Can you give dimension notation for your matrices/vectors? Usually X and Y have some common dimension and in this formulation it looks like they don't agree.
I know that the weighted least squares solution is
B = (X'WX)^-1 . (X'WY)
Where B is the parameters, X the input, Y the targets and W the weight matrix such that Wii = 1/SD, which in this last case, if I understand it, is optimal if the errors are uncorrelated.
But does anyone know how to achieve this derivation in matrix notation from the form
argmin SSE(B) = (Y-XB)'W(Y-XB)?
Many thanks in advance for any insights.