I have an incompatible system of equations like: $y=A*x+n$ with more equations than variables, where $A$ and $y$ are known. $n$ is known to be a vector of random gaussian noise with known variance. How can I find the best aproximation of vector $x$ with all this data?
Note that I don't want to find the Least Squares solution, since I don't want to minimize $|y-A\hat{x}$|. I know the variance of the noise and it should be used to find a better solution for my problem.
Thanks!!!