1. Force models for GPS Orbit modeling
Paul Ries, Jet Propulsion Lab, California Institute of Technology
Copyright 2017 California Institute of Technology. U.S. Government Sponsorship acknowledged.

2. 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries
Outline
Radiation Pressure
Solar radiation pressure
Earth Radiation
Attitude modeling
Thermal forces
Antenna Thrust
Gravity
Based on:
ftp://ftp.igs.org/pub/center/analysis/
giant disclaimer about analysis centers not necessarily being up to date and being cryptic
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

3. Solar Radiation pressure models
Solar radiation pressure results from reflection of sunlight
CODE/ECOMM/DYB model (Beutler et al, 1994)
Estimate SRP during each analysis run with several different components (Direct, y-axis, Direct cross y-axis, once per rev)
JPL Model (Bar-Sever and Kuang 2005)
Empirically determined solar radiation pressure model from several years of data on each satellite, plus tightly constrained terms (solar scale, y-bias, stochastic impulses)
Difference between JPL style model and DYB style model at cm level (Sibthorpe et al 2011)
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

4. Solar radiation pressure models
CODE DYB-style Model
CODE, GFZ, NOAA, USNO
DYB with box-wing model
ESA, GRG
DYB with other apriori
MIT, SIO
empirical GSPM model
NRCAN+JPL
Important to Note: still substantial variations within each category
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

5. 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries
Attitude models
Nominal: keeps solar panels pointed towards the sun and antenna pointed towards earth
Essential component of other radiative forces
Eclipse modeling causes substantial differences (2-3 cm RMS) between solutions
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

6. 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries
Attitude models
None
NOAA, USNO
Nominal
CODE, NRCan, ESA, GFZ, MIT, SIO, WHU
Nominal + eclipse solution
GRG, JPL
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

7. Earth Radiation Pressure
The force of of reflected visible and emitted IR light on a GNSS satellite
Model variations can introduce bias at the cm level (see e.g. Rodriguez et al 2012, Ziebart 2009)
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

8. Earth Radiation Pressure
Rodriguez-Solano et al 2012
GFZ, NOAA, CODE
Knocke-Ries Model
JPL, NRCan
Other similar model
GRG (incorporates ECMWF), ESA
No model
WUH, USNO, SIO, MIT
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

9. Thermal models for the future?
Direct thermal effect
non-uniform temperature and/or non-spherical shape
few meter level, but often absorbed by model parameters (Adhya et al 2005)
Yarkovsky effect
tentatively detected at 10 cm level for Galileo (Svehla et al 2016)
force created by asymmetric thermal emission on rotating body
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

10. 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries
Antenna Thrust
Thrust from transmitting navigation message
typically in radial direction
magnitude of 10s of cm/orbit
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

11. 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries
Antenna Thrust
No information
MIT, GRG, USNO, WHU
None
ESA (as of 2015… but…), SIO
CODE, NRCan, JPL
Rodriguez-Solano 2012 (constant 80W)
GFZ, NOAA
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

12. 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries
Gravity field
EGM2008, 12x12
CODE, NRCan, GFZ, JPL, NOAA
EIGEN-GLO5C 12x12
ESA
EIGEN_6S (TVG)
GRG
EGM 96 9x9
MIT, SIO
JGM3 12x12
USNO
EIGEN-GLO4S1 12x12
WHU
Emphasize that differences for MEO's probably don't matter, but matter much more for LEOs
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

13. Gravity – 3rd body perturbers
Can analytically compute max acceleration at conjunction/opposition and integrate for one MEO orbit
Effects of bodies through Saturn are significant
Differences beyond Saturn make little difference
Body
One orbit effect
Moon
3.8 km
Sun
1.4 km
Venus
5.7 cm
Jupiter
1.1 cm
Mars
7.6 mm
Mercury
7.1 mm
Saturn
0.6 mm
Uranus
12 μm
Ceres
0.1 μm
Pluto
0.4 nm
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

14. Gravity – 3rd body perturbers
Sun and Moon
USNO, MIT, SIO
Sun, Moon, Jupiter, Venus, Mars
CODE, NOAA
All Planets + Sun and Moon
JPL, NRCAN, GRG
All Planets + Sun, Moon, and Pluto
WHU, ESA, GFZ
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

15. Can we eliminate biases?
Force Model
Ease of convergence
Reason
Solar radiation pressure
Challenging
SRP model directly related to estimation strategy
Earth radiation pressure
Earth radiation pressure directly related to estimation strategy (can be absorbed by SRP parameters)
Attitude modeling
Possible
ACs can probably converge on most of attitude model, but more research needed into non-nominal models
Antenna Thrust
Viable
Many ACs already using same model, easy to implement uniformly
3rd body perturbers
Most ACs already have the largest, only a few ACs need to update
Gravity field
A few ACs need to update model, differences probably small at MEO
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

16. Further Consideration
for LEOs:
Time-varying gravity, gravity field agreement
drag
for future GNSS:
orbit normal attitudes
thermal models
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

17. 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries
References
ADHYA, S., ZIEBART, M., SIBTHORPE, A., ARROWSMITH, P. and CROSS, P. (2005), Thermal Force Modeling for Precise Prediction and Determination of Spacecraft Orbits. Navigation, 52: 131–144. doi: /j tb01740.x
Bar-Sever Y, Kuang D (2005) New empirically derived solar radi- ation pressure model for global positioning system satellites during eclipse seasons. The Interplanetary Network Progress Report
Beutler G, Brockmann E, Gurtner W, Hugentobler U, Mervart L, Rothacher M (1994) Extended orbit modeling techniques at the CODE processing center of the International GPS Service for geodynamics (IGS): theory and initial results. Manuscr Geod 19: 367–386
Knocke, P. C., Ries, J. C., Tapley, B. D., American Astronautical Society., American Institute of Aeronautics and Astronautics., & AAS/AIAA Astrodynamics Conference. (1988). Earth radiation pressure effects on satellites. Washington, D.C: American Institute of Aeronautics and Astronautics.
Rodriguez-Solano, C.J., Hugentobler, U., Steigenberger, P. et al. J Geod (2012) 86: 309. doi: /s
Sibthorpe, A., Bertiger, W., Desai, S.D. et al. J Geod (2011) 85: 505. doi: /s
Svelha, D., Rothacher, M., Cacciapouti, L. (2016), Thermal Re-Radiation Acceleration in the GNSS Orbit Modelling Based on Galileo Clock Parameters. IGS Workshop presentation.
Ziebart, M. Springer, T., Flohrer, C., Sibthorpe, A., Haines, B., Bar-Sever, Y. (2009), The GPS-SLR bias: dynamics, attitude and current experiments. International Technical Laser Workshop on SLR Tracking of GNSS Constellations, Metsovo, Greece
2017 Unified Analysis Workshop - Force models for GPS - Paul Ries