Parameter Estimation of Gaussian-Damped Sinusoids from a Geometric Perspective

TL;DR

This paper introduces a geometric approach for efficiently estimating parameters of Gaussian-damped sinusoids, modeling betatron motion in proton bunch signals, by separating parameters and reducing the search space.

Contribution

A novel geometric method for fitting Gaussian-damped sinusoids that simplifies parameter estimation by separating global and local parameters, applicable to similar problems.

Findings

Efficient parameter estimation for betatron motion signals.

Reduction of parameter search space through geometric separation.

Method generalizes to broader classes of problems.

Abstract

The five parameter gaussian damped sinusoid equation is a reasonable model for betatron motion with chromatic decoherence of the proton bunch centroid signal in the ring at the Spallation Neutron Source. A geometric method for efficiently fitting this equation to the turn by turn signals to extract the betatron tune and damping constant will be presented. This method separates the parameters into global and local parameters and allows the use of vector arithmetic to eliminate the local parameters from the parameter search space. Furthermore, this method is easily generalized to reduce the parameter search space for a larger class of problems.