A, B are assumed to be unknown. Minimizing this sum leads to a pair of linear equations. Both regression and kriging are at least partially motivated by conditional expectation.
Multivariate normality is a special case for both.
The coefficients in the regression equation are obtained by using an estimated covariance matrix. In regression there is a response variable and one or more control variables. In kriging there is no response variable. At least one author essentially derived the kriging estimator and the kriging equations from the regression model, A.S. Goldberger, J. American Stat. In the regression model let X be a vector and let the components of the vector be the coordinates of the position variable.