We focus on tracking dynamic sparse signals. Towards this end, we design a
hierarchical Kalman filter based on the so called relevance vector machine,
famous in machine learning literature. The key difference from the standard
Kalman filter is that the variances of the signal innovations are not
pre-defined but learned from the observations. Simulations demonstrate the
advantages of our approach. On the theoretic side, we show that several CS
reconstruction techniques can be borrowed to solve the corresponding
statistical
inference problem and prove the related performance guarantees, which extend
and
refine the Wipf and Rao's analysis.