Rao-Blackwellized Gaussian Smoothing

In this paper, we consider Rao-Blackwellization of linear substructures in sigma-point-based Gaussian assumed density smoothers. We derive marginalized prediction, smoothing, and update steps for the mixed linear/nonlinear Gaussian state-space model as well as for a hierarchical model for both conventional and iterated posterior linearization Gaussian smoothers. The proposed method is evaluated in a numerical example and it is shown that the computational complexity is reduced considerably compared to non-Rao-Blackwellized Gaussian smoothers for systems with high-dimensional linear subspaces.