Decentralised state estimation for linear systems with unknown inputs: a consensus-based approach

This study addresses a problem of decentralised estimation for a class of linear time-invariant systems affected by stochastic disturbances and deterministic unknown inputs. Under certain structural properties of 'strong detectability', the task of reconstructing simultaneously the system state variables and the unknown inputs acting on the system is achieved by a consensus-based decentralised estimator. An optimisation procedure for computing the consensus gain parameters is described. A proportional-integral observer that allows recovering an estimate of the unknown inputs acting on the system is also introduced. All the procedures and methodologies are verified by means of a thoroughly discussed simulation example.