, Luzum, B (2010) IERS Conventions. IERS Technical Note 36, Frankfurt am Main: Verlag des Bundesamts für Kartographie und Geodäsie, 2010. pp 179, ISBN 3-89888-989-6Google Scholar
- Plank L (2014) VLBI satellite tracking for the realization of frame ties. Dissertation, Technische Universität Wien, Geowissenschaftliche Mitteilungen, Heft Nr. 95, 2014, ISSN 1811-8380Google Scholar
- Tang G, Cao J, Han S, Hu S, Ren T, Chen L, Sun J, Wang Mei, Li Y, Li L (2014) Research on Lunar radio measurements by Chang’E-3. In: International VLBI service for geodesy and astrometry 2014 General meeting proceedings: “VGOS: The New VLBI Network”, Eds. Dirk Behrend, Karen D. Baver, Kyla L. Armstrong, Science Press, Beijing, China, ISBN 978-7-03-042974-2, 2014, p. 473-477, 473Google Scholar
- Thompson AR, Moran JM, Swenson GW (2017) In: Astronomy&, (ed) Interferometry and synthesis in radio astronomy, 3.th edn. Astrophysics Library. https://doi.org/10.1007/978-3-319-44431-4