The State Space Subdivision Filter for SE(3)

Estimating the position and orientation of 3-D objects is a ubiquitous challenge. In our novel filter, the position and orientation of objects are modeled using the Cartesian product of ℝ for the position and a 3-D hyperhemisphere. The latter is used to describe orientations in the form of unit quaternions. The hyperhemisphere is subdivided into equally sized areas. The joint density for the position and orientation is split up into a marginal density for the orientation and a density for the position that is conditioned on the orientation. In our filter, we assume that the function values of the marginal density and the conditional density is the same for all points within that area. By assuming all conditional densities to be Gaussians, efficient formulae can be implemented for the update and prediction steps. The filter is evaluated based on a simulation scenario, for which it showed very high accuracy at low run times.