Fast and Accurate Collision Probability Estimation for Autonomous Vehicles using Adaptive Sigma-Point Sampling

2025-07-08

AI Summary

This paper addresses the problem of estimating collision probability under trajectory uncertainty of dynamic objects in autonomous driving. We propose an adaptive sigma-point sampling method that explicitly models temporal dependencies—unlike conventional approaches that assume independence across time steps. Our method dynamically adjusts the sigma-point distribution to align with the time-evolving trajectory covariance and integrates it with efficient probabilistic integration for rapid, accurate collision probability estimation. The key contribution is the first application of adaptive sigma-point sampling to trajectory uncertainty modeling, which effectively mitigates overestimation of collision probability caused by the i.i.d. assumption. Evaluated on 400 real-world autonomous driving logs, our method achieves a median absolute error of only 3.5% and a median runtime of 0.21 ms, demonstrating both high accuracy and real-time capability.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Security and Privacy: Large-scale security measurements

Abstract

A novel algorithm is presented for the estimation of collision probabilities between dynamic objects with uncertain trajectories, where the trajectories are given as a sequence of poses with Gaussian distributions. We propose an adaptive sigma-point sampling scheme, which ultimately produces a fast, simple algorithm capable of estimating the collision probability with a median error of 3.5%, and a median runtime of 0.21ms, when measured on an Intel Xeon Gold 6226R Processor. Importantly, the algorithm explicitly accounts for the collision probability's temporal dependence, which is often neglected in prior work and otherwise leads to an overestimation of the collision probability. Finally, the method is tested on a diverse set of relevant real-world scenarios, consisting of 400 6-second snippets of autonomous vehicle logs, where the accuracy and latency is rigorously evaluated.

Problem

• Estimates collision probability for uncertain vehicle trajectories
• Develops fast algorithm with adaptive sigma-point sampling
• Addresses temporal dependence to avoid probability overestimation

Innovation

• Adaptive sigma-point sampling for collision estimation
• Accounts for temporal dependence in collision probability
• Fast median runtime of 0.21ms with 3.5% error