On sequential data assimilation for scalar macroscopic traffic flow models

Physica D: Nonlinear Phenomena

Volumn 241, Issue 17, 2012, Pages 1421-1440

  Blandin, Sébastien ^a   Couque, Adrien ^b   Bayen, Alexandre ^a,c   Work, Daniel ^d  

^a IBM RESEARCH   (United States)

^b California Center for Innovative Transportation   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d University of Illinois at Urbana Champaign   (United States)

Author keywords

Conservation law; Data assimilation; Macroscopic modeling; Riemann problem; Sequential estimation; Traffic flow

Indexed keywords

SHOCK WAVES; TRAFFIC CONTROL;

CONSERVATION LAW; DATA ASSIMILATION; MACROSCOPIC MODEL; RIEMANN PROBLEM; SEQUENTIAL ESTIMATION; TRAFFIC FLOW;

UNCERTAINTY ANALYSIS;

EID: 84863509580     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2012.05.005     Document Type: Article

References (89)

1. T. Hey, S. Tansley, and K. Tolle The Fourth Paradigm: Data-Intensive Scientific Discovery 2009 Microsoft Research Redmond, WA
2. J. Kaipio, and E. Somersalo Statistical and Computational Inverse Problems 2005 Springer New-York, NY
3. F. Bouttier, P. Courtier, Data assimilation concepts and methods, Training course notes of the European Centre for Medium-Range Weather Forecasts, 1999, Reading, UK.
4. F.-X. Le Dimet, and O. Talagrand Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects Tellus A 38 2 1986 97 110
5. R. Kalman A new approach to linear filtering and prediction problems J. Basic Eng. 82 1 1960 35 45
6. N. Wiener, Extrapolation, interpolation, and smoothing of stationary time series with engineering applications, The Technology Press of The Massachusetts Institute of Technology, Boston, MA, 1949.
7. Y. Bar-Shalom, X. Li, T. Kirubarajan, and J. Wiley Estimation with Applications to Tracking and Navigation 2001 John Wiley and Sons New York, NY
8. S. Schmidt Kalman filter: Its recognition and development for aerospace applications J. Guid. Control 4 1 1981 4 7
9. P. Courtier, E. Andersson, W. Heckley, D. Vasiljevic, M. Hamrud, A. Hollingsworth, F. Rabier, M. Fisher, and J. Pailleux The ECMWF implementation of three-dimensional variational assimilation (3D-Var). I: Formulation Q. J. R. Meteorol. Soc. 124 550 1998 1783 1807 (Pubitemid 29007411)
10. P. Courtier, J. Thepaut, and A. Hollingsworth A strategy for operational implementation of 4D-Var, using an incremental approach Q. J. R. Meteorol. Soc. 120 519 1994 1367 1387
11. B. Anderson, and J. Moore Optimal Filtering 1979 Prentice Hall Upper Saddle River, NJ
12. S. Julier, J. Uhlmann, A new extension of the Kalman filter to nonlinear systems, in: Proceedings of AeroSense: SPIE 11th Annual International Symposium on Aerospace/Defense Sensing, Simulation and Controls, Orlando, FL, 1997.
13. G. Evensen The ensemble Kalman filter: Theoretical formulation and practical implementation Ocean Dynam. 53 4 2003 343 367
14. J. Liu, and R. Chen Sequential Monte Carlo methods for dynamic systems J. Amer. Statist. Assoc. 93 443 1998 1032 1044
15. R. Chen, and J. Liu Mixture Kalman filters J. R. Stat. Soc. Ser. B (Stat. Methodol.) 62 3 2000 493 508
16. D. Gazis, and C. Knapp On-line estimation of traffic densities from time-series of flow and speed data Transp. Sci. 5 3 1971 283 301
17. M. Szeto, and D. Gazis Application of Kalman filtering to the surveillance and control of traffic systems Transp. Sci. 6 4 1972 419 439
