1. Investigations on (radial) offsets between different Swarm orbit solutions 8 September 2015 5th Swarm Data Quality Workshop, IPGP, Paris Heike Peter (PosiTim), Adrian Jäggi, Daniel Arnold (both AIUB), Jose van den IJssel (TUD)

2. 2 Contents  Introduction and motivation  Lessons learned from Sentinel-1A  PosiTim orbit solutions for Swarm  Comparison to TUD and AIUB  SLR validation  Analysis of sytematic offsets  Antenna offset estimation for Swarm  Preliminary results  Summary

3. 3 Introduction and motivation AIUB - TUD Mean rad -12.1 mm alo 0.0 mm cro 11.8 mm Mean rad-14.9 mm alo 8.3 mm cro 2.5 mm Mean rad-14.2 mm alo 2.0 mm cro 10.8 mm A B C Swarm orbits from TUD and AIUB show systematic differences Radial direction is constant Cross-track direction is variable AIUB and TUD use different software packages With respect to the non-gravitational force modelling the orbit parametrization is either pure empirical (AIUB) or partly based on dynamical force models (TUD) The Napeos software package is offering a third orbit parametrization, which is mainly based on dynamical force models. Napeos is also offering the possibility to estimate antenna offsets directly.

4. 4 Lessons learned from Sentinel-1A Comparisons of orbit solutions from different insitutions (e.g., AIUB, TUD and GMV) revealed a radial offset of about 3 cm between different solutions for Sentinel-1A. Due to the purely empirical parametrization in the Bernese GNSS Software (AIUB), the resulting orbits follow the geometry. Due to the dynamical parametrization in Napeos (GMV), the resulting orbits follow the dynamics (mainly in radial); the discrepancy with the given geometry is „moved“ into the PCVs. => Discrepancy in the geometry of the satellite (CoM, antenna offset, PCOs ?)

5. 5 Lessons learned from Sentinel-1A Comparisons of orbit solutions from different insitutions (e.g., AIUB, TUD and GMV) revealed a radial offset of about 3 cm between different solutions for Sentinel-1A. Due to the purely empirical parametrization in the Bernese GNSS Software (AIUB), the resulting orbits follow the geometry. Due to the dynamical parametrization in Napeos (GMV), the resulting orbits follow the dynamics (mainly in radial); the discrepancy with the given geometry is „moved“ into the PCVs. => Discrepancy in the geometry of the satellite (CoM, antenna offset, PCOs ?)  Swarm: a radial offset of about 1 – 1.5cm is observed between the different orbit solutions  Is this a geometrical discrepancy as well? Offset *cos z

6. 6 PosiTim orbit solutions for Swarm A & B & C Data: undifferenced ionosphere-free GPS code & carrier-phase observations from 16 July to 31 December 2014 final ESA GPS ephemeris and 30 sec clocks IGS08.atx PCV map for GPS and (own) estimated PCV map for Swarm attitude from star tracker data Models: Earth gravity (EIGEN6C 120x120) Ocean tides (EOT11a) Atmospheric drag (MSIS90) Solar radiation pressure (coefficient fixed to 1.0) Earth radiation (albedo and infrared, coefficients fixed to 1.0) Macro model for the Swarm satellites (many thanks to ESA, TUD and DLR for providing it) is used in a box-wing model Estimated parameters per 24-hour orbit arc: initial state receiver clock errors 25 drag coefficients 4 sets of CPR coefficients (along-track constant, sine and cosine; cross-track constant, sine and cosine) carrier-phase ambiguities No empirical accelerations in radial direction => radial leveling is fixed to the dynamic models

7. 7 Orbit comparison to TUD and AIUB TUD Swarm A Mean RMS values (PTIM-TUD): radial / along-track / cross-track / 3D 1.47 / 2.62 / 1.93 / 3.63 cm Mean RMS values (PTIM-AIUB): radial / along-track / cross-track / 3D 2.14 / 2.83 / 1.61 / 3.95 cm AIUB Days with 3D-RMS values larger than 10.0 cm are excluded from the statistics 70 mm

8. 8 Orbit comparison to TUD and AIUB TUD Swarm B Mean RMS values (PTIM-TUD): radial / along-track / cross-track / 3D 1.19 / 2.08 / 1.58 / 2.91 cm Mean RMS values (PTIM-AIUB): radial / along-track / cross-track / 3D 1.74 / 2.16 / 1.32 / 3.12 cm AIUB Days with 3D-RMS values larger than 10.0 cm are excluded from the statistics

