Sampling Policy Design for Tracking Time-Varying Graph Signals with Adaptive Budget Allocation

Abstract

There have been many works that focus on the sampling set design for a static graph signal, but few for time-varying graph signals (GS). In this paper, we concentrate on how to select vertices to sample and how to allocate the sampling budget for a time-varying GS to achieve a minimal tracking error for the long-term. In the Kalman Filter (KF) framework, the problem of sampling policy design and budget allocation is formulated as an infinite horizon sequential decision process, in which the optimal sampling policy is obtained by Dynamic Programming (DP). Since the optimal policy is intractable, an approximate algorithm is proposed by truncating the infinite horizon. By introducing a new tool for analyzing the convexity or concavity of composite functions, we prove that the truncated problem is convex. Finally, we demonstrate the performance of the proposed approach through numerical experiments.

arXiv comment6 pages, 4 figures, accepted by APSIPA 2020

References in corpus (9)

• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• Discrete Signal Processing on Graphs: Sampling Theory
• Efficient Sampling Set Selection for Bandlimited Graph Signals Using Graph Spectral Proxies
• Stationary signal processing on graphs
• Sensor Selection Based on Generalized Information Gain for Target Tracking in Large Sensor Networks
• Greedy Sampling of Graph Signals
• Adaptive Graph Signal Processing: Algorithms and Optimal Sampling Strategies
• Filtering Random Graph Processes Over Random Time-Varying Graphs
• Observing and Tracking Bandlimited Graph Processes