Current methods to measure blood flow using ultrafast Doppler imaging often make use of a Singular Value Decomposition (SVD). The SVD has been shown to be an effective way to remove clutter signals associated with slow moving tissue. Conventionally, the SVD is calculated from an ensemble of frames, after which the first dominant eigenvectors are removed. The Power Doppler Image (PDI) is then computed by averaging over the remaining components. The SVD method is computationally intensive and lacks flexibility due to the fixed ensemble length. We propose a method, based on the Projection Approximation Subspace Tracking (PAST) algorithm, which is computationally efficient and allows us to sequentially estimate and remove the principal components, while also offering flexibility for calculating the PDI, e.g. by using any convolutional filter. During a functional ultrasound (fUS) measurement, the intensity variations over time for every pixel were correlated to a known stimulus pattern. The results show that for a pixel chosen around the location of the stimulation electrode, the PAST algorithm achieves a higher Pearson correlation coefficient than the state-of-the-art SVD method, highlighting its potential to be used for fUS measurements.