Estimation for heterogeneous traffic using enhanced particle filters

References

• Aw, A., and M. Rascle. 2000. “Resurrection of ”Second Order” Models of Traffic Flow.” SIAM Journal on Applied Mathematics 60 (3): 916–938. doi:10.1137/S0036139997332099
   Google Scholar
• Benzoni-Gavage, S., and R. M. Colombo. 2002. “An n-Populations Model for Traffic Flow.” European Journal of Applied Mathematics 14: 587–612.
   Google Scholar
• Blandin, S., A. Couque, A. Bayen, and D. Work. 2012. “On Sequential Data Assimilation for Scalar Macroscopic Traffic Flow Models.” Physica D: Nonlinear Phenomena 241 (17): 1421–1440. http://www.sciencedirect.com/science/article/pii/S0167278912001339
   Google Scholar
• Boel, René, and Lyudmila Mihaylova. 2006. “A Compositional Stochastic Model for Real Time Freeway Traffic Simulation.” Transportation Research Part B: Methodological 40 (4): 319–334. https://ideas.repec.org/a/eee/transb/v40y2006i4p319-334.html
   Google Scholar
• Bowman, Adrian W., and Adelchi Azzalini. 2000. Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-Plus Illustrations. Vol. 15. New York: Oxford University Press Inc.
   Google Scholar
• Chalons, C., M. L. Delle Monache, and P. Goatin. 2017. “A Conservative Scheme for Non-classical Solutions to a Strongly Coupled PDE-ODE Problem.” Interfaces and Free Boundaries 19 (4): 553–570. https://hal.inria.fr/hal-01070262
   Google Scholar
• Chen, Z. 2003. “Bayesian Filtering: From Kalman Filters to Particle Filters, and Beyond.” Statistics 182:
   Google Scholar
• Chiarello, F. A., and P. Goatin. 2019. “Non-local Multi-class Traffic Flow Models.” Networks and Heterogeneous Media 14: 371.
   Google Scholar
• Costeseque, G., and A. Duret. 2016, January 27. “Mesoscopic Multiclass Traffic Flow Modeling on Multi-Lane Sections.” In Proceedings of the 95th Annual Meeting Transportation Research Board -- TRB, Washington, DC. https://hal.archives-ouvertes.fr/hal-01250438.
   Google Scholar
• Daganzo, Carlos F. 1994. “The Cell Transmission Model: A Dynamic Representation of Highway Traffic Consistent with the Hydrodynamic Theory.” Transportation Research Part B: Methodological 28 (4): 269–287. http://www.sciencedirect.com/science/article/pii/0191261594900027
   Google Scholar
• Daganzo, Carlos F. 1995. “The Cell Transmission Model, Part II: Network Traffic.” Transportation Research Part B: Methodological 29 (2): 79–93. http://www.sciencedirect.com/science/article/pii/019126159400022R
   Google Scholar
• Doucet, A., and A. Johansen. 2009. “A Tutorial on Particle Filtering and Smoothing: Fifteen Years Later.” Handbook of Nonlinear Filtering 12: 656–704.
   Google Scholar
• Fan, S., and D. B. Work. 2015. “A Heterogeneous Multiclass Traffic Flow Model with Creeping.” SIAM Journal on Applied Mathematics 75 (2): 813–835.
   Google Scholar
• Ferrara, A., S. Simona, and S. Silvia. 2018. Freeway Traffic Modelling and Control. New York, NY: Springer International Publishing.
   Google Scholar
• Garavello, M., K. Han, and B. Piccoli. 2016. Models for Vehicular Traffic on Networks. Vol. 9 of AIMS Series on Applied Mathematics. American Institute of Mathematical Sciences.
   Google Scholar
• Gashaw, S., P. Goatin, and J. Härri. 2018. “Modeling and Analysis of Mixed Flow of Cars and Powered Two Wheelers.” Transportation Research. Part C, Emerging Technologies 89: 1–44. https://hal.inria.fr/hal-01708005.
