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Bounding Sequential Estimation Errors Due to Gauss-Markov Noise with Uncertain Parameters

Langel, Steve and Garcia Crespillo, Omar and Joerger, Mathieu (2019) Bounding Sequential Estimation Errors Due to Gauss-Markov Noise with Uncertain Parameters. Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019), September 16 - 20, 2019, Miami, FL, USA.

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Abstract

This paper describes the derivation and implementation of a new method to overbound Kalman filter (KF) based estimate error distributions in the presence of time-correlated measurement and process noise. The method is specific to problems where each input noise component is first-order Gauss-Markov with a distinct variance sigma^2 in [sigma^2_min, sigma^2_max] and time constant tau in [tau_min, tau_max]. The bounds on sigma^2 and tau are known. Reference [1] derives an overbound for the continuous-time KF, and we extend the result to the more common case of sampled-data systems with discrete-time measurements. We prove that the KF covariance matrix overbounds the estimate error distribution when Gauss-Markov processes are defined using a time constant tau_max and a process noise variance inflated by (tau_max/tau_min). We also show that the overbound is tightest by initializing the variance of the Gauss-Markov process with sigma^2_0 = 2sigma^2_max/ [1 + (tau_min/tau_max)]. The new method is evaluated using covariance analysis for an example application in advanced receiver autonomous integrity monitoring (ARAIM) [2]. [1] Tupysev, V. A., Stepanov, O. A., Loparev, A. V., and Litvinenko, Y. A. “Guaranteed Estimation in the Problems of Navigation Information Processing.” Proceedings of the 18th IEEE International Conference on Control Applications, St. Petersburg, Russia, 2009, pp. 1672 – 1677. [2] Working Group C. “ARAIM Technical Subgroup. Milestone 3.0 Report.” Technical report, EU-US Cooperation on Satellite Navigation, 2016.

Item URL in elib:https://elib.dlr.de/130885/
Document Type:Conference or Workshop Item (Speech)
Title:Bounding Sequential Estimation Errors Due to Gauss-Markov Noise with Uncertain Parameters
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Langel, SteveUNSPECIFIEDUNSPECIFIED
Garcia Crespillo, OmarOmar.GarciaCrespillo (at) dlr.deUNSPECIFIED
Joerger, MathieuUNSPECIFIEDUNSPECIFIED
Date:16 September 2019
Refereed publication:No
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Published
Keywords:Gauss-Markov Noise, Kalman Filter, Overbound, Covariance Matrix, State Augmentation, ARAIM
Event Title:Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019)
Event Location:Miami, FL, USA
Event Type:international Conference
Event Dates:September 16 - 20, 2019
Organizer:ION
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Communication and Navigation
DLR - Research area:Raumfahrt
DLR - Program:R KN - Kommunikation und Navigation
DLR - Research theme (Project):R - Project Navigation 4.0
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Communication and Navigation > Navigation
Deposited By: Garcia Crespillo, Omar
Deposited On:21 Nov 2019 14:01
Last Modified:21 Nov 2019 14:01

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