Efficient Alignment Of Visual-Inertial Maps

In this paper, we address the problem of concurrently computing the transformation between multiple, gravity-aligned maps given common point feature observations. In particular, we formulate the problem as a minimization of the distances between shared features expressed with respect to different maps. We show that by marginalizing the maps' relative positions, the KKT conditions of the resulting minimization problem correspond to a system of multivariate polynomial equations (in the sin and cos of the relative yaw angles) which can be solved analytically for the case of a few maps. Furthermore, and to improve the efficiency when considering numerous maps, we present a fast, iterative process for determining the unknown relative map orientations.