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

Mohammad Khoshkdahan; Pavel Laskov; Alexey Vinel

cs.LGSep 13, 2026

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

Authors: Mohammad Khoshkdahan, Pavel Laskov, Alexey Vinel

Organizations: Karlsruhe Institute of Technology (KIT), Germany · University of Liechtenstein, Vaduz, Liechtenstein · Halmstad University, Sweden

Abstract

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.

Figures & tables

Fig. 1: Overview of the experimental configuration. The figure shows the roadside traffic light unit, vehicle-side sensing and communication system, and the wireless data exchange architecture. The top panel illustrates a representative stopping run with longitudinal acceleration and speed profiles versus distance to the traffic light.

Fig. 2: Summary of experiment-setting and speed-tracking characteristics across instructed-speed conditions. (a) Yellow-onset distance-threshold selection $D_{\mathrm{thr}}$ versus instructed speed $v_{\mathrm{inst}}$ , shown with mean $\pm$ SD. (b) Actual speed at yellow onset $v_{onset}$ for each $v_{\mathrm{inst}}$ , with instructed-speed references and compact tracking statistics (mean speed and speed-error SD). (c) Age-binned mean underspeed magnitude $(\Delta v=v_{\mathrm{inst}}-v_{onset})$ versus $v_{\mathrm{inst}}$ , shown in km/h (raw values, darker blue indicates larger underspeed).

Fig. 3: Dataset statistics summary for TTI and required deceleration

a_{\mathrm{req}}

, including demographic coverage across the observed range.

Fig. 4: Distance–speed stop/go decision surface at yellow onset. The background colormap shows the posterior mean

P(\mathrm{go})

from the Bayesian hierarchical logistic model; the thick contour denotes the decision boundary

P(\mathrm{go})=0.5

, and the hatched band marks the hesitation region

0.4\leq P(\mathrm{go})\leq 0.6

. Overlaid sample points are observed runs (green: go, red: stop), with marker size proportional to normalized driver age. Smooth iso-

a_{\mathrm{req}}

lines are superimposed (light-to-dark purple for low-to-high required deceleration).

	$D_{\rm thr}$	$v_{\rm onset}$	$a_{\rm req}$	TTI	Gender	Age
AME [pp]	$-7.5$	$-4.3$	$\mathbf{+33.7}$	$+0.9$	$+7.7$	$0.0$
$\mathcal{C}_{k}$ [%]	$14.1$	$9.4$	$\mathbf{50.8}$	$10.2$	$12.5$	$3.0$

TABLE I: AME summary for stop–go predictors; AME is in percentage points and

\mathcal{C}_{k}

is relative contribution.

Fig. 5: Physiological and comfort responses in stop-valid runs. (a) Comfort rating versus peak braking magnitude

|a_{\min}|

, with bin-wise means and raw-run overlays. (b) Rating-composition matrix over

|a_{\min}|

bins (cell text: within-bin percentage), with age-group bars showing mean comfort

\pm 1

SD; row labels report disagreement index

A=\sum_{k=1}^{5}p_{k}^{2}

, where

p_{k}

is the proportion in class

R_{k}

(lower

A

indicates higher disagreement). (c) Within-participant relation between

\Delta HR=HR_{\max}-HR_{\min}

and

|a_{\min}|

: thin lines are participant-wise robust trends, shaded bands show ensemble spread (

\pm 0.5

SD and

\pm 1

SD), the thick line is the ensemble mean trend, and dashed vertical lines mark rating-specific mean

|a_{\min}|

(R5 to R1).

Fig. 6: Two-stage decision-conditioned autoregressive trajectory generator with deterministic constraint pipeline and discrete vehicle dynamics feedback.

