A Bayesian method for long AR spectral estimation: a comparative study

Abstract

We address the problem of smooth power spectral density estimation of zero-mean stationary Gaussian processes when only a short observation set is available for analysis. The spectra are described by a long autoregressive model whose coefficients are estimated in a Bayesian regularized least squares (RLS) framework accounting the spectral smoothness prior. The critical computation of the tradeoff parameters is addressed using both maximum likelihood (ML) and generalized cross-validation (GCV) criteria in order to automatically tune the spectral smoothness. The practical interest of the method is demonstrated by a computed simulation study in the field of Doppler spectral analysis. In a Monte Carlo simulation study with a known spectral shape, investigation of quantitative indexes such as bias and variance, but also quadratic, logarithmic, and Kullback distances shows interesting improvements with respect to the usual least squares method, whatever the window data length and the signal-to-noise ratio (SNR).