Dr. Xuesong Zhou & Jeffrey Taylor, Univ. of Utah

1. New Approaches for Traffic State Estimation:Calibrating Heterogeneous Car-Following Behavior using Vehicle Trajectory Data Dr. Xuesong Zhou & Jeffrey Taylor, Univ. of Utah

2. Outline • Background on Dynamic Time Warping (DTW) • Application to Newell’s Simplified CFM • Calibration Results • Important Considerations

3. Motivations: I • Real-time Traffic Management Loop Detector Automatic Vehicle Identification Automatic Vehicle Location Video Image Processing

4. Motivation 2: Self-driving Cars as Mobile Sensor • Controlled , coordinated movements • Proactive approach • Applications • Automated cars • Unmanned aerial vehicles

5. Motivation 3: Detecting Distracted/Risky Drivers

6. Underlying Theory:Cross-resolution Traffic Modeling Space Reaction distance/spacingδ Reaction timelag τ W = δ/ τ Time

7. How to Estimate Driver-specific Car-following Parameters? Input and output

8. Intro to Dynamic Time Warping (DTW) • Matches points by measure of similarity

9. Reference: Eamonn Keogh Computer Science & Engineering DepartmentUniversity of California - Riverside Euclidean Vs Dynamic Time Warping Euclidean Distance Sequences are aligned “one to one”. “Warped” Time Axis Nonlinear alignments are possible.

10. Construct Cost Matrix for Traffic Trajectory Matching

11. Cumulative Cost Matrix • Dynamic programming • Calculate the least cost for matching a pair of points • Warp path • Least cost matching points from end to beginning Singularity

12. Application to Newell’s Model • Follower separated by leader by reaction time and critical jam spacing • Algorithm finds optimal τn (time lag) for best velocity match • Calculate dn for all time steps along the trajectory

13. Calibrated Parameters: Car 1737

14. NGSIM Data: I-80 Lane 4

15. NGSIM Data: I-80 Lane 4: Reaction Time Distribution Mean = 1.48 seconds

16. NGSIM Data: I-80 Lane 4Critical Spacing Distribution Mean = 8.06 meters

17. NGSIM Data: I-80 Lane 4Wave Speed Distribution Mean = 20.55 km/h

18. Current Issues in DTW Application • Singularities • Locations with more than one match solution • Data reduction algorithms • Parameter estimates differ with available methods

19. Singularities

20. Singularity Implications • 1st Interpretation: Many responses to 1 stimulus • 2nd Interpretation: 1 response to many stimuli • 3rd Interpretation: Algorithm drawback • Increases uncertainty in parameter estimates • LCSS force 1-to-1 match LCSS : Longest Common Subsequence

21. Singularities Without Prior Information With Prior Information

22. Data Reduction Algorithms • Piecewise Linear Approximation/Regression • Somewhat subjective in application, needs dynamic parameters • Difficulties creating new points  application with Newell’s model

23. Potential Applications • Analyze intradriver heterogeneity • Markov Chain Monte Carlo method for reaction time/critical jam spacing • Analyze relationships between parameters

24. Markov Chain Transition Matrix Hypothetical case:

25. Trajectory Prediction (MCMC) ~ 5% MAPE