A new recursive subspace identification algorithm is proposed for the problems existed in traditional algorithms
that using fixed factor can easily disturbed by noise. Firstly, input-output Hankel matrices and observation vectors are updated
with variable factor. Then, modified algorithm of gradient subspace tracking is designed for recursive estimation of extended
observation matrix, which is used to estimate system matrices. Finally, with the help of eigenvalues’ Euclidean-distance of
matrix ??, the approach of changing forgetting factor is realized, which ensures the self-adaptation of proposed algorithm. The
simulation results show that the tracking performance of new algorithm is faster and better than that of traditional algorithm.