18. Y. Wang, and M. Papageorgiou Real-time freeway traffic state estimation based on extended Kalman filter: a general approach Transp. Res. 39 2 2005 141 167 (Pubitemid 40032216)
19. Y. Wang, M. Papageorgiou, and A. Messmer Real-time freeway traffic state estimation based on extended Kalman filter: A case study Transp. Sci. 41 2 2007 167
20. M. Papageorgiou, J.-M. Blosseville, and H. Hadj-Salem Modelling and real-time control of traffic flow on the southern part of Boulevard Peripherique in Paris: Part I: Modelling Transp. Res. 24 5 1990 345 359
21. T. Schreiter, C. van Hinsbergen, F. Zuurbier, H. van Lint, S. Hoogendoorn, Data-model synchronization in extended Kalman filters for accurate online traffic state estimation, in: 2010 Proceedings of the Traffic Flow Theory Conference, Annecy, France, 2010.
22. S. Smulders Control of freeway traffic flow by variable speed signs Transp. Res. 24 2 1990 111 132
23. J.-C. Herrera, and A. Bayen Incorporation of lagrangian measurements in freeway traffic state estimation Transp. Res. 44 4 2010 460 481 10.1016/j.trb.2009.10.005
24. X. Sun, L. Muñoz, and R. Horowitz Mixture Kalman filter based highway congestion mode and vehicle density estimator and its application American Control Conference (ACC), 2004 2004 IEEE Boston,MA 2098 2103
25. C. Tampere, L. Immers, An extended Kalman filter application for traffic state estimation using CTM with implicit mode switching and dynamic parameters, in: Intelligent Transportation Systems Conference, 2007. ITSC 2007, Seattle, WA, 2007, pp. 209-216.
26. C. Daganzo The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory Transp. Res. 28 4 1994 269 287
27. C. Daganzo The cell transmission model, part II: Network traffic Transp. Res. 29 2 1995 79 93
28. L. Mihaylova, R. Boel, and A. Hegyi Freeway traffic estimation within particle filtering framework Automatica 43 2 2007 290 300 (Pubitemid 46037591)
29. D. Work, S. Blandin, O.-P. Tossavainen, B. Piccoli, and A. Bayen A traffic model for velocity data assimilation Appl. Math. Res. eXpress 1 1 2010 1 35 10.1093/amrx/abq002
30. N. Gordon, D. Salmond, and A. Smith Novel approach to nonlinear/non-Gaussian Bayesian state estimation Radar and Signal Processing, IEE Proceedings F, vol. 140 1993 IET 107 113
31. L. Mihaylova, R. Boel, A. Hegyi, An unscented Kalman filter for freeway traffic estimation, in: Proceedings of the IFAC Symposium on Control in Transportation Systems, Delft, the Netherlands, 2006, pp. 29-31.
32. M. Lighthill, and G. Whitham On kinematic waves, II: a theory of traffic flow on long crowded roads Proc. R. Soc. Lond. 229 1178 1956 317 345
33. P. Richards Shock waves on the highway Oper. Res. 4 1 1956 42 51
34. S. Godunov A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics Mat. Sb. 89 3 1959 271 306
35. L. Evans Partial Differential Equations 1998 American Mathematical Society Providence, RI
36. G. Evensen Inverse methods and data assimilation in nonlinear ocean models Physica D 77 1-3 1994 108 129
37. H. Sorenson Least-squares estimation: from Gauss to Kalman Spectrum, IEEE 7 7 1970 63 68
38. S. Stigler Gauss and the invention of least squares Ann. Stat. 1981 465 474
39. A. Jazwinski Stochastic Processes and Filtering Theory 1970 Academic Press New York, NY
40. S. Sherman Non-mean-square error criteria IRE Trans. Inform. Theory 4 3 1958 125 126
41. Federal Highway Administration, Next Generation Simulation, http://ngsim-community.org/, 2006.
42. G. Evensen Using the extended Kalman filter with a multilayer quasi-geostrophic ocean model J. Geophys. Res. 97 C11 1992 17905 17924
