Garcia Crespillo, Omar and Langel, Steve and Joerger, Mathieu (2023) Tight Bounds for Uncertain Time-Correlated Errors with Gauss-Markov Structure in Kalman Filtering. IEEE Transactions on Aerospace and Electronic Systems. IEEE - Institute of Electrical and Electronics Engineers. doi: 10.1109/TAES.2023.3242943. ISSN 0018-9251. (In Press)
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Abstract
Safety-critical navigation applications require that estimation errors be reliably quantified and bounded. This can be challenging for linear dynamic systems if the process noise or measurement errors have uncertain time correlation. In many systems (e.g., in satellite-based or inertial navigation systems), there are sources of time-correlated sensor errors that can be well modeled using Gauss-Markov processes (GMP). However, uncertainty in the GMP parameters, particularly in the correlation time constant, can cause misleading error bounds. In this paper, we develop time-correlated models that ensure tight upper bounds on the estimation error variance, assuming that the actual error is a stationary first-order GMP with a variance and time constant that are only known to reside within an interval. We first use frequency-domain analysis to derive stationary GMP models in both the continuous and discrete time domains, which outperform models previously described in the literature. Then, we derive an even tighter estimation error bound using a non-stationary GMP model, for which we determine the minimum initial variance that guarantees bounding conditions. Both models can easily be implemented in a linear estimator like the Kalman filter.
Item URL in elib: | https://elib.dlr.de/193615/ | ||||||||||||||||
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Document Type: | Article | ||||||||||||||||
Title: | Tight Bounds for Uncertain Time-Correlated Errors with Gauss-Markov Structure in Kalman Filtering | ||||||||||||||||
Authors: |
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Date: | 7 February 2023 | ||||||||||||||||
Journal or Publication Title: | IEEE Transactions on Aerospace and Electronic Systems | ||||||||||||||||
Refereed publication: | Yes | ||||||||||||||||
Open Access: | No | ||||||||||||||||
Gold Open Access: | No | ||||||||||||||||
In SCOPUS: | Yes | ||||||||||||||||
In ISI Web of Science: | Yes | ||||||||||||||||
DOI: | 10.1109/TAES.2023.3242943 | ||||||||||||||||
Publisher: | IEEE - Institute of Electrical and Electronics Engineers | ||||||||||||||||
ISSN: | 0018-9251 | ||||||||||||||||
Status: | In Press | ||||||||||||||||
Keywords: | Colored noise, guaranteed estimation, kalman filtering, overbounding, time correlation | ||||||||||||||||
HGF - Research field: | Aeronautics, Space and Transport | ||||||||||||||||
HGF - Program: | Space | ||||||||||||||||
HGF - Program Themes: | Communication, Navigation, Quantum Technology | ||||||||||||||||
DLR - Research area: | Raumfahrt | ||||||||||||||||
DLR - Program: | R KNQ - Communication, Navigation, Quantum Technology | ||||||||||||||||
DLR - Research theme (Project): | R - GNSS Technologies and Services, R - Project Navigation 4.0 | ||||||||||||||||
Location: | Oberpfaffenhofen | ||||||||||||||||
Institutes and Institutions: | Institute of Communication and Navigation > Navigation | ||||||||||||||||
Deposited By: | Garcia Crespillo, Omar | ||||||||||||||||
Deposited On: | 13 Feb 2023 17:27 | ||||||||||||||||
Last Modified: | 19 Oct 2023 15:06 |
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