Time-varying system identification using recursive subspace method based on free response data

A novel recursive subspace method is presented in this paper. The generalized observability matrix is obtained by full rank decomposition of the generalized Hankel matrix consisting of free response data at first. Then the system matrix is calculated according to the shift invariant property of the generalized observability matrix. This method is equal to the Eigen-system Realization Algorithm (ERA). The novel method is obtained using Projection Approximation Subspace Tracking (PAST) method instead of the Eigen Value Decomposition (EVD). The variant of the left singular value vector matrix is tracked while the new data is added. The variant of the system parameter is also tracked according to this. At last a moving mass and simply-supported beam model is presented and the novel method is verified. The novel method is proved to be less computational complexity, more accurate in tracking and more noise-insensitivity.