Skip to main content

Advertisement

We’d like to understand how you use our websites in order to improve them. Register your interest.

Stability of VLBI, SLR, DORIS, and GPS positioning

Abstract

The residual signal in VLBI, SLR, DORIS and GPS station motion, after a linear trend and seasonal components have been removed, is analysed to investigate site-specific and technique-specific error spectra. The study concentrates on 60 sites with dense observation history by two or more space geodetic techniques. Statistical methods include the Allan variance analysis and the three-cornered hat algorithm. The stability of time-series is defined by two parameters, namely the Allan deviation for a one-year sampling time (noise level) and the slope of the Allan variance graph with its spectral interpretation (noise type). The site-specific noise level is found to be in the range 0.5–3.5 mm in either horizontal direction and 1–4.5 mm in height for most sites. The distribution of site-specific noise type includes both white noise and flicker noise. White noise is predominant in the East direction. Both types of noise are found in the North direction, with no particular geographical clustering. In the Up direction, the Northern hemisphere sites seem to be split in two large geographical sectors characterised either by white noise or by flicker noise signatures. Technique-specific noise characteristics are estimated in several ways, leading to a white noise diagnostic for VLBI and SLR in all three local directions. DORIS has also white noise in the horizontal directions, whereas GPS has a flicker noise spectrum. The vertical noise spectrum is indecisive for both DORIS and GPS. The three-dimensional noise levels for the one-year sampling time are 1.7 mm for VLBI, 2.5 mm for SLR, 5.2 mm for DORIS, and 4.1 mm for GPS. For GPS, the long-term analysis homogeneity has a strong influence. In the case of a test solution reanalysed in a fully consistent way, the noise level drops to the VLBI level in horizontal and to the SLR level in vertical. The three-dimensional noise level for a one-year sampling time decreases to 1.8 mm. In addition, the percentage of stations with flicker noise drops to only about 20% of the network.

References

  1. Allan, D. W., Statistics of Atomic Frequency Standards, Proc. IEEE, 54, 221–231, 1966.

  2. Allan, D. W., Time and frequency characterisation, estimation, and prediction of precision clocks and oscillators, IEEE Trans. UFCC, 34, 647–654, 1987.

  3. Allan, D. W. and J. A. Barnes, A Modified “Allan Variance” with Increased Oscillator Characterization Ability, Proceedings of the 35th Annual Frequency Control Symposium, 470–475, 1981.

  4. Altamimi, Z. and X. Collilieux, The status of ITRF2004, IAG Symposium Series, 130, Springer-Verlag, P. Tregoning and C. Rizos (eds), 2007 (in press).

  5. Altamimi, Z., C. Boucher, and P. Sillard, New Trends for the Realization of the International Terrestrial Reference System, Adv. Space Res., 30, 175, 2001.

  6. Altamimi, Z., P. Sillard, and C. Boucher, ITRF2000, A new release of the international terrestrial reference frame for Earth science applications, J. Geophys. Res., 107(B10), 2214, 2002.

  7. Altamimi, Z., C. Boucher, and D. Gambis, Long-term stability of the Terrestrial Reference Frame, Advances in Space Research, 36, 342–349, 2005.

  8. Altamimi, Z., X. Collilieux, and C. Boucher, DORIS contribution to ITRF2005, J. Geod., 80, 625–635, 2006.

  9. Blaha, G., Free networks: minimum norm solution as obtained by the inner adjustment constraint method, Bull. Geod., 56, 209–219, 1982.

  10. Blewitt, G. and D. Lavallée, Effect of annually repeating signals on geodetic velocity estimates, paper presented at The Tenth General Assembly of the WEGENER Project (WEGENER 200), San Fernando, Spain, September 18–20, 2000.

  11. Blewitt, G. and D. Lavallée, Effect of annual signals on geodetic velocity, J. Geophys. Res., 107, B7, ETG 9–1, 2002.

  12. Boucher, C., Z. Altamimi, P. Sillard, and M. Feissel-Vernier, The ITRF2000, IERS Technical Note, 31, 2004.

  13. Collilieux, X., Z. Altamimi, D. Coulot, J. Ray, and P. Sillard, Spectral and correlation analyses of ITRF2005 VLBI, GPS and SLR height residuals: How well do space geodetic techniques agree?, J. Geophys. Res., submitted, 2007.

  14. Coulot, D., Télémétrie laser sur satellites et combinaison de techniques géodésiques. Contribution aux syste`mes de référence et applications, PhD Thesis dissertation, Paris Observatory, Jul. 2005.

