1. Sub-Daily ERP Investigations
Michiel Otten, Tim Springer
ESOC - Navigation Support Office, Darmstadt, Germany
Unified Analysis Workshop 2017, Paris, France
Hobart, Mt. Pleasant Radio Observatory

2. Sub-daily ERP model investigations A bit of history…..
Sub-daily ERP model investigations initially done in 2011
Used different models:
IERS (ortho_eop.f)
GOT4.7
TPXO7.1
Gipson, 2010a.hfeop_v3_cor6_bakcon
Gipson model only one to remove 14-day period in orbit overlap at that time
But nothing visible in ERPs nor CRDs

3. Sub-daily ERP model investigations A bit of history…..
Renewed interest after hearing Gipson presentation in 2014 at UAW in Pasadena:
Despite adding 4 more years of data model is not changing anymore. This is what VLBI gives us
Agreed with Gipson to (re)test his model
Took until 2016 to re-establish contact, testing in 2017
Model: orthow_2016b_withlibra
Other models also considered
Bonn models VLBI, and VLBI&GPS model
Artz and Nothnagel
Vienna model planned, but so far no source code obtained
Robert Weber et. al.

4. Sub-daily ERP model investigations Test set-up
Boundary conditions:
To see the effect clearly at least 1 year of data needed
For station coordinates probably even longer period is needed
Testing should be quick in order to keep it interesting and stay motivated, ideally “overnight”
Selected setup:
Use ESA/ESOC IGS Final processing set-up
But limit tracking station network to 60 stations
Do the preprocessing only once so that all test solutions use exactly the same data, the only difference between the runs is the sub-daily ERP model that is used
Use GPS, GLONASS and Galileo as the near 12 hour periods of GPS may be an issue. The different orbit constellations should also help to separate real model effects from artificial GNSS effects
Processing takes about 12 hours using 8 cores (1 hour per solution day)

5. Processing set-up
Processing settings identical to the ESA IGS Final processing
Used the full year of 2016
Normal 24 hour multi-GNSS processing runs
Limited to 60 multi-GNSS tracking stations
Included Galileo. Up to 68 GNSS satellites were used, i.e., all the available GPS, GLONASS and Galileo satellites
Pre-processing done only in the first run to ensure all runs use the same data set. So all other runs skip the pre-processing
Set-up such that the only difference between the runs is the sub-daily ERP model that is used.
Processing takes about 12 hours using 8 cores (1 hour per solution day)

6. Key aspects of ESOC GNSS Processing
Strict 24 hour (or actually 23:59:30) solutions. These 24 hour solutions are completely independent from each other; no duplication of data used and no constraints between the days.
ESA GNSS processing is undifferenced so we estimate all the station and satellite clocks safe for one reference.
Satellite and station clocks are estimated epoch wise without any constraints from epoch to epoch (white noise parameters).
The good GPS IIF and Galileo satellite clocks may see an effect of an improved sub-daily ERP model (clock stability of IIF and Galileo is at the 50 to 100 ps level over 24 hours).
For ERPs we estimate offset and drift per 24 hours for X, and Y. UT is taken from Bulletin A, LOD estimated. Estimated for mid-day, i.e., 12:00 UTC.
Satellite orbits. We use apriori box-wing models for GPS, GLONASS and Galileo. In addition to the state-vector we estimate 5 parameters from the ECOM (Enhanced CODE Orbit Model) (constants in D, Y, and B, and cosine and sine in B with as argument the latitude of the satellite w.r.t. the latitude of the Sun in the orbital plane) and 3 tightly constraint along-track parameters (a constant and a one per rev sine and cosine term)
Station parameters. Coordinates with minimal constraints (both rotation and translation). Hourly tropospheric zentih delay. And a linear gradient in North-South and East-West direction.
Other parameters. GNSS carrier phase ambiguities.
For both GPS and Galileo integer ambiguity resolution is performed, but not for GLONASS.
Model wise we follow the IERS 2013 conventions as close as possible. For more details see the ESA analysis center summary file.
Processing takes about 12 hours using 8 cores (1 hour per solution day)

7. Sub-daily ERP models used
The following sub-daily ERP models were tested:
Reference run used the IERS conventions model (ortho_eop.f)
Gipson model “hfeop_withlibra” based on VLBI, from 2014
Bonn (Artz et.al.) model based on GPS and VLBI, from 2012
Bonn (Artz et.al.) model based on VLBI only, from 2011
Vienna model planned but no source code yet.
Processing takes about 12 hours using 8 cores (1 hour per solution day)

