Page - 49 - in Contributions to GRACE Gravity Field Recovery - Improvements in Dynamic Orbit Integration, Stochastic Modelling of the Antenna Offset Correction, and Co-Estimation of Satellite Orientations

integrated using the models given in table 6.1, as well as the observations of the GRACE accelerometers. Where the dynamic orbit integration algorithm as described in chapter 5 only fits the initial state of each arc to the approximate orbit used as input, GRACE offers more observations that can be employed here: POD orbits derived from hl-SST observations by the GPS receiver and the ll-SST observations of the KBR system. In ITSG-Grace2016, the dynamic orbit is also fit to both of these observation groups. Accelerometer calibration parametersxcal as described in section 6.4.1 are co-estimated with the initial satellite state for each arc. The observation system for this orbit fit is   lsstlpod,A lpod,B    =    Asst ΦA ΦBApod,A ΦA 0 Apod,B 0 ΦB       xcaly0,A y0,B    , (6.3.1) where the design matricesAare those described in section 6.4.3. The newly estimated initial states yˆ0,A and yˆ0,B are then used to improve the dynamic orbit estimates of GRACE-A and GRACE-B according to eq. (5.1.14). The complete process for integrating the ITSG-Grace2016 dynamic orbits consists of three steps, as illustrated in fig. 6.4. Table 6.1: Background models for dynamic orbit integration in ITSG-Grace2016. Effect Model Mean earth gravity GOCO05s 1 Trend GOCO05s 1 Annual & semi-annual oscillation GOCO05s 1 Atmosphere & ocean dealiasing AOD1B RL05 2 Earth rotation IERS 2010 3 Solid earth tides IERS 2010 3 Pole tides IERS 2010 3 Relativistic effects IERS 2010 3 Third body forces JPL DE421 4 Ocean tides EOT11a 5 Ocean pole tides Desai, 2002 6 Atmospheric tides Atmospheric tide loading calculator 7 1 Mayer-Gu¨rr, Kvas, et al., 2015 2 Flechtner, Dobslaw, and Fagiolini, 2014 3 Petit and Luzum, 2010 4 Folkner, Williams, and Boggs, 2008 5The EOT11a model was produced by DGFI based on multi-mission altimeter data and distributed via OpenADB (http://openadb.dgfi.badw.de). More details on the product are available in (Savcenko et al., 2012). 6Using coefficients published in the IERS Conventions (2010). 7van Dam and Ray, 2010 6.3 Orbit Integration 49