Simultaneous identification of bi-directional paths in closed-loop systems with coloured noise

In this paper, a novel instrumental variable (IV) based identification method is proposed for closed-loop systems in the presence of coloured noise. The key technique lies in constructing an interleaved information matrix with respect to a multiple model structure formulated for the bi-directional paths. Then by utilizing UD factorization, all the parameter estimates for both forward and backward path models with orders possibly from zero to nn, as well as the corresponding minimum loss function values, can be obtained simultaneously. Simulation results are provided to show the effectiveness of the proposed method.