Framework for state and unknown input estimation of linear time-varying systems

The design of unknown-input decoupled observers and lters requires the assumption of an existence condition in the literature.This paper addresses an unknown input ltering problem where the existence condition is not satised. Instead of designing a traditional unknown input decoupled lter, a Double-Model Adaptive Estimation approach is extended to solve the unknown input ltering 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.