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Sensors 2017, 17(10), 2160; doi:10.3390/s17102160

Spatial Copula Model for Imputing Traffic Flow Data from Remote Microwave Sensors

School of Transportation Science and Engineering, Beijing Key Laboratory for Cooperative Vehicle Infrastructure System and Safety Control, Beihang University, Beijing 100191, China
Key Laboratory of Road & Traffic Engineering of the Ministry of Education, Tongji University, 4800 Cao’an Road, Shanghai 201804, China
School of Computer Science and Engineering, the State Key Laboratory of Software Development Environment, Beihang University, Beijing 100191, China
Author to whom correspondence should be addressed.
Received: 24 July 2017 / Revised: 11 September 2017 / Accepted: 16 September 2017 / Published: 21 September 2017
(This article belongs to the Special Issue Sensor Networks for Smart Roads)
View Full-Text   |   Download PDF [1298 KB, uploaded 21 September 2017]   |  


Issues of missing data have become increasingly serious with the rapid increase in usage of traffic sensors. Analyses of the Beijing ring expressway have showed that up to 50% of microwave sensors pose missing values. The imputation of missing traffic data must be urgently solved although a precise solution that cannot be easily achieved due to the significant number of missing portions. In this study, copula-based models are proposed for the spatial interpolation of traffic flow from remote traffic microwave sensors. Most existing interpolation methods only rely on covariance functions to depict spatial correlation and are unsuitable for coping with anomalies due to Gaussian consumption. Copula theory overcomes this issue and provides a connection between the correlation function and the marginal distribution function of traffic flow. To validate copula-based models, a comparison with three kriging methods is conducted. Results indicate that copula-based models outperform kriging methods, especially on roads with irregular traffic patterns. Copula-based models demonstrate significant potential to impute missing data in large-scale transportation networks. View Full-Text
Keywords: traffic flow imputation; spatial interpolation; spatial correlation; marginal distribution; copula model traffic flow imputation; spatial interpolation; spatial correlation; marginal distribution; copula model

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Ma, X.; Luan, S.; Du, B.; Yu, B. Spatial Copula Model for Imputing Traffic Flow Data from Remote Microwave Sensors. Sensors 2017, 17, 2160.

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