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Geodetic time series analysis in earth sciences

Author: Jean-Philippe Montillet; Machiel S Bos
Publisher: Cham : Springer, ©2020.
Series: Springer geophysics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:

This book provides an essential appraisal of the recent advances in technologies, mathematical models and computational software used by those working with geodetic data.

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Genre/Form: Electronic books
Additional Physical Format: Print version:
Montillet, Jean-Philippe
Geodetic Time Series Analysis in Earth Sciences
Cham : Springer,c2019
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jean-Philippe Montillet; Machiel S Bos
ISBN: 9783030217181 3030217183
OCLC Number: 1113902051
Notes: Description based upon print version of record.
6.4.1 Simulating Three Coordinate Components of a GPS Station
Description: 1 online resource (437 p.).
Contents: Intro; Foreword: Welcome to the Not-So-Spherical Cow; Preface; References; Contents; Editors and Contributors; Abbreviations; 1 The Art and Science of Trajectory Modelling; 1.1 Introduction; 1.2 Trajectory Models; 1.3 A Gallery of Geodetic Trajectories; 1.4 Automatic Signal Decomposition Using GrAtSiD; 1.5 Conclusions; References; 2 Introduction to Geodetic Time Series Analysis; 2.1 Gaussian Noise and the Likelihood Function; 2.2 Linear Models; 2.3 Models for the Covariance Matrix; 2.4 Power Spectral Density; 2.5 Numerical Examples; 2.6 Discussion; References 3 Markov Chain Monte Carlo and the Application to Geodetic Time Series Analysis3.1 Introduction; 3.2 Markov Chain Monte Carlo as a Parameter Estimation Method; 3.2.1 Fundamentals; 3.2.2 The Random-Walk Metropolis-Hasting Algorithm; 3.2.3 The Markov Chain Monte Carlo Algorithm; 3.3 General Considerations for Markov Chain Monte Carlo; 3.3.1 The Equilibrium State; 3.3.2 The Acceptance Rate; 3.3.3 The Spectrum of the Markov Chain; 3.4 Applications; 3.4.1 Position Time Series; 3.4.2 Plate Motion Models; 3.4.3 Gravity Time Series; 3.4.4 Mean Sea Level Time Series; 3.5 Summary; References 4 Introduction to Dynamic Linear Models for Time Series Analysis4.1 Introduction to Dynamic Linear Models; 4.2 State Space Description; 4.2.1 Example: Spline Smoothing; 4.3 DLM as Hierarchical Statistical Model; 4.4 State and Parameter Estimation; 4.5 Recursive Kalman Formulas; 4.6 Simulation Smoother; 4.7 Estimating the Static Structural Parameters; 4.8 Analysing Trends; 4.9 Examples of Different DLM Models; 4.9.1 The Effect of Level and Trend Variance Parameters; 4.9.2 Seasonal Component; 4.9.3 Autoregressive Process; 4.9.4 Regression Covariates and Proxy Variables 4.10 Synthetic GNSS Example4.11 Computer Implementation; 4.12 Conclusions; References; 5 Fast Statistical Approaches to Geodetic Time Series Analysis; 5.1 Introduction; 5.2 Motivation and Statistical Impact of Temporal Correlations; 5.3 The First-Order Gauss-Markov Extrapolation (FOGMEX) Algorithm; 5.3.1 Weighted Least-Squares Algorithm; 5.3.2 Kalman Filter Extension; 5.3.3 Impact of Flicker Noise; 5.3.4 Dependence of Results on Data Duration and Noise Ratios; 5.3.5 Time Series Data Weighting; 5.4 Comparisons to Hector Results; 5.4.1 Comparison for Time Series with no Breaks 5.4.2 Comparison for Time Series with Breaks5.5 Performance Using Real Data; 5.5.1 Comparison of Least-Squares and Kalman Filter Estimates; 5.5.2 Comparison of FOGMEX and Hector; 5.5.3 Comparison of Run Times; 5.6 Conclusions; References; 6 Least Squares Contribution to Geodetic Time Series Analysis; 6.1 Introduction and Background; 6.2 Univariate Geodetic Time Series Analysis; 6.2.1 Functional Model; 6.2.2 Stochastic Model; 6.3 Multivariate Geodetic Time Series Analysis; 6.3.1 Functional Model; 6.3.2 Stochastic Model; 6.4 Simulated Results on GPS Time Series
Series Title: Springer geophysics.
Responsibility: Jean-Philippe Montillet, Machiel S. Bos, editors.

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