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.