Efficient Traffic State Estimation and Prediction Based on the Ensemble Kalman Filter with a Fast Implementation and Localized Deterministic Scheme

Traffic state estimation and forecasting are central components in dynamic traffic management and information applications. This paper proposes a traffic state estimation approach based on an improved formulation of the traditional Ensemble Kalman filter (EnKF), including a fast implementation and a localized deterministic scheme. A reformulation of the EnKF equations leads to efficient computation. The deterministic scheme implies that we use the same observations for each of the ensembles instead of randomized observations. The use of a deterministic algorithm can reduce the impact of coincidental sampling and associated sampling errors. Localization is in contrast with a global method. In the global method, both the evolution of system states and the incorporation of observations are considered as an entity (within a global matrix). Here, the inclusion of localization has several potential advantages for large-scale applications: blocking spurious correlations, decreasing computation time due to smaller matrix inversions, increasing the accuracy by increasing the effective ensemble size. The proposed implementation of the EnKF for traffic state estimation and prediction is tested and validated in a realistic Dutch freeway network. The experiment studies deliver promising results for large-scale practical applications.

[1]  G. Evensen,et al.  Analysis Scheme in the Ensemble Kalman Filter , 1998 .

[2]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

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

[4]  William W. Hager,et al.  Updating the Inverse of a Matrix , 1989, SIAM Rev..

[5]  A. Bayen,et al.  A traffic model for velocity data assimilation , 2010 .

[6]  Peter R. Oke,et al.  A deterministic formulation of the ensemble Kalman filter : an alternative to ensemble square root filters , 2008 .

[7]  Alexandre M. Bayen,et al.  An ensemble Kalman filtering approach to highway traffic estimation using GPS enabled mobile devices , 2008, 2008 47th IEEE Conference on Decision and Control.

[8]  Henk J. van Zuylen,et al.  Localized Extended Kalman Filter for Scalable Real-Time Traffic State Estimation , 2012, IEEE Transactions on Intelligent Transportation Systems.

[9]  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.

[10]  Pavel Sakov,et al.  Relation between two common localisation methods for the EnKF , 2011 .

[11]  S. A. Smulders.  Control of Freeway Traffic Flow , 1988 .

[12]  Jeffrey P. Walker,et al.  Extended versus Ensemble Kalman Filtering for Land Data Assimilation , 2002 .

[13]  J. Whitaker,et al.  Ensemble Data Assimilation without Perturbed Observations , 2002 .

[14]  Serge P. Hoogendoorn,et al.  Real-Time Lagrangian Traffic State Estimator for Freeways , 2012, IEEE Transactions on Intelligent Transportation Systems.

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

[16]  J. Mandel.  A Brief Tutorial on the Ensemble Kalman Filter , 2009, 0901.3725.

[17]  Jan Mandel,et al.  Efficient Implementation of the Ensemble Kalman Filter Efficient Implementation of the Ensemble Kalman Filter , 2022 .

[18]  Slobodan Vucetic,et al.  Traffic State Estimation from Aggregated Measurements with Signal Reconstruction Techniques , 2012 .

[19]  D. Stensrud,et al.  The Ensemble Kalman Filter for Combined State and Parameter Estimation , 2009 .

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