State estimation for a class of linear time-invariant systems with distributed output measurements (distributed sensors) and
unknown inputs is addressed in this paper. The objective is to design a network of observers such that the state vector
of the entire system can be estimated, while each observer has access to only local output measurements that may not be
sufficient on their own to reconstruct the entire system’s state. Existing results in the literature on distributed state estimation
assume either that the system does not have inputs, or that all the system’s inputs are globally known to all the observers.
Accordingly, we address this gap by proposing a distributed observer capable of estimating the overall system’s state in the
presence of inputs, while each observer only has limited local information on inputs and outputs. We provide a design method
that guarantees convergence of the estimation errors to zero under joint detectability conditions. This design suits undirected
communication graphs that may have switching topologies and also applies to strongly connected directed graphs.We also give
existence conditions that are consistent with existing results on unknown input observers. Finally, simulation results verify
the effectiveness of the proposed estimation scheme for various scenarios.
