generalized least squares (GLS) is a technique for estimating the unknown parameters in a linear regression model.
The GLS is applied when the variances of the observations are unequal or when there is a certain degree of correlation between the observations.

In a typical linear regression model we observe data \{y_i,x_{ij}\}_{i=1..n,j=1..p} on n statistical units. The response values are placed in a vector Y = (y1, ..., yn)′, and the predictor values are placed in the design matrix X = [[xij]], where xij is the value of the jth predictor variable for the ith unit. The model assumes that the conditional mean of Y given X is a linear function of X, whereas the conditional variance of the error term given X is a known matrix Ω. This is usually written as

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