Uncertainty-Aware Optimization for Physics-Aware Highway Trajectory Prediction

Aanchal Rajesh Chugh; Sebastian Dorn

cs.LGOct 8, 2026

Uncertainty-Aware Optimization for Physics-Aware Highway Trajectory Prediction

Authors: Aanchal Rajesh Chugh, Sebastian Dorn

Organizations: Technische Hochschule Augsburg TTZ Landsberg am Lech

Abstract

Accurate trajectory forecasting and well-defined predictive uncertainty are crucial for reliable, safety-critical applications such as autonomous driving. Most trajectory prediction approaches provide point estimates only, while uncertainty-aware approaches typically quantify uncertainty only in the trajectory space. In physics-aware approaches, uncertainty in the predicted motion variables should be explicitly modeled and propagated through the vehicle dynamics. Otherwise, the resulting trajectory-space uncertainty may not fully reflect the variability introduced by the underlying motion prediction. Therefore, in this work, uncertainty-aware extensions of X-TRACK (X-TRACK-DE and X-TRACK-MCD), a physics-aware trajectory prediction framework, are proposed. The proposed framework predicts future vehicle motion variables and models both aleatoric and epistemic uncertainties by propagating motion space uncertainty to trajectory space. Additionally, conformal prediction is applied to the trajectory space predictive covariance to construct uncertainty regions targeting a desired marginal coverage level. Evaluation on the highD dataset shows that X-TRACK-DE improves trajectory prediction accuracy over the deterministic baseline, while both uncertainty-aware variants provide predictive uncertainty that can be conformally calibrated to the desired marginal coverage level.

Figures & tables

Figure 1: Overview of the uncertainty-aware X-TRACK framework. Aleatoric uncertainty is estimated by sampling from the predicted motion distributions, and epistemic uncertainty is obtained using MC Dropout or Deep Ensembles. The sampled vehicle motion variables are propagated through the physics-based kinematic layer to obtain uncertainty in trajectory space. To obtain calibrated trajectory uncertainty regions, conformal prediction is applied.

Architecture	ADE $\downarrow$	FDE $\downarrow$	minADE $\downarrow$	minFDE $\downarrow$
X-TRACK ( Chugh et al., 2025 )	0.56	1.76	-	-
X-TRACK-MCD (Ours)	0.54	1.79	0.20	0.41
X-TRACK-DE (Ours)	0.44	1.49	0.15	0.33
MHA-LSTM ( Messaoud et al., 2021 )	1.97	4.72	-	-
iNATran ( Chen et al., 2022 )	1.84	3.95	-	-
GFTNNv2 ( Neumeier et al., 2023 )	0.92	2.20	-	-

Table 1: ADE and FDE (in meters) evaluated at a

5s

prediction horizon for the evaluated models

Architecture	1s	2s	3s	4s	5s
X-TRACK ( Chugh et al., 2025 )	0.10	0.31	0.71	1.31	2.16
X-TRACK-MCD (Ours)	0.06	0.22	0.66	1.34	2.23
X-TRACK-DE (Ours)	0.04	0.16	0.51	1.09	1.87
MHA-LSTM ( Messaoud et al., 2021 )	0.71	1.62	2.85	4.31	6.06
iNATran ( Chen et al., 2022 )	0.88	1.62	2.35	3.58	4.95
GFTNNv2 ( Neumeier et al., 2023 )	0.47	0.61	1.05	1.75	2.69

Table 2: Comparison of the proposed variants with the baseline models evaluated in the considered highway trajectory prediction setting in terms of RMSE at different prediction horizons.

Metric	X-TRACK MCD	X-TRACK DE	cVMDx
NLL $\downarrow$	0.47	0.51	11.32
ECE $\downarrow$	0.17	0.12	0.10
Pearson Correlation ( $\rho$ ) $\uparrow$	0.34	0.33	0.05
Mean Predictive Uncertainty ( $\mathrm{m}^{2}$ )	1.32	0.75	4.04
Miss Rate (MR) @ $2\,\mathrm{m}$ $\downarrow$	0.02	0.01	0.31
CP Coverage@ $95\%$	95.72%	95.39%	-

Table 3: Uncertainty quantification and calibration performance of the evaluated uncertainty-aware trajectory prediction approaches.

