Abstract-In this paper, we present an algorithm for autonomous stair climbing with a tracked vehicle. The proposed method achieves robust performance under real-world conditions, without assuming prior knowledge of the stair geometry, the dynamics of the vehicle's interaction with the stair surface, or lighting conditions. Our approach relies on fast and accurate estimation of the robot's heading and its position relative to the stair boundaries. An extended Kalman filter is used for quaternion-based attitude estimation, fusing rotational velocity measurements from a 3-axial gyroscope, and measurements of the stair edges acquired with an onboard camera. A twotiered controller, comprised of a centering-and a headingcontrol module, utilizes the estimates to guide the robot fast, safely, and accurately upstairs. Both the theoretical analysis and implementation of the algorithm are presented in detail, and extensive experimental results demonstrating the algorithm's performance are described.