   Google Scholar
• Gazis, D. C., and C. H. Knapp. 1971. “On-Line Estimation of Traffic Densities From Time-Series of Flow and Speed Data.” Transportation Science 5 (3): 283–301. https://doi.org/10.1287/trsc.5.3.283
   Google Scholar
• Godunov, S. K. 1959. “A-difference Method for Numerical Calculation of Discontinuous Solutions of the Equations of Hydrodynamics.” Mat. Sb. (N.S.) 47 (89): 271–306. http://mi.mathnet.ru/msb4873
   Google Scholar
• Hegyi, A., D. Girimonte, R. Babuska, and B. De Schutter. 2006, September. “A Comparison of Filter Configurations for Freeway Traffic State Estimation.” In Proceedings of 2006 IEEE Intelligent Transportation Systems Conference, 1029–1034.
   Google Scholar
• Hill, Peter D. 1985. “Kernel Estimation of a Distribution Function.” Communications in Statistics -- Theory and Methods 14 (3): 605–620. https://doi.org/10.1080/03610928508828937
   Google Scholar
• Kaipio, J., and E. Somersalo. 2006. Statistical and Computational Inverse Problems. Vol. 160. Springer-Verlag New York: Springer Science & Business Media.
   Google Scholar
• Kanagaraj, Venkatesan, Gowri Asaithambi, Tomer Toledo, and Tzu-Chang Lee. 2015. “Trajectory Data and Flow Characteristics of Mixed Traffic.” Transportation Research Record 2491 (1): 1–11. https://doi.org/10.3141/2491-01
   Google Scholar
• Krajewski, Robert, Julian Bock, Laurent Kloeker, and Lutz Eckstein. 2018. “The highD Dataset: A Drone Dataset of Naturalistic Vehicle Trajectories on German Highways for Validation of Highly Automated Driving Systems.” In 2018 21st International Conference on Intelligent Transportation Systems (ITSC), 2118–2125.
   Google Scholar
• Li, L., R. Jiang, Z. He, and X. Zhou. 2020. “Trajectory Data-based Traffic Flow Studies: A Revisit.” Transportation Research Part C: Emerging Technologies 114: 225–240. http://www.sciencedirect.com/science/article/pii/S0968090X19312987
   Google Scholar
• Lighthill, M. J., and G. B. Whitham. 1955. “On Kinematic Waves II. A Theory of Traffic Flow on Long Crowded Roads.” In Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 229, 317–345. https://royalsocietypublishing.org/doi/abs/10.1098/rspa.1955.0089.
   Google Scholar
• Mallikarjuna, C., and K. R. Rao. 2009. “Cellular Automata Model for Heterogeneous Traffic.” Journal of Advanced Transportation 43 (3): 321–345. https://onlinelibrary.wiley.com/doi/abs/10.1002/atr.56-70430305
   Google Scholar
• Martino, L., V. Elvira, and F. Louzada. 2017. “Effective Sample Size for Importance Sampling Based on Discrepancy Measures.” Signal Processing 131: 386–401. http://www.sciencedirect.com/science/article/pii/S0165168416302110
   Google Scholar
• Mihaylova, L., R. K. Boel, and A. Hegyi. 2007. “Freeway Traffic Estimation Within Particle Filtering Framework.” Automatica 43: 290–300.
   Google Scholar
• Mihaylova, L., A. Hegyi, A. Gning, and R. K. Boel. 2012. “Parallelized Particle and Gaussian Sum Particle Filters for Large-Scale Freeway Traffic Systems.” IEEE Transactions on Intelligent Transportation Systems 13 (1): 36–48.
   Google Scholar
• Mohan, R., and G. Ramadurai. 2019, January. “Multi-class Traffic Flow Model Based on Three-Dimensional Flow-Concentration Surface.” In Proceedings of the 98th Annual Meeting Transportation Research Board -- TRB, Washington, DC, 19–04534. https://trid.trb.org/view/1573120.