Method	$\varepsilon_{a(\cdot)}$	$\varepsilon_{a(\cdot)}$	$\varepsilon_{d(\cdot)}$	$\varepsilon_{v(\cdot)}$	$\rho_{\mathrm{stop}}^{\mathrm{band}}$
	MAE	RMSE	MAE	MAE	success
$a(t)=-a_{\mathrm{req}}\,[1-y]$	0.865	1.170	1.404	0.854	100.0
Mixture of primitives	0.856	1.331	1.470	1.781	90.0
Neural ODE	1.058	1.686	1.447	1.715	75.5
DCAR Transformer w/o physics	0.559	1.032	0.666	0.426	98.2
DCAR Transformer ( ours )	0.499	0.850	0.628	0.373	95.5

TABLE II: Trajectory-model comparison on the stratified split. Lower is better for

\varepsilon

-metrics; higher is better for

\rho_{\mathrm{stop}}^{\mathrm{band}}

(%).

$V_{\mathrm{onset}}$	$D_{\mathrm{thr}}$	TTI	$a_{\mathrm{req}}$	Age	Gender	Random (stratified) split					Participant-disjoint split
$V_{\mathrm{onset}}$	$D_{\mathrm{thr}}$	TTI	$a_{\mathrm{req}}$	Age	Gender	$\eta_{\mathrm{acc}}$	AUC	F1	Prec.	$\eta_{\mathrm{BA}}$	$\eta_{\mathrm{acc}}$	AUC	F1	Prec.	$\eta_{\mathrm{BA}}$
✓	$\times$	$\times$	$\times$	$\times$	$\times$	59.9	69.4	54.0	41.1	65.3	60.4	64.7	44.9	34.8	61.3
$\times$	✓	$\times$	$\times$	$\times$	$\times$	79.0	84.8	69.7	61.3	79.5	79.2	89.2	69.3	55.6	83.4
$\times$	$\times$	✓	$\times$	$\times$	$\times$	91.1	95.8	86.5	78.9	92.4	83.2	97.8	75.2	60.3	88.7
$\times$	$\times$	$\times$	✓	$\times$	$\times$	84.1	93.0	77.5	67.2	86.2	83.9	95.2	75.0	62.1	87.5
✓	✓	$\times$	$\times$	$\times$	$\times$	89.8	96.2	84.3	78.2	90.3	84.6	98.2	76.8	62.3	89.6

TABLE III: Stage 1 stop/go ablation (by onset features) under random (stratified run-level) and participant-disjoint splits. All metric entries are percentages (%), where

\eta_{\mathrm{acc}}

and

\eta_{\mathrm{BA}}

denote accuracy and balanced accuracy, respectively. Bold values denote the highest values in each metric column.

Input features

Validation metrics

V_{t}

D_{t}

TTI

a_{req}

Age

\hat{y}

p_{go}

\varepsilon_{a(\cdot)}

\varepsilon_{v(\cdot)}

\varepsilon_{d(\cdot)}

\varepsilon_{d_{f}}

\varepsilon_{v_{f}}

\rho_{\mathrm{stop-band}}

\checkmark

\checkmark

\times

\times

\times

\times

\times

1.15

0.80

1.15

1.54

1.53

94.55

\checkmark

\checkmark

\times

\checkmark

\times

\times

\times

1.33

0.89

1.23

1.44

1.65

96.36

\times

\times

\checkmark

\checkmark

\checkmark

\times

\times

1.34

1.01

1.33

1.70

1.63

100.00

\checkmark

\checkmark

\checkmark

\checkmark

\times

\times

\times

0.96

0.91

2.42

3.13

1.70

69.09

\times

\times

\checkmark

\checkmark

\times

\checkmark

\times

0.51

0.41

0.76

0.98

0.45

99.09

TABLE IV: Stage 2 input-modality ablation on the stratified split. All

\varepsilon

-metrics are MAE values in corresponding physical units. Lower is better for

\varepsilon

-metrics and higher is better for

\rho_{\mathrm{stop-band}}

. Bold values denote the best values columns.

Fig. 7: Twelve trajectory estimation examples (rows 1–2 stop and row 3 go). Each panel shows predicted and measured acceleration and distance trajectories in physical time with panel-level TTI,

v_{onset}

a_{\mathrm{req}}

, acceleration MAE, and outcome annotations

d_{f}

for stop and

v_{f}

for go.

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