Assimilating Eulerian and Lagrangian data in traffic-flow models

Chao Xia, Courtney Cochrane, Joseph DeGuire, Gaoyang Fan, Emma Holmes, Melissa McGuirl, Patrick Murphy, Jenna Palmer, Paul Carter, Laura Slivinski, Björn Sandstede

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Data assimilation of traffic flow remains a challenging problem. One difficulty is that data come from different sources ranging from stationary sensors and camera data to GPS and cell phone data from moving cars. Sensors and cameras give information about traffic density, while GPS data provide information about the positions and velocities of individual cars. Previous methods for assimilating Lagrangian data collected from individual cars relied on specific properties of the underlying computational model or its reformulation in Lagrangian coordinates. These approaches make it hard to assimilate both Eulerian density and Lagrangian positional data simultaneously. In this paper, we propose an alternative approach that allows us to assimilate both Eulerian and Lagrangian data. We show that the proposed algorithm is accurate and works well in different traffic scenarios and regardless of whether ensemble Kalman or particle filters are used. We also show that the algorithm is capable of estimating parameters and assimilating real traffic observations and synthetic observations obtained from microscopic models.

Original languageEnglish (US)
Pages (from-to)59-72
Number of pages14
JournalPhysica D: Nonlinear Phenomena
StatePublished - May 1 2017
Externally publishedYes

Bibliographical note

Funding Information:
The authors gratefully acknowledge support by the National Science Foundation through grant DMS-1148284. We thank the anonymous referees for their constructive and helpful comments.

Publisher Copyright:
© 2017 Elsevier B.V.


  • Data assimilation
  • Eulerian observations
  • Lagrangian observations
  • Traffic flow


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