  In this paper we consider the continuous--time nonlinear filtering problem,
which has an infinite--dimensional solution in general, as proved by
Chaleyat--Maurel and Michel. There are few examples of nonlinear systems for
which the optimal filter is finite dimensional, in particular Kalman's, Benes',
and Daum's filters. In the present paper, we construct new classes of scalar
nonlinear filtering problems admitting finite--dimensional filters. We consider
a given (nonlinear) diffusion coefficient for the state equation, a given
(nonlinear) observation function, and a given finite--dimensional exponential
family of probability densities. We construct a drift for the state equation
such that the resulting nonlinear filtering problem admits a
finite--dimensional filter evolving in the prescribed exponential family
augmented by the observaton function and its square.
