Sparse Semi-Parametric Estimation of Harmonic Chirp Signals

In this paper, we present a method for estimating the parameters detailing an unknown number of linear, possibly harmonically related, chirp signals, using an iterative sparse reconstruction framework. The proposed method is initiated by a re-weighted group-sparsity approach, followed by an iterative relaxation-based refining step, to allow for high-resolution estimates. Numerical simulations illustrate the achievable performance, offering a notable improvement as compared to other recent approaches. The resulting estimates are found to be statistically efficient, achieving the corresponding Cramér-Rao lower bound.