The ability to estimate a specific set of parameters, without regard to an unknown set of other parameters that influence the measured data, or nuisance parameters, is described by the Fisher Information matrix (FIM), and its inverse the Cramer-Rao bound. In many adaptive gradient algorithm, the effect of multiplication by the latter is to make the update larger in directions in which the variations of the parameter θ have less statistical significance. In this paper, we examine the relationship between the Fisher information and the covariance of the estimation error under the scope of the source separation problem.