On the Convergence of the Extended Kalman Filter on Stiefel Manifolds when Observing a Constant Particle with Measurement Errors

In this paper we first introduce the setting of filtering on Stiefel manifolds. Then, assuming the underlying system process is constant, the convergence of the extended Kalman filter with Stiefel manifold-valued observations is proved. This corresponds to the case where one has measurement errors that needs to be filtered. Finally, some simulations are presented for a selected few Stiefel manifolds and the speed of convergence is studied.