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Journal of Geodesy

, 84:31 | Cite as

Global optimization of core station networks for space geodesy: application to the referencing of the SLR EOP with respect to ITRF

  • David CoulotEmail author
  • Arnaud Pollet
  • Xavier Collilieux
  • Philippe Berio
Original Article

Abstract

We apply global optimization in order to optimize the referencing (and consequently the stability) of the Earth Orientation Parameters (EOP) with respect to ITRF2005. These EOP are derived at a daily sampling from SLR data, simultaneously with weekly station positions. The EOP referencing is carried out with minimum constraints applied weekly to the three rotations and over core station networks. Our approach is based on a multi objective genetic algorithm, a particular stochastic global optimization method, the reference system effects being the objectives to minimize. We thus use rigorous criteria for the optimal weekly core station selection. The results evidence an improvement of 10% of the stability for Polar Motion (PM) series in comparison to the results obtained with the network specially designed for EOP referencing by the Analysis Working Group of the International Laser Ranging Service. This improvement of nearly 25 μas represents 50% of the current precision of the IERS 05 C04 PM reference series. We also test the possibility of averaging the weekly networks provided by our algorithm (the Genetically Modified Networks—GMN) over the whole time period. Although the dynamical nature of the GMN is clearly a key point of their success, we can derive such a global mean core network, which could be useful for practical applications regarding EOP referencing. Using this latter core network moreover provides more stable EOP series than the conventional network does.

Keywords

Global optimization Earth orientation parameters Minimum constraints Core station networks Genetic algorithms Satellite laser ranging 

Supplementary material

190_2009_342_MOESM1_ESM.pdf (571 kb)
ESM (PDF 571 kb)
190_2009_342_MOESM2_ESM.pdf (42 kb)
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References