  15. Ding, X. L., D. W. Zheng, D. N. Dong, C. Ma, Y. Q. Chen, and G. L. Wang, Seasonal and secular positional variations at eight collocated GPS and VLBI stations, J. Geod., 79, 71–81, 2005.

  16. Dong, D., P. Fang, Y. Bock, M. K. Cheng, and S. Miyazaki, Anatomy of apparent seasonal variations from GPS-derived site position time series, J. Geophys. Res., 107, 9–1, 2002.

  17. Feissel-Vernier, M. and K. Le Bail, Spectral characteristics of the measurement of station motion with GPS, IGS 2004-2005 Technical report, Edited by IGS Central Bureau, 2006 (in press).

  18. Feissel-Vernier, M., K. Le Bail, P. Berio, D. Coulot, G. Ramillien, and J. J. Valette, Geocenter motion measured by DORIS and SLR and geophysical evidence, J. Geod., 80, 637–648, 2006.

  19. Ferland, R., J. Kouba, and D. Hutchison, Analysis methodology and recent results of the IGS network combination, Earth Planets Space, 52, 953–957, 2000.

  20. Gontier, A.-M., K. Le Bail, M. Feissel, and T. M. Eubanks, Stability of the extragalactic VLBI reference frame, Astron. Astrophys., 375, 661–674, 2001.

  21. Gontier, A.-M., M. Feissel-Vernier, and C. Barache, Paris Observatory Analysis Center OPAR: Report on Activities, January-December 2005, IVS Annual Report, 2005, 256–259, 2006.

  22. Gray, J. E. and D. W. Allan, A method for estimating the frequency stability of an individual oscillator, Proc. 28th Annual Symp. on Frequency Control, May 1974, 243–246, 1974.

  23. Hugentobler, U. and G. Beutler, Measurement of Geocenter Variations With GNSS, American Geophysical Union, Fall Meeting 2005, abstract G31A-02, 2005.

  24. Koot, L., O. de Viron, and V. Dehant, Atmospheric angular momentum time-series: characterization of their internal noise and creation of a combined series, J. Geod., 79, 663–674, 2006.

  25. Langbein, J. and H. Johnson, Correlated errors in geodetic time-series: Implications for time-dependant deformation, J. Geophys. Res., 102, 591–604, 1997.

  26. Le Bail, K., Etude statistique de la stabilité des stations de géodésie spatiale. Application a` DORIS, PhD Thesis dissertation, Observatoire de Paris, Dec. 2004.

  27. Le Bail, K., Estimating the noise in space-geodetic positioning. The case of DORIS, J. Geod., 80, 541–565, 2006.

  28. Le Bail, K., M. Feissel-Vernier, J.-J. Valette, and W. Zerhouni, Long term consistency of multi-technique terrestrial reference frames, a spectral approach, IAG Symposium Series, 130, Springer-Verlag, P. Tregoning and C. Rizos (eds), 2006 (in press).

  29. Lindman, H. R., Analysis of variance in complex experimental designs, Edited by W. H. Freeman and Co, San Francisco, 1974.

  30. Ma, C., E. F. Arias, T. M. Eubanks, A. L. Fey, A.-M. Gontier, C. S. Jacobs, O. J. Sovers, B. A. Archinal, and P. Charlot, The International Celestial Reference Frame as realized by Very Long Baseline Interferometry, Astron. J., 116, 516, 1998.

  31. Mangiarotti, S., A. Cazenave, L. Soudarin, and J.-F. Crétaux, Annual vertical crustal motions predicted from surface mass redistribution and observed by space geodesy, J. Geophys. Res., 106, 4277–4292, 2001.

  32. Mao, A., C. G. A. Harrison, and T. H. Dixon, Noise in GPS coordinate times series, J. Geophys. Res., 104, 2797–2816, 1999.

  33. McCarthy, D. D., G. Petit, (eds) IERS Standards (2003), IERS Technical Note, 32, BKG, Frankfurt am Main, Germany, 2004.

  34. McMillan, D. S. and C. Ma, Atmospheric gradients and the VLBI terrestrial and celestial reference frames, Geophys. Res. Lett., 24, 453, 1997.

  35. Meisel, B., D. Angermann, M. Kruegel, H. Drewes, M. Gerstl, R. Kelm, H. Mueller, W. Seemueller, and V. Tesmer, Refined approaches for terrestrial reference frame computations, Adv. in Space Res., 36, 350–357, 2005.

