Many papers use the NMSE function without ever explicitly defining it. I have always assumed that MSE(x,y)=1N∑i(xi−yi)2 and NMSE(x,y)=MSEx,yMSE(x,0)=||x−y||22||x||22 where y is the approximation to x. This gives a simple relation between NMSE and relative l2 error. An internet search however only shows strange definitions like ∑i(xi−yi)2N∑i(xi)2 or N∑i(xi−yi2)∑ixi∑iyi Is my interpretation not the standard definition?

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GaceCoect5v · Accepted Answer

Matlab System Identification toolbox uses the following definiton:  NMSE=1−||x−y||2||x−x―||  where x―=1N∑ixi;y is the approximation of x

Many papers use the NMSE function without ever explicitly defining it.

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