Maximum non-bounded difference method for overbounding Global Navigation Satellite System errors
File(s)
Published version
Author(s)
Alghananim, Ma’mon Saeed
Ochieng, Washington Yotto
Type
Journal Article
Abstract
Global Navigation Satellite Systems (GNSS) support numerous applications, including mission-critical ones that require high integrity for safe operations such as air, maritime, and land-based navigation. These applications require ensuring the upper bound of the positioning computation, including overbounding any assumptions made in positioning algorithms. One of the main assumptions in the GNSS positioning algorithm is that the error follows a Probability Density Function (PDF), widely assumed to be Gaussian. This assumption should be overbounded to ensure safety. Two mathematical definitions of distribution overbounding have been proposed: Cumulative Distribution Function (CDF) overbounding and paired overbounding. Achieving these definitions has been an open problem for the past 20 years, and to date, no methods have effectively achieved either definition in multimode datasets. This paper proposes the first overbounding method, the Maximum non-Bounded Difference (MnBD) method, capable of achieving both definitions. Its effectiveness is assessed by comparison with the combined CDF bounding and paired overbounding approach. The results show that the MnBD method successfully achieves overbounding in both real datasets and 1000 simulated multimode data, tested on Gaussian and Generalized Extreme Value (GEV) distributions. The latter demonstrates MnBD’s ability to handle asymmetric distributions. The developed approach can be utilized in overbounding the GNSS error at the system level and user level to ensure the system integrity.
Date Issued
2024-11-16
Date Acceptance
2024-10-25
Citation
GPS Solutions, 2024, 29
ISSN
1080-5370
Publisher
Springer Science and Business Media LLC
Journal / Book Title
GPS Solutions
Volume
29
Copyright Statement
© The Author(s) 2024 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
10.1007/s10291-024-01772-x
Subjects
GNSS
Mission-critical applications
Error distribution overbounding
SBAS
Publication Status
Published
Article Number
22
Date Publish Online
2024-11-16