Recursive non parametric spectral estimation from irregularly sampled observations

In this paper, the nonparametric spectral analysis of a randomly sampled signal is discussed. In particular, a class of estimators is introduced: the IRINCORREL class. This class is composed of recursive algorithms which both take into account the sampling irregularity and the correlation of the signal values. The study of the mean square estimation error shows that there is a trade off between bias and convergence rate. The minimization of this mean square estimation error leads to the adapted window IRINCORREL estimators. Statistical properties of the proposed estimators are illustrated by means of numerical examples.