In the recent past, estimating brain activity with magneto/electroencephalography (M/EEG) has been increasingly employed as a noninvasive technique for understanding the brain functions and neural dynamics. However, one of the main open problems when dealing with M/EEG data is its non-Gaussian and nonstationary structure. In this paper, we introduce a methodology for enhancing the data covariance estimation using a weighted combination of multiple Gaussian kernels, termed WM-MK, that relies on the Kullback-Leibler divergence for associating each kernel weight to its relevance. From the obtained results of validation on nonstationary and non-Gaussian brain activity (simulated and real-world EEG data), WM-MK proves that the accuracy of the source estimation raises by more effectively exploiting the measured nonlinear structures with high time and space complexity.