Details
| Original language | English |
|---|---|
| Title of host publication | 2018 IEEE/ION Position, Location and Navigation Symposium (PLANS) |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 355-366 |
| Number of pages | 12 |
| ISBN (electronic) | 9781538616475 |
| Publication status | Published - 7 Jun 2018 |
| Event | 2018 IEEE/ION Position, Location and Navigation Symposium, PLANS 2018 - Monterey, United States Duration: 23 Apr 2018 → 26 Apr 2018 |
Publication series
| Name | 2018 IEEE/ION Position, Location and Navigation Symposium, PLANS 2018 - Proceedings |
|---|
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
ASJC Scopus subject areas
- Engineering(all)
- Automotive Engineering
- Engineering(all)
- Aerospace Engineering
- Mathematics(all)
- Control and Optimization
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2018 IEEE/ION Position, Location and Navigation Symposium (PLANS). Institute of Electrical and Electronics Engineers Inc., 2018. p. 355-366 (2018 IEEE/ION Position, Location and Navigation Symposium, PLANS 2018 - Proceedings).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Comparison of Different Bounding Methods for Providing GPS Integrity Information
AU - Dbouk, Hani
AU - Schön, Steffen
N1 - 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.
PY - 2018/6/7
Y1 - 2018/6/7
N2 - 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.
AB - 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.
KW - GNSS
KW - Integrity
KW - Interval Analysis
KW - Linear Programming
KW - SIVIA
KW - Zonotopes
UR - http://www.scopus.com/inward/record.url?scp=85048862475&partnerID=8YFLogxK
U2 - 10.1109/plans.2018.8373401
DO - 10.1109/plans.2018.8373401
M3 - Conference contribution
AN - SCOPUS:85048862475
T3 - 2018 IEEE/ION Position, Location and Navigation Symposium, PLANS 2018 - Proceedings
SP - 355
EP - 366
BT - 2018 IEEE/ION Position, Location and Navigation Symposium (PLANS)
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 IEEE/ION Position, Location and Navigation Symposium, PLANS 2018
Y2 - 23 April 2018 through 26 April 2018
ER -