Parameter estimation of exponentially damped sinusoids using second order statistics

K. Abed-Meraim* A. Belouchrani** A. Mansour*** and Y. Hua*
             
  * department of Electrical and Electronics Engineering,
The University of Melbourne, Parklike, Victoria 3052, Australia 
 
** Department of electrical engineering and computer Sciences,
The University of California Berkeley CA 94720, USA,
  
*** LTIRF - into, 46 Av. Felix Viallet 38031 Grenoble 
 
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     to
cyclo-correlation statistics domain. The proposed method
exploits the nullity smart: on the cyclo-correlation of  
stationary process at non-zero cyclo-frequency.   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 : (i) first it deals only with second
order statistics which requiers 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 moire. The effectiveness of
the proposed method is illustrated by some numerical  
simulation.