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

TL;DR

This paper proves the convergence of the extended Kalman filter on Stiefel manifolds for constant systems with measurement errors and demonstrates this through simulations, advancing filtering techniques on complex geometric spaces.

Contribution

It introduces filtering on Stiefel manifolds and establishes convergence results for the extended Kalman filter in this setting, which was previously unexplored.

Findings

Convergence of the extended Kalman filter on Stiefel manifolds is proven for constant systems.

Simulations confirm the theoretical convergence and analyze the speed of convergence.

The study extends filtering methods to complex geometric spaces like Stiefel manifolds.

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.