Maximum likelihood estimation of amplitude-modulated time series

The concern of this paper is to study a class of nonstationary signals of t he form x(t)c(t) where x(t) is a stationary Gaussian stochastic process and c(t) is a deterministic signal. The process x(t) is modeled by an autoregr essive (AR) process. The deterministic signal c(t) is a known function of a finite-dimensional unknown vector. Closed-form expressions are derived for the finite-sample Cramer-Rao bound. Algorithms for the maximum likelihood estimation of c(t) and the spectral density of x(t) are developed. The prop osed methods are applied to the problem of estimating abrupt change in mult iplicative noise. (C) 1999 Elsevier Science B.V. All rights reserved.