The Interacting Multiple Model Filter on Boxplus-Manifolds

The interacting multiple model filter is the standard in state estimation where different dynamic models are required to model the behavior of a system. It performs a probabilistic mixing of estimates. Up to now, it is undefined how to perform this mixing properly on manifold spaces, e.g. quaternions. We present the proper probabilistic mixing on differentiable manifolds based on the boxplus-method. The result is the interacting multiple model filter on boxplus-manifolds. We prove that our approach is a first order correct approximation of the optimum. The approach is evaluated in a simulation and performs as good as the ad-hoc solution for quaternions. A generic implementation of the boxplus interacting multiple model filter for differentiable manifolds is published alongside with this paper.