9. 9 Orbit comparison to TUD and AIUB TUD Swarm C Mean RMS values (PTIM-TUD): radial / along-track / cross-track / 3D 1.46 / 2.60 / 1.82 / 3.54 cm Mean RMS values (PTIM-AIUB): radial / along-track / cross-track / 3D 1.97 / 2.78 / 1.53 / 3.78 cm AIUB Days with 3D-RMS values larger than 10.0 cm are excluded from the statistics

10. 10 SLR validation A Mean / RMS values (cm): A: 0.07 / 2.75 cm B C B: -0.38 / 2.05 cmC: -0.11 / 2.37 cm

11. 11 Systematic orbit differences – mean daily offsets (m) TUD - PTIM AIUB - PTIM AIUB - TUD Mean rad -2.9 mm alo 3.8 mm cro11.6 mm Mean rad -2.8 mm alo 3.3 mm cro 5.2 mm Mean rad -3.9 mm alo 4.6 mm cro 9.7 mm Mean rad -8.2 mm alo -4.6 mm cro 2.1 mm Mean rad -12.1 mm alo 0.0 mm cro 11.8 mm Mean rad-14.9 mm alo 8.3 mm cro 2.5 mm Mean rad-14.2 mm alo 2.0 mm cro 10.8 mm Mean rad-11.3 mm alo -1.8 mm cro -0.9 mm Mean rad-12.2 mm alo 5.1 mm cro -2.8 mm A B C 0.03 -0.03

12. 12 PCV maps from different institutions TUD PTIM AIUB A B C TUD - PTIMPTIM - AIUB Note: Time span used for the generation of the PCV maps is different in all three cases AIUB - TUD

13. 13 Antenna offset estimation – first test The estimation of antenna offsets in Napeos is implemented for the satellite body- fixed system  antenna phase center offsets (PCOs) are given in the antenna reference frame and have to be rotated into the satellite body-fixed system  no problem in the case of Swarm, because PCOs are zero and the axes of the antenna reference system are (anti-)parallel to the satellite body-fixed system Since systematic offsets in radial and cross-track are observed, the estimation is done for the y-(cross-track) and z-(radial) direction The constant accelerations of the CPR parameters in cross-track are fully correlated with the y-offset => switch off the constant accelerations in cross-track direction PCO only solution is done, because the PCVs may induce offsets in the orbits, which has to be avoided for the antenna offset estimation

14. 14 Antenna offset estimation Y antenna offset – delta (m) -0.05 0.01 The estimation of antenna offsets in y-/cross-track direction is correlated to beta (angle of the Sun over the orbital plane). Swarm A Swarm B Swarm C

15. 15 Antenna offset estimation Y and Z antenna offset – delta (m) -0.05 0.02 The estimation of antenna offsets in y-/cross-track direction is correlated to beta (angle of the Sun over the orbital plane). Test for Swarm A: The orbit parametrization is changed => solar radiation pressure coefficient is fixed to 0.8 instead of 1.0 => the y-offset estimation gives different results (up to 5 mm) =>The estimated values for the z-offset, however, do not change significantly. => y-offset estimation is not very reliable

16. 16 Antenna offset estimation Mean Swarm A 12.7 mm Swarm B 13.4 mm Swarm C 11.0 mm Z antenna offset – delta (m) 0.02 0.004 The estimation of antenna offsets in z-/radial direction is much more stable. From July to September the values for all satellites are very close; from October onwards they diverge. The mean values are in-between the offsets observed between TUD and PTIM and between AIUB and PTIM.  First test for Swarm A with a modified PCO Up Offset = -12.5 mm (original 0.0 mm)

17. 17 New PCV map for Swarm A – PCO Up = -12.5mm PTIMPTIM Up-125PTIM – PTIM Up-125 Mean 0.07 cm RMS 2.75 cm Carrier phase RMS (mm) SLR residuals (m) Mean 0.06 cm RMS 2.75 cm PCO only solutions How would the modification of the PCO-Up value impact the other orbit solutions?

18. 18 Summary Systematic orbit offsets are observed between solutions from different institutions. The radial offsets are stable and show little variation. The solutions from PosiTim offer additional orbits for validation. Comparison to TUD and AIUB show a 3-D RMS of 3-4 cm. SLR validation gives RMS values between 2.05 and 2.75 cm. The estimation of antenna offsets is possible in Napeos. Estimation of y-/cross-track offsets is not reliable, because it is correlated to the beta angle of the sun over the orbital plane. Estimation in z-/radial direction results in values between 11.0 and 13.4 mm. First test with a modified PCO Up-value of -12.5 mm for Swarm A shows a reduced carrier phase RMS, which is an indicator for a better modelling. SLR validation shows no improvement (radial levelling is fixed in Napeos) => Further tests with other software packages are needed for validation.