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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access April 16, 2015

Spatio-temporal filtering for determination ofcommon mode error in regional GNSS networks

Janusz Bogusz, Maciej Gruszczynski, Mariusz Figurski and Anna Klos
From the journal Open Geosciences

Abstract

The spatial correlation between different stationsfor individual components in the regional GNSS networksseems to be significant. The mismodelling in satelliteorbits, the Earth orientation parameters (EOP), largescaleatmospheric effects or satellite antenna phase centrecorrections can all cause the regionally correlated errors.This kind of GPS time series errors are referred to ascommon mode errors (CMEs). They are usually estimatedwith the regional spatial filtering, such as the "stacking".In this paper, we show the stacking approach for the setof ASG-EUPOS permanent stations, assuming that spatialdistribution of the CME is uniform over the whole regionof Poland (more than 600 km extent). The ASG-EUPOSis a multifunctional precise positioning system based onthe reference network designed for Poland. We used a 5-year span time series (2008-2012) of daily solutions in theITRF2008 from Bernese 5.0 processed by the Military Universityof Technology EPN Local Analysis Centre (MUTLAC). At the beginning of our analyses concerning spatialdependencies, the correlation coefficients between eachpair of the stations in the GNSS network were calculated.This analysis shows that spatio-temporal behaviour of theGPS-derived time series is not purely random, but there isthe evident uniform spatial response. In order to quantifythe influence of filtering using CME, the norms L1 and L2were determined. The values of these norms were calculatedfor the North, East and Up components twice: beforeperforming the filtration and after stacking. The observedreduction of the L1 and L2 norms was up to 30% dependingon the dimension of the network. However, the questionhow to define an optimal size of CME-analysed subnetworkremains unanswered in this research, due to thefact that our network is not extended enough.

References

[1] Bosy J., Graszka W., Leończyk M. (2007): "ASG-EUPOS - A multifunctionalprecise satellite positioning system in Poland". EuropeanJournal of Navigation, vol. 5 (4) September 2007, pp. 2-6Search in Google Scholar

[2] Krypiak-Gregorczyk A., Wielgosz P., Gosciewski D., Paziewski J.(2013): "Validation of Approximation Techniques for Local TotalElectron Content Mapping". Acta Geodynamica et GeomaterialiaVol. 10, No. 3 (171), 275–283 (DOI: 10.13168/AGG.2013.0027)Search in Google Scholar

[3] Bosy J. (2014): "Global, Regional and National Geodetic ReferenceFrames for Geodesy and Geodynamics". Pure Appl. Geophys.171 (2014), 783–808, DOI 10.1007/s00024-013-0676-8.Search in Google Scholar

[4] Gross, R., Beutler, G., and Plag, H.-P. (2009): "Integrated scientificand societal user requirements and functional specificationsfor theGGOS". In: H.-G. Plag, M. Pearlman (eds.), Global GeodeticObserving System: Meeting the Requirements of a Global Societyon a Changing Planet in 2020, Springer, Berlin, 2009, 209-224.Search in Google Scholar

[5] Mao A., Harrision C., Dixon T. (1999): "Noise in GPS coordinatetime series." J Geophys Res 104(B2): 2797–2816.10.1029/1998JB900033Search in Google Scholar

[6] Williams S. D. P. (2003): "The effect of coloured noise on the uncertaintiesof rates estimated from geodetic time series." J Geod76:483–494, DOI 10.1007/s00190-002-0283-4.Search in Google Scholar

[7] Williams S. D. P., Y. Bock, P. Fang, P. Jamason, R. M. Nikolaidis, L.Prawirodirdjo, M. Miller, and D. J. Johnson (2004): "Error analysisof continuous GPS position time series", J. Geophys. Res., 109,B03412, doi:10.1029/2003JB002741.10.1029/2003JB002741Search in Google Scholar

[8] Kenyeres, A., Bruyninx, C.: (2009): "Noise and Periodic Terms inthe EPN Time Series. Geodetic Reference Frames", InternationalAssociation of Geodesy Symposia Volume 134, 2009, pp. 143-148.Search in Google Scholar

[9] Klos A., Bogusz J., Figurski M., Kosek W. (2014a): "Uncertaintiesof geodetic velocities from permanent GPS observations: Sudetencase study". Acta Geodynamica et Geomaterialia, vol. 11, no.3(175), pp. 201-209, 2014, DOI: 10.13168/AGG.2014.0005.10.13168/AGG.2014.0005Search in Google Scholar

[10] Teferle N. (2010): "Spatial filtering of coordinate time series: Abrief review". COST Action ES0701 WG3 Workshop, Nottingham,18-19 March 2010.Search in Google Scholar

[11] Dong, D., P. Fang, Y. Bock, F. Webb, L. Prawirodirdjo, S. Kedar,and P. Jamason (2006): "Spatiotemporal filtering using principalcomponent analysis and Karhunen-Loeve expansion approachesfor regional GPS network analysis". J. Geophys. Res.,111, B03405, DOI:10.1029/2005JB003806.10.1029/2005JB003806Search in Google Scholar

[12] Nikolaidis R. (2002): "Observation of geodetic and seismic deformationwith the Global Positioning System", Ph.D. thesis,Univ. of Calif., San Diego, 2002.Search in Google Scholar

