In this paper exact finite-dimensional filters are derived for a class of doubly stochastic auto-regressive models. The parameters of the doubly stochastic auto-regressive process vary according to a nonlinear function of a Gauss-Markov process. We develop a difference equation for the evolution of an unnormalized conditional density related to the state of the doubly stochastic auto-regressive process. We then give a characterization of the general solution followed by examples for which the state of the filter is determined by a finite number of sufficient statistics. These new finite-dimensional filters build upon the discrete-time Kalman filter.