Certified Vision-Based State Estimation for Autonomous Landing Systems Using Reachability Analysis

This paper studies the problem of designing a certified vision-based state estimator for autonomous landing systems. In such a system, a neural network (NN) processes images from a camera to estimate the aircraft's relative position with respect to the runway. We propose an algorithm to design such NNs with certified properties in terms of their ability to detect runways and provide accurate state estimation. At the heart of our approach is the use of geometric models of perspective cameras to obtain a mathematical model that captures the relation between the aircraft states and the inputs. We show that such geometric models enjoy mixed monotonicity properties that can be used to design state estimators with certifiable error bounds. We show the effectiveness of the proposed approach using an experimental testbed on data collected from event-based cameras.