Maximum likelihood estimation of amplitude-modulated time series

Abstract The concern of this paper is to study a class of nonstationary signals of the 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 autoregressive (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 proposed methods are applied to the problem of estimating abrupt change in multiplicative noise.

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