8. Sub-daily ERP model evaluations
Look at orbit overlaps:
Radial, along-, and cross-track
Some signals cross-track but not very clear, and some signal in radial direction
Look at overlap of the Kepler elements
Very clear signal in right ascension of the ascending node (RAAN), small signals in semi-major axis.
Look at ERP differences to IERS pole series
Some signals in the pole rates and LOD
Look at repeatability of the station coordinates
Seems 60 stations may be too limited
And/or one year timeframe to little to separate signal from other station related effects
Processing takes about 12 hours using 8 cores (1 hour per solution day)

9. GPS Amplitude Spectrum IERS Model: Cross-track orbit overlaps
Some power at ~14 days but not much,
and looks like two peaks
No clear signal in cross-track and seems to have 2 peaks.
Cross-track overlap is not at the same orbital position for every satellite!

10. GPS Amplitude Spectrum IERS Model: Right Ascension of the Ascending Node
Very clear signal for all GPS satellites
Signal much clearer in the overlap in the RAAN. Indication that it is a UT1 sub-daily model?
RAAN has same orbital location of the overlap and clear rotation around Z-axis.

11. RAAN Amplitude Spectrum for GPS: Gipson model
Signal mostly gone with Gipson model
14-day period for ALL GPS satellites gone! Gipson model, but also for both Artz models.

12. RAAN Amplitude Spectrum for GLONASS: IERS model
Same 14-day period signal in GLONASS.
Also lots of power around 8 days, GLONASS orbital repeat period, indicating orbit modelling issues for GLONASS

13. RAAN Amplitude Spectrum for GLONASS: Gipson model
14-day period for ALL GLONASS satellites gone! Gipson model, but also for Artz models.

14. RAAN Amplitude Spectrum for Galileo: IERS model
Same 14-day period signal in Galileo.
Notice how the amplitude spectrum is much better/flatter then that of GLONASS.
The power around ~7 days is the repeat period of the two eccentric Galileo satellites (GAL-201 and GAL-202)

15. RAAN Amplitude Spectrum for Galileo: Gipson model
14-day period for ALL Galileo satellites gone! Gipson model, but also for Artz models.
The power around ~7 days is the repeat period of the two eccentric Galileo satellites (GAL-201 and GAL-202) remains, indicates some orbit model issues.

16. RAAN Amplitude Spectrum for ALL: IERS model
Same 14-day period for ALL GNSS satellites
This is NOT the case in cross-track, due to different inclinations and orbit repeat periods

17. RAAN Amplitude Spectrum for ALL: Gipson model
14-day period for ALL GNSS satellites gone! Gipson model, but also for Artz models.

18. Amplitude Spectra: LOD
14 day (0.0714/day) peak reduced with Gipson model and with Artz

19. Amplitude Spectra: X-pole rate
14 day peak reduced but only with Gipson model not with Artz

20. Amplitude Spectra: Y-pole rate
14 day peak reduced but only with Gipson model not with Artz

21. Sub-daily ERP model conclusions
The results confirm what we saw in 2011 with the 2010 Gipson model
But in 2011 it was based only on using GPS, now we also included GLONASS and Galileo which gives more confidence in these results
Different orbital periods, altitudes, and inclinations and even the two “eccentric” Galileo satellites
14 day period most clearly seen in RAAN
Indicates largest model errors to be in UT/LOD?
14 day period in RAAN completely gone with both Gipson and Artz (Bonn) models
These models also reduce the 14-day peak in LOD
Gipson model also reduces the 14-day peaks in X- and Y-pole rates
Artz (Bonn) models do not

22. Sub-daily ERP model way forward
Real improvements offered by the Gipson model!
Only model of the 3 tested to also show improvements in the ERP rates
Gipson model holds the promise to significantly reduce the 14-day periods observed in several of the IGS/GNSS products
Model change has been proposed to the IERS conventions!
A model derived from one of the latest ocean tidal models would be preferred but given the lack of such models the Gipson model does seem to offer a very suited alternative.
Fully acceptable for GNSS in general and the IGS in particular, and very much needed to reduce 14-day periods in the products
Should also be acceptable for IDS and ILRS
What about using it in the IVS?

23. THANK YOU Michiel Otten Tim Springer Michiel.Otten@esa.int
Tim Springer

24. Multi-GNSS data processing 2014-2015
ESA and MGEX sites
GPS-IIA
GPS-IIR/RM
GPS-IIF
GLONASS-M
QZSS
Galileo
BeiDou
~68-75 satellites