Structure from Motion with variable focal length: Interconnected fuzzy observer

In this paper, a 3D point feature depth and camera focal length estimation is proposed, using a partially calibrated low cost monocular camera. The camera intrinsic parameters are known, except for the focal length, which may vary across different views. The camera perspective projection model is augmented using dynamic extension approach, then decomposed into two interconnected subsystems. The subsystems are described as quasi-Linear Parameter Varying (qLPV) systems with unmeasured premise variables for which an interconnected fuzzy observer is designed. Necessary and sufficient conditions to ensure the observer existence are presented. The error convergence analysis is performed based on Lyapunov theory associated with Lipchitz condition. Gains that guarantee the asymptotic stability of the estimation error are computed in terms of Linear Matrix Inequalities (LMI) with eigenvalues clustering in LMI region to improve the estimation performance.