Frequency estimation with missing measurements

The frequency estimation problem is studied in this work in the presence of missing measurements. The approach developed in this work is mainly inspired by sparse signal theory. To find a sparse representation of frequency estimation problem, a DFT-like matrix is created in which the frequency sparsity is discovered. The missing measurements are modeled by a sparse representation as well where missing samples are set to be zeros. Based on this model, the missing pattern represented by a vector in this work is indeed sparse since it only contains zeros and ones. Therefore, by exploring the sparsity of both frequency and missing petters, a joint estimation is devised under optimization framework. To solve that optimization problem, a two-step process is proposed as well. Numerical studies demonstrate that the joint estimation offers precise and consistent results.