FRF Smoothing to Improve Initial Estimates for Transfer Function Identification

Good initial values are crucial to obtain solutions of nonconvex optimization problems. When estimating the transfer function of physical systems from measured noisy data, obtaining good initial parameter estimates is therefore a primordial step. In this paper, it is shown that smoothing the measured frequency response function of a linear time-invariant system enhances the construction of initial estimates significantly, resulting in the optimization schemes to converge to a better optimum. This is achieved with minimal user interaction. Two smoothing techniques, the time-truncated local polynomial method and the regularized finite impulse response, are compared with the existing generalized total least squares and the bootstrapped total least squares initial estimates. The improvement attributable to smoothing is demonstrated by a simulation and by measurements of an electrical filter. The results ultimately show that the parametric models obtained using the proposed starting values are much more likely to give a good description of the measured system and hence lead to more useful models.