Uncertainty quantification of first fix in a time-differenced carrier phase observation model

© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/)

Bibliographic Details
Authors: Cherfi, Hakim|||0009-0004-5893-9616, Lesouple, Julien, Solà Ortega, Joan|||0000-0002-2933-3381, Thevenon, Paul|||0000-0002-9600-1029
Format: article
Publication Date:2025
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/439472
Online Access:https://hdl.handle.net/2117/439472
https://dx.doi.org/10.3390/s25113480
Access Level:Open access
Keyword:GNSS
TDCP
Uncertainty quantification
Odometry
Positioning error
Navigation
Àrees temàtiques de la UPC::Informàtica::Automàtica i control
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oai_identifier_str oai:upcommons.upc.edu:2117/439472
network_acronym_str ES
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repository_id_str
spelling Uncertainty quantification of first fix in a time-differenced carrier phase observation modelCherfi, Hakim|||0009-0004-5893-9616Lesouple, JulienSolà Ortega, Joan|||0000-0002-2933-3381Thevenon, Paul|||0000-0002-9600-1029GNSSTDCPUncertainty quantificationOdometryPositioning errorNavigationÀrees temàtiques de la UPC::Informàtica::Automàtica i control© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/)This paper presents an uncertainty quantification analysis of the first fix in a time-differenced carrier phase (TDCP) observation model. TDCP is a widely used method in GNSS-based odometry for precise positioning and displacement estimation. A key point in the TDCP modeling is the assumption that the GNSS receiver’s initial position is perfectly known, which is never exactly the case in real-world applications. This study assesses the impact of initial position errors on estimated displacement by formulating a correct TDCP model and a misspecified one, where the first position is not correct. Theoretical derivations provide a generic framework of estimation under the misspecified model and its associated mean squared error (MSE), as well as estimation performance bounds through the misspecified Cramér-Rao bound (MCRB) for the considered case. These theoretical considerations are then used to build an estimator of the receiver’s displacement, with comparisons to the MCRB for performance evaluation. Extensive simulations using realistic GNSS geometry assess the influence of a first-fix error under various conditions, including different time intervals, first-fix error norms, and first-fix error direction. As an example, it is shown that for the considered geometry, if a TDCP of $t_2 - t_1 = 1~\text{s}$ is built with an initial first fix error norm $\|\Delta \mathbf{r}_1\| = 10~\text{m}$, then it introduces an estimation of the displacement, with an error of norm equal to $1.3~\text{mm}$ at most. The results indicate that the displacement estimation error is linearly related to the initial position error and the time interval between observations, highlighting the importance of accurate first-fix estimation for reliable TDCP-based odometry. The findings contribute to highlighting the order of magnitude of errors on solutions as a function of the error on parameters.This work was supported in part by the EBCON Project under Grant PID2020119244GB-I00, and in part by the Consolidated Research Group RAIG under Grant 2021 SGR 00510 of the Departament de Recerca i Universitats de la Generalitat de Catalunya.Peer ReviewedMultidisciplinary Digital Publishing Institute (MDPI)20252025-06-0120252025-07-25journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/439472https://dx.doi.org/10.3390/s25113480reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-119244GB-I00 ESTIMACION Y CONTROL DE MOVIMIENTO CON CAMARAS DE EVENTOSopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4394722026-05-27T15:37:01Z
dc.title.none.fl_str_mv Uncertainty quantification of first fix in a time-differenced carrier phase observation model
title Uncertainty quantification of first fix in a time-differenced carrier phase observation model
spellingShingle Uncertainty quantification of first fix in a time-differenced carrier phase observation model
Cherfi, Hakim|||0009-0004-5893-9616
GNSS
TDCP
Uncertainty quantification
Odometry
Positioning error
Navigation
Àrees temàtiques de la UPC::Informàtica::Automàtica i control
title_short Uncertainty quantification of first fix in a time-differenced carrier phase observation model
title_full Uncertainty quantification of first fix in a time-differenced carrier phase observation model
title_fullStr Uncertainty quantification of first fix in a time-differenced carrier phase observation model
title_full_unstemmed Uncertainty quantification of first fix in a time-differenced carrier phase observation model
title_sort Uncertainty quantification of first fix in a time-differenced carrier phase observation model
dc.creator.none.fl_str_mv Cherfi, Hakim|||0009-0004-5893-9616
Lesouple, Julien
Solà Ortega, Joan|||0000-0002-2933-3381
Thevenon, Paul|||0000-0002-9600-1029
author Cherfi, Hakim|||0009-0004-5893-9616
author_facet Cherfi, Hakim|||0009-0004-5893-9616
Lesouple, Julien
Solà Ortega, Joan|||0000-0002-2933-3381
Thevenon, Paul|||0000-0002-9600-1029
author_role author
author2 Lesouple, Julien
Solà Ortega, Joan|||0000-0002-2933-3381
Thevenon, Paul|||0000-0002-9600-1029
author2_role author
author
author
dc.subject.none.fl_str_mv GNSS
TDCP
Uncertainty quantification
Odometry
Positioning error
Navigation
Àrees temàtiques de la UPC::Informàtica::Automàtica i control
topic GNSS
TDCP
Uncertainty quantification
Odometry
Positioning error
Navigation
Àrees temàtiques de la UPC::Informàtica::Automàtica i control
description © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/)
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-06-01
2025
2025-07-25
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/439472
https://dx.doi.org/10.3390/s25113480
url https://hdl.handle.net/2117/439472
https://dx.doi.org/10.3390/s25113480
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-119244GB-I00 ESTIMACION Y CONTROL DE MOVIMIENTO CON CAMARAS DE EVENTOS
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute (MDPI)
publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute (MDPI)
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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