Quantifying Estimation Errors in Robust Vision-Based Control: An Extreme Value Theory Approach

Abstract

Modern autonomous systems—from classical state-estimators to deep learning based visual inertial odometry (VIO)—depend on noisy, high- dimensional sensor data to estimate their state. Quantifying and bound- ing these perceptual errors presents itself as a necessity for integration into a control framework that with provable safety guarantees. Since, neural networks are highly complex “black boxes", we prefer statistical methods for estimating error bounds that can be reliably embedded in robust controllers. In this thesis, we propose to use Extreme Value Theory (EVT), which deals with modeling distributions for extreme events, as an algorithm-agnostic, data-driven framework for quantifying high–con- fidence error bounds on perception outputs. We treat unusually large perceptual errors as “extreme events” and model them through the EVT framework to derive statistical error bounds—first for a Kalman Filter state estimator and then for a deep VIO network. Our simulations show that these bounds are not violated with unseen perceptual data. We fur- ther demonstrate through simulated robust control examples how these bounds can be integrated into a control framework. By empirically validat- ing EVT as a scalable, systematic approach to uncertainty quantification, our findings underscore its value and feasibility for strengthening the safety margins of robust control designs.