To solve the problem of distributed multisensor fusion, the optimal linear methods can be used in Gaussian noise models. In practice, channel noise distributions are usually non-Gaussian, possibly heavy-tailed, making linear methods fail. By combining a classical tool of optimal linear fusion and a robust statistical method, the two-stage MAD robust fusion (MADRF) algorithm is proposed. It effectively performs both in symmetrically and asymmetrically contaminated Gaussian channel noise with contamination parameters varying over a wide range.