Analytical method for error analysis of high-low satellite-to-satellite tracking missions

We present an analytical relationship between the high-low satellite-to-satellite tracking measurement errors and the accuracy of the gravity field recovery from the point of view of signal theory, which concerns the field where geodesy is in contact with physics and technical sciences. This method enables us to gain a better understanding of the effects of the instrument noise and the mission parameters on the gravity field recovery directly, especially for the analysis of the noise spectral characteristics. It is a helpful tool for the pre-mission analysis before full-scale simulations are conducted. By taking the advantage of the analytical expression, this study discusses how the orbit errors and accelerometer noise degrade the accuracy of the gravity field recovery from high-low satellite-to-satellite tracking observations. The results show that the noise level of orbit errors is at least one to four orders of magnitude larger than that of accelerometers in the measurement bandwidth with the state-of-the-art technologies, which indicates that the accuracy of the gravity field coefficients is mainly limited by the level of orbit errors for high-low satellite-to-satellite tracking observations.

[1]  A. Jäggi,et al.  Combined satellite gravity field model GOCO01S derived from GOCE and GRACE , 2010 .

[2]  Lin Cai,et al.  Analytical error analysis for satellite gravity field determination based on two-dimensional Fourier method , 2012, Journal of Geodesy.

[3]  Jeongrae Kim,et al.  Simulation study of a low-low satellite-to-satellite tracking mission , 2000 .

[4]  R. Koop.  Global gravity field modelling using satelite gravity gradiometry , 1993 .

[5]  H. Bock,et al.  GPS-only gravity field recovery with GOCE, CHAMP, and GRACE , 2011 .

[6]  Peter Schwintzer,et al.  Accelerometry Aboard CHAMP , 2000 .

[7]  P. Steigenberger,et al.  A CHAMP‐only gravity field model from kinematic orbits using the energy integral , 2003 .

[8]  N. Sneeuw.  A Semi-Analytical Approach to Gravity Field Analysis from Satellite Observations , 2000 .

[9]  Zhou Ze.  Spectral analysis for recovering the Earth′s gravity potential by satellite gravity gradients , 2012 .

[10]  P. Touboul.  Space Accelerometers: Present Status , 2001 .

[11]  J. Lemoine,et al.  A high‐quality global gravity field model from CHAMP GPS tracking data and accelerometry (EIGEN‐1S) , 2002 .

[12]  C. Jekeli.  The determination of gravitational potential differences from satellite-to-satellite tracking , 1999 .

[13]  Assessment of two methods for gravity field recovery from GOCE GPS-SST orbit solutions , 2003 .

[14]  M. Watkins,et al.  The gravity recovery and climate experiment: Mission overview and early results , 2004 .

[15]  Ernst J. O. Schrama,et al.  Gravity field error analysis - Applications of Global Positioning System receivers and gradiometers on low orbiting platforms , 1991 .

[16]  L. Cai,et al.  Error analysis for satellite gravity field determination based on two-dimensional Fourier methods , 2012 .

[17]  L. P. Pellinen.  Physical Geodesy , 1972 .

[18]  H. Hornik,et al.  Towards an Integrated Global Geodetic Observing System (IGGOS) , 2000 .

[19]  Fernando Sansò,et al.  Space-wise approach to satellite gravity field determination in the presence of coloured noise , 2004 .

[20]  P. Touboul,et al.  Accelerometers for CHAMP, GRACE and GOCE space missions: synergy and evolution , 1999 .

[21]  R. Klees,et al.  On the joint inversion of SGG and SST data from the GOCE mission , 2003 .

[22]  Oscar L. Colombo,et al.  Ephemeris errors of GPS satellites , 1986 .

[23]  B. Frommknecht,et al.  Integrated Sensor Analysis of the GRACE Mission , 2007 .

[24]  P. Touboul,et al.  Capacitive detection scheme for space accelerometers applications , 1999 .

[25]  O. Colombo.  Numerical Methods for Harmonic Analysis on the Sphere , 1981 .

[26]  Richard Biancale,et al.  On Board Evaluation of the STAR Accelerometer , 2003 .

[27]  Nico Sneeuw,et al.  Energy integral method for gravity field determination from satellite orbit coordinates , 2003 .

[28]  Jun Luo,et al.  Lunar gravity gradiometry and requirement analysis , 2013 .

[29]  J. Lemoine,et al.  The CHAMP-only earth gravity field model EIGEN-2 , 2003 .

[30]  Christian Gruber,et al.  FFT-based high-performance spherical harmonic transformation , 2011 .

[31]  M. Weigelt,et al.  GOCE orbit analysis: Long-wavelength gravity field determination using the acceleration approach , 2012 .

[32]  C. Reigber,et al.  First champ mission results for gravity, magnetic and atmospheric studies , 2003 .

[33]  Katsuhiko Ogata,et al.  Modern Control Engineering , 1970 .