This paper presents an optimal reduced-order Kalman filter for discrete-time dynamic stochastic linear systems with unknown inputs. The problem is to estimate a part of the state vector in the case where none of the observations are assumed to be noise-free. The proposed filter is obtained by minimizing the trace of the estimation error covariance matrix with respect to the remaining degrees of freedom after noninteresting state and unknown inputs decoupling. The necessary and sufficient conditions for stability and convergence of the filter are established.