Estimating parameters in the damped exponential model

In this paper we consider the problem of estimation of the frequencies and damping factors of exponential signals in the presence of noise. We propose a non-iterative method based on using forward-backward linear prediction and the notion of extended order modeling. In addition to providing estimators of the unknown parameters in the model, the proposed method can be used to specify initial values in any standard minimization algorithm to obtain the least-squares estimators. For the undamped exponential model, it is well known that any estimator is inconsistent under the usual definition of consistency. We redefine the model so that the sampling interval is finite, and prove the consistency and asymptotic normality of the least-squares estimators under this new assumption. It is observed that the dispersion matrix of the least-squares estimators attains the Cramer-Rao bound. (C) 2001 Elsevier Science B.V. All rights reserved.