A robust interpolation algorithm for spectral analysis

We propose a robust interpolation algorithm for model-based spectral analysis. Instead of estimating the spectral model directly, the so-called half spectrum, which has a one-to-one relationship with the spectrum through standard spectral decomposition, is estimated using an interpolation approach. The interpolation data consists of the values and the derivatives of the half spectrum function at a set of user-specified points, and can be easily estimated using an input-to-state filter. Our algorithm allows a large number of noisy interpolation data to be used to optimally fit a half spectrum function of a fixed order. The capability of handling large number of interpolation data makes our algorithm robust to the inherent finite sample noise in the interpolation data. The algorithm involves solving some least-squares problems and semidefinite programming problems, and is thus numerically efficient. Numerical tests show that our algorithm gives very reliable spectral estimates.