Generating High-Accuracy Simulation Models Using Problem-Tailored Orthogonal Polynomials Basis

Abstract

The problem of computing high-accuracy simulation models for systems described by tabulated frequency data is of paramount importance in the modeling arena. Standard algorithms for this task involve generating rational function approximations to the data. However, for complicated data sets, high-order approximations are required. Unfortunately, numerical conditioning problems arise when attempting to fit high-order rational approximations to the data, effectively limiting the accuracy of the models that can be generated. While robust fitting schemes based on orthogonal polynomial exist, they usually pose strict constraints on the data points, which are either hard or even impossible to guarantee. Furthermore, the approximation must still be translated such that it can directly be used inside a simulator. In this paper, we present an algorithm for robustly generating such a model using only the data given. The model is supported on a problem-tailored orthogonal polynomial basis. We also present a method for directly generating a state-space model associated with a rational function described in terms of such polynomials, effectively making the model amenable for simulation. An extension to the MIMO case is described and it is shown that the method is easily included with existing passivity enforcing procedures. Finally, we demonstrate the proposed technique by constructing approximations to several real-world data sets