Tracking Dynamic Sparse Signals with Hierarchical Kalman Filters: A Case Study

J. Filos, E. Karseras, W. Dai., and Shulin Yan.
International Conference on Digital Signal Processing (DSP) (2013) (2013)

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.
Index Terms—Kalman filtering; compressed sensing; sparse
Bayesian learning; sparse representations.