Distributed State Estimation for Discrete-Time Observable Linear Time-Invariant Systems with Unknown Exogenous Inputs

This paper presents a Distributed Unknown Input Observer (D-UIO) design methodology based on node-wise observability decomposition to estimate the state of discrete-time linear time-invariant (LTI) systems affected by measurement noise and unknown inputs. The framework models sensors as integral components of logical units, which together constitute the nodes of a distributed observer network. Each node of the network has only partial access to system information - restricted to local measurements - and can exchange data solely with its direct neighbors. The observer design challenge is therefore split into two complementary tasks: (i) determining local output injection gains to intelligently use locally available data, and (ii) defining diffusive coupling gains that, through a consensus mechanism, compensate for incomplete information. The proposed synthesis is cast as a set of linear matrix inequalities (LMI) conditions, which can be efficiently solved via semidefinite programming, yielding a tractable design procedure. The effectiveness of the distributed observer is finally demonstrated through a numerical simulation example.