An approach to stochastic system identification in riemannian manifolds

Estimation problems on manifolds e.g. Stiefel manifolds, and Lie groups e.g. SE(3), SO(3) have emerged in several applications such as computer vision pose estimation and aerospace attitude estimation. But the random process construction methods available in the probability literature rely on abstract stochastic differential geometry and are accessible with difficulty to an engineering audience. Here we review and expand to matrix manifolds a recent much simpler approach developed by the author. Using that approach we give a simple interpretation of some important recent results based on a notion of state conversion. We then show how these conversion results can be used to do system identification. We illustrate throughout with Stiefel manifold examples.