The problem of multiple emitters geolocation using sensor arrays is addressed, in the case of fading channels. A sparsity-based covariance-matrix fitting method is described. The procedure consists of finding a sparse representation of the sample covariance matrices obtained at the arrays, by representing each matrix by an over-complete basis. Sparsity is encouraged by an ℓ1-norm based penalty function. The penalty function is minimized by semi-definite programming. The proposed method provides useful insight and it does not require the identification of the signal and noise subspaces. Therefore, the method does not rely on a good estimate of the number of emitters. Some of the approach properties are super-resolution, robustness to noise, robustness to emitter correlation, no sensitivity to initialization and no need for synchronizing the arrays. Special emphasis is given to uncorrelated sources and uniform linear arrays.