Bounding the Residual Tropospheric Error by Interval Analysis

authored by: Jingyao Su, Steffen Schön
Abstract: GNSS integrity monitoring requires proper bounding to characterize all ranging error sources. Unlike classical approaches based on probabilistic assumptions, our alternative integrity approach depends on deterministic interval bounds as inputs. The intrinsically linear uncertainty propagation with intervals is adequate to describe remaining systematic uncertainty, the so-called imprecision. In this contribution, we make a proposal on how to derive the required intervals in order to quantify and bound the residual error for empirical troposphere models, based on the refined sensitivity analysis via interval arithmetic. We evaluated experimentally the Saastamoinen model with (i) a priori ISO standard atmosphere, and (ii) on-site meteorological measurements from IGS and Deutscher Wetterdienst (DWD) stations as inputs. We obtain consistent and complete enclosure of residual ZPD errors w.r.t IGS ZPD products. Thanks to the DWD dense network, interval maps for meteorological parameters and residual ZPD errors are generated for Germany as by-products. These experimental results and products are finally validated, taking advantage of the high-quality tropospheric delays estimated by the Vienna Ray Tracer. Overall, the results indicate that our strategy based on interval analysis successfully bounds tropospheric model uncertainty. This will contribute to a realistic uncertainty assessment of GNSS-based single point positioning.
Organisation(s): Institute of Geodesy
Type: Contribution to book/anthology
Pages: 367-376
No. of pages: 10
Publication date: 25.12.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computers in Earth Sciences, Geophysics
Electronic version(s): https://doi.org/10.1007/1345_2022_184 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@inbook{a173004b248647c391eb669b2b885aa3,
title = "Bounding the Residual Tropospheric Error by Interval Analysis",
abstract = "GNSS integrity monitoring requires proper bounding to characterize all ranging error sources. Unlike classical approaches based on probabilistic assumptions, our alternative integrity approach depends on deterministic interval bounds as inputs. The intrinsically linear uncertainty propagation with intervals is adequate to describe remaining systematic uncertainty, the so-called imprecision. In this contribution, we make a proposal on how to derive the required intervals in order to quantify and bound the residual error for empirical troposphere models, based on the refined sensitivity analysis via interval arithmetic. We evaluated experimentally the Saastamoinen model with (i) a priori ISO standard atmosphere, and (ii) on-site meteorological measurements from IGS and Deutscher Wetterdienst (DWD) stations as inputs. We obtain consistent and complete enclosure of residual ZPD errors w.r.t IGS ZPD products. Thanks to the DWD dense network, interval maps for meteorological parameters and residual ZPD errors are generated for Germany as by-products. These experimental results and products are finally validated, taking advantage of the high-quality tropospheric delays estimated by the Vienna Ray Tracer. Overall, the results indicate that our strategy based on interval analysis successfully bounds tropospheric model uncertainty. This will contribute to a realistic uncertainty assessment of GNSS-based single point positioning.",
keywords = "Error bounding, Global navigation satellite systems, Integrity, Interval analysis, Residual tropospheric error",
author = "Jingyao Su and Steffen Sch{\"o}n",
note = "This work was supported by the German Research Foundation (DFG) as part of the Research Training Group i.c.sens [RTG 2159]. The authors gratefully acknowledge Deutscher Wetterdienst (DWD) for providing climate data, Helmholtz-Centre Potsdam GFZ German Research Centre for Geosciences for providing measurement data at POTS and OBE4 stations, International GNSS Service (IGS) for providing GNSS data and products, TU Wien for providing access to the online Ray-Tracer.; IAG 2021 : Scientific Assembly of the International Association of Geodesy ; Conference date: 28-06-2021 Through 04-07-2021",
year = "2022",
month = dec,
day = "25",
doi = "10.1007/1345_2022_184",
language = "English",
isbn = "978-3-031-29506-5",
series = "International Association of Geodesy Symposia",
publisher = "Springer, Cham",
pages = "367--376",
editor = "Freymueller, {Jeffrey T.} and Laura S{\'a}nchez",
booktitle = "Geodesy for a Sustainable Earth",
url = "https://www.iag2021.com/en/web/index/",
}