Advertisement

The correlation process in Very Long Baseline Interferometry

  • Axel NothnagelEmail author
Original Paper
  • 4 Downloads

Abstract

The correlation process is an important element of geodetic Very Long Baseline Interferometry (VLBI). For many decades there has been constant progress in the capabilities of geodetic VLBI correlators following technical development and the need for ever higher precision of the results. In this publication, we describe the concept and some of the important practical aspects of VLBI correlation for a better understanding of the general geodetic readership. Time-lag correlators provide the easiest approach to the concept and to the individual steps necessary for the operations. More modern approaches then use the path where the data streams are Fourier transformed first before the cross correlation is actually performed. These correlators are called FX correlators, in contrast to XF correlators, where the cross-multiplications are done before the Fourier transform. Both concepts lead to the same results, the cross power spectrum. Following the correlation process proper, the VLBI observables, time delay and delay rate, have to be found in a fringe fitting process.

Keywords

Very Long Baseline Interferometry Correlation Cross power spectrum 

Mathematics Subject Classification

62M10 65T50 

Notes

References

  1. Altamimi, Z., Rebischung, P., Métivier, L., Collilieux, X.: ITRF2014: a new release of the International Terrestrial Reference Frame modeling nonlinear station motions. J. Geophys. Res. Solid Earth 121, 6109–6131 (2016).  https://doi.org/10.1002/2016JB013098 CrossRefGoogle Scholar
  2. Bare, C., Clark, B.G., Kellermann, K.I., Cohen, M.H., Jauncey, D.L.: Interferometer experiment with independent local oscillators. Science 157(3785), 189–191 (1967)CrossRefGoogle Scholar
  3. Broten, N.W., Legg, T.H., Locke, J.L., McLeish, C.W., Richards, R.S., Chisholm, R.M., Gush, H.P., Yen, J.L., Galt, J.A.: Long base line interferometry: a new technique. Science 156(3782), 1592–1593 (1967).  https://doi.org/10.1126/science.156.3782.1592 CrossRefGoogle Scholar
  4. Cohen, M.H., Shaffer, D.B.: Positions of radio sources from long-baseline interferometry. Astron. J. 76, 76–91 (1971)CrossRefGoogle Scholar
  5. Deller, A.T., Tingay, S.J., Bailes, M., West, C.: DiFX: a software correlator for very long baseline interferometry using multiprocessor computing environments. Publ. Astron. Soc. Pac. 119, 318–336 (2007)CrossRefGoogle Scholar
  6. Fey, A.L., Gordon, D., Jacobs, C.S., Ma, C., Gaume, R.A., Arias, E.F., Bianco, G., Boboltz, D.A., Böckmann, S., Bolotin, S., Charlot, P., Collioud, A., Engelhardt, G., Gipson, J., Gontier, A.M., Heinkelmann, R., Kurdubov, S., Lambert, S., Lytvyn, S., MacMillan, D.S., Malkin, Z., Nothnagel, A., Ojha, R., Skurikhina, E., Sokolova, J., Souchay, J., Sovers, O.J., Tesmer, V., Titov, O., Wang, G., Zharov, V.: The second realization of the international celestial reference frame by very long baseline interferometry. Astron. J. 150(2), 58 (2015).  https://doi.org/10.1088/0004-6256/150/2/58 CrossRefGoogle Scholar
  7. Han, S., Nothnagel, A., Zhang, Z., Haas, R., Zhang, Q.: Fringe fitting and group delay determination for geodetic VLBI observations of DOR tones. Adv. Space Res. 63(5), 1754–1767 (2019).  https://doi.org/10.1016/j.asr.2018.11.018 CrossRefGoogle Scholar
  8. Hinteregger, H.F., Shapiro, I.I., Robertson, D.S., Knight, C.A., Ergas, R.A., Whitney, A.R., Rogers, A.E.E., Moran, J.M., Clark, T.A., Burke, B.F.: Precision geodesy via radio interferometry. Science 178, 396–398 (1972).  https://doi.org/10.1126/science.178.4059.396 CrossRefGoogle Scholar
  9. Hobiger, T., Kondo, T.: An FX software correlator based on Matlab. In: Proceedings of the 17th Working Meeting on European VLBI for Geodesy and Astrometry held at Noto, 22–23 April 2005, pp. 34–38 (2005)Google Scholar
  10. Krasbutter, I., Kargoll, B., Schuh, W.D.: Magic Square of real spectral and time series analysis with an application to moving average processes. In: Kutterer, H., Seitz, F., Alkhatib, H., Schmidt, M. (eds.) The 1st International Workshop on the Quality of Geodetic Observation and Monitoring Systems (QuGOMS’11), IAG Symposia, vol. 140, pp. 9–14. Springer, Berlin (2015)Google Scholar
