Closed-loop identification using generalized orthonormal basis functions

This paper presents a closed-loop identification method based on the construction of generalized orthonormal basis functions (GOBF). It modifies the two-stage method, which applies the finite impulse response (FIR) model structure to one that uses GOBF functions. Identification of a FIR model has some important advantages, however it fails to be successful when the number of coefficients to be estimated becomes large. With appropriately chosen basis functions where the basis is generated by all-pass functions having poles close to the poles of the system, the convergence rate of the series expansion can be extremely fast. The paper gives the algorithm of the closed-loop identification, and it demonstrates the method in a numerical example