The Interacting Multiple Model Filter and Smoother on Boxplus-Manifolds †

Hybrid systems are subject to multiple dynamic models, or so-called modes. To estimate the state, the sequence of modes has to be estimated, which results in an exponential growth of possible sequences. The most prominent solution to handle this is the interacting multiple model filter, which can be extended to smoothing. In this paper, we derive a novel generalization of the interacting multiple filter and smoother to manifold state spaces, e.g., quaternions, based on the boxplus-method. As part thereof, we propose a linear approximation to the mixing of Gaussians and a Rauch–Tung–Striebel smoother for single models on boxplus-manifolds. The derivation of the smoother equations is based on a generalized definition of Gaussians on boxplus-manifolds. The three, novel algorithms are evaluated in a simulation and perform comparable to specialized solutions for quaternions. So far, the benefit of the more principled approach is the generality towards manifold state spaces. The evaluation and generic implementations are published open source.