Parameter estimation of exponentially damped sinusoids using second order statistics

Abstract

In this contribution, we present a new approach for the estimation of the parameters of exponentially damped sinusoids based on the second order statistics of the observations. The method may be seen as an extension of the minimum norm principal eigenvectors method (see [1]) to cydo-correlation statistics domain. The proposed method exploits the nullity property of the cy do-correlation of stationary processes at non-zero cyclo-frequencies [2], This property allows in a pre-processing step to get rid from stationary additive noise. This approach presents many advantages in comparison with existing higher order statistics based approaches [3]: (i) First it deals only with second order statistics which require generally few samples in contrast to higher-order methods, (ii) it deals either with Gaussian and non-Gaussian additive noise, and (iii) also deals either with white or temporally colored (with unknown autocorrelation sequence) additive noise. The effectiveness of the proposed method is illustrated by some numerical simulations.