The asymptotic Cramer-Rao lower bound and maximum likelihood estimation of parameters of exponentially damped sinusoid from noisy measurements

The problem of estimating the frequency, damping, phase, and amplitude of exponentially damped sinusoidal signal is considered. An expression of asymptotic Cramer-Rao lower bound (CRLB) for any unbiased estimator of the estimation problem under consideration is derived. A simplified maximum likelihood Gauss Newton algorithm is developed. The analytic and numerical studies show that the algorithm provides asymptotically efficient estimates of the parameters. A numerical example is presented to illustrate the performance of the proposed estimation procedure. A comparison to the Cramer-Rao lower bounded performance is also presented using the simple expression for the asymptotic CRLB covariance matrix derived in the paper