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Simulation-based methods for blind maximum-likelihood filter identification. (English) Zbl 0926.93066

Summary: 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, which allow 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.

MSC:

93E12 Identification in stochastic control theory
93E11 Filtering in stochastic control theory
93E25 Computational methods in stochastic control (MSC2010)
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