Provably stable nonlinear and adaptive observers for dynamic structure and motion estimation
Ola Dahl, Anders Heyden, Fredrik Nyberg · 2007
Abstract. Structure and motion estimation from long image sequences is a hard problem, especially when it comes to proving stability and convergence of different methods. We propose a novel approach based on nonlinear and adaptive observers based on a dynamic model of the motion. The estimation of the three-dimensional position and velocity of the camera as well as the three-dimensional structure of the scene is done by observing states and parameters of a nonlinear dynamic system, containing a perspective transformation in the output equation, often referred to as a perspective dynamic system. The paper presents a stability analysis for a class of observers for the estimation of position. The analysis provides conditions for convergence, and insight into feasible motions. An advantage of the proposed method is that it is filter-based, i.e. it provides an estimate of structure and motion at each time instance, which is then updated based on a novel image in the sequence. Finally, the performance of the proposed method is shown in simulated experiments.