Parameter estimation of exponentially damped sinusoids using higher order statistics

A new approach for the estimation of the parameters of exponentially damped sinusoids is introduced based on third- or fourth-order statistics of the observation signal. The method may be seen as an extension of the minimum norm principal eigenvectors method to higher order statistics domains. The strong points and limitations of the method are discussed as well as sufficient conditions for the existence of the solution. The utilization of the method in the case of finite length signals in the presence of additive Gaussian noise (white or colored) is addressed. Monte Carlo simulations demonstrate the effectiveness of the new method when the additive noise is colored Gaussian with unknown autocorrelation sequence for different signal-to-noise ratios and a single data record. The case of an ensemble of data records is studied when the exponentially damped sinusoids are assumed to have random phase