In this paper, a novel Kalman filter based noise suppression algorithm for hearing aids, using spatial information for estimating the required noise and speech models, is proposed. The main assumption of the scheme is that the target (usually the speech signal) is directly in front of the hearing aid user while the interference (usually the noise signal) comes from the back hemisphere. While in an earlier paper [1], a related approach based on instantaneous Wiener filters using a Weighted Overlap Add (WOLA) decomposition has been presented, this paper focuses on a time domain approach employing a time varying Kalman filter. Clearly, with the proper noise and speech models, one would expect a better performance of a time varying Kalman filter than of a WOLA Wiener filter. Hearing tests as well as objective performance measures show the excellent performance of the Kalman filter based noise suppression algorithm.