This paper deals with speech enhancement in dual-microphone smartphones using beamforming along with postfiltering techniques. The performance of these algorithms relies on a good estimation of the acoustic channel and speech and noise statistics. In this work we present a speech enhancement system that combines the estimation of the relative transfer function (RTF) between microphones using an extended Kalman filter framework with a novel speech presence probability estimator intended to track the noise statistics’ variability. The available dual-channel information is exploited to obtain more reliable estimates of clean speech statistics. Noise reduction is further improved by means of postfiltering techniques that take advantage of the speech presence estimation. Our proposal is evaluated in different reverberant and noisy environments when the smartphone is used in both close-talk and far-talk positions. The experimental results show that our system achieves improvements in terms of noise reduction, low speech distortion and better speech intelligibility compared to other state-of-the-art approaches.