  The problem of discrete universal filtering, in which the components of a
discrete signal emitted by an unknown source and corrupted by a known DMC are
to be causally estimated, is considered. A family of filters are derived, and
are shown to be universally asymptotically optimal in the sense of achieving
the optimum filtering performance when the clean signal is stationary, ergodic,
and satisfies an additional mild positivity condition. Our schemes are
comprised of approximating the noisy signal using a hidden Markov process (HMP)
via maximum-likelihood (ML) estimation, followed by the use of the forward
recursions for HMP state estimation. It is shown that as the data length
increases, and as the number of states in the HMP approximation increases, our
family of filters attain the performance of the optimal distribution-dependent
filter.
