GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering

TL;DR

This paper introduces GSP-KalmanNet, a hybrid neural and model-based approach for tracking graph signals that improves accuracy, robustness, and computational efficiency over traditional Kalman filter methods in complex dynamic systems.

Contribution

The paper develops GSP-KalmanNet, integrating graph signal processing and deep learning to enhance state tracking in graph-based systems with reduced complexity and increased robustness.

Findings

Achieves higher accuracy than traditional Kalman filter variants.

Demonstrates improved robustness to model misspecifications.

Offers faster processing suitable for high-dimensional signals.

Abstract

Dynamic systems of graph signals are encountered in various applications, including social networks, power grids, and transportation. While such systems can often be described as state space (SS) models, tracking graph signals via conventional tools based on the Kalman filter (KF) and its variants is typically challenging. This is due to the nonlinearity, high dimensionality, irregularity of the domain, and complex modeling associated with real-world dynamic systems of graph signals. In this work, we study the tracking of graph signals using a hybrid model-based/data-driven approach. We develop the GSP-KalmanNet, which tracks the hidden graphical states from the graphical measurements by jointly leveraging graph signal processing (GSP) tools and deep learning (DL) techniques. The derivations of the GSP-KalmanNet are based on extending the KF to exploit the inherent graph structure via graph frequency domain filtering, which considerably simplifies the computational complexity entailed in processing high-dimensional signals and increases the robustness to small topology changes. Then, we use data to learn the Kalman gain following the recently proposed KalmanNet framework, which copes with partial and approximated modeling, without forcing a specific model over the noise statistics. Our empirical results demonstrate that the proposed GSP-KalmanNet achieves enhanced accuracy and run time performance as well as improved robustness to model misspecifications compared with both model-based and data-driven benchmarks.