Abstract
The ionospheric effect is one of the major errors in GPS data processing over long baselines. As a dispersive medium, it is possible to compute its influence on the GPS signal with the ionosphere-free linear combination of L1 and L2 observables, requiring dual-frequency receivers. In the case of single-frequency receivers, ionospheric effects are either neglected or reduced by using a model. In this paper, an alternative for single-frequency users is proposed. It involves multiresolution analysis (MRA) using a wavelet analysis of the double-difference observations to remove the short- and medium-scale ionosphere variations and disturbances, as well as some minor tropospheric effects. Experiments were carried out over three baseline lengths from 50 to 450 km, and the results provided by the proposed method were better than those from dual-frequency receivers. The horizontal root mean square was of about 0.28 m (1σ).
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References
Camargo PO, Monico JFG, Ferreira LDD (2000) Application of ionospheric corrections in the equatorial region for L1 GPS users. Earth Planets Space 52:1083–1089
Chui CK (1992) An introduction to wavelets. Academic, Boston
Daubechies I (1992) Ten lectures on wavelets, vol. 61 of CBMS-NSF regional conference (series in applied mathematics). SIAM, Philadelphia
Daubechies I, Mallat S, Willsky A (1992) Introduction to the special issue on wavelet transforms and multiresolution signal analysis. IEEE Trans Inf Theory 38(2):528–531
Donoho DL, Johnstone IM (1994) Ideal spatial adaptation by wavelet shrinkage. Biometrika 81:425–455
Fortes LPS, Luz R, Pereira KD, Costa SMA, Blitzkow D (1998) The Brazilian network for continuous monitoring of GPS (RBMC): operation and products. In: Brunner FK, (ed) (Org) Advances in positioning and reference frames, vol. 118. Springer, Berlin, pp 73–78
Fengler MJ, Freeden W, Kohlhaas A, Michel V, Peters T (2007) Wavelet modeling of regional and temporal variations of the earth’s gravitational potential observed by GRACE. J Geodesy 81(1):5–15. doi:10.1007/s00190-006-0040-1
Foster DJ, Lane FD, Mosher CC, Wu RS (1997) Wavelet transforms for seismic data processing. SEG 67th annual meeting. pp 1318–1321
Hopfield HS (1971) Tropospheric effect on electromagnetically measured range: prediction from surface weather data. Radio Sci 6:357–367
Keller W (2004) Wavelets in geodesy and geodynamics. Walter de Gruyter, Berlin, 279p
Klobuchar JA (1991) Ionospheric effects on GPS. GPS World. pp 48–51
Machado WC, Monico JFG (2002) Utilização do software GPSeq na Solução rápida das ambigüidades GPS no Posicionamento Relativo Cinemático de Bases Curtas. Pesquisas em Geociências, 29, 2, pp 89–99. Available in: http://www.pesquisasemgeociencias.ufrgs.br/arquivos/29-2%20Wagner.pdf
Mautz R, Ping J, Heki K, Schaffrin B, Shum C, Potts L (2005) Efficient spatial and temporal representations of global ionosphere maps over Japan using B-spline wavelets. J Geodesy 78(11): 660–667. doi:10.1007/s00190-004-0432-z
McNamara LF (1991) The ionosphere: communications, surveillance, and direction finding. Krieger, Malabar
Monico JFG (1995) High precision intercontinental GPS network Univeristy Of Nottinhgam, PhD. Thesis, IESSG, UK, 205p
Percival DB, Walden AT (2000) Wavelet methods for time Series analysis. Cambridge University Press, Cambridge, 594p
Potts L, Schmidt M, Shum C, Ge S (2003) Wavelet based regional multi-resolution TEC model. In: EGS—AGU—Eug joint assembly. Abstracts from the meeting held in Nice. France
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran 90: the Art of parallel scientific computing. Cambridge, New York, 994p
Sauli P, Abry P, Boska J (2002) Wavelet-based analysis of wave-like structures in the ionospheric F-region electron concentration. American Geophysical Union, Fall Meeting
Sauli P, Abry P, Boska J (2004) Fourier and wavelet based characterization of the ionospheric response to the solar eclipse of August, the 11th, 1999, measured through 1-minute Vertical Ionospheric sounding. American Geophysical Union, Spring meeting
Seeber G (2003) Satellite geodesy: foundations, methods and applications. Walter de Gruyter. p 586 Berlin New York
Soltanpour A, Nahavandchi H, Featherstone WE (2006) The use of second-generation wavelets to combine a gravimetric quasigeoid model with GPS-levelling data. J Geodesy 80(2):82–93. doi:10.1007/s00190-006-0033-0
Souza EM, Monico JFG (2004) Wavelet shrinkage: high frequency multipath reduction from GPS relative positioning. GPS Solutions, 8, 3:152–159. doi:10.1007/s10291-004-0100-z
Wang Y-J, Wilkinson P, Caruana J (2001) Using GPS to monitor ionospheric irregularities in the southern high latitude Region. Anare Reports 146: Australian solar terrestrial and space physics research. Australian National Antarctic. Australia: Australian Antarctic Division. Available in: http://www.its-db.aad.gov.au/proms/pubn/pubshow.asp?pub_id=10051
Teunissen PJG (1998) Quality control and GPS. In: Teunissen PJG, kleusberg A. (eds). GPS for Geodesy. Springer, Berlin, pp 271–318
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Souza, E.M.d., Monico, J.F.G. The wavelet method as an alternative for reducing ionospheric effects from single-frequency GPS receivers. J Geod 81, 799–804 (2007). https://doi.org/10.1007/s00190-007-0150-4
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DOI: https://doi.org/10.1007/s00190-007-0150-4