Deterministic Approaches for Bounding GNSS Uncertainty

A Comparative Analysis

authored by: Jingyao Su, Steffen Schon
Abstract: Uncertainty modeling and bounding are of vital importance for high-integrity GNSS applications. Classical approaches are mostly developed in a stochastic manner with probabilistic assumptions. However, the exact error distribution is often unknown, and remaining systematics may persist, so that a purely stochastic modeling of all error sources will not be adequate, and alternative uncertainty bounding and propagation should be studied. This paper introduces two deterministic approaches for GNSS uncertainty bounding and compares them with the conventional least-squares method theoretically and experimentally with simulated and real measurements. Both methods use deterministic intervals to denote observation un-certainty, subsequently following a linear uncertainty propagation instead of quadratic one. The interval extension of least-squares transfers the uncertainty into the position domain in the form of zonotope and further bound the stochasticity by the extended point confidence domain. As a comparison, the other method takes advantage of geometrical constraints and convex optimization, leading to a poly topic solution set and zonotopic confidence region. We show their theoretical similarities and high-light different interpretations in practice. Nevertheless, both are sufficient to account for both random and systematic components of uncertainty.
Organisation(s): Institute of Geodesy
Graduiertenkolleg 2159: Integrität und Kollaboration in dynamischen Sensornetzen
Type: Conference contribution
Publication date: 2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Instrumentation, Control and Optimization, Computer Networks and Communications, Signal Processing, Aerospace Engineering
Electronic version(s): https://doi.org/10.1109/NAVITEC53682.2022.9847545 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@inproceedings{d20ec6b6a96740bbbee639d7a1150c38,
title = "Deterministic Approaches for Bounding GNSS Uncertainty: A Comparative Analysis",
abstract = "Uncertainty modeling and bounding are of vital importance for high-integrity GNSS applications. Classical approaches are mostly developed in a stochastic manner with probabilistic assumptions. However, the exact error distribution is often unknown, and remaining systematics may persist, so that a purely stochastic modeling of all error sources will not be adequate, and alternative uncertainty bounding and propagation should be studied. This paper introduces two deterministic approaches for GNSS uncertainty bounding and compares them with the conventional least-squares method theoretically and experimentally with simulated and real measurements. Both methods use deterministic intervals to denote observation un-certainty, subsequently following a linear uncertainty propagation instead of quadratic one. The interval extension of least-squares transfers the uncertainty into the position domain in the form of zonotope and further bound the stochasticity by the extended point confidence domain. As a comparison, the other method takes advantage of geometrical constraints and convex optimization, leading to a poly topic solution set and zonotopic confidence region. We show their theoretical similarities and high-light different interpretations in practice. Nevertheless, both are sufficient to account for both random and systematic components of uncertainty.",
keywords = "confidence region, Global Navigation Satellite System, interval mathematics, polytope, uncertainty bounding, zonotope",
author = "Jingyao Su and Steffen Schon",
note = "Funding Information: This work was supported by the German Research Foundation as part of the Research Training Group 2159: Integrity and Collaboration in Dynamic Sensor Networks (i.c.sens).; 10th Workshop on Satellite Navigation Technology, NAVITEC 2022 ; Conference date: 05-04-2022 Through 07-04-2022",
year = "2022",
doi = "10.1109/NAVITEC53682.2022.9847545",
language = "English",
isbn = "978-1-6654-1617-7",
series = "ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
booktitle = "2022 10th Workshop on Satellite Navigation Technology, NAVITEC 2022",
address = "United States",
}