This contribution presents a modified Kalman filter approach for single channel speech enhancement which is operating in the frequency domain. In the first step, temporal correlation of successive frames is exploited yielding estimates of the current speech and noise DFT coefficients. This first prediction is updated in the second step applying an SNR dependent MMSE estimator which is adapted to the (measured) statistics of the speech prediction error signal. Objective measurements show consistent improvements compared to estimators which do not take into account the temporal correlation or the influence of the input SNR on the statistics of the prediction error signal.