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Driver Behavior Estimation at Signalized Intersections Using a Physics-Constrained Decision-Conditioned Autoregressive Transformer

Mohammad Khoshkdahan, Pavel Laskov, Alexey Vinel

arXiv:2609.16058v1cs.LGcs.AIcs.CYcs.SYeess.SY

TL;DR

At signalized intersections, drivers must choose whether to stop or proceed during the yellow phase, with abrupt braking and late crossing posing safety risks. The paper combines high-precision real-world measurements with a two-stage, physics-constrained Transformer to predict that choice and generate trajectories. The model reports low trajectory errors and estimates stopping comfort from a yellow-onset observation.

  • Problem

    At yellow onset, drivers must choose between stopping and proceeding under time pressure, where abrupt braking risks rear-end collisions and late crossing risks severe intersection crashes.

    Source: §I · p. 1

  • Method

    The paper combines real-world driver and vehicle measurements with a two-stage decision-conditioned autoregressive Transformer that predicts maneuver choice and generates the longitudinal trajectory under physics-based constraints.

    Source: §I · p. 1

  • Results

    The model achieves an acceleration MAE of 0.49 m/s2 and a distance-trajectory MAE of 0.62 m, and its braking profiles match ground-truth driver comfort levels in 84.5% of stop cases.

    Source: §VI · p. 7, §VIII · p. 8

  • Takeaways & Limitations

    The results indicate that maneuver intent and comfort-related braking behavior can be predicted early from onset-level kinematics, supporting predictive intersection safety systems and infrastructure-assisted driver support.

    Source: §VIII · p. 8

Abstract

from arXiv · show

Red-light violations and harsh braking at signalized intersections are major contributors to traffic accidents. This paper analyzes and predicts human driver decision-making and longitudinal trajectory behavior during traffic light signal transitions. We collected a diverse real-world dataset comprising 449 approach runs under varying speed and distance conditions. Vehicle motion was recorded using RTK-corrected GNSS with centimeter-level accuracy, and driver heart rate and multi-level comfort ratings were monitored. Spatial and temporal calibration ensured precise alignment between vehicle state and signal timing. Statistical analysis identifies required deceleration as the dominant single predictor of the stop-go decision, and heteroscedastic Gaussian modeling of peak deceleration reveals five empirical comfort ranges derived from human stopping behavior. Based on this insight, we propose a two-stage modeling framework. Stage 1 predicts the binary maneuver decision, and Stage 2 generates the longitudinal acceleration trajectory using a decision-conditioned autoregressive Transformer with physics constraints, including target-state conditioning and jerk limits. The proposed architecture outperforms baseline methods and achieves 0.49m/s^2 acceleration MAE and 0.62m distance MAE. It also estimates the future stopping-comfort level of the human driver from a single yellow-onset snapshot. Qualitative results demonstrate realistic human-like braking behavior. The dataset and source code are publicly available.

I. INTRODUCTION

At yellow onset, drivers must balance stopping smoothly against proceeding safely, and models need to capture both maneuver choice and trajectory execution. Prior work has treated these aspects largely separately; this paper combines high-precision real-world data with a physics-constrained, decision-conditioned trajectory model.

I. INTRODUCTION

  • Models of both stop–go choice and braking trajectories could support adaptive signal timing and V2I systems that anticipate unsafe maneuvers.The introduction links early speed adaptation to avoiding late harsh braking and premature deceleration, targeting safety and comfort together.Source: §I · p. 1
  • The paper introduces a real-world dataset combining centimeter-level vehicle motion, synchronized driver physiology, and stopping-comfort feedback, then proposes a two-stage Transformer that predicts maneuver choice and generates the full deceleration trajectory.The model uses a single yellow-onset snapshot and physics-based constraints on acceleration profiles.Source: §I · p. 1

