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Various speech enhancement techniques (e.g. noise suppression, dereverberation) rely on the knowledge of the statistics of the clean signal and the noise process. In practice, however, these statistics are not explicitly available, and the overall enhancement accuracy critically depends on the estimation quality of the unknown statistics. With this respect, subspace based approaches have shown to allow for reduced estimation delay and perform a good tracking vs. final misadjustment tradeoff [1,2]. For an accurate noise non-stationarity tracking, these schemes have the challenge to estimate the correlation matrix of the observed signal from a limited number of samples. In this paper, we investigate the effect of the covariance estimation artifacts on the noise PSD tracking. We show that the estimation downsides could be alleviated using an appropriate selection scheme.