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

2. Outline 2 Background on Dynamic Time Warping (DTW) Application to Newells Simplified CFM Calibration Results Important Considerations

3. Motivations: I 3 Real-time Traffic Management Automatic Vehicle IdentificationAutomatic Vehicle LocationLoop Detector Video Image Processing

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

5. Motivation 3: Detecting Distracted/Risky Drivers 5

6. Underlying Theory: Cross-resolution Traffic Modeling 6 Reaction distance/spacing δ Reaction time lag τ W = δ / τ Time Space

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

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

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

10. Construct Cost Matrix for Traffic Trajectory Matching 10

11. Cumulative Cost Matrix 11 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 Newells Model 12 Follower separated by leader by reaction time and critical jam spacing Algorithm finds optimal τ n (time lag) for best velocity match Calculate d n for all time steps along the trajectory

13. Calibrated Parameters: Car 1737 Reaction Time Lag (sec) Critical Spacing (m) Backward Wave Speed (km/h) Avg2.6213.3918.46 St. Dev0.412.081.05

14. NGSIM Data: I-80 Lane 4 14

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

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

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

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

19. Singularities 19

20. Singularity Implications 20 1 st Interpretation: Many responses to 1 stimulus 2 nd Interpretation: 1 response to many stimuli 3 rd 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 21

22. Data Reduction Algorithms 22 Piecewise Linear Approximation/Regression – Somewhat subjective in application, needs dynamic parameters – Difficulties creating new points application with Newells model

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

24. Markov Chain Transition Matrix 24 Reaction Time+++000--- Acceleration+0-+0-+0- + 0.10.0500.0010.0480.0360.1990.1020.0580.043 0.00.9500.9490.9520.9180.8010.8980.9420.8580.751 - 0.10.0010.0490.0000.0460.000 0.0990.207 Sum1.000 Hypothetical case:

25. Trajectory Prediction (MCMC) 25 ~ 5% MAPE