Optimal Hankel-norm approximation and rational function models using impulse response data

The motivation of this work is rational function modeling of transfer functions using impulse response data from underwater acoustic transducers. However, since such data does not, in general, correspond to a rational model even in the abscence of noise, an effective rational function approximation criterion is necessary. In this report, the approximation error measure used is the Hankel-norm. Approximation using the Hankel-norm is a linear algebra method with an assured global minimum while the usual least-squares approximation is a nonlinear method satisfying only local minimum criteria. There are three outstanding features of this Hankel-norm approach: (1) the rational model is uniquely determined by the optimality criterion; (2) this rational model is guaranteed to be stable; and (3) the exact error approximation is given by a singular value of the corresponding Hankel operator and can be easily computed. The main contribution of this report is to extend Kung's model reduction algorithm to approximating systems not exactly described by rational function models of finite order and to requiring only the solution of simple instead of generalized eigenvalue problems required in Kung's method.