  We present a representation theorem for a filtering model with
first-passage-type stopping time. The model is constructed from two
unobservable processes and one observable process that is under the influence
of two unobservable processes.A filter is constructed using Brownian motion in
the observable process and a first-passage-type stopping time in an
unobservable process.Though our theorems are similar to those of
Nakagawa\cite{Nakagawa}, we do not use pinned Brownian motion measure, which is
difficult to deal with. In addition, we describe a representation theorem for
another filtration that was not discussed by Nakagawa
