Continuous-Discrete Filtering and Smoothing on Submanifolds of Euclidean Space
This addresses filtering problems in constrained geometric settings, such as robotics or orientation tracking, but is incremental as it extends existing projection methods to submanifolds.
The paper tackles filtering and smoothing for state variables evolving on submanifolds of Euclidean space, deriving formal expressions and showing that approximate equations match Euclidean cases, with application to von Mises-Fisher distributions.
In this paper the issue of filtering and smoothing in continuous discrete time is studied when the state variable evolves in some submanifold of Euclidean space, which may not have the usual Lebesgue measure. Formal expressions for prediction and smoothing problems are derived, which agree with the classical results except that the formal adjoint of the generator is different in general. For approximate filtering and smoothing the projection approach is taken, where it turns out that the prediction and smoothing equations are the same as in the case when the state variable evolves in Euclidean space. The approach is used to develop projection filters and smoothers based on the von Mises-Fisher distribution.