Smooth 2-D frequency estimation using covariance fitting

In this paper, we introduce a non-parametric 2-D spectral estimator for smooth spectra, allowing for irregularly sampled measurements. The estimate is formed by assuming that the spectrum is smooth and will vary slowly over the frequency grids, such that the spectral density inside any given rectangle in the spectral grid may be approximated well as a plane. Using this framework, the 2-D spectrum is estimated by finding the solution to a convex covariance fitting problem, which has an analytic solution. Numerical simulations indicate the achievable performance gain as compared to the Blackman-Tukey estimator.