Unit Quaternion-Based Parameterization for Point Features in Visual Navigation

Abstract

In this paper, we propose to use unit quaternions to represent point features in visual navigation. Contrary to the Cartesian 3D representation, the unit quaternion can well represent features at both large and small distances from the camera without suffering from convergence problems. Contrary to inverse-depth, homogeneous points, or anchored homogeneous points, the unit quaternion has error state of minimum dimension of three. In contrast to prior representations, the proposed method does not need to approximate an initial infinite depth uncertainty. In fact, the unit-quaternion error covariance can be initialized from the initial feature observations without prior information, and the initial error-states are not only bounded, but the bound is identical for all scene geometries. To the best of our knowledge, this is the first time bearing-only recursive estimation (in covariance form) of point features has been possible without using measurements to initialize error covariance. The proposed unit quaternion-based representation is validated on numerical examples.