II. RELATED WORK

  • Prior comfort findings report tolerated decelerations around −3.5 m/s2 and an acceptable −4 m/s2 limit for automated collision avoidance, but quantified multi-level comfort profiles for red-light decelerations remain unaddressed.These thresholds are cited from prior studies,.Source: §II · p. 2
  • Prior intersection studies modeled stopping probabilities, nonlinear decisions, or temporal evolution, but generally did not combine decision logic with physically consistent deceleration-trajectory generation.The review also notes that many earlier approaches used camera or roadside sensing and omitted detailed demographics.Source: §II · p. 2
  • Existing datasets and simulations leave gaps for this task: SIND lacks extended tracking, driver-specific features, and RTK-GNSS accuracy, while virtual subjects do not experience real deceleration forces.The paper identifies a need for intersection data combining high-precision motion, participant profiles, physiology, and multi-level stopping-comfort ratings.Source: §II · p. 2

III. EXPERIMENTAL SETUP

The experimental setup combines controlled yellow-onset trials with synchronized vehicle, signal, heart-rate, and comfort measurements. Spatial projection and latency-aware timing calibration align vehicle position with the signal transition.

A. Data Collection

  • Thirty licensed drivers completed repeated approach runs at instructed speeds, with voluntary stop/go decisions and forced-stop trials followed by five-point braking-stress ratings.Trials used a straight, traffic-free road and varied yellow-onset distances to sample the hesitation region as well as clearer decisions.Source: A. Data Collection · p. 2

B. Vehicle, Sensor, and Traffic Light Setup

  • The system recorded vehicle position, speed, acceleration, signal state, and continuous heart rate using RTK-corrected GNSS, a wearable sensor, and a remotely controlled roadside traffic light.RTK provided centimeter-level vehicle-position accuracy; data were logged at 10 Hz, and heart-rate recording continued after standstill.Source: A. Data Collection · p. 2, B. Vehicle, Sensor, and Traffic Light… · p. 3

C. Distance Calibration and Longitudinal Correction

  • Vehicle-to-light distance is projected onto the road axis, removing lateral-offset bias from direct geodetic distance.The signed distance is positive upstream, zero at the light reference, and negative after passing it.Source: C. Distance Calibration and… · p. 3
  • Figure 2 summarizes yellow-onset distance thresholds by instructed speed, actual yellow-onset speeds with instructed-speed references and tracking statistics, and age-binned mean underspeed, defined as instructed minus onset speed.Source: Figure 2 · p. 3
  • Latency-aware yellow-command timing reduced spatial onset error to below 30 cm, while further reduction was limited by unknown, time-varying GNSS-logger latency.The procedure repeatedly predicts time to the target onset distance from corrected distance and speed, accounting for measured fixed and ping-based communication latency.Source: C. Distance Calibration and… · p. 3

A. Run Distribution and Speed Tracking

The study covers a broad range of intersection approaches and examines how kinematic conditions relate to stop–go decisions. Required deceleration is the dominant single predictor, while the decision boundary also varies with distance.

A. Run Distribution and Speed Tracking

  • 449 runs include 392 normal decision runs; 40, 50, and 60 km/h each had 112 runs, versus 56 at 70 km/h.The remaining runs were dedicated to high-deceleration forced-stop evaluation.Source: A. Run Distribution and Speed Tracking · p. 3
  • 78.8% of drivers traveled below instructed speed, averaging −2.26 ± 2.83 km/h; age-related tracking differences were not statistically significant.Underspeed mostly increased with instructed speed.Source: A. Run Distribution and Speed Tracking · p. 4

B. Kinematic Variables

  • Kinematic coverage spans low-TTI, high-deceleration and high-TTI, moderate-deceleration cases, with both genders and all three age groups represented.TTI is time-to-intersection, and required deceleration is the constant deceleration needed to stop at the signal.Source: B. Kinematic Variables · p. 4

C. Determinants of the Stop–Go Decision

  • Required deceleration is the dominant stop–go predictor, and the decision boundary shifts with distance rather than following a fixed threshold.The hesitation band is concentrated around 2–4 m/s² and aligns with intermediate-to-high deceleration demand.Source: C. Determinants of the Stop–Go Decision · p. 4, Figure 4 · p. 4

D. Braking Magnitude, Comfort, and Physiological Response

Comfort ratings decline as braking demand rises, while the intermediate braking range shows the greatest disagreement among drivers. Heart-rate responses and comfort ratings also vary with age, and one reported ordering reversal is attributed to differing internal reference frames.

