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 -