GPS Stochastic Modelling : Signal Quality Measures and ARMA Processes.
Global Navigation Satellite Systems (GNSS), such as GPS, have become an efficient, reliable and standard tool for a wide range of applications. However, when processing GNSS data, the stochastic model characterising the precision of observations and the correlations between them is usually simplifie...
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| Format: | eBook |
| Language: | English |
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Dordrecht :
Springer,
2013.
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| Series: | Springer theses.
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Table of Contents:
- Supervisor's Foreword; Acknowledgments; Contents; Acronyms; 1 Introduction; 1.1 Problem Statement; 1.2 State of the Art; 1.3 Objectives of this Thesis; 1.4 Outline of the Thesis; References; 2 Mathematical Background; 2.1 Parameter Estimation in Linear Models; 2.1.1 Estimators and Optimisation Criteria; 2.1.2 Weighted Least-Squares Estimation; 2.1.3 Best Linear Unbiased Estimation; 2.2 Time Series Analysis; 2.2.1 Classical Decomposition Model; 2.2.2 (Partial) Autocorrelation Function; 2.2.3 Autoregressive Moving Average Processes; 2.2.4 An Example of the Classical Decomposition Model.
- 2.3 Statistical Hypothesis Tests2.3.1 Hypothesis Testing; 2.3.2 Tests for Normality; 2.3.3 Tests for Trend; 2.3.4 Tests for Stationarity; 2.3.5 Tests for Uncorrelatedness; 2.4 Wavelet Transforms; 2.4.1 Wavelets and Morlet Wavelet; 2.4.2 Continuous Wavelet Transform; 2.4.3 Discrete Wavelet Transform; 2.4.4 An Example of Wavelet Transforms; References; 3 Mathematical Models for GPS Positioning; 3.1 Global Positioning System; 3.1.1 Reference and Time Systems; 3.1.2 GPS Segments; 3.1.3 GPS Signals; 3.1.4 GPS Observations; 3.1.5 Linear Combinations; 3.2 Precise Point Positioning.
- 3.2.1 Introduction3.2.2 Functional Model; 3.2.3 Error Sources and Effects; 3.2.4 Stochastic Model; 3.3 Relative Positioning; 3.3.1 Introduction; 3.3.2 Functional Model; 3.3.3 Error Sources and Effects; 3.3.4 Stochastic Model; References; 4 Data and GPS Processing Strategies; 4.1 Selecting Sites and Forming Baselines; 4.2 Relative Positioning Processing Strategies; 4.2.1 Processing Steps; 4.2.2 A Long-Term Case Study; 4.2.3 A Short-Term Case Study; 4.3 PPP Processing Strategies; 4.3.1 Processing Steps; 4.3.2 A Long-Term Case Study; References.
- 5 Observation Weighting Using Signal Quality Measures5.1 Signal-to-Noise Ratio; 5.2 Review of Previous Work; 5.3 SNR-Based Weighting Model; 5.3.1 Model Realisation; 5.3.2 Model Comparison; 5.3.3 Model Implementation; 5.4 Concluding Remarks; References; 6 Results of SNR-Based Observation Weighting; 6.1 Case Study 1: Long-Term Relative Positioning; 6.1.1 SNR Extremes and Observation Weights; 6.1.2 Effects on Ambiguity Resolution; 6.1.3 Effects on Troposphere Parameters; 6.1.4 Effects on Coordinate Estimates; 6.2 Case Study 2: Short-Term Relative Positioning.
- 6.2.1 SNR Extremes and Observation Weights6.2.2 Effects on Ambiguity Resolution; 6.2.3 Effects on Troposphere Parameters; 6.2.4 Effects on Coordinate Estimates; 6.3 Concluding Remarks; References; 7 Residual-Based Temporal Correlation Modelling; 7.1 Review of Previous Work; 7.2 Residual Decomposition; 7.2.1 Studentised Residuals; 7.2.2 Decomposition Model; 7.2.3 Vondrák Filtering; 7.2.4 Outlier Handling; 7.2.5 Sidereal Stacking; 7.3 ARMA Modelling; 7.3.1 AR Estimation; 7.3.2 MA Estimation; 7.3.3 ARMA Estimation; 7.3.4 AR-MA Identification; 7.4 Concluding Remarks; References.