Extended Kalman Filtering on Stiefel Manifolds

TL;DR

This paper extends the Kalman filter to handle measurements on Stiefel manifolds, demonstrating improved estimation accuracy through simulations on the 2-sphere and orthogonal matrices.

Contribution

It introduces a generalized extended Kalman filter tailored for Stiefel manifold-valued data, enhancing filtering performance for such geometric measurements.

Findings

Significant improvement over raw measurements in simulations

Effective filtering on the 2-sphere and orthogonal matrices

Demonstrates the applicability of the method to manifold-valued data

Abstract

A generalisation of the extended Kalman filter for Stiefel manifold-valued measurements is presented. 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.