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On the probability distribution of GNSS carrier phase observations

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Abstract

When processing observational data from global navigation satellite systems (GNSS), the carrier phase measurements are generally assumed to follow a normal distribution. Although full knowledge of the probability distribution of the observables is not required for parameter estimation, for example when using the least-squares method, the distributional properties of GNSS observations play a key role in quality control procedures, such as outlier and cycle-slip detection, in ambiguity resolution, as well as in the reliability assessment of estimation results. In addition, when applying GNSS positioning under critical observation conditions with respect to multipath and atmospheric effects, the validity of the normal distribution assumption of GNSS observables certainly comes into doubt. This paper illustrates the discrepancies between the normal distribution assumption and reality, based on a large and representative data set of GPS phase measurements covering a range of factors, including multipath impact, baseline length, and atmospheric conditions. The statistical inferences are made using the first through fourth sample moments, hypothesis tests, and graphical tools such as histograms and quantile–quantile plots. The results show clearly that multipath effects, in particular the near-field component, produce the dominant influence on the distributional characteristics of GNSS observables. Additionally, using surface meteorological data, considerable correlations between distributional deviations from normality on the one hand and atmospheric relative humidity on the other are detected.

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Acknowledgments

We would like to thank the state survey office of Baden-Württemberg for providing the GNSS data and absolute antenna calibration values. The German Research Foundation (DFG) is gratefully acknowledged for supporting the research project “Improving the stochastic model of GPS observations by modeling physical correlations”. We also appreciate very much the professional comments from two anonymous reviewers as well as the valuable suggestions from the editorial office.

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  1. Geodetic Institute, Karlsruhe Institute of Technology (KIT), Englerstr. 7, 76131, Karlsruhe, Germany

    Xiaoguang Luo, Michael Mayer & Bernhard Heck

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  1. Xiaoguang Luo
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  2. Michael Mayer
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  3. Bernhard Heck
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Correspondence to Xiaoguang Luo.

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Luo, X., Mayer, M. & Heck, B. On the probability distribution of GNSS carrier phase observations. GPS Solut 15, 369–379 (2011). https://doi.org/10.1007/s10291-010-0196-2

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