Subspace identification identifies the state space model directly based on the process input and output data.Due to its simplicity and efficiency

subspace identification method is widely used in MIMO process identification.The main obstacle towards implementing adaptive subspace identification is developing online QR and SVD decomposition algorithms.A fast QR decomposition procedure was proposed by simultaneously applying data updating and downdating

which outperformed traditional algorithms in terms of computational efficiency.Complexity analysis showed that fast QR decomposition could save 8.3% computational cost compared with the two-step approach.Numerical simulation study demonstrated the efficiency of the proposed algorithm.