4D Flow MRI is the state of the art technique for measuring blood flow velocity, 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. Due to this, usually only a part of the frequency space is acquired, where then further assumptions need to be made in order to obtain an image. Inverse problems from 4D Flow MRI data have the potential to compute clinically relevant quantities without the need for invasive procedures, and/or expanding the set of biomarkers for a more accurate diagnosis. However, reconstructing 4D flow with Compressed Sensing techniques introduces 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 unclear which of them is preferable. Here, we present a parameter estimation problem directly using highly undersampled frequency space measurements. This problem is numerically solved by a Reduced-Order Unscented Kalman Filter (ROUKF). 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 how the quality of the parameter estimation depends on the choice of the sampling pattern.