This paper considers the optimal minimum-variance estimation for systems with unknown inputs which affect both the system model and the measurements. By making use of a parametrized filter structure, the constrained optimization method, and an optimal switching rule, an optimal parametrized minimum-variance filter (OPMVF) is derived to achieve an optimal compromise between the conventional exact unknown inputs decoupled filter and the well-known Kalman filter. A numerical example is included in order to illustrate the proposed results.