elib
DLR-Header
DLR-Logo -> http://www.dlr.de
DLR Portal Home | Imprint | Privacy Policy | Contact | Deutsch
Fontsize: [-] Text [+]

Tight Bounds for Uncertain Time-Correlated Errors with Gauss-Markov Structure in Kalman Filtering

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, 59 (4), pp. 4347-4362. IEEE - Institute of Electrical and Electronics Engineers. doi: 10.1109/TAES.2023.3242943. ISSN 0018-9251.

[img] PDF - Only accessible within DLR - Postprint version (accepted manuscript)
1MB

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/
Document Type:Article
Title:Tight Bounds for Uncertain Time-Correlated Errors with Gauss-Markov Structure in Kalman Filtering
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Garcia Crespillo, OmarUNSPECIFIEDhttps://orcid.org/0000-0002-2598-7636UNSPECIFIED
Langel, SteveMITREUNSPECIFIEDUNSPECIFIED
Joerger, MathieuVirginia TechUNSPECIFIEDUNSPECIFIED
Date:August 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
Volume:59
DOI:10.1109/TAES.2023.3242943
Page Range:pp. 4347-4362
Publisher:IEEE - Institute of Electrical and Electronics Engineers
ISSN:0018-9251
Status:Published
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:26 Jan 2024 16:13

Repository Staff Only: item control page

Browse
Search
Help & Contact
Information
electronic library is running on EPrints 3.3.12
Website and database design: Copyright © German Aerospace Center (DLR). All rights reserved.