Journal of Geodesy

, Volume 91, Issue 5, pp 547–562 | Cite as

Model improvements and validation of TerraSAR-X precise orbit determination

  • S. HackelEmail author
  • O. Montenbruck
  • P. Steigenberger
  • U. Balss
  • C. Gisinger
  • M. Eineder
Original Article


The radar imaging satellite mission TerraSAR-X requires precisely determined satellite orbits for validating geodetic remote sensing techniques. Since the achieved quality of the operationally derived, reduced-dynamic (RD) orbit solutions limits the capabilities of the synthetic aperture radar (SAR) validation, an effort is made to improve the estimated orbit solutions. This paper discusses the benefits of refined dynamical models on orbit accuracy as well as estimated empirical accelerations and compares different dynamic models in a RD orbit determination. Modeling aspects discussed in the paper include the use of a macro-model for drag and radiation pressure computation, the use of high-quality atmospheric density and wind models as well as the benefit of high-fidelity gravity and ocean tide models. The Sun-synchronous dusk–dawn orbit geometry of TerraSAR-X results in a particular high correlation of solar radiation pressure modeling and estimated normal-direction positions. Furthermore, this mission offers a unique suite of independent sensors for orbit validation. Several parameters serve as quality indicators for the estimated satellite orbit solutions. These include the magnitude of the estimated empirical accelerations, satellite laser ranging (SLR) residuals, and SLR-based orbit corrections. Moreover, the radargrammetric distance measurements of the SAR instrument are selected for assessing the quality of the orbit solutions and compared to the SLR analysis. The use of high-fidelity satellite dynamics models in the RD approach is shown to clearly improve the orbit quality compared to simplified models and loosely constrained empirical accelerations. The estimated empirical accelerations are substantially reduced by 30% in tangential direction when working with the refined dynamical models. Likewise the SLR residuals are reduced from \(-3\,\pm \,17\) to \(2\,\pm \,13\) mm, and the SLR-derived normal-direction position corrections are reduced from 15 to 6 mm, obtained from the 2012–2014 period. The radar range bias is reduced from \(-10.3\) to \(-6.1\) mm with the updated orbit solutions, which coincides with the reduced standard deviation of the SLR residuals. The improvements are mainly driven by the satellite macro-model for the purpose of solar radiation pressure modeling, improved atmospheric density models, and the use of state-of-the-art gravity field models.


Atmospheric density models Radar ranging Reduced-dynamic orbit determination Satellite macro-model Solar radiation pressure 



The work was partly funded by the German Helmholtz Association HGF through its DLR@Uni Munich Aerospace project “Hochauflösende geodätische Erdbeobachtung”. We thank our cooperation partners—the Federal Agency for Cartography and Geodesy (BKG) and the Finnish Geodetic Institute (FGI)—for their kind allowance to install the corner reflectors at their property in Wettzell and Metsähovi, respectively, and for their local support. We thank our colleagues from DLR’s Remote Sensing Date Center (DFD), who installed and maintained the corner reflectors at GARS O’Higgins. In addition, we would like to thank Airbus DS for providing satellite- related information.


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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.German Space Operations Center, Deutsches Zentrum für Luft- und Raumfahrt (DLR)WeßlingGermany
  2. 2.Remote Sensing Technology InstituteDeutsches Zentrum für Luft- und Raumfahrt (DLR)WeßlingGermany
  3. 3.Lehrstuhl für Astronomische und Physikalische GeodäsieTechnische Universität MünchenMünchenGermany

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