[13] Wdowinski, S., Y. Bock, J. Zhang, P. Fang, and J. Genrich(1997): "Southern California permanent GPS geodetic array:Spatial filtering of daily positions for estimating coseismicand postseismic displacements induced by the 1992 Landersearthquake". J. Geophys. Res., 102(B8), pp. 18057-18070,DOI:10.1029/97JB01378.10.1029/97JB01378Search in Google Scholar

[14] Teferle, F. N., R. M. Bingley, A. H. Dodson, N. T. Penna, and T. F.Baker (2002): "Using GPS to separate crustal movements andsealevel changes at tide gauges in the UK", in Vertical Reference Systems,edited by H. Drewes, et al., pp. 264-269, Springer-Verlag,Heidelberg Berlin.10.1007/978-3-662-04683-8_50Search in Google Scholar

[15] Teferle, F. N., R. M. Bingley, S. D. P. Williams, T. F. Baker, and A.H. Dodson (2006): "Using continuous GPS and absolute gravityto separate vertical land movements and changes in sea level attide gauges in the UK", Philosophical Transactions of the RoyalSociety, Part A, 364, 917-930, 910.1098/rsta.2006.1746.Search in Google Scholar

[16] Prawirodirdjo, L., Y. Ben-Zion, and Y. Bock (2006): "Observationand modeling of thermoelasticstrain in Southern California IntegratedGPS Network daily position time series", Journal of GeophysicalResearch, 111, 10.1029/2005JB003716.Search in Google Scholar

[17] Menke, W. (1984): "Geophysical Data Analysis, Discrete InverseTheory". Elsevier, New York.10.1016/B978-0-12-490920-5.50014-4Search in Google Scholar

[18] Van Trees HL. (1968): "Detection; Estimation and ModulationTheory", Part 1. Wiley: New York, 1968.Search in Google Scholar

[19] Shen Y., Li W., Xu G., Li B.(2013): "Spatiotemporal filtering of regionalGNSS network’s position time serieswith missing data usingprinciple component analysis." Journal of Geodesy vol 88, pp.351–360, DOI 10.1007/s00190-013-0663-y, Springer-Verlag, HeidelbergBerlin.10.1007/s00190-013-0663-ySearch in Google Scholar

[20] Márquez-Azúa, B., and C. DeMets (2003): "Crustal velocity fieldof Mexico from continuous GPS measurements". 1993 to June2001: Implications for the neotectonics of Mexico, J. Geophys.Res., 108(B9), 2450, DOI:10.1029/2002JB002241.10.1029/2002JB002241Search in Google Scholar

[21] Altamimi Z., Collilieux X. and Metivier L. (2011): "ITRF2008:an improved solution of the International Terrestrial ReferenceFrame". Journal of Geodesy, vol. 85, issue 8, pp. 457-473, DOI: 10.1007/s00190-011-0444-4. Published: 2011.10.1007/s00190-011-0444-4Search in Google Scholar

[22] Dach, R., Hugentobler, U., Fridez, S. and Meindl, M. (eds.):(2007): "Bernese GPS software version 5.0". Astonomical Institute,the University of Bern.Search in Google Scholar

[23] Szafranek K., Bogusz J., Figurski M. (2013): "GNSS referencesolution for permanent station stability monitoring andgeodynamical investigations: the ASG-EUPOS case study".Acta Geodynamica et Geomaterialia v. 10, No. 1(169), DOI:10.13168/AGG.2013.0006, 2013 pp. 67-75.10.13168/AGG.2013.0006Search in Google Scholar

[24] Bogusz J., Figurski M. (2014): „Annual signals observed in regionalGPS networks". Acta Geodynamica et Geomaterialia vol.11 No. 2(174), 2014, pp. 1-7, DOI: 10.13168/AGG.2014.0003.10.13168/AGG.2014.0003Search in Google Scholar

[25] Mosteller F. and Tukey J. (1977): "Data Analysis and Regression".Upper Saddle River, NJ: Addison-Wesley.Search in Google Scholar

[26] Sachs L. (1984): "Applied Statistics: A Handbook of Techniques".New York: Springer-Verlag, pp. 253.Search in Google Scholar

[27] Klos A., Bogusz J., Figurski M., Kosek W. (2014b): „On the handlingof outliers in the GNSS time series by means of the noiseand probability analysis". Accepted for publication in the InternationalAssociation of Geodesy Symposia, proceedings of theIAG Scientific Assembly 2014.10.1007/1345_2015_78Search in Google Scholar

[28] Rodionov S. (2004): "A sequential algorithm for testing climateregime shifts". Geophysical Research Letters, vol. 31, L09204,DOI: 10.1029/2004GL019448, 2004.10.1029/2004GL019448Search in Google Scholar

[29] Rodionov S. and Overland J.E. (2005): "Application of a sequentialregime shift detection method to the Bering Sea ecosystem".ICES Journal of Marine Science, 62, pp. 328-332, DOI:10.1016/j.icesjms.2005.01.013.10.1016/j.icesjms.2005.01.013Search in Google Scholar

[30] Wessel P., SmithW. H. F., Scharroo R., Luis J. F., Wobbe F. (2013):"GenericMapping Tools: Improved version released", EOS Trans.AGU, 94, pp. 409-410, 2013.Search in Google Scholar

Received: 2014-04-17
Accepted: 2014-11-14
Published Online: 2015-04-16

©2015 J. Bogusz et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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