1. Reference Frame Representations: The ITRF from the user perspective
Zuheir Altamimi
Paul Rebischung
Laurent Métivier
Xavier Collilieux
Kristel Chanard
IGN, France

2. Key Points Possible reference frame representations and:
the reality of a deformable Earth
Linear motion
Nonlinear variations
technique systematic errors
User needs
The ITRF from the user perspective
Science applications
Operational geodesy
The ITRF should satisfy both types of applications

3. What is a Reference Frame in practice?
Earth fixed/ centered RF: allows determination of station locations/positions as a function of time
It appears simple, but … we have to deal with:
Relativity theory
Forces acting on the satellite
The atmosphere
Earth rotation
Solid Earth and ocean tides …
Whatever the mathematical formulation
you choose, you need to precisely specify
the frame definition:
Origin, Scale, Orientation & their time evolution

4. Why a Reference System/Frame is needed?
Precise Orbit Determination for:
GNSS: Global Navigation Satellite Systems
Other satellite missions: Altimetry, Oceanography, Gravity
Earth Sciences Applications
Tectonic motion and crustal deformation
Mean sea level variations
Earth rotation …
Operational geodesy applications (today: via GNSS only!)
National geodetic systems/frames (see next)
Positioning : Real Time or a posteriori
Navigation: Aviation, Terrestrial, Maritime
Require the availability of the orbits and the RF (ITRF)
Many, many users…

5. National/Regional Reference Frames
Use of GNSS technology only (no SLR, VLBI or DORIS)
Use of and rely on the IGS products (orbits, clocks,..)
Rely on the ITRF
More than 80% of National RFs are aligned to the ITRF (source: UN-GGIM GGRF questionnaire)
Materialized by station coordinates at a given epoch + possibly a deformation model or minimized velocities
May need to apply PSD corrections (if ITRF2014 is used)
Some countries will move soon to a “dynamic” RF, ITRF-compatible, e.g. Australia

6. How to define the frame parameters ?
Origin: CoM (Satellite Techniques, mainly SLR, and potentially DORIS but subject to uncertainties)
Scale: Depends on physical parameters (SLR, VLBI and potentially DORIS, but subject to biases anyway)
Orientation: Conventional
Time evolution: Geophysical meaning (e.g. NNR condition)
==> Lack of information for some parameters:
Orientation & time evolution (all techniques)
Origin & time evolution in case of VLBI
==> Rank Deficiency in terms of Normal Equation System

7. “Motions” of the deformable Earth & technique systematic errors
Nearly linear motion:
Tectonic motion: mainly horizontal (Plate Motion Model)
Post-Glacial Rebound: Vertical & Horizontal
Nonlinear motion:
Loading deformation, including Annual, Semi & Inter-Annual, etc.
Co- & Post-seismic deformations,
Transient deformations, Volcano Eruptions, local events…
Systematic errors, e.g. draconitics, fortnightly,…

8. Crust-based TRF The instantaneous position of a point on the Earth
surface at epoch t could be written as :
𝑋 𝑡 =𝑋 𝑡0 + 𝑋 . 𝑡− 𝑡 ∆𝑋 𝑐 𝑡 𝑋 𝑛𝑐 (𝑡)
𝑿 𝒕𝟎 : position at a reference epoch t0
𝑿 : linear velocity
∆𝑿 𝒄 (𝒕) : Class 1 Conventional models, e.g. :
- Solid Earth, Ocean & Pole tides (models, IERS Conv.)
∆𝑿 𝒏𝒄 (𝒕) : : Class 2 models or estimated quantities:
- Loading deformation (seasonal and non-seasonal)
- Post-Seismic Deformation
- …

9. Reference Frame Representations
Long-Term linear Frame: mean station positions at a reference epoch (t0) and station velocities:
The indispensable basis for science and operational geodesy applications
Secular Frame + corrections (PSDs, Seasonals, Geocenter motion) ==> modeled “Quasi-Instantaneous” station positions
"Quasi-Instantaneous" RF: mean station positions at a "short” & “regular” interval:
Daily or weekly representations
Nonlinear motion embedded in their time series
Still rely on the ITRF for at least the orientation definition
<= Regularized Position
With piece-wise linear function
𝑋 𝑡 =𝑋 𝑡0 + 𝑋 . 𝑡− 𝑡 0 +𝑋(𝑡)𝑃𝑆𝐷+𝑋 𝑡 𝑆+𝑋(𝑡)𝐺

10. “Instantaneous” position: linear & nonlinear parts
Regularized position
𝑋 𝑡 =𝑋 𝑡0 + 𝑋 . 𝑡− 𝑡 0 +𝑋(𝑡)𝑃𝑆𝐷+𝑋 𝑡 𝑆+𝑋(𝑡)𝐺
Post-Seismic Deformations
Seasonal Signals of all frequencies
Caution: significant discrepancies between techniques
Or a Loading model with ALL contributions (ATM, …) in CF
Geocenter Motion
Caution: different models exist, with significant differences
All the 𝑿 corrections could be part of future ITRF products

11. Up annual signals : VLBI
January A f
April
Dh = A.cos( 2p f (t – t0 ) + f )

12. Up annual signals : VLBI + GNSS
January A f
April
Dh = A.cos( 2p f (t – t0 ) + f )

13. “Instantaneous” position: linear & nonlinear parts
Science Applications in general
𝑋 𝑡 =𝑋 𝑡0 + 𝑋 . 𝑡− 𝑡 0 +𝑋(𝑡)𝑃𝑆𝐷+𝑋 𝑡 𝑆+𝑋(𝑡)𝐺
Operational Geodesy
& certain science applications

14. ITRF2014 error propagation: GNSS coordinates
Spherical error = sqrt(sigx^2 + sigy^2 + sigz^2 + 2sigxy + 2sigxz + 2sigyz)

15. ITRF2014 error propagation: VLBI coordinates

16. ITRF2014 error propagation: SLR coordinates

17. ITRF2014 error propagation: DORIS coordinates

18. Conclusion
The ITRF as a secular frame is the basis for Science and operational geodesy applications
ITRF “Instantaneous” station position, if needed, can easily be derived. Cautions:
Seasonal signals: discrepancies among techniques at colocation sites, due to technique systematic errors
Different & discrepant Geocenter motion models exist
Time series of “Quasi-instantaneous” frames: scientifically sound approach. Cautions:
Predictability ?
Less practical for Operational Geodesy & some geophysical applications
Co-motion constraints at co-location sites ??
If needed: Identify users and how to do it ?

19. Backup

20. Up annual signals : GNSS
January A f
April
Dh = A.cos( 2p f (t – t0 ) + f )