© 2013

GPS Stochastic Modelling

Signal Quality Measures and ARMA Processes


Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Xiaoguang Luo
    Pages 1-6
  3. Xiaoguang Luo
    Pages 7-53
  4. Xiaoguang Luo
    Pages 55-116
  5. Xiaoguang Luo
    Pages 117-136
  6. Xiaoguang Luo
    Pages 163-191
  7. Xiaoguang Luo
    Pages 193-225
  8. Xiaoguang Luo
    Pages 289-293
  9. Back Matter
    Pages 295-331

About this book


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 simplified and incomplete, leading to overly optimistic accuracy estimates.

This work extends the stochastic model using signal-to-noise ratio (SNR) measurements and time series analysis of observation residuals. The proposed SNR-based observation weighting model significantly improves the results of GPS data analysis, while the temporal correlation of GPS observation noise can be efficiently described by means of autoregressive moving average (ARMA) processes. Furthermore, this work includes an up-to-date overview of the GNSS error effects and a comprehensive description of various mathematical methods.


ARMA Process AutoRegressive Moving Average Process Hypothesis Testing Signal-to-Noise Ratio (SNR) Stochastic Model of GNSS Observations Wavelet Analysis

Authors and affiliations

  1. 1., Geodetic InstituteKarlsruhe Institute of Technology (KIT)KarlsruheGermany

About the authors

Xiaoguang Luo is currently a research associate at the Geodetic Institute of Karlsruhe Institute of Technology (KIT), Germany. He received his Ph.D. in Geodesy and Geoinformatics from KIT in 2012. He is interested in analysing the stochastic model, atmospheric and site-specific effects of GNSS observations, with a special focus on statistical testing and time series modelling.

Bibliographic information

Industry Sectors
Oil, Gas & Geosciences


From the reviews:

“The book is mathematical in that it is intended for readers who have a working knowledge of mathematical tools for communications systems. While the book is reasonably self-contained in terms of reviewing mathematical prerequisites and giving a broad view of the physical elements affecting GPS performance, at a technical level it is really intended for readers interested in designing components of GPS systems, or in policies pertaining to GPS systems.” (Joseph D. Lakey, Mathematical Reviews, March, 2014)