Fundamental limits of missing traffic data estimation in urban networks

Wang, S; Mao, G

Fundamental limits of missing traffic data estimation in urban networks

Wang, S

Mao, G

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Publisher:: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Publication Type:: Journal Article
Citation:: IEEE Transactions on Intelligent Transportation Systems, 2020, 21, (3), pp. 1191-1203
Issue Date:: 2020-03-01

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Field	Value	Language
dc.contributor.author	Wang, S https://orcid.org/0000-0003-4347-6669
dc.contributor.author	Mao, G https://orcid.org/0000-0002-3598-4949
dc.date.accessioned	2021-01-10T00:41:27Z
dc.date.available	2021-01-10T00:41:27Z
dc.date.issued	2020-03-01
dc.identifier.citation	IEEE Transactions on Intelligent Transportation Systems, 2020, 21, (3), pp. 1191-1203
dc.identifier.issn	1524-9050
dc.identifier.issn	1558-0016
dc.identifier.uri	http://hdl.handle.net/10453/145241
dc.description.abstract	© 2000-2011 IEEE. Traffic data estimation plays an important role because traffic data often suffers from missing data problems, caused by a variety of reasons, i.e., temporary deployment of sensors, sensor malfunction and communication failure. Existing research on missing data estimation has mostly focused on using data-driven or model-driven models to estimate the missing data, and there is a lack of study on the achievable estimation accuracy and the conditions to achieve accurate missing data estimation. In this paper, we investigate the fundamental limits of missing traffic data estimation accuracy in urban networks using the spatial-temporal random effects model. We derive the squared flow error bound (SFEB) for the cases of the Fisher matrix being a singular and non-singular matrix, respectively. We show that the sufficient and necessary condition of the existence of an unbiased estimator is that the number of missing points is less than or equal to the rank of the Fisher matrix. For the case that no unbiased estimator can be found, we derive an inequality for the SPEB and show that the SFEB is readily determined by the covariance matrix of the unknown (missing) parameter vector, flow correlation between the unknown and the available data, and the sensor locations. Furthermore, we develop an optimal spatial-temporal Kriging estimator which is efficient in both cases where the causal relationship among available data points exists or does not exist. Our theoretical findings can be used to develop a sensor location optimization strategy to minimize the SFEB.
dc.language	English
dc.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
dc.relation.ispartof	IEEE Transactions on Intelligent Transportation Systems
dc.relation.isbasedon	10.1109/TITS.2019.2903524
dc.rights	© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.	en_US
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0801 Artificial Intelligence and Image Processing, 0905 Civil Engineering, 1507 Transportation and Freight Services
dc.subject.classification	Logistics & Transportation
dc.title	Fundamental limits of missing traffic data estimation in urban networks
dc.type	Journal Article
utslib.citation.volume	21
utslib.for	0805 Distributed Computing
utslib.for	0801 Artificial Intelligence and Image Processing
utslib.for	0905 Civil Engineering
utslib.for	1507 Transportation and Freight Services
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - CRIN - Realtime Information Networks
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Electrical and Data Engineering
pubs.organisational-group	/University of Technology Sydney
utslib.copyright.status	closed_access	*
dc.date.updated	2021-01-10T00:41:06Z
pubs.issue	3
pubs.publication-status	Published
pubs.volume	21
utslib.citation.issue	3

Abstract:

© 2000-2011 IEEE. Traffic data estimation plays an important role because traffic data often suffers from missing data problems, caused by a variety of reasons, i.e., temporary deployment of sensors, sensor malfunction and communication failure. Existing research on missing data estimation has mostly focused on using data-driven or model-driven models to estimate the missing data, and there is a lack of study on the achievable estimation accuracy and the conditions to achieve accurate missing data estimation. In this paper, we investigate the fundamental limits of missing traffic data estimation accuracy in urban networks using the spatial-temporal random effects model. We derive the squared flow error bound (SFEB) for the cases of the Fisher matrix being a singular and non-singular matrix, respectively. We show that the sufficient and necessary condition of the existence of an unbiased estimator is that the number of missing points is less than or equal to the rank of the Fisher matrix. For the case that no unbiased estimator can be found, we derive an inequality for the SPEB and show that the SFEB is readily determined by the covariance matrix of the unknown (missing) parameter vector, flow correlation between the unknown and the available data, and the sensor locations. Furthermore, we develop an optimal spatial-temporal Kriging estimator which is efficient in both cases where the causal relationship among available data points exists or does not exist. Our theoretical findings can be used to develop a sensor location optimization strategy to minimize the SFEB.

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http://hdl.handle.net/10453/145241