Noise variance estimation based on measured maximums of sampled subsets

In this paper, an estimation of the Gaussian noise variance based on observed (measured) maximums of subsets of samples is given. Circumstances of the measurement environment being limited, only maximums of subsets of samples are available and the non-constant variance of the Gaussian noise can be estimated. In the case of power line noise, the variance of the zero mean Gaussian noise is a periodic function of the a-priory known parameterization. Variance function parameters estimation is computed in two steps, first the estimation formula of the constant variance Gaussian noise is applied to a certain subset of samples and second, the least mean square criterion (LMS) is applied to fit the parametrized variance function to estimated variances. The Maximum likelihood estimation (MLE) criterion is applied to derive estimators of the variance function parameters. Beside that, the quotient of the variance of the zero mean Gaussian noise and its maximums is evolved explicitly. Experimental results on real and simulated data are given to demonstrate their accuracy.