Matrix factorization based instrumental variable approach for simultaneous identification of Bi-directional path models

This paper proposes a closed-loop identification approach to integrate matrix factorization algorithms with generalized instrumental variable (GIV) techniques to simultaneously identify the parameters and orders for both forward and backward path models. Aside from the technique of UD factorization, the QR factorization technique, which possesses good numerical property, is utilized for the proposed GIV-based method. The major difficulty and novelty of the proposed approach lies in how to properly construct instruments, number of instruments, and weighting matrices to obtain enhanced identification performance. To the end, the identification accuracy properties, in terms of the covariance matrix of the parameter estimates, are provided. In addition, a sufficient condition of consistent parameter estimates for the GIV-based approach is discussed. The effectiveness of the proposed identification method is demonstrated by simulation results.