Comparison of Different Bounding Methods for Providing GPS Integrity Information

authored by: Hani Dbouk, Steffen Schön
Abstract: Reliable computation of confidence domains for point position, and inconsistency check of the observations is of great importance for any navigation system, especially for safety critical applications. In this work, non-stochastic error bound for reaming observation errors are introduced as intervals. Using concepts from interval mathematics four different deterministic bounding methods will be applied on GPS positioning, namely: Least Squares Adjustments based on Interval Analysis (LSA-IA), extension of LSA-IA by means of Zonotopes, Linear Programing (LP) applied to the navigation equation linearized by Taylor expansion, and finally solving the non-linear navigation equation by Set Inversion Via Interval Analysis (SIVIA). These methods provide different type of confidence regions and inconsistency measures. Each method will be investigated alone, then conducting a comparison study of the mathematical properties of these methods, and providing geometrical interpretation with respect to the navigation problem (e.g. form and orientation of the bounding area w.r.t. line-of-sight and number of satellites in view). Thanks to a reduced position scatter and the implicit inconsistence measure, the LP approach seems especially promising for further investigation towards an alternative integrity concept.
Organisation(s): Institute of Geodesy
Type: Conference contribution
Pages: 355-366
No. of pages: 12
Publication date: 07.06.2018
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Automotive Engineering, Aerospace Engineering, Control and Optimization
Electronic version(s): https://doi.org/10.1109/plans.2018.8373401 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@inproceedings{398bce33e2e64ca99b82cf17565e6c83,
title = "Comparison of Different Bounding Methods for Providing GPS Integrity Information",
abstract = "Reliable computation of confidence domains for point position, and inconsistency check of the observations is of great importance for any navigation system, especially for safety critical applications. In this work, non-stochastic error bound for reaming observation errors are introduced as intervals. Using concepts from interval mathematics four different deterministic bounding methods will be applied on GPS positioning, namely: Least Squares Adjustments based on Interval Analysis (LSA-IA), extension of LSA-IA by means of Zonotopes, Linear Programing (LP) applied to the navigation equation linearized by Taylor expansion, and finally solving the non-linear navigation equation by Set Inversion Via Interval Analysis (SIVIA). These methods provide different type of confidence regions and inconsistency measures. Each method will be investigated alone, then conducting a comparison study of the mathematical properties of these methods, and providing geometrical interpretation with respect to the navigation problem (e.g. form and orientation of the bounding area w.r.t. line-of-sight and number of satellites in view). Thanks to a reduced position scatter and the implicit inconsistence measure, the LP approach seems especially promising for further investigation towards an alternative integrity concept.",
keywords = "GNSS, Integrity, Interval Analysis, Linear Programming, SIVIA, Zonotopes",
author = "Hani Dbouk and Steffen Sch{\"o}n",
note = "Funding information: VII. ACKNOWLEDGMENT This work was supported by the German Research Foundation (DFG) as a part of the Research Training Group i.c.sens [GRK2159]. Thomas Krawinkel is thanked for supporting the measurements and the computation of the reference trajectory.; 2018 IEEE/ION Position, Location and Navigation Symposium, PLANS 2018 ; Conference date: 23-04-2018 Through 26-04-2018",
year = "2018",
month = jun,
day = "7",
doi = "10.1109/plans.2018.8373401",
language = "English",
series = "2018 IEEE/ION Position, Location and Navigation Symposium, PLANS 2018 - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "355--366",
booktitle = "2018 IEEE/ION Position, Location and Navigation Symposium (PLANS)",
address = "United States",
}