A System Parameterization for Direct Data-Driven Estimator Synthesis

This letter introduces a novel parameterization to characterize unknown linear time-invariant systems using noisy data. The presented parameterization describes exactly the set of all systems consistent with the available data. We then derive verifiable conditions when the consistency constraint reduces the set to the true system and when it does not have any impact. Furthermore, we demonstrate how to use this parameterization to perform a direct data-driven estimator synthesis with guarantees on the ${\mathcal{H}}_{\infty }$ -norm. Lastly, we conduct numerical experiments to compare our approach to existing methods.