Model-based parameter estimation in electromagnetics: Part I. Background and theoretical development

Electromagnetics (EM), as is true of other scientific disciplines, utilizes solution tools that range from rigorous analytical formulations to approximate, engineering estimates. One goal in EM, especially for design applications where specific performance is desired, is that of expending only enough solution effort to obtain a quantitative result commensurate with the problem requirements. Included among the possible approaches for achieving such a goal is model-based parameter estimation (MBPE). MBPE is used to circumvent the requirement of obtaining all samples of desired observables (e.g., impedance, gain, RCS, etc.) from a first-principles model (FPM) or from measured data (MD) by instead using a reduced-order, physically-based approximation of the sampled data, called a fitting model (FM). One application of a fitting model is interpolating between, or extrapolating from, samples of first-principles-model or measured data observables, to reduce the amount of data needed. A second is to use a fitting model in first-principles-model computations by replacing needed mathematical expressions with simpler analytical approximations, to reduce the computational cost of the first-principles model itself. As an added benefit, the fitting models can be more suitable for design and optimization purposes than the usual numerical data that comes from a first-principles model or measured data, because the fitting models can normally be handled analytically rather than via operations on the numerical samples. This article first provides a background and motivation for using MBPE in electromagnetics, focusing on the use of fitting models that are described by exponential and pole series. How data obtained from various kinds of sampling procedures can be used to quantify such models, i.e., to determine numerical values for their coefficients is also presented. It continues by illustrating applications of MBPE to various kinds of EM observables. It concludes by discussing how MBPE might be used to improve the efficiency of first-principles models based on frequency-domain integral equations (IEs).