D. Braking Magnitude, Comfort, and Physiological Response

  • ρ = −0.675 (p = 2.76 × 10−45) across stop-valid runs and ρ = −0.806 (p = 4.00×10−14) in forced-stop runs, with comfort declining as |amin| rises.The forced-stop linear trend decreases by approximately 0.483 rating units per 1 m/s2.Source: D. Braking Magnitude, Comfort, and… · p. 5, Figure 5 · p. 5
  • Heteroscedastic Gaussian Bayes boundaries between R5|R4, R4|R3, R3|R2, and R2|R1 occur at 4.07, 5.15, 7.54, and 9.11 m/s2, respectively.Unequal class variances and imbalanced sample sizes motivate prior-weighted boundaries rather than midpoint thresholds.Source: D. Braking Magnitude, Comfort, and… · p. 5
  • Agreement is highest in [1.5,3.0) m/s2 (A = 0.745) and lowest in [4.5,6.0) m/s2 (A = 0.386), where perceptual dispersion is greatest.The intermediate range lacks a well-separated posterior crossing between adjacent rating densities, contributing to an outward-shifted Bayes boundary.Source: D. Braking Magnitude, Comfort, and… · p. 5
  • One reported ordering reversal is attributed more likely to differing internal reference frames than to sampling effects.Source: D. Braking Magnitude, Comfort, and… · p. 5
  • Heart-rate elevation rises by an overall mean of 1.173 bpm per 1 m/s2; age-stratified slopes decrease with age, while older drivers report higher comfort at comparable deceleration.Younger drivers generally give lower comfort ratings for the same braking magnitude, except in [6.0,7.5) m/s2.Source: D. Braking Magnitude, Comfort, and… · p. 5

A. Training Setup

The experiments use stratified train-validation splits, with an additional participant-disjoint evaluation. The two-stage model predicts a maneuver at signal onset, then conditions a trajectory rollout on that fixed decision.

A. Training Setup

  • The random stratified split uses 60% training and 40% validation, with additional evaluation under a participant-disjoint split.Stage 1 is trained for 200 epochs with Adam; Stage 2 is trained for 200 epochs with AdamW and gradient clipping.Source: A. Training Setup · p. 5

B. Two-Stage Trajectory Generator

  • A maneuver decision is predicted once at yellow onset and held fixed while a causal Transformer generates a physically constrained longitudinal acceleration trajectory in closed loop.Figure 6 depicts the two-stage generator and deterministic constraint pipeline.Source: B. Two-Stage Trajectory Generator · p. 6, Figure 6 · p. 6

1) Stage 1: Maneuver Decision Modeling:

  • The Stage 1 onset-level MLP maps speed, threshold distance, time to intersection, required deceleration, age, and gender to pgo and a thresholded binary decision.The predicted decision and pgo condition the full Stage 2 trajectory rollout.Source: 1) Stage 1: Maneuver Decision Modeling · p. 6

2) Stage 2: Autoregressive Trajectory Modeling:

Stage 2 predicts longitudinal acceleration autoregressively from vehicle-state and decision-related inputs, then applies deterministic constraints before integrating vehicle motion. Its objective combines trajectory fidelity, terminal feasibility, and smoothness.

2) Stage 2: Autoregressive Trajectory Modeling:

  • The Transformer predicts signed longitudinal acceleration stepwise from autoregressive tokens including vehicle state, required deceleration, time to intersection, prior acceleration, demographics, and the Stage 1 decision.For stopping cases, the target state is vtarget = 0 and dtarget = 0.5.Source: 2) Stage 2: Autoregressive Trajectory… · p. 6
  • A decision-aware actuator clamp prevents positive acceleration in stop trajectories while allowing bounded acceleration in go trajectories, and a hard jerk constraint limits acceleration-rate changes.Jmax = 15 m/s3 is set slightly above the maximum observed absolute jerk of 12.69 m/s3.Source: 2) Stage 2: Autoregressive Trajectory… · p. 6
  • After discrete-kinematics integration, a terminal freeze sets acceleration and velocity to zero upon entering the stopping deadband or reaching near-zero velocity.Stop-band success is defined as final position within [−0.5, 1.5] m relative to the stop line; training uses post-constraint trajectories.Source: 2) Stage 2: Autoregressive Trajectory… · p. 6
  • The training objective combines trajectory fidelity, terminal feasibility, and smoothness regularization to support accurate tracking and physically consistent terminal behavior.Source: 2) Stage 2: Autoregressive Trajectory… · p. 6

VI. RESULTS

The DCAR Transformer has the lowest reported trajectory errors among learned models and matches human stopping-comfort levels in most stop cases. The results also identify effective onset cues for stop/go prediction and show how Stage 2 errors change when inputs are ablated.

