4D Flow MRI is the state of the art technique for measuring blood flow, and it provides valuable information for inverse problems in the cardiovascular system. However, 4D Flow MRI has a very long acquisition time, straining healthcare resources and inconveniencing patients. Due to this, usually only a (small) part of the frequency space is acquired, where then further assumptions need to be made in order to obtain an image. Reconstructing these measurements with Compressed Sensing techniques introduces potential artifacts and inaccuracies, which can compromise the results of the inverse problems. Additionally, there is a high number of different sampling patterns available, and it is often unclear which of them is preferable. Here, we present an inverse problem using highly undersampled frequency space measurements by using a Reduced-Order Unscented Kalman Filter (ROUKF) with a novel objective function. We show that this results in more accurate parameter estimation for boundary conditions in a synthetic aortic blood flow than using measurements reconstructed with Compressed Sensing. We also compare different sampling patterns, demonstrating that the quality of the parameter estimation is strongly dependent on the choice of sampling pattern.