1. Insensitivity of GNSS to geocenter motion through the network shift approach Paul Rebischung, Zuheir Altamimi, Tim Springer AGU Fall Meeting 2013, San Francisco, December 9-13, 2013 1

2. Observing geocenter motion with GNSS 2 Degree-1 deformation approach (Blewitt et al., 2001): –Based on the fact that loading-induced geocenter motion is accompanied by deformations of the Earth’s crust. –Gives satisfying results. –But can only sense non-secular, loading-induced geocenter motion. Network shift approach: –Weekly AC solutions theoretically CM-centered. –AC → ITRF translations should reflect geocenter motion. –But unlike SLR, GNSS have so far not proven able to reliably observe geocenter motion through the network shift approach. –Why?

3. 3 Example of network shift results –The translations of the different IGS ACs show various features. –But none properly senses the X & Z components of geocenter motion. — SLR (smoothed) — GPS (ESA) — GPS (ESA, smoothed) Annual signal missed Spurious peaks at harmonics of 1.04 cpy Why?

4. 4 (Multi-) Collinearity Consider the linear regression model: y = Ax + v = Σ A i x i + v –A i = ∂y / ∂x i = « signature » of x i on the observations Collinearity = existence of quasi-dependencies among the A i ’s Consequences: –Some (linear combinations of) parameters cannot be reliably inferred, –are extremely sensitive to any modeling or observation error, –have large formal errors. observationsparametersresiduals

5. Is the estimation of a particular parameter x i subject to collinearity issues? –θ i = angle between A i and the hyper- plane K i containing all other A j ’s –VIF i = 1 / sin²θ i –θ i = π/2(VIF i = 1) : x i is uncorrelated with any other parameter. –θ i → 0(VIF i → ∞) : x i tends to be indistinguishable from the other parameters. If yes, why? –The orthogonal projection α i of A i on K i corresponds to the linear combination of the x j ’s which is the most correlated with x i. 5 Variance inflation factor (VIF)

6. Geocenter coordinates are not explicitly estimated parameters. –They are implicitly realized through station coordinates. →Extend previous notions to such « implicit parameters ». There are perfect orientation singularities. →Extend previous notions so as to handle singularities supplemented by minimal constraints. The whole normal matrix is not available. –Clock parameters are either reduced or annihilated by forming double-differenced observations. →Practical collinearity diagnosis (next slide) 6 Mathematical difficulties

7. 7 0) 1) 2) –Simulate « perfect » observations x 0 → y 0 –Introduce a 1 cm error on the Z geocenter coordinate: x 1 = x 0 + [0, 0, 0.01, …, 0, 0, 0.01, 0, …0] T –Re-compute observations → y 1 –Solve the constrained LSQ problem: (How can the introduced geocenter error be compensated / absorbed by the other parameters?) → x 2, y 2 Practical diagnosis

8. 8 « Signature » of a geocenter shift From the satellite point of view: GPSLAGEOS δZ gc = 1 cm δX gc = 1 cm · impact on a particular observation — epoch mean impact

9. 9 1 st issue: satellite clock offsets Satellite clocks ↔ constant per epoch and satellite →The epoch mean geocenter signature is 100% absorbable by (indistinguishable from) the satellite clock offsets. →The GNSS geocenter determination can only rely on a 2 nd order signature. In case of SLR : –The epoch mean signatures of X gc and Y gc are directly observable. → No collinearity issue for X gc and Y gc (VIF ≈ 1) –The epoch mean signature of Z gc is absorbable by the satellite osculating elements. → Slight collinearity issue for Z gc (VIF ≈ 9)

10. 2 nd order geocenter signature 10 δZ gc = 1 cmδX gc = 1 cm 2 nd issue: collinearity with station parameters –Positions, clock offsets, tropospheric parameters

11. 11 So what’s left? δX gc = 1 cm: From the point of view of a satellite……and of a station VIF > 2000 for the 3 geocenter coordinates! (More than 99.96% of the introduced signal could be absorbed.) · impact on an observation, before compensation · impact on an observation, after compensation

12. 12 Role of the empirical accelerations –The insensitivity of GNSS to geocenter motion is mostly due to the simultaneous estimation of clock offsets and tropospheric parameters. –The ECOM empirical accelerations only slightly increase the collinearity of the Z geocenter coordinate. –This increase is due to the simultaneous estimation of D 0, B C and B S :

13. 13 Conclusions (1/2) Current GNSS are barely sensitive to geocenter motion. –The 3 geocenter coordinates are extremely collinear with other GNSS parameters, especially satellite clock offsets and all station parameters. –Their VIFs are huge (at the same level as for the terrestrial scale when the satellite z-PCOs are estimated). –The GNSS geocenter determination can only rely on a tiny 3rd order signal. –Other parameters not considered here (unfixed ambiguities) probably worsen things even more (cf. GLONASS).

14. 14 Conclusions (2/2) The empirical satellite accelerations do not have a predominant role. –Contradicts Meindl et al. (2013)’s conclusions What can be done? –Reduce collinearity issues (highly stable satellite clocks?) –Reduce modeling errors (radiation pressure, higher-order ionosphere…) –Continue to rely on SLR…

15. Thanks for your attention! For more: Rebischung P, Altamimi Z, Springer T (2013) A collinearity diagnosis of the GNSS geocenter determination. Journal of Geodesy. DOI: 10.1007/s00190-013-0669-5 15

16. Parameter response to δZ gc = 1 cm Network distortion: → Explains the significant correlations between origin & degree-1 deformations observed in the IGS AC solutions ZWDs: (as a function of time, for each station) And their means: (as a function of latitude) Station clock offsets: (as a function of time, for each station) And their means: (as a function of latitude) Tropo gradients: (as a function of latitude) N/S gradients W/E gradients 16

17. Z gc collinearity issue in SLR 17 δZ gc = 1 cm: –This slight collinearity issue probably contributes to the lower quality of the Z component of SLR-derived geocenter motion. –To be further investigated… · impact on an observation, before compensation · impact on an observation, after compensation — radial orbit difference –The epoch mean signature of δZ gc is compensated by a periodic change of the orbit radius obtained through: →VIF ≈ 9.0