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This paper considers estimation of the noise spectral variance from speech signals contaminated by highly nonstationary noise sources. The method can accurately track fast changes in noise power level (up to about 10 dB/s). In each time frame, for each frequency bin, the noise variance estimate is updated recursively with the minimum mean-square error (mmse) estimate of the current noise power. A time- and frequency-dependent smoothing parameter is used, which is varied according to an estimate of speech presence probability. In this way, the amount of speech power leaking into the noise estimates is kept low. For the estimation of the noise power, a spectral gain function is used, which is found by an iterative data-driven training method. The proposed noise tracking method is tested on various stationary and nonstationary noise sources, for a wide range of signal-to-noise ratios, and compared with two state-of-the-art methods. When used in a speech enhancement system, improvements in segmental signal-to-noise ratio of more than 1 dB can be obtained for the most nonstationary noise sources at high noise levels.