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

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

paper · doi:10.48550/arxiv.2511.02680

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

Abstract

In this paper we first introduce the setting of filtering on Stiefel manifolds. Then, assuming the underlying system process is constant, the convergence of the extended Kalman filter with Stiefel manifold-valued observations is proved. This corresponds to the case where one has measurement errors that needs to be filtered. Finally, some simulations are presented for a selected few Stiefel manifolds and the speed of convergence is studied.

Citations

• Extended Kalman Filtering on Stiefel Manifolds
• On parameter estimation for N(μ,σ² I₃) based on projected data into \mathbbS²
• Fisher's Legacy of Directional Statistics, and Beyond to Statistics on Manifolds
• StiefelGen: A Simple, Model Agnostic Approach for Time Series Data Augmentation over Riemannian Manifolds
• Central limit theorem for intrinsic Frechet means in smooth compact Riemannian manifolds
• Modeling animal movement with directional persistence and attractive points

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• Extended Kalman Filtering on Stiefel Manifolds

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