43. R. Miller, E. Carter, and S. Blue Data assimilation into nonlinear stochastic models Tellus A 51 2 1999 167 194 (Pubitemid 29335120)
44. R. Miller, M. Ghil, and F. Gauthiez Advanced data assimilation in strongly nonlinear dynamical systems J. Atmospheric Sci. 51 8 1994 1037 1056
45. S. Julier, J. Uhlmann, and H. Durrant-Whyte A new method for the nonlinear transformation of means and covariances in filters and estimators IEEE Trans. Automat. Control 45 3 2000 477 482
46. A. Hegyi, D. Girimonte, R. Babuška, B. De Schutter, A comparison of filter configurations for freeway traffic state estimation, in: Intelligent Transportation Systems Conference, 2006, ITSC 2006, Toronto, CA, 2006, pp. 1029-1034. (Pubitemid 351492306)
47. G. Evensen Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics J. Geophys. Res. 99 1994 10143 10162
48. G. Burgers, P. van Leeuwen, and G. Evensen Analysis scheme in the ensemble Kalman filter Mon. Weather Rev. 126 6 1998 1719 1724 (Pubitemid 128597660)
49. J. Anderson An ensemble adjustment Kalman filter for data assimilation Mon. Weather Rev. 129 12 2001 2884 2903 (Pubitemid 34004796)
50. C. Andrieu, N. De Freitas, A. Doucet, and M. Jordan An introduction to MCMC for machine learning J. Mach. Learn. 50 1 2003 5 43
51. N. Metropolis, and S. Ulam The Monte Carlo method J. Amer. Statist. Assoc. 44 247 1949 335 341
52. W. Hastings Monte Carlo sampling methods using Markov chains and their applications Biometrika 57 1 1970
53. R. Boel, and L. Mihaylova A compositional stochastic model for real time freeway traffic simulation Transp. Res. 40 4 2006 319 334 (Pubitemid 43033366)
54. C. Snyder, T. Bengtsson, P. Bickel, and J. Anderson Obstacles to high-dimensional particle filtering Mon. Weather Rev. 136 12 2008 4629 4640
55. R. Van Der Merwe, A. Doucet, N. De Freitas, and E. Wan The unscented particle filter Adv. Neural Inform. Process. Syst. 13 2001 584 590
56. A. Chorin, and X. Tu Implicit sampling for particle filters Proc. Nat. Acad. Sci. 106 41 2009 17249 17254
57. B. Greenshields A study of traffic capacity Proc. Highway Res. Board 14 1 1935 448 477
58. G. Newell A simplified theory of kinematic waves in highway traffic, Part II: queueing at freeway bottlenecks Transp. Res. 27 4 1993 289 303
59. T. Li Nonlinear dynamics of traffic jams Physica D 207 1-2 2005 41 51 (Pubitemid 40851775)
60. H. Greenberg An analysis of traffic flow Oper. Res. 7 1 1959 79 85
61. M. Van Aerde, Single regime speed-flow-density relationship for congested and uncongested highways, in: 74th Annual Meeting of the Transportation Research Board, Washington, DC, 1995.
62. G. Coclite, M. Garavello, and B. Piccoli Traffic flow on a road network SIAM J. Math. Anal. 36 6 2005 1862 1886 (Pubitemid 41640446)
63. H. Holden, and N. Risebro A mathematical model of traffic flow on a network of unidirectional roads SIAM J. Math. Anal. 26 4 1995 999 1017
64. J.-P. Lebacque, First-order macroscopic traffic flow models: Intersection modeling, network modeling, in: Proceedings of the 16th International Symposium on Transportation and Traffic Theory, Flow, Dynamics and Human Interaction, College Park, MD, 2005.
65. M. Garavello, and B. Piccoli Traffic Flow on Networks American Institute of Mathematical Sciences 2006 Springfield, MO
66. J. Glimm Solutions in the large for nonlinear hyperbolic systems of equations Commun. Pure Appl. Math. 18 1965 697 715
67. R. Leveque Finite Volume Methods for Hyperbolic Problems 2002 Cambridge University Press Cambridge, UK
