Abstract
This study investigates the applicability of the recursive least-squares (RLS) adaptive filter for gravity field modelling applications. Simulated satellite gravity gradients are used to assess the performance of the algorithm. The synthetic data follow the behavior of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission observations. An analysis is carried out, where the convergence speed, computational efficiency and optimal impulse response of the adaptive filter are examined. The behavior of the filtered gravity gradients in the time and spectral domain is also studied. The algorithm is capable of converging to a mean-square error (MSE) of 0.013 Eötvös, which is very close to the level of Gaussian noise (0.011 Eötvös) added to the synthetic observations. Although the RLS algorithm shows a fast convergence speed, a strong disadvantage that should be considered before its implementation is its reduced time efficiency.
Similar content being viewed by others
References
Bendat JS, Piersol AG (1993) Engineering applications of correlation and spectral analysis, 2nd edn. Wiley, New York
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. https://doi.org/10.1007/s00190-011-0498-3
Förste C, Bruinsma SL, Abrikosov O et al (2014) EIGEN-6C4 The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. In: EGU General Assembly 2014, Vienna, 27 April--2 May 2014. https://doi.org/10.5880/icgem.2015.1
Gatti A, Reguzzoni M, Sansò F, Migliaccio F 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 November 2014
Ge L, Chen H-Y, Han S, Rizos C (2000) Adaptive filtering of continuous GPS results. J Geod 74:572–580. https://doi.org/10.1007/s001900000120
Haykin SS (2014) Adaptive filter theory, 5th edn. Pearson, Upper Saddle River
Ince ES, Pagiatakis SD (2016) Effects of space weather on GOCE electrostatic gravity gradiometer measurements. J Geod 90(12):1389–1403. https://doi.org/10.1007/s00190-016-0931-8
Krasbutter I, Brockmann JM, Kargoll B, Schuh W-D (2014) Adjustment of digital filters for decorrelation of GOCE SGG data. In: Flechtner F, Sneeuw N, Schuh W-D (eds) Observation of the system earth from space - CHAMP, GRACE, GOCE and future missions. Springer, Berlin, Heidelberg, pp 109–114
Liu H, Li X, Ge L et al (2009) Variable length LMS adaptive filter for pseudorange multipath mitigation based on SydNET stations. J Appl Geod 3:35–46. https://doi.org/10.1515/JAG.2009.004
Moustakides GV (1997) Study of the transient phase of the forgetting factor RLS. IEEE Trans Signal Process 45:2468–2476. https://doi.org/10.1109/78.640712
Pail R, Bruinsma S, Migliaccio F et al (2011) First GOCE gravity field models derived by three different approaches. J Geod 85:819–843. https://doi.org/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. https://doi.org/10.1029/2011JB008916
Piretzidis D, Sideris MG (2017) Adaptive filtering of GOCE-derived gravity gradients of the disturbing potential in the context of the space-wise approach. J Geod 91(9):1069–1086. https://doi.org/10.1007/s00190-017-1010-5
Reguzzoni M, Tselfes N (2008) Optimal multi-step collocation: application to the space-wise approach for GOCE data analysis. J Geod 83:13–29. https://doi.org/10.1007/s00190-008-0225-x
Sesay A (2014) Lecture notes on adaptive signal processing. The University of Calgary, Calgary
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, Heidelberg
Wang RJ (1977) Adaptive predictive deconvolution of seismic data. Geophys Prospect 25:342–381. https://doi.org/10.1111/j.1365-2478.1977.tb01174.x
Wolf K, Müller J (2008) Accuracy analysis of external reference data for GOCE evaluation in space and frequency domain. In: Sideris MG (ed) Observing our changing earth. Springer, Berlin, Heidelberg, pp 345–352
Yi W, Rummel R (2014) A comparison of GOCE gravitational models with EGM2008. J Geodyn 73:14–22. https://doi.org/10.1016/j.jog.2013.10.004
Young PPC (2011) Recursive least squares estimation. In: Recursive estimation and time-series analysis. Springer, Berlin, Heidelberg, pp 29–46
Acknowledgments
This work is financially aided by a grant from Canada’s Natural Sciences and Engineering Research Council (NSERC) to the second author. The GOCE Level 2b data were provided by Prof. I.N. Tziavos of the Aristotle University of Thessaloniki within the GOCESeaComb project. The two anonymous reviewers are thanked for their comments and suggestions for the improvement of this paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Piretzidis, D., Sideris, M.G. (2017). Application of the Recursive Least-Squares Adaptive Filter on Simulated Satellite Gravity Gradiometry Data. In: Vergos, G., Pail, R., Barzaghi, R. (eds) International Symposium on Gravity, Geoid and Height Systems 2016. International Association of Geodesy Symposia, vol 148. Springer, Cham. https://doi.org/10.1007/1345_2017_24
Download citation
DOI: https://doi.org/10.1007/1345_2017_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-95317-5
Online ISBN: 978-3-319-95318-2
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)