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

Abstract: 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.