  11. Lambeck, K.: The Earth’s Variable Rotation: Geophysical Causes and Consequences. Cambridge Monographs on Mechanics. Cambridge University Press, Cambridge (1980)CrossRefGoogle Scholar
  12. Loth, I., Kargoll, B., Schuh, WD.: Non-recursive representation of an autoregressive process within the Magic Square. In: IX. Hotine-Marussi-Symposium, IAG Symposia, Lecture Notes in Earth Science. Springer (2019).  https://doi.org/10.1007/1345_2019_60 Google Scholar
  13. Matveenko, L.I., Kardashev, N.S., Sholomitskii, G.B.: Large base-line radio interferometers. Soviet Radiophys. 8(4), 461–463 (1965).  https://doi.org/10.1007/bf01038318 CrossRefGoogle Scholar
  14. Michelson, A.A.: On the application of interference methods to astronomical measurements. Astrophys. J. 51, 257–262 (1920)CrossRefGoogle Scholar
  15. Moran, J.M.: Very long baseline interferometric observations and data reduction. Methods Exp. Phys. 12, 228–260 (1976).  https://doi.org/10.1016/S0076-695X(08)60711-5 CrossRefGoogle Scholar
  16. Moran, J.M., Crowther, P.P., Burke, B.F., Barrett, A.H., Rogers, A.E.E., Ball, J.A., Carter, J.C., Bare, C.C.: Spectral line interferometry with independent time standards at stations separated by 845 kilometers. Science 157(3789), 676–677 (1967).  https://doi.org/10.1126/science.157.3789.676 CrossRefGoogle Scholar
  17. Napier, P.J., Bagri, D.S., Clark, B.G., Rogers, A.E.E., Romney, J.D., Thompson, A.R., Walker, R.C.: The very long baseline array. Proc. IEEE 82(5), 658–671 (1994)CrossRefGoogle Scholar
  18. Niell, A., Barrett, J., Burns, A., Cappallo, R., Corey, B., Derome, M., Eckert, C., Elosegui, P., McWhirter, R., Poirier, M., Rajagopalan, G., Rogers, A., Ruszczyk, C., SooHoo, J., Titus, M., Whitney, A., Behrend, D., Bolotin, S., Gipson, J., Gordon, D., Himwich, W.E., Petrachenko, B.: Demonstration of a broadband very long baseline interferometer system: a new instrument for high-precision space geodesy. Radio Sci. 53(10), 1269–1291 (2018).  https://doi.org/10.1029/2018RS006617 CrossRefGoogle Scholar
  19. Nothnagel, A.: Very long baseline interferometry. In: Freeden, W., Rummel, R. (eds.) Handbuch der Geodäsie. Springer Reference Naturwissenschaften Book Series, pp. 1–58. Springer Spektrum, Berlin (2019).  https://doi.org/10.1007/978-3-662-46900-2_110-1 CrossRefGoogle Scholar
  20. Nothnagel, A., Nilsson, T., Schuh, H.: Very long baseline interferometry: dependencies on frequency stability. Space Sci. Rev. 214, 66 (2018).  https://doi.org/10.1007/s11214-018-0498-1 CrossRefGoogle Scholar
  21. Petrov, L., Gordon, D., Gipson, J., MacMillan, D., Ma, C., Fomalont, E., Walker, R.C., Carabajal, C.: Precise geodesy with the very long baseline array. J. Geod. 83(9), 859–876 (2009).  https://doi.org/10.1007/s00190-009-0304-7 CrossRefGoogle Scholar
  22. Rogers, A.E.E.: Very Long Baseline Interferometry with large effective bandwidth for phase-delay measurement. Radio Sci. 5(10), 1239–1247 (1970)CrossRefGoogle Scholar
  23. Shapiro, I.I., Robertson, D.S., Knight, C.A., Counselman, C.C., Rogers, A.E.E., Hinteregger, H.F., Lippincott, S., Whitney, A.R., Clark, T.A., Niell, A.E., Spitzmesser, D.J.: Transcontinental baseline and the rotation of the earth measured by radio interferometry. Science 186, 920–922 (1974)CrossRefGoogle Scholar
  24. Sovers, O.J., Fanselow, J.L., Jacobs, C.S.: Astrometry and geodesy with radio interferometry: experiments, models, results. Rev. Modern Phys. 70(4), 1393–1454 (1998).  https://doi.org/10.1103/RevModPhys.70.1393 CrossRefGoogle Scholar
  25. Thompson, A.R., Moran, J., Swenson, G.W.: Interferometry and Synthesis in Radio Astronomy. Springer, Berlin (2017)CrossRefGoogle Scholar
  26. Whitney, A.R.: How do VLBI correlators work? In: Vandenberg, N.R., Baver, K.D. (eds.) International VLBI Service for Geodesy and Astrometry 2000 General Meeting Proceedings, NASA/CP-2000-209893, pp. 187–205 (2000)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Geodesy and GeoinformationUniversity of BonnBonnGermany

Personalised recommendations