Simulation-based methods for blind maximum-likelihood filter identification

Blind linear system identification consists in estimating the parameters of a linear time-invariant system given its (possibly noisy) response to an u nobserved input signal. Blind system identification is a crucial problem in many applications which range from geophysics to telecommunications, eithe r for its own sake or as a preliminary step towards blind deconvolution (i. e. recovery of the unknown input signal). This paper presents a survey of r ecent stochastic algorithms, related to the expectation-maximization (EM) p rinciple, that make it possible to estimate the parameters of the unknown l inear system in the maximum likelihood sense. Emphasis is on the computatio nal aspects rather than on the theoretical questions. A large section of th e paper is devoted to numerical simulations techniques, adapted from the Ma rkov chain Monte Carlo (MCMC) methodology, and their efficient application to the noisy convolution model under consideration. (C) 1999 Published by E lsevier Science B.V. All rights reserved.