  1. Altamimi Z, Boucher C, Sillard P (2002) New trends for the realization of the International Terrestrial Reference System. Adv Space Res 30(2): 175–184CrossRefGoogle Scholar
  2. Altamimi Z, Sillard P, Boucher C (2002) ITRF2000: a new release of the International Terrestrial Reference Frame for Earth science applications. J Geophys Res 107(B10): 2214. doi: 10.1029/2001JB000561 CrossRefGoogle Scholar
  3. Altamimi Z, Collilieux X, Legrand J, Garayt B, Boucher C (2007) ITRF2005: a new release of the International Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters. J Geophys Res 112: B09401. doi: 10.1029/2007JB004949 CrossRefGoogle Scholar
  4. Altamimi Z, Gambis D, Bizouard C (2008) Rigorous combination to ensure ITRF and EOP consistency. In: Capitaine N (ed) Proceedings of the journées 2007: systèmes de référence spatio-temporels: the celestial reference frame for the future, Observatoire de Paris, pp 151–154Google Scholar
  5. Baarda W (1973) S-transformations and criterion matrices, vol 5(1), Geodetic New Series. Netherlands Geodetic Commission Publications, DelftGoogle Scholar
  6. Baselga S, García-Asenjo L (2008) GNSS differential positioning by robust estimation. J Surv Eng 134(1): 21–25CrossRefGoogle Scholar
  7. Berné JL, Baselga S (2004) First-order design of geodetic networks using the simulated annealing method. J Geod 78: 47–54. doi: 10.1007/s00190-003-0365-y CrossRefGoogle Scholar
  8. Bizouard C, Gambis D (2009) The combined solution C04 for Earth Orientation Parameters consistent with the International Reference Frame 2005. In: Proceedings of the IAG symposium GRF2006: geodetic reference frames, IAG Springer SeriesGoogle Scholar
  9. Bjerhammar A (1973) Theory of errors and generalized matrix inverses. Elsevier, AmsterdamGoogle Scholar
  10. Blaha G (1971) Inner adjustment constraints with emphasis on range observations. Technical Report 48, Department of Geodetic Science, The Ohio State University, ColumbusGoogle Scholar
  11. Blaha G (1982) Free networks: minimum norm solution as obtained by the inner adjustment constraint method. Bull Geod 56: 209–219CrossRefGoogle Scholar
  12. Coello Coello CA (2000) Handling preferences in evolutionary multiobjective optimization: a survey. In: Proceedings of the 2000 congress on evolutionary computation (CEC’2000), vol 1. IEEE Press, pp 30–37Google Scholar
  13. Coello Coello CA et al (2005) Recent trends in evolutionary multiobjective optimization. In: Abraham A (eds) Evolutionary multi-objective optimization: theoretical advances and applications, advanced information and knowledge processing ser. Springer, London, pp 7–32Google Scholar
  14. Coello Coello CA (2006) Twenty years of evolutionary multi-objective optimization: a historical view of the field. IEEE Comput Intell Mag 1(1): 28–36CrossRefGoogle Scholar
  15. Coulot D, Berio P, Biancale R, Loyer S, Soudarin L, Gontier AM (2007) Toward a direct combination of space-geodetic techniques at the measurement level: methodology and main issues. J Geophys Res 112: B05410. doi: 10.1029/2006JB004336 CrossRefGoogle Scholar
  16. Cvetković D, Coello Coello CA (2004) Human preferences and their applications in evolutionary multi-objective optimization. In: Yaochu J (eds) Knowledge incorporation in evolutionary computation. Springer, Berlin, pp 479–503Google Scholar
  17. Dare P, Saleh H (2000) GPS network design: logistics solution using optimal and near-optimal methods. J Geod 74: 467–478CrossRefGoogle Scholar
  18. Deb K, Agrawal S, Pratap A, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2): 182–197CrossRefGoogle Scholar
  19. de Caritat Condorcet MJAN (1785) Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. Imprimerie RoyaleGoogle Scholar
  20. Dermanis A (1994) Free networks solutions with the Direct Linear Transformation (DLT) method. ISPRS J Photogram Rem Sens 49: 2–12CrossRefGoogle Scholar
  21. Gambis D (2004) Monitoring earth orientation using space-geodetic techniques: state-of-the-art and prospective. J Geod 78: 295–303. doi: 10.1007/s00190-004-0394-1 CrossRefGoogle Scholar
  22. Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading, MAGoogle Scholar
  23. Grafarend EW (1974) Optimization of geodetic networks. Boll Geod Sc Aff 33(4): 351–406Google Scholar
  24. Grafarend EW, Schaffrin B (1974) Unbiased free net adjustment. Surv Rev 22(171): 200–218Google Scholar
  25. Grafarend EW, Schaffrin B (1976) Equivalence of estimable quantitiess and invariants in geodetic networks. Z Vermess 101: 485–491Google Scholar
  26. Knowles J, Corne D et al (2004) Memetic algorithms for multiobjective optimization: issues, methods, and prospects. In: Krasnogor N (eds) Recent advances in memetic algorithms. Springer, Berlin, pp 313–352Google Scholar
  27. Koch KR (1987) Parameter estimation and hypothesis testing in linear models. Springer, BerlinGoogle Scholar
  28. Konak A, Coit DW, Smith AE (2006) Multi-Objective optimization using genetic algorithms: a tutorial. Reliab Eng Syst Saf 91: 992–1007CrossRefGoogle Scholar
  29. Leguizamón G, Michalewicz Z (1999) A new version of ant system for subset problems. In: Angeline PJ et al (eds) Proceedings of the 1999 congress on evolutionary computation (CEC’99), IEEE Press, pp 1459–1464Google Scholar
  30. Meissel P (1965) Über die innere Genauigkeit dreidimensionaler Punkthaufens. Z Vermess 90: 109–118Google Scholar
  31. Pearlman M, Degnan JJ, Bosworth JM (2002) The international laser ranging service. Adv Space Res 30(2): 135–143CrossRefGoogle Scholar
  32. Penrose R (1956) On best approximate solution of linear matrix equations. In: Proceedings of the Cambridge Philosophical Society, vol 52, pp 17–19Google Scholar
  33. Ray J, Altamimi Z (2005) Evaluation of co-location ties relating the VLBI and GPS reference frames. J Geod 79: 189–195. doi: 10.1007/s00190-005-0456-z CrossRefGoogle Scholar
  34. Saleh HA, Chelouah R (2004) The design of the global navigation satellite system surveying networks using genetic algorithms. Eng Appl Artif Intell 17: 111–122. doi: 10.1016/j.engappai.2003.11.001 CrossRefGoogle Scholar
  35. Schaffrin B (1985) Aspects of network design. In: Grafarend EW, Sansò F (eds) Optimization and design of geodetic networks. Springer, BerlinGoogle Scholar
  36. Sillard P, Boucher C (2001) A review of algebraic constraints in terrestrial reference frame datum definition. J Geod 75: 63–73CrossRefGoogle Scholar
  37. Ulrich T, Brockhoff D, Zitzler E (2008) Pattern identification in Pareto-set Approximations. In: Kejzer M et al (eds) Proceedings of the 2008 genetic and evolutionary computation conference (GECCO-2008), ACM, pp 737–744Google Scholar
  38. Vergidis T, Vergidis K, Tiwari A (2008) The evaluation line: a posteriori preference articulation approach. In: Proceedings of the 2008 conference on evolutionary computation (CEC 2008), IEEE Press, pp 2694–2700. doi: 10.1109/CEC.2008.4631160
  39. Zhu SY, Mueller II (1983) Effects of adopting new precession, nutation and equinox corrections on the terrestrial reference frame. Bull Geod 57: 29–42CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • David Coulot
    • 1
    Email author
  • Arnaud Pollet
    • 1
  • Xavier Collilieux
    • 1
  • Philippe Berio
    • 2
  1. 1.IGN/LAREG et ENSGMarne la Vallée Cedex 2France
  2. 2.Observatoire de la Côte d’AzurNice Cedex 4France

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