  36. Michel, V., G. Roesch, and J. Long, Hartebeesthoek Co-location Survey, Proceedings of the IERS Workshop on site co-location. IERS Technical Note, 33, Edited by W. R. Dick and B. Richter, 34–36, BKG, Frankfurt am Main, Germany, 2005.

  37. Nicolas, J., J.-M. Nocquet, M. van Camp, T. van Dam, J.-P. Boy, J. Hinderer, P. Gegout, E. Calais, and M. Amalvict, Seasonal effect on vertical positioning by Satellite Laser Ranging and Global Positioning System and on absolute gravity at the OCA geodetic station, Grasse, France, Geophys. J. Int., 167, 1127–1137, 2006.

  38. Penna, N. T. and M. P. Stewart, Aliased tidal signatures in continuous GPS height time-series, Geophys. Res. Lett., 30, 2184–2187, 2003.

  39. Percival, D. B., Stochastic models and statistical analysis for clock noise, Metrologia, 40, S289–S304, 2003.

  40. Petrov, L. and J. Boy, Study of the atmospheric pressure loading signal in very long baseline interferometry observations, J. Geophys. Res., 109, B03405, 2004.

  41. Petrov, L. and C. Ma, Study of harmonic site position variations determined by very long baseline interferometry, J. Geophys. Res., 108, B4, ETG 5-1, 2003.

  42. Premoli, A. and P. Tavella, A Revisited Three-Cornered-Hat Method for Estimating Frequency Standards Instability, IEEE Trans. on instrumentation and measurement, 42, 1–10, 1993.

  43. Ray, J. and Z. Altamimi, Evaluation of co-location ties relating the VLBI and GPS reference frames, J. Geod., 79, 189–195, 2005.

  44. Richter, B., W. R. Dick, and W. Schwegmann, (eds) Proceedings of the IERS Workshop on site co-location, Matera, Italy, 23–24 October 2003, IERS Technical Note, 33, 2005.

  45. Soudarin, L. and J.-F. Crétaux, ftp://cddis.gsfc.nasa.gov/doris/products/-sinex_series/lcawd/lcawd14_snx_dsc.txt, 2006a.

  46. Soudarin, L. and J.-F. Crétaux, A model of present-day plate motions from 12 years of DORIS measurements, J. Geod., 80, 609–624, 2006b.

  47. Steigenberger, P., M. Rothacher, R. Dietrich, M. Fritsche, A. Ruelke, and S. Vey, Reprocessing of a global GPS network, J. Geophys. Res., 111, B05402, 2003.

  48. Tavernier, G., H. Fagard, M. Feissel-Vernier, K. Le Bail, F Lemoine, C. Noll, J. Ries, L. Soudarin, J.-J. Valette, and P. Willlis, The International DORIS Service: genesis and early achievements, J. Geod., 80, 403–417, 2006.

  49. Titov, O. and H. Yakovleva, Seasonal variation in radial components of VLBI stations, Astron. and Astrophys. Trans., 18, 593–606, 1999.

  50. Williams S. D. P., Offsets in Global Positioning System time series, J. Geophys. Res., 108 (B6), 2310, 2003.

  51. Williams, S. D. P. and P. Willis, Error analysis of weekly station coordinates in the DORIS network, J. Geod., 80, 525–539, 2006.

  52. Williams, S. D. P., Y. Bock, P. Fang, P. Jamason, R. M. Nikolaidis, L. Prawirodirdjo, M. Miller, and D. J. Johnson, Error analysis of continuous GPS position time-series, J. Geophys. Res., 109, B03412, 2004.

  53. Woppelmann, G., B. Martin-Miguez, M.-N. Bouin, and Z. Altamimi, Geocentric sea-level trend estimates from GPS analyses at relevant tide gauges world-wide, Global and Planetary change, 2007 (in press).

  54. Zhang, J., U. Bock, H. Johnson, P. Fang, S. Williams, J. Genrich, S. Wdowinski, and J. Behr, Southern California Permanent GPS Geodetic Array: error analysis of daily position estimates and site velocities, J. Geophys.Res., 102, 18035–18056, 1997.

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to M. Feissel-Vernier.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Feissel-Vernier, M., de Viron, O. & Le Bail, K. Stability of VLBI, SLR, DORIS, and GPS positioning. Earth Planet Sp 59, 475–497 (2007). https://doi.org/10.1186/BF03352712

Download citation

Key words

  • Reference frames
  • station positions
  • station stability
  • Allan variance
  • three-cornered hat