Incremental estimation without specifying a-priori covariance matrices for the novel parameters

Christian Beder, Richard Steffen

Abstract: We will present a novel incremental algorithm for the task of online least-squares estimation. Our approach aims at combining the accuracy of least-squares estimation and the fast computation of recursive estimation techniques like the Kalman filter. Analyzing the structure of least-squares estimation we devise a novel incremental algorithm, which is able to introduce new unknown parameters and observations into an estimation simultaneously and is equivalent to the optimal overall estimation in case of linear models. It constitutes a direct generalization of the well-known Kalman filter allowing to augment the state vector inside the update step. In contrast to classical recursive estimation techniques no artificial initial covariance for the new unknown parameters is required here. We will show, how this new algorithm allows more flexible parameter estimation schemes especially in the case of scene and motion reconstruction from image sequences. Since optimality is not guaranteed in the non-linear case we will also compare our incremental estimation scheme to the optimal bundle adjustment on a real image sequence. It will be shown that competitive results are achievable using the proposed technique.