Noise-interference suppression and data-processing acceleration are crucial to aeroacoustic measurements with phased array in wind tunnels. In this paper, we develop a "multi-window" beamforming algorithm that recursively processes data based on an array-acquisition model. This spatial filtering algorithm is derived from the Kalman filter theory for signal processing. The simulated results show that by using recursive operations, accurate signal estimation is acquired with incoherent and coherent background noise removed in the presence of both channel noise and phase noise. The convergence rate of this recursive algorithm is faster than the existing algorithms. As a result, considerable storage space and computational resources are saved, while testing defects in wind tunnel measurement are revealed and corrected immediately on-site. It has a great potential for real-time localization of sound sources in a noisy environment.