Consider the following regression model :
Y = AX + BU
where the size of Y is $N \times n$, A is $N \times n$, X is $n \times n$, B is $N \times n$ and U is $n \times 1$.
The matrices X,Y and U are kown and the matrices A and U have to be estimated.
Is there an optimal method (in the sense of minimal residual error between Y and its estimate) for estimating A and U simultaneously ?