GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering
Itay Buchnik Guy Sagi Nimrod Leinwand Yuval Loya Nir Shlezinger Tirza Routtenberg
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.