Motivated by fault detection and isolation problems, we present an approach to the design of state observers for linear time-variant stochastic systems with unknown parameters and disturbances. The novelties with respect to more conventional techniques are as follows: (a) the joint estimation of state, disturbances and parameters can be carried out; (b) it is a full-stochastic approach: the unknown parameters and disturbances are random quantities and prior information, in terms of means and covariances, can be easily taken into account; (c) the observer structure is not fixed a priori, rather derived from the optimal one by means of a sliding window approximation; (d) contrary to descriptor system techniques, which estimate the state starting from a restricted set of disturbance-free equations, our approach is focused on disturbance estimation, from which state estimates are derived straightforwardly.