Tracking dynamic sparse signals with hierarchical Kalman filters: A case study

Tracking and recovering dynamic sparse signals using traditional Kalman filtering techniques tend to fail. Compressive sensing (CS) addresses the problem of reconstructing signals for which the support is assumed to be sparse but is not fit for dynamic models. This paper provides a study on the performance of a hierarchical Bayesian Kalman (HB-Kalman) filter that succeeds in promoting sparsity and accurately tracks time varying sparse signals. Two case studies using real-world data show how the proposed method outperforms the traditional Kalman filter when tracking dynamic sparse signals. It is shown that the Bayesian Subspace Pursuit (BSP) algorithm, that is at the core of the HB-Kalman method, achieves better performance than previously proposed greedy methods.