Filtering from Observations on Stiefel Manifolds

2014/09/25 by Jérémie Boulanger, Salem Said, Boulanger, Jeremie +5 · 1 citation
Computer Science · Engineering · #FOS: Computer and information sciences #Inertial Sensor and Navigation #Other Computer Science (cs.OH) #Structural Health Monitoring Techniques #Target Tracking and Data Fusion in Sensor Networks

paper · doi:10.48550/arxiv.1409.7442

openalex publication_date 2014/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Extended Kalman Filtering on Stiefel Manifolds

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