STATISTICAL EVALUATION OF THE STABILITY OF VLBI, SLR, DORIS AND GPS STATIONS

Transcription

1 STATISTICAL EVALUATION OF THE STABILITY OF VLBI, SLR, DORIS AND GPS STATIONS K. Le Bail (1), O. de Viron (), M. Feissel-Vernier (3), (1) Institut Géographique National/LAREG, Marne La Vallée, France and Observatoire de la Côte d'azur/gemini, Grasse, France () Institut de Physique du Globe de Paris/Géodésie et Gravimétrie, Paris, France (3) Observatoire de Paris/SYRTE, Paris, France and Institut Géographique National/LAREG, Marne La Vallée, France

2 Contents Goal of this study : Statistical study of time-series of geodetic station coordinates (signal, noise). Used tools : Allan variance; Principal Component Analysis applied in the time domain; Three-cornered hat method.

3 The studied data DORIS, GPS, VLBI, SLR individual solutions Time-series of station position (15 stations in 57 s) Software Solution by Referencing in a TRF #stat DORIS GINS-DYNAMO L. Soudarin J.-J. Valette (CATREF) 46 GPS BERNESE Soft. U. Hugentobler et al. R. Ferland (IGS) 58 SLR GINS-DYNAMO D. Coulot et al. D. Coulot (CATREF) 0 VLBI CALC-SOLVE C. Ma C. Ma 40

4 Geodetic time-series Time-series = reflect of the measurement technique, the instrumentation, the analysis strategy, insufficient modeling, local geophysical phenomena Deterministic part : Periodic signals : seasonal (annual, semi-annual,...), aliasing (13.6 days for GPS, 118 days for TOPEX/Poseidon),... Drift (velocity); Bias,... Noise.

5 PART I : Individual 1D noise characteristics Allan variance; Results for each component, each station and each technique.

6 The Allan variance If (x i ) are the measurements and T the sampling time : σ T ) 0.5 < ( x i x DORIS ( = + 1 i ) >

7 Individual type and level of noise

8 PART II : Individual 3D signal and noise characteristics Principal Component Analysis applied in the time domain; Results for each station and each technique.

9 The Principal Component Analysis applied in the time domain Let A a matrix as: - A(i,1) is the East coordinate of the considered station at the date t i ; - A(i,)=North(t i ); - A(i,3)=Height(t i ). Cross variance-covariance matrix : COV A ( k, l) = n i= 1 ( A( i, k) A k )( A( i, l) n A l )

10 The Principal Component Analysis Projection : applied in the time domain ( PC1, PC, PC3) = ( East, Explained variance percentage : North, Height). V Transformation of 3D series of coordinates into its eigenspace in the time-domain: it allows to separate independent noise components. λ 3 i= 1 k λ i

11 The Principal Component Analysis applied in the time domain Study of each Principal Component can suggest different origins for the detected noise. Hartebeesthoek (DORIS station):

12 The Principal Component Analysis applied in the time domain Information about the geometry of the technique (network, satellite passes over the stations, ) by study of the covariance matrix; Indication of a privileged direction (eigenvectors and explained variance percentage). DORIS

13 PART III : collocation s Assumption : x = S + ε i x), Three-cornered hat method (resolution: least-squares, L1-norm/simplex); Results about "technique" noise : Per station; Per network ε station = ε + αε technique (resolution: least-squares, L1-norm/simplex).

14 The three-cornered Assumption : x i = S + ε x), Standard method : technique independence σ ( x y) = σ ( ε σ ( x z) = σ ( ε σ ( y z) = σ ( ε x), x), y), hat method ) + σ ( ε ) + σ ( ε ) + σ ( ε y), z), z), ) ) )

15 The generalized three-cornered Assumption : Generalized method : σ ( x y) = σ ( ε σ ( x z) = σ ( ε σ ( y z) = σ ( ε x), x), y), Example of Hartebeesthoek station (South Africa) x i = S + ε x), ) + σ ( ε ) + σ ( ε ) + σ ( ε y), z), z), hat method ) + cov( ε ) + cov( ε ) + cov( ε x), x), y), East (mm) North (mm), ε, ε, ε y), z), z), GPS,18 6,7 7,80 DORIS 7,79 3,00 3,65 LASER 3,48,9 3,48 VLBI 1,87 3,60 6,08 ) ) ) Height (mm)

16 Outlook "Site" noise and "technique" noise per network; Application to all the studied stations.

17 Conclusion and discussion Separation of different noises ("", "technique" per network, "technique" per station); These different tools (simple and rapid) give an overview of the composition of geodetic timeseries. One should be cautious : different referencing results of ITRF005!

18 Conclusion and discussion Thanks for your attention!