Abstract Although better progress has been made in the area of speech enhancement, a significant performance degradation still exists under highly non-stationary noisy conditions. These conditions have a detrimental impact on the performance of the speech processing applications such as automatic speech recognition, speech encoding, speaker verification, speaker identification, and speaker recognition. Therefore, in this work, a robust noise estimation technique is proposed for speech enhancement under highly non-stationary noisy scenarios. The proposed work introduces an optimal smoothing and minima controlled (OSMC) through an iterative averaging method for noise estimation. Firstly, the computation of smooth power spectrum of degraded speech data and tracking the minima by continuously taking the past spectral average values are considered. Then, to find the activity of speech in each frequency bin, the ratio of degraded speech spectrum to its local minimum is considered, and a Bayes minimum-cost rule is applied for the decision-making. Finally, the spectrum of noise is estimated using the time-frequency dependent smoothing factors which mainly depend on the estimation of the probability of speech presence. The experiments are conducted on NOIZEUS and Kannada speech databases. The evaluated results demonstrated that the proposed OSMC technique exhibits better speech quality and intelligibility performance compared to existing algorithms under highly non-stationary noisy conditions.