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Least Squares Contribution to Geodetic Time Series Analysis

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Geodetic Time Series Analysis in Earth Sciences

Part of the book series: Springer Geophysics ((SPRINGERGEOPHYS))

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Abstract

This chapter introduces the least squares framework to the analysis of geodetic time series. The geodetic time series analysis is based on the correct formulation of both functional and stochastic models. The ultimate goal of all geodetic time series studies is to discriminate between the functional and the stochastic effects in the series. Both effects are relevant in geodetic and geophysical phenomena and hence the subject of discussion in this contribution. Functional effects, such as a linear trend, offsets, and potential periodicities, can be well explained by a deterministic model, while the remaining unmodeled effects can be described by a proper stochastic model. Both models should optimally be selected and analyzed for proper analysis of the time series. This can be implemented both for a single and multiple time series, resulting in the univariate and multivariate time series analysis. The first part of the chapter is devoted to the functional model identification in which the presence and identification of outlying observations, offsets, and possible periodic signals in the series will be discussed. The second part deals with the parameter estimation in the stochastic model. Identification and estimation of different noise components in GNSS time series analysis will be discussed. A few simulated time series are used to illustrate the theory.

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Change history

  • 26 February 2020

    In the original version of the book, the following belated corrections have been incorporated: Electronic Supplementary Materials have been included in Chapters 2 and 6, ESM logo has been added to the cover, and ESM information has been added to the opening page of both the chapters. The erratum chapters and book have been updated with the changes.

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Acknowledgements

I would like to acknowledge Machiel S. Bos and Jean-Philippe Montillet, the editors, for providing me with the Python script of the LS-VCE. Their helpful remarks and corrections on earlier versions of this chapter is greatly acknowledged.

Author information

Authors and Affiliations

  1. Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, 81746-73441, Isfahan, Iran

    Alireza Amiri-Simkooei

  2. Acoustics Group, Faculty of Aerospace Engineering, Delft University of Technology, 2629 HS, Delft, The Netherlands

    Alireza Amiri-Simkooei

Authors
  1. Alireza Amiri-Simkooei
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Corresponding author

Correspondence to Alireza Amiri-Simkooei .

Editor information

Editors and Affiliations

  1. Space and Earth Geodetic Analysis Laboratory, Universidade da Beira Interior, Covilha, Portugal

    Jean-Philippe Montillet

  2. Instituto Dom Luiz, Universidade da Beira Interior, Covilha, Portugal

    Machiel S. Bos

6.1 Electronic Supplementary Material

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Supplementary material 1 (zip 144 KB)

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Amiri-Simkooei, A. (2020). Least Squares Contribution 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_6

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