INFO-F422 - Statistical foundations of machine learning - 202425

🗓️ Seminar MLG - April 25th 2025, 10AM
❓ Probability of Collision in Nonlinear Dynamics by Moment Propagation
👨‍⚕️ Dr. Théo Verhelst
📍 Campus de La Plaine - NO.800G (Rotule)

Abstract:
Estimating the probability of collision between spacecraft is crucial for risk management and collision-avoidance strategies. Current methods often rely on Gaussian assumptions and simplifications, which can be inaccurate in highly nonlinear scenarios. We present a general and efficient approach for computing collision probabilities without relying on such assumptions. Using high-order multivariate Taylor polynomials, we propagate statistical moments of initial uncertainties to the point of closest approach between the spacecraft. To compute the probability of collision, we derive a semi-analytical expression for the probability density function (PDF) of the closest approach distance, inferred from the propagated moments using orthogonal polynomials. Tested on various short-term and long-term encounters in low-Earth orbit, our method accurately handles nonlinear dynamics, non-Gaussian uncertainties, and irregular distributions. This versatile framework advances space situational awareness by providing precise collision probability estimates in complex dynamical environments. Moreover, our methodology applies to any dynamical system with uncertainty in its initial state and is therefore not restricted to collision probability estimation.

About Théo Verhelst:
Researcher in causal machine learning, autonomous and continuously learning. Theo holds a PhD in computer science on causal inference and machine learning for customer churn prediction.