   Google Scholar
• Nair, R., H. S. Mahmassani, and E. Miller-Hooks. 2011. “A Porous Flow Approach to Modeling Heterogeneous Traffic in Disordered Systems.” Procedia -- Social and Behavioral Sciences 17: 611–627. http://www.sciencedirect.com/science/article/pii/S1877042811010937
   Google Scholar
• Ngoduy, D. 2008. “Applicable Filtering Framework for Online Multiclass Freeway Network Estimation.” Physica A: Statistical Mechanics and Its Applications 387 (2–3): 599–616.
   Google Scholar
• Ngoduy, D., and R. Liu. 2007. “Multiclass First-order Simulation Model to Explain Non-linear Traffic Phenomena.” Physica A: Statistical Mechanics and Its Applications 385 (2): 667–682. http://www.sciencedirect.com/science/article/pii/S0378437107007911
   Google Scholar
• Ngoduy, D., and A. Sumalee. 2010. “Adaptive Estimation of Noise Covariance Matrices in Unscented Kalman Filter for Multiclass Traffic Flow Model.” Transportation Research Record 2188 (1): 119–130. https://doi.org/10.3141/2188-13
   Google Scholar
• NGSIM. 2006. “The Next Generation Simulation Program.” U.S. Department of Transportation Federal Highway Administation. http://ops.fhwa.dot.gov/trafficanalysistools/ngsim.htm.
   Google Scholar
• Olivier, L. E., B. Huang, and I. K. Craig. 2012. “Dual Particle Filters for State and Parameter Estimation with Application to a Run-of-mine Ore Mill.” Journal of Process Control 22 (4): 710–717. http://www.sciencedirect.com/science/article/pii/S0959152412000583
   Google Scholar
• Polson, N., and V. Sokolov. 2018. “Bayesian Particle Tracking of Traffic Flows.” IEEE Transactions on Intelligent Transportation Systems 19 (2): 345–356.
   Google Scholar
• Richards, P. I. 1956. “Shock Waves on the Highway.” Operations Research 4 (1): 42–51. https://doi.org/10.1287/opre.4.1.42
   Google Scholar
• Risso, M. A., N. Bhouri, A. J. Rubiales, and P. A. Lotito. 2020. “A Constrained Filtering Algorithm for Freeway Traffic State Estimation.” Transportmetrica A: Transport Science 16 (2): 316–336. https://doi.org/10.1080/23249935.2018.1549618
   Google Scholar
• Seo, T., A. M. Bayen, T. Kusakabe, and Y. Asakura. 2017. “Traffic State Estimation on Highway: A Comprehensive Survey.” Annual Reviews in Control 43: 128–151. http://www.sciencedirect.com/science/article/pii/S1367578817300226
   Google Scholar
• Simon, D. 2006. Optimal State Estimation. Hoboken, NJ: John Wiley & Sons, Inc.
   Google Scholar
• Sun, Y., and D. B. Work. 2017. “Scaling the Kalman Filter for Large-scale Traffic Estimation.” IEEE Transactions on Control of Network Systems 5 (3): 968–980.
   Google Scholar
• Sun, Y., and D. B. Work. 2018. “Error Bounds for Kalman Filters on Traffic Networks.” Networks & Heterogeneous Media 13 (2): 261–295.
   Google Scholar
• Surace, S. C., A. Kutschireiter, and J. Pfister. 2019. “How to Avoid the Curse of Dimensionality: Scalability of Particle Filters with and Without Importance Weights.” SIAM Review 61 (1): 79–91. https://doi.org/10.1137/17M1125340
   Google Scholar
• Szeto, M. W., and D. C. Gazis. 1972. “Application of Kalman Filtering to the Surveillance and Control of Traffic Systems.” Transportation Science 6 (4): 419–439. https://doi.org/10.1287/trsc.6.4.419
   Google Scholar
• Tang, T. Q., H. J. Huang, S. G. Zhao, and H. Y. Shang. 2009. “A New Dynamic Model for Heterogeneous Traffic Flow.” Physics Letters A 373 (29): 2461–2466. http://www.sciencedirect.com/science/article/pii/S0375960109005799
   Google Scholar
• van Lint, J. W. C., S. P. Hoogendoorn, and A. Hegyi. 2008. “Dual EKF State and Parameter Estimation in Multi-Class First-Order Traffic Flow Models.” IFAC Proceedings Volumes 41 (2): 14078–14083. http://www.sciencedirect.com/science/article/pii/S1474667016412486
   Google Scholar
• van Lint, J. W. C., S. P. Hoogendoorn, and M. Schreuder. 2008. “Fastlane: New Multiclass First-Order Traffic Flow Model.” Transportation Research Record: Journal of the Transportation Research Board 2088: 177–187.