VI. RESULTS

  • The DCAR Transformer achieves the lowest acceleration and trajectory-tracking errors among learned models, while constant deceleration guarantees 100% stop-band success but has substantially larger tracking errors.The mixture-of-primitives improves on constant deceleration but remains clearly inferior to the DCAR Transformer.Source: §VI · p. 6, Table II · p. 7
  • The (Vonset,areq) configuration achieves 92.4% accuracy and the strongest F1 and precision in both splits among tested onset-feature combinations.Among single cues, areq and TTI are strongest; the full-input model has the highest random-split AUC and remains competitive under participant-disjoint evaluation.Source: Table III · p. 7, §VI · p. 7
  • 84.5% of stop cases have braking profiles whose predicted comfort level matches the ground-truth driver comfort level.The result indicates future stopping comfort can be anticipated from a single yellow-onset observation.Source: §VI · p. 7
  • Performance decreases under the participant-disjoint split compared with the random split, indicating lost benefit from implicit memorization of driver-specific decision boundaries.Participant ID is not an input in either setting.Source: §VI · p. 7
  • Ablating the Stage 1 decision increases acceleration error by up to 2.6×, while using all inputs except age minimizes primary tracking and terminal errors.Stop-band success peaks under two configurations, including the full model.Source: Table IV · p. 7, §VI · p. 7
  • Figure 7 presents twelve trajectory-estimation examples: the first two rows are stop cases and the third is go cases.Panels show predicted and measured acceleration and distance trajectories in physical time, with panel-level annotations.Source: Figure 7 · p. 7

VII. DISCUSSION AND OUTLOOK

The RTK-GNSS measurement setup provides higher positioning accuracy than camera-based collection and supports precise association of comfort ratings with stopping trajectories. The dataset’s German setting and driver sample constrain its scope, motivating cross-region data collection and passenger-side measurements.

VII. DISCUSSION AND OUTLOOK

  • RTK-GNSS provides substantially higher positioning accuracy than camera-based collection and enables precise correlation of acceleration-induced comfort with each stopping trajectory.The discussion identifies additional context such as following vehicles, pedestrians, lighting, and weather as possible dataset extensions.Source: §VII · pp. 7–8
  • The dataset was collected in Germany and primarily includes drivers with German licenses, so cross-region data are needed to evaluate generalization and behavioral variability.Driving habits, stopping strategies, and comfort perception may differ across countries and traffic cultures, particularly outside Europe.Source: §VII · p. 8
  • Passenger comfort and physiological response may differ from the driver’s because passengers do not control the vehicle, motivating passenger-side measurements.The paper identifies those measurements as a possible way to improve human-centered automated braking system design.Source: §VII · p. 8

VIII. CONCLUSION

The paper combines a position-triggered signal-transition setup and real-world driver data with a two-stage, decision-conditioned autoregressive Transformer. It reports low acceleration and distance-trajectory errors, and says onset-level kinematics can support estimates of future braking stress.

VIII. CONCLUSION

  • The experimental setup triggers traffic-light timing from RTK-corrected vehicle position and collects vehicle kinematics, braking-comfort ratings, and physiological responses from human drivers.The setup allows accurate and repeatable yellow-onset generation.Source: §VIII · p. 8
  • The model achieves an acceleration MAE of 0.49 m/s2 and a distance-trajectory MAE of 0.62 m while maintaining high stop-band success and accurate final stopping positions.It predicts stop/go decisions and generates the full longitudinal trajectory from a single yellow-onset observation.Source: §VIII · p. 8
  • Learned trajectories allow future braking stress to be estimated from onset-level kinematics alone and support predictive intersection safety systems and infrastructure-assisted driver support.The results indicate that both maneuver intent and comfort-related braking behavior can be predicted early.Source: §VIII · p. 8
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