An advanced residual error model for tropospheric delay estimation
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ORIGINAL ARTICLE
An advanced residual error model for tropospheric delay estimation Szabolcs Rózsa1 · Bence Ambrus1 · Ildikó Juni1 · Pieter Bastiaan Ober2 · Máté Mile3,4 Received: 10 November 2019 / Accepted: 30 July 2020 © The Author(s) 2020
Abstract Global navigation satellite systems (GNSS) are widely used for safety-of-life positioning applications. Such applications require high integrity, availability, and continuity of the positioning service. Integrity is assessed by the definition of a protection level, which is an estimation of the maximum positioning error at extremely low probability levels. The emergence of multi-frequency civilian signals and the availability of satellite-based augmentation systems improve the modeling of ionospheric disturbances considerably. As a result, in many applications the tropospheric delay tends to become one of the limiting factors of positioning—especially at low elevation angles. The currently adopted integrity concepts employ a global constant to model the variance of the residual tropospheric delay error. We introduce a new approach to derive residual tropospheric delay error models using the extreme value analysis technique. Seventeen years of global numerical weather model fields are analyzed, and new residual error models are derived for some recently developed tropospheric delay models. Our approach provides models that consider both the geographical location and the seasonal variation of meteorological parameters. Our models are validated with a 17-year-long time series of zenith tropospheric delay estimates as provided by the International GNSS Service. The results show that the developed models are still conservative, while the maximal residual error of the tropospheric delay is still improved by 39–55%. This improvement yields higher service availability and continuity in safety-of-life applications of GNSS. Keywords Residual tropospheric delay error · Safety-of-life applications · Integrity · GPT2w · Aeronautics
Introduction In safety-of-life (SoL) navigation applications using Global Navigation Satellite Systems (GNSS), the main performance parameter of interest is integrity. A protection level * Szabolcs Rózsa [email protected] Bence Ambrus [email protected] Ildikó Juni [email protected] Máté Mile [email protected] 1
Department of Geodesy and Surveying, Budapest University of Technology and Economics, Budapest, Hungary
2
IntegriCom, Leiden, The Netherlands
3
Unit of Methodology Development, Hungarian Meteorological Service, Budapest, Hungary
4
Development Centre of Weather Forecasting, Norwegian Meteorological Institute, Oslo, Norway
is calculated that bounds the positioning error even at very small probability levels to assess the integrity (Zhu et al. 2018). The user predicts the protection level on the basis of error models of each of the contributing ranging error sources. To ensure that the protection level is not underestimated, each of these separate error sources needs to be modeled conservatively (Ober
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