  The design of unknown-input decoupled observers and filters requires the
assumption of an existence condition in the literature. This paper addresses an
unknown input filtering problem where the existence condition is not satisfied.
Instead of designing a traditional unknown input decoupled filter, a
Double-Model Adaptive Estimation approach is extended to solve the unknown
input filtering problem. It is proved that the state and the unknown inputs can
be estimated and decoupled using the extended Double-Model Adaptive Estimation
approach without satisfying the existence condition. Numerical examples are
presented in which the performance of the proposed approach is compared to
methods from literature.
