Filtering from Observations on Stiefel Manifolds

TL;DR

This paper develops a particle filtering method for estimating signals on Stiefel manifolds, addressing partial observations and noise in 3D rigid body attitude estimation.

Contribution

It introduces a novel filtering approach on Stiefel manifolds using anti-development and particle filters, with interpolation techniques for sampling issues.

Findings

Successfully estimates angular velocity from partial observations.

Demonstrates effectiveness on synthetic 3D data.

Addresses sampling and interpolation challenges in manifold filtering.

Abstract

This paper considers the problem of optimal filtering for partially observed signals taking values on the rotation group. More precisely, one or more components are considered not to be available in the measurement of the attitude of a 3D rigid body. In such cases, the observed signal takes its values on a Stiefel manifold. It is demonstrated how to filter the observed signal through the anti-development built from observations. A particle filter implementation is proposed to perform the estimation of the signal partially observed and corrupted by noise. The sampling issue is also addressed and interpolation methods are introduced. Illustration of the proposed technique on synthetic data demonstrates the ability of the approach to estimate the angular velocity of a partially observed 3D system partially observed.