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 -