Parameter estimation for random amplitude chirp signals

We consider the problem of estimating the parameters of a chirp signal obse rved in multiplicative noise, i.e., whose amplitude is randomly time-varyin g. Two methods for solving this problem are presented. First, an unstructur ed nonlinear least-squares approach ((NLS) is proposed. It is shown that by minimizing the NLS criterion with respect to all samples of the time-varyi ng amplitude, the problem reduces to a two-dimensional (2-D) maximization p roblem, A theoretical analysis of the NLS estimator is presented, and an ex pression for its asymptotic variance is derived. It is shown that the NLS e stimator has a variance that is very close to the Cramer-Rao bound. The sec ond approach combines the principles behind the high-order ambiguity functi on (HAF) and the NLS approach, It provides a computationally simpler but su boptimum estimator. A statistical analysis of the HAF-based estimator is al so carried out, and closed-form expressions are derived for the asymptotic variance of the HAF estimators based on the data and on the squared data. N umerical examples attest to the validity of the theoretical analyzes and es tablish a comparison between the tno proposed methods.