  We consider the problem of estimating a variable number of parameters with a
dynamic nature. A familiar example is finding the position of moving targets
using sensor array observations. The problem is challenging in cases where
either the observations are not reliable or the parameters evolve rapidly.
Inspired by the sparsity based techniques, we introduce a novel Bayesian model
for the problems of interest and study its associated recursive Bayesian
filter. We propose an algorithm approximating the Bayesian filter, maintaining
a reasonable amount of calculations. We compare by numerical evaluation the
resulting technique to state-of-the-art algorithms in different scenarios. In a
scenario with a low SNR, the proposed method outperforms other complex
techniques.
