Continuous-Time Data-Driven Unknown-Input Observers

State estimation in the presence of unknown inputs remains a fundamental challenge in control and monitoring applications. Traditional unknown-input observer (UIO) relies on explicit system models; however, it applicability is often constrained by system complexity and modeling uncertainties. Recent advancements in data-driven approaches have facilitated state estimation using solely pre-collected input-output data, eliminating the need for explicit system identification. Nevertheless, existing data-driven UIO designs have primarily been developed for discrete-time systems, leaving a significant gap in the continuous-time framework. This paper addresses this gap by introducing a novel data-driven UIO (D-UIO) for continuous-time linear time-invariant (LTI) systems. The proposed method directly constructs the observer from offline input-output-state data, circumventing the need for knowledge of the system matrices. By leveraging historical data, we derive necessary and sufficient conditions for the existence of a continuous-time D-UIO and provide theoretical guarantees regarding its stability and convergence. Numerical simulations validate the proposed methodology, showcasing estimation performance comparable to model-based UIO, despite the absence of any a priori knowledge of the system dynamics.