Original Article

GPS Solutions

, Volume 9, Issue 1, pp 21-31

First online:

Precise GRACE baseline determination using GPS

  • Remco KroesAffiliated withDepartment of Earth Observation and Space Systems, Delft University of Technology Email author 
  • , Oliver MontenbruckAffiliated withGerman Space Operations Center, Deutsches Zentrum für Luft- und Raumfahrt
  • , William BertigerAffiliated withJet Propulsion Laboratory
  • , Pieter VisserAffiliated withDepartment of Earth Observation and Space Systems, Delft University of Technology

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Precision relative navigation is an essential aspect of spacecraft formation flying missions, both from an operational and a scientific point of view. When using GPS as a relative distance sensor, dual-frequency receivers are required for high accuracy at large inter-satellite separations. This allows for a correction of the relative ionospheric path delay and enables double difference integer ambiguity resolution. Although kinematic relative positioning techniques demonstrate promising results for hardware-in-the-loop simulations, they were found to lack an adequate robustness in real-world applications. To overcome this limitation, an extended Kalman Filter modeling the relative spacecraft dynamics has been developed. The filter processes single difference GPS pseudorange and carrier phase observations to estimate the relative position and velocity along with empirical accelerations and carrier phase ambiguities. In parallel, double difference carrier phase ambiguities are resolved on both frequencies using the least square ambiguity decorrelation adjustment (LAMBDA) method in order to fully exploit the inherent measurement accuracy. The combination of reduced dynamic filtering with the LAMBDA method results in smooth relative position estimates as well as fast and reliable ambiguity resolution. The proposed method has been validated with data from the gravity recovery and climate experiment (GRACE) mission. For an 11-day data arc, the resulting solution matches the GRACE K-Band Ranging System measurements with an accuracy of 1 mm, whereby 83% of the double difference ambiguities are resolved.


Spacecraft formation flying Relative positioning GRACE Integer ambiguity resolution