Title :

Filtering from Observations on Stiefel Manifolds

Author(s) :

Boulanger, Jérémie [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Said, Salem [Auteur]
Laboratoire de l'intégration, du matériau au système [IMS]
Le Bihan, Nicolas [Auteur]
GIPSA - Communication Information and Complex Systems [GIPSA-CICS]
Manton, Jonathan H. [Auteur]
Department of Electrical and Electronic Engineering [Melbourne]

Journal title :

Signal Processing

Pages :

52-64

Publisher :

Elsevier

Publication date :

2015-12

ISSN :

0165-1684

English keyword(s) :

Rotation group
Stochastic process
Particle filtering
Interpolation
Stiefel manifold
Partial observation
Angular velocity estimation

HAL domain(s) :

Sciences de l'ingénieur [physics]/Traitement du signal et de l'image [eess.SP]

English abstract : [en]

This paper adresses the problem of filtering processes on the rotation group SO(n)SO(n) when partial observations, i.e. processes on the Stiefel manifold, are only available. In particular, we consider the problem of ...
Show more >This paper adresses the problem of filtering processes on the rotation group SO(n)SO(n) when partial observations, i.e. processes on the Stiefel manifold, are only available. In particular, we consider the problem of estimating the angular velocity of an object when only partial observation of its orientation is available. Interpolation schemes are proposed to overcome the discrete nature of observations and a practical numerical solution (particle filtering) is developed for filtering on the Stiefel manifold. The proposed solution to the filtering problem is based on the anti-development signal concept, which allows to overcome the non-additivity nature of the noise present in the observed signal. The solutions proposed are general and can be transposed to many manifolds. However, the presented examples and simulations consider the case of partially observed signals taking values on the special orthogonal group when one or more components are missing. In this particular case, the observed process takes its values in the Stiefel manifold. A comparison of the proposed particle filter with the extended Kalman filter is presented. Results on synthetic and real (sport science) data show the behaviour of the proposed algorithm.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL