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 unobserved input signal. Blind system identification is a crucial problem in many applications which range from geophysics to telecommunications, either 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 recent stochastic algorithms, related to the expectation-maximization (EM) principle, that make it possible to estimate the parameters of the unknown linear system in the maximum likelihood sense. Emphasis is on the computational aspects rather than on the theoretical questions. A large section of the paper is devoted to numerical simulations techniques, adapted from the Markov chain Monte Carlo (MCMC) methodology, and their efficient application to the noisy convolution model under consideration.