Localized Extended Kalman Filter for Scalable Real-Time Traffic State Estimation

Current or historic traffic states are essential input to advanced traveler information, dynamic traffic management, and model predictive control systems. As traffic states are usually not perfectly measured and are everywhere, they need to be estimated from local and noisy sensor data. One of the most widely applied estimation methods is the Lighthill-Whitham and Richards (LWR) model with an extended Kalman filter (EKF). A large disadvantage of the EKF is that it is too slow to perform in real time on large networks. To overcome this problem, the novel localized EKF (L-EKF) is proposed in this paper. The logic of the traffic network is used to correct only the state in the vicinity of a detector. The L-EKF does not use all information available to correct the state of the network; the resulting accuracy is equal, however, if the radius of the local filters is sufficiently large. In two experiments, it is shown that the L-EKF is much faster than the traditional Global EKF (G-EKF), that it scales much better with the network size, and that it leads to estimates with nearly the same accuracy as the G-EKF and when the spacing between detectors is varied somewhere between 0.7 and 5.1 km. Compared with the G-EKF, the L-EKF is a highly scalable solution to the state estimation problem.

[1]  Markos Papageorgiou,et al.  Real-time freeway traffic state estimation based on extended Kalman filter: a general approach , 2005 .

[2]  Bart De Schutter,et al.  Model predictive control for optimal coordination of ramp metering and variable speed limits , 2005 .

[3]  V. Strassen Gaussian elimination is not optimal , 1969 .

[4]  Helbing Gas-kinetic derivation of Navier-Stokes-like traffic equations. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  M. Rascle An improved macroscopic model of traffic flow: Derivation and links with the Lighthill-Whitham model , 2002 .

[6]  Ludovic Leclercq,et al.  The Lagrangian Coordinates and What it Means for First Order Traffic Flow Models , 2007 .

[7]  Serge P. Hoogendoorn,et al.  State-of-the-art of vehicular traffic flow modelling , 2001 .

[8]  D. Gingras,et al.  Comparison between the unscented Kalman filter and the extended Kalman filter for the position estimation module of an integrated navigation information system , 2004, IEEE Intelligent Vehicles Symposium, 2004.

[9]  P. I. Richards Shock Waves on the Highway , 1956 .

[10]  R. Courant,et al.  Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .

[11]  A. Jazwinski Stochastic Processes and Filtering Theory , 1970 .

[12]  Carlos F. Daganzo,et al.  THE CELL TRANSMISSION MODEL, PART II: NETWORK TRAFFIC , 1995 .

[13]  R. Horowitz,et al.  Mixture Kalman filter based highway congestion mode and vehicle density estimator and its application , 2004, Proceedings of the 2004 American Control Conference.

[14]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[15]  Markos Papageorgiou,et al.  Real-Time Freeway Traffic State Estimation Based on Extended Kalman Filter: A Case Study , 2007, Transp. Sci..

[16]  A. Hegyi,et al.  Parallelized particle filtering for freeway traffic state tracking , 2007, 2007 European Control Conference (ECC).

[17]  H. J. Van Zuylen,et al.  Online estimation of Kalman Filter parameters for traffic state estimation , 2010 .

[18]  Peter S. Maybeck,et al.  Stochastic Models, Estimation And Control , 2012 .

[19]  Bart De Schutter,et al.  A comparison of filter configurations for freeway traffic state estimation , 2006, 2006 IEEE Intelligent Transportation Systems Conference.

[20]  J. V. van Lint,et al.  Improving a Travel-Time Estimation Algorithm by Using Dual Loop Detectors , 2003 .

[21]  Dipankar Ghosh,et al.  Estimation of traffic variables using a linear model of traffic flow , 1978 .

[22]  Stef Smulders,et al.  Control of freeway traffic flow by variable speed signs , 1990 .

[23]  Harold J Payne,et al.  MODELS OF FREEWAY TRAFFIC AND CONTROL. , 1971 .

[24]  Dirk Helbing,et al.  Reconstructing the spatio-temporal traffic dynamics from stationary detector data , 2002 .

[25]  H. M. Zhang A NON-EQUILIBRIUM TRAFFIC MODEL DEVOID OF GAS-LIKE BEHAVIOR , 2002 .

[26]  L. H. Immers,et al.  An Extended Kalman Filter Application for Traffic State Estimation Using CTM with Implicit Mode Switching and Dynamic Parameters , 2007, 2007 IEEE Intelligent Transportation Systems Conference.

[27]  J. Lebacque THE GODUNOV SCHEME AND WHAT IT MEANS FOR FIRST ORDER TRAFFIC FLOW MODELS , 1996 .

[28]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.