An exponential observer for systems on SE(3) with implicit outputs

Abstract

This paper considers the state estimation problem of a class of systems described by implicit outputs and whose state lives in the special Euclidean group SE(3). This type of systems are motivated by applications in dynamic vision such as the estimation of the motion of a camera from a sequence of images. We propose an observer in the group of motion SE(3) and discuss conditions under which the linearized state estimation error converges exponentially fast. We also analyze the problem when the system is subject to disturbances and noises. We show that the estimate converges to a neighborhood of the real solution. The size of the neighborhood increases/decreases gracefully with the bound of the disturbance and noise. © Springer-Verlag Berlin Heidelberg 2011.