Reliable bounding zones and inconsistency measures for GPS positioning using geometrical constraints

authored by: Hani Dbouk, Steffen Schön
Abstract: Reliable confidence domains for positioning with Global Navigation Satellite System (GNSS) and inconsistency measures for the observations are of great importance for any navigation system, especially for safety critical applications. In this work, deterministic error bounds are introduced in form of intervals to assess remaining observation errors. The intervals can be determined based on expert knowledge or - as in our case - based on a sensitivity analysis of the measurement correction process. Using convex optimization, bounding zones are computed for GPS positioning, which satisfy the geometrical constraints imposed by the observation intervals. The bounding zone is a convex polytope. When exploiting only the navigation geometry, a confidence domain is computed in form of a zonotope. We show that the relative volume between the polytope and the zonotope can be considered as an inconsistency measure. A small polytope volume indicates bad consistency of the observations. In extreme cases, empty sets are obtained which indicates large outliers. We explain how shape and volume of the polytopes are related to the positioning geometry. Furthermore, we propose a new concept of Minimum Detectable Biases. Using the example of the Klobuchar ionospheric model and Saastamoinen tropospheric model, we show how observation intervals can be determined via sensitivity analysis of these correction models for a real measurement campaign. Taking GPS code data from simulations and real experiments, a comparison analysis between the proposed deterministic bounding method and the classical least-squares adjustment has been conducted in terms of accuracy and reliability. It shows that the computed polytopes always enclose the reference trajectory. In case of large outliers, large position deviations persist in the least-squares solution while the polytope algorithm yields empty sets and thus successfully detects the cases with outliers.
Organisation(s): Institute of Geodesy
Type: Article
Journal: Acta Cybernetica
Volume: 24
Pages: 573-591
No. of pages: 19
ISSN: 0324-721X
Publication date: 19.03.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Software, Computer Science (miscellaneous), Computer Vision and Pattern Recognition, Management Science and Operations Research, Information Systems and Management, Electrical and Electronic Engineering
Electronic version(s): https://doi.org/10.14232/actacyb.24.3.2020.16 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{70dd2b124df04d829cc0cb7435d1ffff,
title = "Reliable bounding zones and inconsistency measures for GPS positioning using geometrical constraints",
abstract = "Reliable confidence domains for positioning with Global Navigation Satellite System (GNSS) and inconsistency measures for the observations are of great importance for any navigation system, especially for safety critical applications. In this work, deterministic error bounds are introduced in form of intervals to assess remaining observation errors. The intervals can be determined based on expert knowledge or - as in our case - based on a sensitivity analysis of the measurement correction process. Using convex optimization, bounding zones are computed for GPS positioning, which satisfy the geometrical constraints imposed by the observation intervals. The bounding zone is a convex polytope. When exploiting only the navigation geometry, a confidence domain is computed in form of a zonotope. We show that the relative volume between the polytope and the zonotope can be considered as an inconsistency measure. A small polytope volume indicates bad consistency of the observations. In extreme cases, empty sets are obtained which indicates large outliers. We explain how shape and volume of the polytopes are related to the positioning geometry. Furthermore, we propose a new concept of Minimum Detectable Biases. Using the example of the Klobuchar ionospheric model and Saastamoinen tropospheric model, we show how observation intervals can be determined via sensitivity analysis of these correction models for a real measurement campaign. Taking GPS code data from simulations and real experiments, a comparison analysis between the proposed deterministic bounding method and the classical least-squares adjustment has been conducted in terms of accuracy and reliability. It shows that the computed polytopes always enclose the reference trajectory. In case of large outliers, large position deviations persist in the least-squares solution while the polytope algorithm yields empty sets and thus successfully detects the cases with outliers.",
keywords = "GPS, Integrity, Intervals, Polytope, Reliability, Zonotope",
author = "Hani Dbouk and Steffen Sch{\"o}n",
note = "Funding information: This work was supported by the German Research Foundation (DFG) as a part of the Research Training Group i.c.sens [GRK2159]. Leibniz Universit{\"a}t Hannover, Institut f{\"u}r Erdmessung, Schneiderberg 50, 30167 Hannover, Germany, E-mail: {dbouk,schoen}@ife.uni-hannover.de",
year = "2020",
month = mar,
day = "19",
doi = "10.14232/actacyb.24.3.2020.16",
language = "English",
volume = "24",
pages = "573--591",
journal = "Acta Cybernetica",
issn = "0324-721X",
publisher = "University of Szeged, Institute of Informatics",
number = "3",
}