68. A. Bressan Hyperbolic Systems of Conservation Laws: The One-dimensional Cauchy Problem 2000 Oxford University Press Oxford, UK
69. C. Claudel, and A. Bayen Lax-hopf based incorporation of internal boundary conditions into hamilton-jacobi equation. part i: Theory IEEE Trans. Automat. Control 55 5 2010 1142 1157
70. C. Claudel, and A. Bayen Lax-hopf based incorporation of internal boundary conditions into hamilton-jacobi equation. part ii: Computational methods IEEE Trans. Automat. Control 55 5 2010 1158 1174
71. P.E. Mazare, A. Dehwah, C.G. Claudel, and A.M. Bayen Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model Transp. Res. Part B 45 10 2011 1727 1748
72. S. Wong, and G. Wong An analytical shock-fitting algorithm for LWR kinematic wave model embedded with linear speed-density relationship Transp. Res. 36 8 2002 683 706 (Pubitemid 34724890)
73. J.-P. Lebacque, The Godunov scheme and what it means for first order macroscopic traffic flow models, in: Proceedings of the 13th International Symposium on Transportation and Traffic Theory, Lyon, France, 1996, pp. 647-677.
74. H. Payne Models of freeway traffic and control Math. Models Public Syst. 1 1 1971 51 61
75. G. Whitham Linear and Nonlinear Waves 1974 John Wiley and Sons New York, NY
76. A. Aw, and M. Rascle Resurrection of second order models of traffic flow SIAM J. Appl. Math. 60 3 2000 916 938
77. M. Zhang A non-equilibrium traffic model devoid of gas-like behavior Transp. Res. 36 3 2002 275 290
78. S. Blandin, D. Work, P. Goatin, B. Piccoli, and A. Bayen A general phase transition model for vehicular traffic SIAM J. Appl. Math. 71 1 2011 107 121 10.1137/090754467
79. R. Colombo On a 2 × 2 hyperbolic traffic flow model Math. Comput. Model. 35 5-6 2002 683 688
80. D. Helbing Improved fluid-dynamic model for vehicular traffic Phys. Rev. E 51 4 1995 3164 3169
81. H. Zhang Structural properties of solutions arising from a nonequilibrium traffic flow theory Transp. Res. 34 7 2000 583 603 (Pubitemid 30491730)
82. C. Huang, Y. Fallah, R. Sengupta, and H. Krishnan Adaptive intervehicle communication control for cooperative safety systems IEEE Netw. 24 1 2010 6 13
83. X. Sun, L. Muñoz, R. Horowitz, Highway traffic state estimation using improved mixture Kalman filters for effective ramp metering control, in: Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, 2003, pp. 6333-6338.
84. M. Bocquet, C. Pires, and L. Wu Beyond Gaussian statistical modeling in geophysical data assimilation Mon. Weather Rev. 138 2010 2997 3023
85. J. Chandrasekar, A. Ridley, D. Bernstein, A comparison of the extended and unscented Kalman filters for discrete-time systems with nondifferentiable dynamics, in: American Control Conference, ACC, 2007, pp. 4431-4436.
86. M. Cunha, and F. Dorini Statistical moments of the solution of the random Burgers-Riemann problem Math. Comput. Simulation 79 5 2009 1440 1451
87. J. Huttunen, and J. Kaipio Approximation errors in nonstationary inverse problems Inverse Probl. Imaging 1 1 2007 77 93
88. J. Huttunen, and J. Kaipio Approximation error analysis in nonlinear state estimation with an application to state-space identification Inverse Problems 23 2007 2141 2157 (Pubitemid 351453862)
89. O.-P. Tossavainen, J. Percelay, M. Stacey, J. Kaipio, and A. Bayen State estimation and modeling error approach for 2D shallow water equations and Lagrangian measurements Water Resources Research 47 10 2011 W10510