Recursive subspace model identification based on orthogonal projection and principal component analysis

Most subspace identification methods are developed for linear time-invariant system. However, in reality, most systems are time-varying. Hence the recursive version of subspace identification methods is urgently desired. In this paper, we propose a unifying framework of recursive subspace model identification algorithm, which is based on the orthogonal projection and principal component analysis (PCA). Based on our framework, the bona fide recursive algorithm is applied to update the QR factorization. Two recursive subspace model identification algorithms are developed for open loop and closed loop condition, respectively. The numerical simulations demonstrate the efficiency of the two algorithms comparing with other algorithms.