Geodetic time series analysis in earth sciences [electronic resource] / Jean-Philippe Montillet, Machiel S. Bos, editors.
This book provides an essential appraisal of the recent advances in technologies, mathematical models and computational software used by those working with geodetic data. It explains the latest methods in processing and analyzing geodetic time series data from various space missions (i.e. GNSS, GRAC...
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| Format: | Electronic eBook |
| Language: | English |
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Springer,
©2020.
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| Series: | Springer geophysics.
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Table of 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.