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

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

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

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

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Motivation 3: Detecting Distracted/Risky Drivers 5

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

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

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

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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

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Construct Cost Matrix for Traffic Trajectory Matching 10

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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

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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

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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

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NGSIM Data: I-80 Lane 4 14

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

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

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

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

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Singularities 19

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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

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Singularities Without Prior Information With Prior Information 21

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

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

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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:

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Trajectory Prediction (MCMC) 25 ~ 5% MAPE

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