   Google Scholar
• van Wageningen-Kessels, F., H. van Lint, K. Vuik, and S. Hoogendoorn. 2015. “Genealogy of Traffic Flow Models.” EURO Journal on Transportation and Logistics 4 (4): 445–473. https://doi.org/10.1007/s13-676-014-0045-5
   Google Scholar
• Vivas, C., S. Siri, A. Ferrara, S. Sacone, G. Cavanna, and F. R. Rubio. 2015. “Distributed Consensus-Based Switched Observers for Freeway Traffic Density Estimation.” In 2015 54th IEEE Conference on Decision and Control (CDC), 3445–3450. IEEE.
   Google Scholar
• Wang, R., Y. Li, and D. B. Work. 2017. “Comparing Traffic State Estimators for Mixed Human and Automated Traffic Flows.” Transportation Research Part C: Emerging Technologies 78: 95–110. http://www.sciencedirect.com/science/article/pii/S0968090X17300517
   Google Scholar
• Wang, Y., and M. Papageorgiou. 2005. “Real-time Freeway Traffic State Estimation Based on Extended Kalman Filter: a General Approach.” Transportation Research Part B: Methodological 39 (2): 141–167. http://www.sciencedirect.com/science/article/pii/S0191261504000438
   Google Scholar
• Wang, Y., and D. B. Work. 2019. “Heterogeneous Traffic Estimation With Particle Filtering.” In 2019 IEEE Intelligent Transportation Systems Conference (ITSC), 2551–2556.
   Google Scholar
• Work, D. B., O.-P. Tossavainen, S. Blandin, A. M. Bayen, T. Iwuchukwu, and K. Tracton. 2008, December. “An Ensemble Kalman Filtering Approach to Highway Traffic Estimation Using GPS Enabled Mobile Devices.” In Proceedings of 2008 47th IEEE Conference on Decision and Control, 5062–5068.
   Google Scholar
• Wright, M., and R. Horowitz. 2016. “Fusing Loop and GPS Probe Measurements to Estimate Freeway Density.” IEEE Transactions on Intelligent Transportation Systems 17 (12): 3577–3590.
   Google Scholar
• Zhang, H. M. 2002. “A Non-equilibrium Traffic Model Devoid of Gas-like Behavior.” Transportation Research Part B: Methodological 36 (3): 275–290. https://ideas.repec.org/a/eee/transb/v36y2002i3-p275-290.html
   Google Scholar
• Zhang, Peng, Ru-xun Liu, S. C. Wong, and Shi-qiang Dai. 2006. “Hyperbolicity and Kinematic Waves of a Class of Multi-population Partial Differential Equations.” European Journal of Applied Mathematics 17 (2): 171–200.
   Google Scholar
• Zhang, Peng, S. C. Wong, and Chi-Wang Shu. 2006. “A Weighted Essentially Non-oscillatory Numerical Scheme for a Multi-class Traffic Flow Model on An Inhomogeneous Highway.” Journal of Computational Physics 212 (2): 739–756. http://www.sciencedirect.com/science/article/pii/S00219991050-03542
   Google Scholar
• Zhang, Peng, S. C. Wong, and Zhenli Xu. 2008. “A Hybrid Scheme for Solving a Multi-class Traffic Flow Model with Complex Wave Breaking.” Computer Methods in Applied Mechanics and Engineering 197 (45): 3816–3827. http://www.sciencedirect.com/science/article/pii/S0045782508001175
   Google Scholar