Abstract
We present fast algorithms for estimating common parameters in geodetic time series based on statistical approaches to assess the impact of temporal correlations. One such assessment is based on the characteristics of the time series residuals averaged over different durations and with the statistical characteristics extrapolated with a first-order Gauss–Markov process to infinite averaging time. This approach circumvents a limitation of spectral methods, which cannot reliably account for the impact of temporal correlations over periods longer than the length of a given time series. The subsequent fast approach is the use of a Kalman filter with process noise values determined from the first-order Gauss–Markov characteristics to estimate all parameters. These methods are particularly useful for assessing long and numerous geodetic time series, which are nowadays ubiquitous, because they are much less computationally intensive than comprehensive methods, such as maximum likelihood estimators. Our approaches are compared to other commonly used programs, such as Hector, to understand the speed and impact of outliers on the algorithms, and to provide advice and suggestions on the uses of such algorithms in operational geodetic processing.
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References
Bartlett M S (1935) Some aspects of the time-correlation problem in regard to tests of significance. J. R. Stat. Soc. 98 (3). Wiley, Royal Statistical Society: 536. https://doi.org/10.2307/2342284.
Bos M S, Fernandes R M S, Williams S D P et al (2013) Fast error analysis of continuous GNSS observations with missing data. J. Geod. 87:351–360. https://doi.org/10.1007/s00190-012-0605-0.
Herring T (2003) MATLAB Tools for viewing GPS velocities and time series. GPS Solut. 7:194–199. https://doi.org/10.1007/s10291-003-0068-0.
Herring T A, King R W, Floyd M A et al (2018) GAMIT Reference Manual, Release 10.7, Massachusetts Institute of Technology, Cambridge, MA, http://geoweb.mit.edu/gg/GAMIT_Ref.pdf.
Herring T A, Floyd M A, King R W et al (2015) GLOBK Reference Manual, Release 10.6, Massachusetts Institute of Technology, Cambridge, MA, http://geoweb.mit.edu/gg/GLOBK_Ref.pdf.
Leith C E (1973) The standard error of time-average estimates of climatic means. J. Appl. Meteorol. 12 (6): 1066–69. https://doi.org/10.1175/1520-0450(1973)012%3c1066:tseota%3e2.0.co;2.
Reilinger R, McClusky S, Vernant P et al (2006) GPS constraints on continental deformation in the Africa-Arabia-Eurasia continental collision zone and implications for the dynamics of plate interactions. J. Geophys. Res.: Solid Earth 111:B05411. https://doi.org/10.1029/2005jb004051.
Wang L, Herring T (2019) Impact of data breaks on the uncertainties of GNSS site velocity estimates. Submitted J. Geophys. Res., March.
Zhang J, Bock Y, Johnson H et al (1997) Southern California permanent GPS geodetic array: Error analysis of daily position estimates and site velocities. J. Geophys. Res.: Solid Earth 102:18035–18055. https://doi.org/10.1029/97jb01380.
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Floyd, M.A., Herring, T.A. (2020). Fast Statistical Approaches to Geodetic Time Series Analysis. In: Montillet, JP., Bos, M. (eds) Geodetic Time Series Analysis in Earth Sciences. Springer Geophysics. Springer, Cham. https://doi.org/10.1007/978-3-030-21718-1_5
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DOI: https://doi.org/10.1007/978-3-030-21718-1_5
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