Extended Kalman Filtering on Stiefel Manifolds

2025/11/04 by Figueras, Jordi-Lluís, Persson, Aron, Viitasaari, Lauri · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #53Z30 (Secondary) #62R30 (Primary) #Applications (stat.AP) #Computation (stat.CO) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Morphological variations and asymmetry #Statistical Mechanics and Entropy #Target Tracking and Data Fusion in Sensor Networks

paper · doi:10.48550/arxiv.2511.02682

openalex publication_date 2025/11/04 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

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.

Citations

• On the Convergence of the Extended Kalman Filter on Stiefel Manifolds when Observing a Constant Particle with Measurement Errors
• On parameter estimation for N(μ,σ² I₃) based on projected data into \mathbbS²
• On the Injectivity Radius of the Stiefel Manifold: Numerical investigations and an explicit construction of a cut point at short distance
• Associating Uncertainty to Extended Poses for on Lie Group IMU\n Preintegration with Rotating Earth
• Orthogonal Convolutional Neural Networks
• Can We Gain More from Orthogonality Regularizations in Training Deep CNNs?
• A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric
• The invariant extended Kalman filter as a stable observer
• Filtering from Observations on Stiefel Manifolds
• The Geometry of Algorithms with Orthogonality Constraints

Cited by

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

Related

• On the Convergence of the Extended Kalman Filter on Stiefel Manifolds when Observing a Constant Particle with Measurement Errors
• A Note on the Extended Kalman Filter on a Manifold
• Filtering from Observations on Stiefel Manifolds
• The Geometry of Extended Kalman Filters on Manifolds with Affine Connection
• A Quick Guide for the Iterated Extended Kalman Filter on Manifolds