Distributed Data-driven Unknown-input Observers for State Estimation

Unknown inputs related to, e.g., sensor aging, modeling errors, or device bias, represent a major concern in wireless sensor networks, as they degrade the state estimation performance. To improve the performance, unknown-input observers (UIOs) have been proposed. Most of the results available to design UIOs are based on explicit system models, which can be difficult or impossible to obtain in real-world applications. Data-driven techniques, on the other hand, have become a viable alternative for the design and analysis of unknown systems using only data. In this context, a novel data-driven distributed unknown-input observer (D-DUIO) for unknown continuous-time linear time-invariant (LTI) systems is developed, which requires solely some data collected offline, without any prior knowledge of the system matrices. In the paper, first, a model-based approach to the design of a DUIO is presented. A sufficient condition for the existence of such a DUIO is recalled, and a new one is proposed, that is prone to a data-driven adaption. Moving to a data-driven approach, it is shown that under suitable assumptions on the input/output/state data collected from the continuous-time system, it is possible to both claim the existence of a D-DUIO and to derive its matrices in terms of the matrices of pre-collected data. Finally, the efficacy of the D-DUIO is illustrated by means of numerical examples.