Distributed State Estimation for Discrete-Time LTI Systems in the Presence of Unknown Inputs

This paper addresses the distributed state estimation problem for a discrete-time linear and time-invariant (LTI) state-space model, whose state equation is affected by disturbances. A connected sensor network, in which each sensor has access only to part of the control inputs and provides its own output signal (that represents a partial indirect measurement of the state), is deployed to reconstruct the state of a system. Such sensors exchange information with the goal of achieving consensus and providing an asymptotically correct estimate of the global system state. Necessary and sufficient conditions for the existence of distributed unknown input observers (DUIOs) with augmented states that achieve both goals are derived. Moreover, an algorithmic procedure to design the matrices of the proposed DUIO is presented. The problem solution leverages the theory of decentralized output feedback control, thus making it possible to exploit the algorithms available for the solution of that problem.