Iterative Selection of GOB Poles in the Context of System Modeling

This paper is concerned with the problem of system identification using expansions on generalized orthonormal bases (GOB). Three algorithms are proposed to optimize the poles of such a basis. The first two algorithms determine a GOB with optimal real poles while the third one determines a GOB with optimal real and complex poles. These algorithms are based on the estimation of the dominant mode associated with a residual signal obtained by iteratively filtering the output of the process to be modelled. These algorithms are iterative and based on the quadratic error between the linear process output and the GOB based model output. They present the advantage to be very simple to implement. No numerical optimization technique is needed, and in consequence there is no problem of local minima as is the case for other algorithms in the literature. The convergence of the proposed algorithms is proved by demonstrating that the modeling quadratic error between the process output and the GOB based model is decreasing at each iteration of the algorithm. The performance of the proposed pole selection algorithms are based on the quadratic error criteria and illustrated by means of simulation results.