The first step in innovations-based failure detection is the construction of an innovations generator, i.e. a filter which, in the absence of failures from the inputs and the outputs of the system, generates a zero-mean white process with known covariance called innovations. A decision on whether a failure has occurred is then made by monitoring and applying statistical tests to this innovations process. In this paper, a method for constructing innovations in the case where the model contains unknown inputs and disturbances is presented. The solution is complete in the sense that it covers ’singular’ cases.