Model based parameter estimation as a model abstraction technique

In this paper it is demonstrated that the technique of Model Based Parameter Estimation (MBPE), specifically Cauchy's Method, can be used in the frequency domain to extrapolate/interpolate a narrowband set of system data or information to a broadband set of data or information. The information can be either computed data or measured experimental data over a frequency band. For computed data the sampled values of the function and a few derivative values are used to reconstruct the function. For measured data only sampled values of the function are used as derivative values are too noisy. Cauchy's method is based on applying the principle of analytic continuation to a complex, hard to specify function, analytic except at isolated poles, that represents the frequency domain property of interest. Such a function can be represented by a ratio of two polynomials, a reduced order model, which can be considered to be a variant of model abstraction [3]. A procedure is outlined for determining the order of the polynomials and their coefficients using the methods of Singular Value Decomposition (SVD) and Least Squares. The method is applied to a selected set of frequency domain problems to illustrate the accuracy and versatility of the method.