Arnaud Doucet

Simulation-based methods for blind maximum-likelihood filter identification

Abstract 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.

An Introduction to Monte Carlo Methods for Bayesian Data Analysis

Often it is natural to describe a signal processing or dynamical modeling problem in terms of probability distributions, and in particular tin Bayesian terms, where the unknown parameters are taken to be random variables and their distributions are updated by applying Bayes’ theorem to gave the distributions of the parameters conditional on the data. In the past, it was not possible to handle many non-trivial problems in this way because the distributions seldom took tractable forms. Considerable progress has been made in recent years in applying Monte Carla methods to overcome this, and in this chapter we describe some of the new results that have made a full Bayesian approach to signal processing tractable as well as powerful.