Traffic Density Estimation for Multiple Segment Freeways
Traffic density, an indicator of traffic
conditions, is one of the most critical characteristics to
Intelligent Transport Systems (ITS). This paper investigates
recursive traffic density estimation using the information
provided from inductive loop detectors. On the basis of the
phenomenological relationship between speed and density, the
existing studies incorporate a state space model and update the
density estimate using vehicular speed observations via the
extended Kalman filter, where an approximation is made
because of the linearization of the nonlinear observation
equation. In practice, this may lead to substantial estimation
errors. This paper incorporates a suitable transformation to
deal with the nonlinear observation equation so that the
approximation is avoided when using Kalman filter to
estimate the traffic density. A numerical study is conducted. It
is shown that the developed method outperforms the existing
methods for traffic density estimation.
[1] T. Z. Qiu,., X. Y. Lu, A. H. F. Chow, & S. Shladover, "Real-time
density estimation on freeway with loop detector and probe data,"
Transportation Science, 2009, vol. 31, pp. 324-335.
[2] D. Gazis, & C. Liu, "Kalman filtering estimation of traffic counts for
two network links in tandem," Transportation Research Part B, 2003,
vol. 37(8), pp. 737-745.
[3] Y. Wang, & M. Papageorgiou, "Real-time freeway traffic state
estimation based on extended Kalman filter: A general approach,"
Transportation Research Part B, 2005, vol. 39(2), pp. 141-167.
[4] J. S. Drake, J. L. Schofer, and A. D. May. "A Statistical Analysis of
Speed Density Hypotheses," Highway Research Record, 1967, vol. 154,
pp. 53-87.
[5] B. Li, "A non-Gaussian Kalman filter with application to the estimation
of vehicular speed," Technometrics, 2009, vol. 51(2), pp. 162-172.
[6] B. D. Greenshields, "The Photographic Method of studying Traffic
Behaviour," Proceedings of the 13th Annual Meeting of the Highway
Research Board, 1933
[7] B. D. Greenshields, "A study of highway capacity," Proceedings
Highway Research Record, Washington, 1935, vol. 14, pp. 448-477.
[8] M. W. Szeto, , & D. C. Gazis, "Application of kalman filtering to the
surveillance and control of traffic systems," Transportation Science,
1972, vol. 6(4), pp. 419.
[9] X. Sun, L. Mu├▒oz, & R. Horowitz, "Mixture Kalman filter based
highway congestion mode and vehicle density estimator and its
application," Proceedings of the 2004 American Control Conference, pp.
2098-2103.
[10] G. Vigos, M. Papageorgiou, & Y. Wang, "Real-time estimation of
vehicle-count within signalized links," Transportation Research Part C,
2008, vol. 16(1), pp. 18-35.
[1] T. Z. Qiu,., X. Y. Lu, A. H. F. Chow, & S. Shladover, "Real-time
density estimation on freeway with loop detector and probe data,"
Transportation Science, 2009, vol. 31, pp. 324-335.
[2] D. Gazis, & C. Liu, "Kalman filtering estimation of traffic counts for
two network links in tandem," Transportation Research Part B, 2003,
vol. 37(8), pp. 737-745.
[3] Y. Wang, & M. Papageorgiou, "Real-time freeway traffic state
estimation based on extended Kalman filter: A general approach,"
Transportation Research Part B, 2005, vol. 39(2), pp. 141-167.
[4] J. S. Drake, J. L. Schofer, and A. D. May. "A Statistical Analysis of
Speed Density Hypotheses," Highway Research Record, 1967, vol. 154,
pp. 53-87.
[5] B. Li, "A non-Gaussian Kalman filter with application to the estimation
of vehicular speed," Technometrics, 2009, vol. 51(2), pp. 162-172.
[6] B. D. Greenshields, "The Photographic Method of studying Traffic
Behaviour," Proceedings of the 13th Annual Meeting of the Highway
Research Board, 1933
[7] B. D. Greenshields, "A study of highway capacity," Proceedings
Highway Research Record, Washington, 1935, vol. 14, pp. 448-477.
[8] M. W. Szeto, , & D. C. Gazis, "Application of kalman filtering to the
surveillance and control of traffic systems," Transportation Science,
1972, vol. 6(4), pp. 419.
[9] X. Sun, L. Mu├▒oz, & R. Horowitz, "Mixture Kalman filter based
highway congestion mode and vehicle density estimator and its
application," Proceedings of the 2004 American Control Conference, pp.
2098-2103.
[10] G. Vigos, M. Papageorgiou, & Y. Wang, "Real-time estimation of
vehicle-count within signalized links," Transportation Research Part C,
2008, vol. 16(1), pp. 18-35.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:50705", author = "Karandeep Singh and Baibing Li", title = "Traffic Density Estimation for Multiple Segment Freeways", abstract = "Traffic density, an indicator of traffic
conditions, is one of the most critical characteristics to
Intelligent Transport Systems (ITS). This paper investigates
recursive traffic density estimation using the information
provided from inductive loop detectors. On the basis of the
phenomenological relationship between speed and density, the
existing studies incorporate a state space model and update the
density estimate using vehicular speed observations via the
extended Kalman filter, where an approximation is made
because of the linearization of the nonlinear observation
equation. In practice, this may lead to substantial estimation
errors. This paper incorporates a suitable transformation to
deal with the nonlinear observation equation so that the
approximation is avoided when using Kalman filter to
estimate the traffic density. A numerical study is conducted. It
is shown that the developed method outperforms the existing
methods for traffic density estimation.", keywords = "Density estimation, Kalman filter, speed-densityrelationship, Traffic surveillance.", volume = "4", number = "6", pages = "641-5", }