Comparison of Different Bounding Methods for Providing GPS Integrity Information

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.
Published in: 2018 IEEE/ION Position, Location and Navigation Symposium (PLANS)
April 23 - 26, 2018
Hyatt Regency Hotel
Monterey, CA
Pages: 355 - 366
Cite this article: Dbouk, Hani, Schön, Steffen, "Comparison of Different Bounding Methods for Providing GPS Integrity Information," 2018 IEEE/ION Position, Location and Navigation Symposium (PLANS), Monterey, CA, April 2018, pp. 355-366.
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