Data Assimilation of the Minimal Flow Unit

State-estimation and prediction are central challenges in turbulent flows. Data-driven approaches can provide accurate representations of these systems thus improving modeling and control. Techniques in data assimilation, a sequential time-stepping strategy which seeks to optimally combine a model forecast and system observations, provide an opportunity for improved state estimation using limited measurements. Reconstruction using sparse measurements is advantageous due to limited availability of sensors. We utilize a high-dimensional model efficiently using ensemble Kalman methods. These methods are demonstrated on a turbulent channel simulation of the minimal flow unit. The measurements and model outputs are assimilated following short episodes of simulation advancement. Using a perfect model or assimilation with synthetic observations, where the simulation provides data for both the model and measurement, we assimilate these data streams for improved state estimation.