3D blood velocity estimation in medical ultrasound systems is revolutionizing the diagnosis of vascular diseases. However, the accuracy of blood velocity estimation is greatly affected by clutter signals from the vessel wall and the tissues surrounding the vessel. Filters used today to remove clutter are computationally expensive, limiting their practicality in portable 3D systems. In this paper, we present clutter filters for arterial flow that reduce computational complexity by orders of magnitude while maintaining the clutter removal performance of existing techniques. We achieve this goal by combining the existing Hankel-SVD clutter filter with the power iteration method to eliminate unnecessary SVD calculations. For the filters which use power iteration exclusively, we achieve excellent filtering performance with only 14.2% computational overhead to our previous flow estimation system. With these filtering methods, our pipelined architecture can compute velocity fields at a rate of 85 frames per second.