These are numerical algorithms for subspace state space system identification. The book that use as reference it will be "Subspace Methods for System Identification" from Tohru Katayama
Step 1: Compute the LQ decomposition of (6.32).
Step 2: Compute the SVD of (6.39), and let and define the extended observability matrix as
Step 3: Obtain C and A from (6.41) and (6.42), respectively.
Step 4: Solve (6.44) by the least-squares method to estimate B and D .
You can enter see the code complete in python and use as a reference: MOESP_ALGORITHM.ipynb