Abstract
Filtering and signal processing techniques have been widely used in the processing of satellite gravity observations to reduce measurement noise and correlation errors. The parameters and types of filters used depend on the statistical and spectral properties of the signal under investigation. Filtering is usually applied in a non-real-time environment. The present work focuses on the implementation of an adaptive filtering technique to process satellite gravity gradiometry data for gravity field modeling. Adaptive filtering algorithms are commonly used in communication systems, noise and echo cancellation, and biomedical applications. Two independent studies have been performed to introduce adaptive signal processing techniques and test the performance of the least mean-squared (LMS) adaptive algorithm for filtering satellite measurements obtained by the gravity field and steady-state ocean circulation explorer (GOCE) mission. In the first study, a Monte Carlo simulation is performed in order to gain insights about the implementation of the LMS algorithm on data with spectral behavior close to that of real GOCE data. In the second study, the LMS algorithm is implemented on real GOCE data. Experiments are also performed to determine suitable filtering parameters. Only the four accurate components of the full GOCE gravity gradient tensor of the disturbing potential are used. The characteristics of the filtered gravity gradients are examined in the time and spectral domain. The obtained filtered GOCE gravity gradients show an agreement of 63–84 mEötvös (depending on the gravity gradient component), in terms of RMS error, when compared to the gravity gradients derived from the EGM2008 geopotential model. Spectral-domain analysis of the filtered gradients shows that the adaptive filters slightly suppress frequencies in the bandwidth of approximately 10–30 mHz. The limitations of the adaptive LMS algorithm are also discussed. The tested filtering algorithm can be connected to and employed in the first computational steps of the space-wise approach, where a time-wise Wiener filter is applied at the first stage of GOCE gravity gradient filtering. The results of this work can be extended to using other adaptive filtering algorithms, such as the recursive least-squares and recursive least-squares lattice filters.
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References
Albertella A, Migliaccio F, Reguzzoni M, Sansò F (2004) Wiener filters and collocation in satellite gradiometry. In: Sansò PDF (ed) V Hotine-Marussi symposium on mathematical geodesy. Springer, Berlin, pp 32–38
Albertella A, Migliaccio F, Sansó F (2002) GOCE: the earth gravity field by space gradiometry. In: Celletti A, Ferraz-Mello S, Henrard J (eds) Modern celestial mechanics: from theory to applications. Springer, Dordrecht, pp 1–15
Alessio SM (2016) Digital signal processing and spectral analysis for scientists. Springer International Publishing, Cham
Amjadiparvar B, Rangelova E, Sideris MG (2015) The GBVP approach for vertical datum unification: recent results in North America. J Geod 90:45–63. doi:10.1007/s00190-015-0855-8
Bartlett MS (1948) Smoothing periodograms from time-series with continuous spectra. Nature 161:686–687. doi:10.1038/161686a0
Bartlett MS (1950) Periodogram analysis and continuous spectra. Biometrika 37:1–16. doi:10.1093/biomet/37.1-2.1
Bendat JS, Piersol AG (1993) Engineering applications of correlation and spectral analysis, 2nd edn. Wiley, New York
Cesare S (2008) Performance requirements and budgets for the gradiometric mission. Thales Alenia Space, Torino
Eshagh M (2009) On satellite gravity gradiometry. PhD Thesis, Royal Institute of Technology (KTH)
Eshagh M, Abdollahzadeh M (2010) Semi-vectorization: an efficient technique for synthesis and analysis of gravity gradiometry data. Earth Sci Inform 3:149–158. doi:10.1007/s12145-010-0062-3
Eshagh M, Abdollahzadeh M (2012) Software for generating gravity gradients using a geopotential model based on an irregular semivectorization algorithm. Comput Geosci 39:152–160. doi:10.1016/j.cageo.2011.06.003
Floberghagen R, Fehringer M, Lamarre D et al (2011) Mission design, operation and exploitation of the gravity field and steady-state ocean circulation explorer mission. J Geod 85:749–758. doi:10.1007/s00190-011-0498-3
Fuchs MJ, Bouman J (2011) Rotation of GOCE gravity gradients to local frames. Geophys J Int 187:743–753. doi:10.1111/j.1365-246X.2011.05162.x
Gatti A, Reguzzoni M, Venuti G (2012) The height datum problem and the role of satellite gravity models. J Geod 87:15–22. doi:10.1007/s00190-012-0574-3
Gatti A, Reguzzoni M, Migliaccio F, Sansò F (2014) Space-wise grids of gravity gradients from GOCE data at nominal satellite altitude. In: 5th international GOCE user workshop, Paris, 25–28 Nov 2014
Ghobadi-Far K, Sharifi MA, Sneeuw N (2015) GOCE gradiometry data processing using the Rosborough approach. J Geod 89:1245–1261. doi:10.1007/s00190-015-0849-6
