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

A representation theorem on a filtering model with first-passage-type stopping time