Fokker-Planck Prediction on the Cylindric Manifold Using Tensor Decomposition of a Regular Grid

The Fokker-Planck propagator is derived for prediction on cylindric manifolds. We exploit the low-rank tensor decomposition technique that is already being used in the Euclidean domain. With only a small change to the finite difference matrix, we can readily apply it to certain manifolds such as the cylinder. Our application example is estimating the angular position and velocity of a rotating shaft. This state estimation problem may seem linear at first glance, but since the underlying state space is nonlinear due to the periodicity of the angular coordinate, it is an inherently nonlinear estimation problem.