Sparse coloured system identification with guaranteed stability

We develop a method for sparse transfer function estimation in the presence of coloured noise. Unlike most previous sparse transfer function estimation methods our approach via Laguerre polynomials guarantees stability. Also unlike previous methods the new procedure can handle coloured noise. We discuss both l₁ and l₀ penalized procedures. Simulation results are presented to demonstrate the effectiveness of this approach and to compare the performance of the two penalties that are considered.