Details
| Original language | English |
|---|---|
| Title of host publication | 2022 10th Workshop on Satellite Navigation Technology, NAVITEC 2022 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| ISBN (electronic) | 9781665416160 |
| ISBN (print) | 978-1-6654-1617-7 |
| Publication status | Published - 2022 |
| Event | 10th Workshop on Satellite Navigation Technology, NAVITEC 2022 - Noordwijk, Netherlands Duration: 5 Apr 2022 → 7 Apr 2022 |
Publication series
| Name | ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing |
|---|---|
| ISSN (Print) | 2325-5439 |
| ISSN (electronic) | 2325-5455 |
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
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Instrumentation
- Mathematics(all)
- Control and Optimization
- Computer Science(all)
- Computer Networks and Communications
- Computer Science(all)
- Signal Processing
- Engineering(all)
- Aerospace Engineering
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2022 10th Workshop on Satellite Navigation Technology, NAVITEC 2022. Institute of Electrical and Electronics Engineers Inc., 2022. (ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Deterministic Approaches for Bounding GNSS Uncertainty
T2 - 10th Workshop on Satellite Navigation Technology, NAVITEC 2022
AU - Su, Jingyao
AU - Schon, Steffen
N1 - 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).
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - confidence region
KW - Global Navigation Satellite System
KW - interval mathematics
KW - polytope
KW - uncertainty bounding
KW - zonotope
UR - http://www.scopus.com/inward/record.url?scp=85135374398&partnerID=8YFLogxK
U2 - 10.1109/NAVITEC53682.2022.9847545
DO - 10.1109/NAVITEC53682.2022.9847545
M3 - Conference contribution
AN - SCOPUS:85135374398
SN - 978-1-6654-1617-7
T3 - ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing
BT - 2022 10th Workshop on Satellite Navigation Technology, NAVITEC 2022
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 5 April 2022 through 7 April 2022
ER -