# Recursive QR-factorisation for N4SID - What does this equation mean?

I was reading a paper about recursive subspace identification, where they are using N4SID-algorithm with some extantion for the recursive method.

http://www.iaescore.com/journals/index.php/IJEECS/article/viewFile/6557/6368

I reason why I'm asking this question, is because I don't know how to compute the right hand side of equation (9) when the rigth hand side looks like this. I can't even write this out in LaTeX becase I don't know if $$\begin{bmatrix} u_f(\psi +1) \\ w_p(\psi +1)\\ y_f(\psi +1) \end{bmatrix}$$

What does $$\psi$$ come frome?

is a vector or not, because I cannot see any brackets in the formula. What do you think?