Maximum likelihood, weighted Kalman and subspace linear prediction algorithms for system identification

For the problem of estimating parameters of a linear system from its input and output sequences, the authors present iterative quadratic maximum-likelihood (IQML), iterative quadratic weighted Kalman (IQWK), and noniterative subspace linear prediction (SLP) algorithms. The presence of forced response, free response, and noise is taken into account. The IQML algorithm is only for the case where either the free response or the forced response is absent from the output. The IQWK algorithm is provided as another classical method for the system identification problem. The SLP algorithms are based on a novel subspace deconvolution of the output. In particular, a double total-least-squares SLP algorithm is provided.