Reliability and integrity measures of GPS positioning via geometrical constraints

authored by: Hani Dbouk, Steffen Schön
Abstract: Confidence domains for Global Navigation Satellite System (GNSS) positioning and inconsistency measures of the observations are of great importance for any navigation system, especially for safety critical applications. In this work, deterministic error bounds are derived from a sensitivity analysis of the observation correction models and introduced in form of intervals to assess remaining observation errors. Using convex optimization, bounding zones are computed for GPS positioning using geometrical constraints imposed by the observation intervals. The bounding zone is a convex polytope. We show that the volume of the polytope is an inconsistency measures rather than confidence measures, since small polytopes indicates bad consistency of the observations. In extreme cases empty sets are obtained which indicates large outliers. We explain how the shape and the volume of the polytope are related to the positioning geometry and how observations of maximum impact can be revealed. In a first attempt, a point position can by associated to the solution set by its barycenter. However, we show that this assignment has based to be interpreted with care. Furthermore, we propose a new concept of Minimum Detectable Biases (MDB) on the geometric relations. Taking GPS data from simulations and real experiments, a comparison analysis between the proposed deterministic bounding method and the classical least-squares adjustment has been conduct in terms of accuracy and reliability. This helps validating that our proposed deterministic bound methods shows high internal and external reliability compared to the probabilistic approaches and that it provides rigorous inconsistency measures.
Organisation(s): Institute of Geodesy
Type: Conference contribution
Pages: 730-743
No. of pages: 14
Publication date: 2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computer Science Applications, Aerospace Engineering, Ocean Engineering, Transportation, Electrical and Electronic Engineering
Electronic version(s): https://doi.org/10.33012/2019.16722 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@inproceedings{e5e6b4b31b0f44d58bed12bdd12b116b,
title = "Reliability and integrity measures of GPS positioning via geometrical constraints",
abstract = "Confidence domains for Global Navigation Satellite System (GNSS) positioning and inconsistency measures of the observations are of great importance for any navigation system, especially for safety critical applications. In this work, deterministic error bounds are derived from a sensitivity analysis of the observation correction models and introduced in form of intervals to assess remaining observation errors. Using convex optimization, bounding zones are computed for GPS positioning using geometrical constraints imposed by the observation intervals. The bounding zone is a convex polytope. We show that the volume of the polytope is an inconsistency measures rather than confidence measures, since small polytopes indicates bad consistency of the observations. In extreme cases empty sets are obtained which indicates large outliers. We explain how the shape and the volume of the polytope are related to the positioning geometry and how observations of maximum impact can be revealed. In a first attempt, a point position can by associated to the solution set by its barycenter. However, we show that this assignment has based to be interpreted with care. Furthermore, we propose a new concept of Minimum Detectable Biases (MDB) on the geometric relations. Taking GPS data from simulations and real experiments, a comparison analysis between the proposed deterministic bounding method and the classical least-squares adjustment has been conduct in terms of accuracy and reliability. This helps validating that our proposed deterministic bound methods shows high internal and external reliability compared to the probabilistic approaches and that it provides rigorous inconsistency measures.",
author = "Hani Dbouk and Steffen Sch{\"o}n",
year = "2019",
doi = "10.33012/2019.16722",
language = "English",
series = "Proceedings of the Institute of Navigation",
publisher = "Institute of Navigation",
pages = "730--743",
booktitle = "Proceedings of the 2019 International Technical Meeting of The Institute of Navigation",
note = "Institute of Navigation International Technical Meeting 2019, ITM 2019 ; Conference date: 28-01-2019 Through 31-01-2019",
}