Consistent estimate of Kalman gain in subspace identification method

This paper proposes a consistent estimates of the Kalman gain and the covariance of the innovations in the framework of subspace identification. The estimates of the system matrices in PO-MOESP method are known to be consistent while the estimates of (A, C) matrices in N4SID method are asymptotically consistent, i.e., each estimate converges in probability to the true value if not only the data length but also the past horizon goes to infinity. The conventional estimates of the Kalman gain and the innovations covariance are asymptotically consistent. To consider the gap relating amount, consistent estimates of the Kalman gain and the innovations covariance are obtained.