A methodology for non-invasive estimation of the pressure in internal carotid arteries is proposed. It uses data assimilation and Ensemble Kalman filters in order to identify unknown parameters in a mathematical description of the cerebral network. The approach uses patient specific blood flow rates extracted from Magnetic Resonance Angiography and Magnetic Resonance Imaging. This construction is necessary as the simulation of blood flows in complex arterial networks, such as the circle of Willis, is not straightforward because hemodynamic parameters are unknown as well as the boundary conditions necessary to close this complex system with many outlets. For instance, in clinical cases, the values of Windkessel model parameters or the Young's modulus and the thickness of the arteries are not available on per-patient cases. To make the approach computational efficient, a reduced order zero-dimensional compartment model is used for blood flow dynamics. Using this simplified model, the proof-of-concept study demonstrates how to use the EnKF as an optimization tool to find parameters and how to make the inverse hemodynamic problem tractable. The predicted blood flow rates in the internal carotid arteries and the predicted systolic and diastolic brachial blood pressures are found to be in good agreement with the clinical measurements.