Rethinking Gaussian Trajectory Predictors: Calibrated Uncertainty for Safe Planning

2026-03-11

AI Summary

This work addresses the unreliable confidence estimates produced by Gaussian trajectory predictors, which often lead uncertainty-aware planners to exhibit either unsafe or overly conservative behaviors. To mitigate this issue, the paper introduces a novel calibration loss function that, for the first time, integrates Gaussian prediction uncertainty calibration with chi-squared distribution theory. The method constructs an empirical confidence distribution via kernel density estimation and enforces its alignment with the theoretical chi-squared distribution, while preserving mean squared error to maintain accuracy in predicted trajectory means. Evaluated on real-world trajectory datasets, the approach significantly enhances the reliability of confidence estimates across multiple state-of-the-art Gaussian predictors. When integrated into model predictive control (MPC), it enables safer and more efficient collision-free navigation.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationPlanning, Routing, and Scheduling: Planning under UncertaintyIntelligent Robots: State Estimation

Application Category

Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAISearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Accurate trajectory prediction is critical for safe autonomous navigation in crowded environments. While many trajectory predictors output Gaussian distributions to represent the multi-modal distribution over future pedestrian positions, the reliability of their confidence levels often remains unaddressed. This limitation can lead to unsafe or overly conservative motion planning when the predictor is integrated with an uncertainty-aware planner. Existing Gaussian trajectory predictors primarily rely on the Negative Log-Likelihood loss, which is prone to predict over- or under-confident distributions, and may compromise downstream planner safety. This paper introduces a novel loss function for calibrating prediction uncertainty which leverages Kernel Density Estimation to estimate the empirical distribution of confidence levels. The proposed formulation enforces consistency with the properties of a Gaussian assumption by explicitly matching the estimated empirical distribution to the Chi-squared distribution. To ensure accurate mean prediction, a Mean Squared Error term is also incorporated in the final loss formulation. Experimental results on real-world trajectory datasets show that our method significantly improves the reliability of confidence levels predicted by different State-Of-The-Art Gaussian trajectory predictors. We also demonstrate the importance of providing planners with reliable probabilistic insights (i.e. calibrated confidence levels) for collision-free navigation in complex scenarios. For this purpose, we integrate Gaussian trajectory predictors trained with our loss function with an uncertainty-aware Model Predictive Control on scenarios extracted from real-world datasets, achieving improved planning performance through calibrated confidence levels.

Problem

• trajectory prediction
• uncertainty calibration
• Gaussian predictors
• autonomous navigation
• confidence reliability

Innovation

• Uncertainty Calibration
• Gaussian Trajectory Prediction
• Kernel Density Estimation
• Chi-squared Distribution
• Model Predictive Control