Extended Kalman filtering on Stiefel manifolds

A generalization of the extended Kalman filter for Stiefel manifold-valued measurements is presented. Our approach is based on translating between manifold-valued measurements and the ambient space through an injective mapping between scalar true variance on the manifold and the variance of the noise. This mapping inherently takes into account the curvature of the manifold corresponding to the higher order derivatives. To illustrate our approach, we provide simulations on the 2-sphere and the space of orthogonal 4-by-2 matrices which show significant improvement of the Extended Kalman Filter compared to only relying on raw measurements. We also compare our approach to classical Extended Kalman Filter and second order Extended Kalman Filter, and complement our results by physically informed application related to spacecraft measurements. Our results indicate that our algorithm has similar performance as the second order Extended Kalman Filter without requiring the costly computations of the second order derivatives.