Differential And Autoregressive Linear Regression Models For Lorentzian Profile Fitting Problem

The paper presents a formulation of a lorentzian profile fitting problem as a linear regression problem, solvable in closed-form. This is essentially a parameter estimation problem for resonance peak profile. The resulting linear regression problems/models (differential and autoregressive forms) are solved for a simulated data under different scenarios in order to demonstrate the effectiveness of the linear regression formulation. In the first scenario (intended as proof of principle and reference) the linear model is subjected to noiseless data with small discretization size and the parameters are accurately estimated. The next scenarios subject the linear model to varying levels of data noise and discretization size, which demonstrates that the model is sensitive to data noise and discretization size. It was also found that the differential linear model is more prone to noise than the autoregressive linear model.