VAMP-Based Kalman Filtering Under Non-Gaussian Process Noise

Estimating time-varying signals becomes particularly challenging in the face of non-Gaussian (e.g., sparse) and/or rapidly time-varying process noise. By building upon the recent progress in the approximate message passing (AMP) paradigm, this paper unifies the vector variant of AMP (i.e., VAMP) wit...

Full description

Saved in:
Bibliographic Details
Main Authors: Tiancheng Gao, Mohamed Akrout, Faouzi Bellili, Amine Mezghani
Format: Article
Language:English
Published: IEEE 2025-01-01
Series:IEEE Open Journal of Signal Processing
Subjects:
Online Access:https://ieeexplore.ieee.org/document/10947573/
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Estimating time-varying signals becomes particularly challenging in the face of non-Gaussian (e.g., sparse) and/or rapidly time-varying process noise. By building upon the recent progress in the approximate message passing (AMP) paradigm, this paper unifies the vector variant of AMP (i.e., VAMP) with the Kalman filter (KF) into a unified message passing framework. The new algorithm (coined VAMP-KF) does not restrict the process noise to a specific structure (e.g., same support over time), thereby accounting for non-Gaussian process noise sources that are uncorrelated both component-wise and over time. For the sake of theoretical performance prediction, we conduct a state evolution (SE) analysis of the proposed algorithm and show its consistency with the asymptotic empirical mean-squared error (MSE). Numerical results using sparse noise dynamics with different sparsity ratios demonstrate unambiguously the effectiveness of the proposed VAMP-KF algorithm and its superiority over state-of-the-art algorithms both in terms of reconstruction accuracy and computational complexity.
ISSN:2644-1322