Parametric estimation of hidden signals by likelihood maximization

Many important problems in signal processing can be reduced to the estimation of a hidden (unobserved) signal from a series of arbitrarily distorted observations by means of a digital filter. We analyze a novel criterion that relies on the ability to characterize statistically the desired signal to be obtained after filtering. Using this statistical reference, the filter coefficients can be optimized by maximizing the likelihood of the output signal under the desired probability distribution. We assess the asymptotic properties of this method and establish necessary and sufficient conditions for convergence that apply to a broad class of systems.