Figure 2: Qualitative comparison of ground truth with deterministic X-TRACK and predictive means of X-TRACK-MCD and X-TRACK-DE .

Figure 3: Decomposition of uncertainty into individual components for both variants.

Figure 4: Comparing empirical coverage and nominal confidence for raw predictive distributions of X-TRACK-MCD and X-TRACK-DE .

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Model	Architectural Changes
Baseline	Default architecture
Wider Encoder	Encoder: $96$ , Decoder: $160$ , Dynamic Embedding: $96$
Wider Embedding	Input Embedding: $48$ , Dynamic Embedding: $80$
More Heads	GAT Heads: $6$
Deeper Decoder	Number of Decoder LSTM Layers: $3$ , Dropout: $0.25$

Appendix

Table 4: Architectural modification of X-TRACK for the Deep Ensemble members.

Architecture	ADE $\downarrow$	FDE $\downarrow$	Pre-CP C@95% $\uparrow$	ECE $\downarrow$
Homogeneous Ensemble	0.65	1.85	25.2%	0.25
Heterogeneous Ensemble	0.58	1.72	42.4%	0.08

Appendix

Table 5: Comparison of homogeneous and heterogeneous ensembles to assess the impact of architectural diversity.

	X-TRACK-MCD		X-TRACK-DE
Metric	Pre-CP	Post-CP	Pre-CP	Post-CP
Coverage@95% $\uparrow$	67.47%	95.72%	62.01%	95.39%
MPIW $\downarrow$	2.24	2.61	1.57	2.11
ECE $\downarrow$	0.17	0.11	0.12	0.11

Appendix

Table 6: Effect of conformal prediction on the uncertainty-aware variants.

Figure 5: Comparison of total predictive uncertainty for X-TRACK-MCD and X-TRACK-DE over different prediction horizons.

Figure 6: Total predictive uncertainty in trajectory space over the prediction horizon for X-TRACK-MCD and X-TRACK-DE. The same mean uncertainty is shown using (a) linear, (b) semi-logarithmic, and (c) log-log scales.

Figure 7: Comparison of predictive multiple trajectories obtained by X-TRACK-DE and X-TRACK-MCD.

Figure 8: Qualitative comparison of ground-truth trajectories with deterministic X-TRACK and the predictive means of its uncertainty-aware variants.

Figure 9: Decomposition of trajectory space predictive uncertainty (different scales) into aleatoric, epistemic, and total components for X-TRACK-MCD and X-TRACK-DE.

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Most trajectory forecasting models are trained on clean annotated histories, and are often evaluated under the same idealized assumption, although practical deployments rely on trajectories produced by imperfect multi-object trackers. The real-world observations exhibit localization jitter, missed or unstable detections, and data-association ambiguity, which are usually either ignored or removed through denoising. This paper instead treats tracking-derived reliability cues as an informative signal to be propagated to the predictor. We propose a plug-in uncertainty-aware formulation in which each observed state is encoded as an uncertain state representation, modeled by a Gaussian distribution whose covariance combines detection-level localization uncertainty and association-level ambiguity through the law of total variance. Existing backbones are adapted with minimal architectural changes: input trajectories are represented as Gaussian observations, and predicted trajectories are produced as Gaussian forecasts rather than deterministic coordinates. To train predictors that remain robust under structured observation noise, we combine temporally correlated Ornstein-Uhlenbeck perturbations with response-based knowledge distillation from a teacher trained on clean trajectories. Experiments on Oxford Town Centre and VIRAT using real tracker outputs, together with a complementary ETH/UCY pseudo-detection protocol, show that the proposed formulation improves displacement accuracy and the reliability-sharpness trade-off of probabilistic forecasts.

Abstract

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