On Time-Variable Seasonal Signals: Comparison of SSA and Kalman Filtering Based Approach

Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 142)

Abstract

Seasonal signals (annual and semi-annual) in GPS time series are of great importance for understanding the evolution of regional mass, e.g. ice and hydrology. Conventionally, these signals are derived by least-squares fitting of harmonic terms with a constant amplitude and phase. In reality, however, such seasonal signals are modulated, i.e., they have time-variable amplitudes and phases. Davis et al. (J Geophys Res 117(B1):B01,403, 2012) used a Kalman filtering (KF) based approach to investigate seasonal behavior of geodetic time series. Singular spectrum analysis (SSA) is a data-driven method that also allows to derive time-variable periodic signals from the GPS time series. In Chen et al. (J Geodyn 72:25–35, 2013), we compared time-varying seasonal signals obtained from SSA and KF for two GPS stations and received comparable results. In this paper, we apply SSA to a global set of 79 GPS stations and further confirm that SSA is a viable tool for deriving time variable periodic signals from the GPS time series. Moreover, we compare the SSA-derived periodic signals with the seasonal signals from KF with two different input process noise variances. Through the comparison, we find both SSA and KF obtain promising results from the stations with strong seasonal signals. While for the stations dominated by the long-term variations, SSA seems to be superior. We also find that KF with input process noise variance based on variance rates performs better than KF with the input process noise variance based on simulations.

Keywords

Kalman filtering Singular spectrum analysis Time variable seasonal signals 

References

  1. Bennett RA (2008) Instantaneous deformation from continuous GPS: contributions from quasi-periodic loads. Geophys J Int 174(3):1052–1064. doi:10.1111/j.1365-246X.2008.03846.xCrossRefGoogle Scholar
  2. Broomhead D, King GP (1986) Extracting qualitative dynamics from experimental data. Physica D 20:217–236. doi:10.1016/0167-2789(86)90031-XCrossRefGoogle Scholar
  3. Chen Q, van Dam T, Sneeuw N, Collilieux X, Weigelt M, Rebischung P (2013) Singular spectrum analysis for modeling seasonal signals from GPS time series. J Geodyn 72:25–35. doi:10.1016/j.jog.2013.05.005CrossRefGoogle Scholar
  4. Collilieux X, van Dam T, Ray J, Coulot D, Métivier L, Altamimi Z (2012) Strategies to mitigate aliasing of loading signals while estimating gps frame parameters. J Geod 86:1–14. 10.1007/s00190-011-0487-6CrossRefGoogle Scholar
  5. Davis JL, Wernicke BP, Bisnath S, Niemi NA, Elosegui P (2006) Subcontinental-scale crustal velocity changes along the Pacific-North America plate boundary. Nature 441(7097):1131–1134. doi:10.1038/nature04781CrossRefGoogle Scholar
  6. Davis JL, Wernicke BP, Tamisiea ME (2012) On seasonal signals in geodetic time series. J Geophys Res 117(B1):B01,403. doi:10.1029/2011JB008690Google Scholar
  7. Dong D, Fang P, Bock Y, Cheng MK, Miyazaki S (2002) Anatomy of apparent seasonal variations from GPS-derived site position time series. J Geophys Res 107(B4):2075. doi:10.1029/2001JB000573CrossRefGoogle Scholar
  8. Freymueller J (2009) Seasonal position variations and regional reference frame realization. In: Drewes H (ed) Geodetic reference frames, IAG symp, vol 134, pp 191–196. doi:10.1007/978-3-642-00860-3_30CrossRefGoogle Scholar
  9. Murray JR, Segall P (2005) Spatiotemporal evolution of a transient slip event on the San Andreas fault near Parkfield, California. J Geophys Res 110(B9):B09,407. doi:10.1029/2005JB003651Google Scholar
  10. Plaut G, Vautard R (1994) Spells of low-frequency oscillations and weather regimes in the northern hemisphere. J Atmos Sci 51(2):210–236. doi:10.1175/1520-0469(1994)051¡0210:SOLFOA¿2.0.CO;2CrossRefGoogle Scholar
  11. Rauch HE, Striebel C, Tung F (1965) Maximum likelihood estimates of linear dynamic systems. AIAA J 3(8):1445–1450. doi:10.2514/3.3166CrossRefGoogle Scholar
  12. Schoellhamer DH (2001) Singular spectrum analysis for time series with missing data. Geophys Res Lett 28(16):3187–3190. doi:10.1029/2000GL012698CrossRefGoogle Scholar
  13. Tesmer V, Steigenberger P, Rothacher M, Boehm J, Meisel B (2009) Annual deformation signals from homogeneously reprocessed VLBI and GPS height time series. J Geod 83:973–988. doi:10.1007/s00190-009-0316-3CrossRefGoogle Scholar
  14. Vautard R, Ghil M (1989) Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Physica D 35(3):395–424. doi:10.1016/0167-2789(89)90077-8CrossRefGoogle Scholar
  15. Vautard R, Yiou P, Ghil M (1992) Singular-spectrum analysis: a toolkit for short, noisy chaotic signals. Physica D 58(1-4):95–126. doi:10.1016/0167-2789(92)90103-TGoogle Scholar
  16. Weigelt M, van Dam T, Jäggi A, Prange L, Tourian MJ, Keller W, Sneeuw N (2013) Time-variable gravity signal in Greenland revealed by high-low satellite-to-satellite tracking. J Geophys Res 118:3848–3549. doi:10.1002/jgrb.50283CrossRefGoogle Scholar
  17. Williams SDP, Bock Y, Fang P, Jamason P, Nikolaidis RM, Prawirodirdjo L, Miller M, Johnson DJ (2004) Error analysis of continuous GPS position time series. J Geophys Res 109(B3):B03,412. doi:10.1029/2003JB002741Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of GeodesyUniversity of StuttgartStuttgartGermany
  2. 2.Faculté des Science, de la Technologie et de la CommunicationUniversity of LuxembourgEsch-sur-AlzetteLuxembourg

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