Grebenitcharsky R, Moore P (2014) Application of wavelets for along-track multi-resolution analysis of GOCE SGG data. In: Marti U (ed) Gravity, geoid and height systems. Springer International Publishing, Cham, pp 41–50
Gruber T, Abrikosov O, Hugentobler U (2010a) GOCE High Level Processing Facility. GOCE Standards. Technical Report GO-TN-HPFGS-0111, Issue 3.2
Gruber T, Rummel R, Abrikosov O, van Hees R (2010b) GOCE High Level Processing Facility. GOCELevel 2 Product Data Handbook. Technical Report GO-MA-HPF-GS-0110, Issue 4.3
Haykin SS (2014) Adaptive filter theory, 5th edn. Pearson, Upper Saddle River
Hofmann-Wellenhof B, Moritz H (2005) Physical geodesy. Wien, New York
Ince ES, Pagiatakis SD (2016) Effects of space weather on GOCE electrostatic gravity gradiometer measurements. J Geod 90:1–15. doi:10.1007/s00190-016-0931-8
Ince S, Pagiatakis S (2014) Improvement of GOCE level 1b gradiometer data processing over magnetic poles. CGUs Newsl Elem 32:39
Jekeli C (1999) The determination of gravitational potential differences from satellite-to-satellite tracking. Celest Mech Dyn Astron 75:85–101. doi:10.1023/A:1008313405488
Kern M, Preimesberger T, Allesch M et al (2005) Outlier detection algorithms and their performance in GOCE gravity field processing. J Geod 78:509–519. doi:10.1007/s00190-004-0419-9
Klees R, Ditmar P (2004) How to handle colored noise in large least-squares problems in the presence of data gaps? In: Sansò PDF (ed) V Hotine-Marussi symposium on mathematical geodesy. Springer, Berlin, pp 39–48
Lemoine FG, Smith DE, Kunz L et al (1997) The development of the NASA GSFC and NIMA joint geopotential model. In: Segawa PDJ, Fujimoto PDH, Okubo PDS (eds) Gravity, geoid and marine geodesy. Springer, Berlin, pp 461–469
Migliaccio F, Reguzzoni M, Sansò F (2004) Space-wise approach to satellite gravity field determination in the presence of coloured noise. J Geod 78:304–313. doi:10.1007/s00190-004-0396-z
Moritz H (1980) Advanced physical geodesy. Wichmann [u.a.], Karlsruhe
Pail R, Bruinsma S, Migliaccio F et al (2011) First GOCE gravity field models derived by three different approaches. J Geod 85:819–843. doi:10.1007/s00190-011-0467-x
Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the earth gravitational model 2008 (EGM2008). J Geophys Res Solid Earth 117:B04406. doi:10.1029/2011JB008916
Polgár Z, Sujbert L, Földváry L et al (2013) Filter design for GOCE gravity gradients. Geocarto Int 28:28–36. doi:10.1080/10106049.2012.687401
Reguzzoni M (2003) From the time-wise to space-wise GOCE observables. Adv Geosci 1:137–142. doi:10.5194/adgeo-1-137-2003
Reguzzoni M, Tselfes N (2008) Optimal multi-step collocation: application to the space-wise approach for GOCE data analysis. J Geod 83:13–29. doi:10.1007/s00190-008-0225-x
Rummel R, Yi W, Stummer C (2011) GOCE gravitational gradiometry. J Geod 85:777–790. doi:10.1007/s00190-011-0500-0
Sansò F, Tscherning CC (2003) Fast spherical collocation: theory and examples. J Geod 77:101–112. doi:10.1007/s00190-002-0310-5
Sideris MG, Rangelova E, Amjadiparvar B (2014) First results on height system unification in North America using GOCE. In: Marti U (ed) Gravity, geoid and height systems. Springer International Publishing, Cham, pp 221–227
Tziavos IN, Vergos GS, Grigoriadis VN et al (2015) Validation of GOCE/GRACE satellite only and combined global geopotential models over greece in the frame of the GOCESeaComb project. Springer, Berlin
Visser PNAM, van den IJssel JAA (2015) Calibration and validation of individual GOCE accelerometers by precise orbit determination. J Geod 90:1–13. doi:10.1007/s00190-015-0850-0
Wan X-Y, Yu J-H, Zeng Y-Y (2012) Frequency analysis and filtering processing of gravity gradient data from GOCE. Chin J Geophys 55:530–538. doi:10.1002/cjg2.1747
Yu J, Zhao D (2010) The gravitational gradient tensor’s invariants and the related boundary conditions. Sci China Earth Sci 53:781–790. doi:10.1007/s11430-010-0014-2
Zhou R, Wu X (2015) An iterative Wiener filtering method based on the gravity gradient invariants. Geod Geodyn 6:286–291. doi:10.1016/j.geog.2015.06.002
Acknowledgements
Financial support for this work has been provided by a grant from Canada’s Natural Sciences and Engineering Research Council (NSERC) to the second author. The GOCE data used in this study were provided by Prof. I. N. Tziavos within the GOCESeaComb project. Dr. Andrea Gatti, Researcher at Politecnico di Milano, is thanked for his useful insights and comments concerning the space-wise approach.
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Piretzidis, D., Sideris, M.G. Adaptive filtering of GOCE-derived gravity gradients of the disturbing potential in the context of the space-wise approach. J Geod 91, 1069–1086 (2017). https://doi.org/10.1007/s00190-017-1010-5
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DOI: https://doi.org/10.1007/s00190-017-1010-5