# Least square ellipsoid fitting using iterative orthogonal transformations

## TL;DR

This paper introduces a numerically stable iterative method for fitting ellipsoids to minimal data points, accurately determining shape, orientation, and axes, with applications in gravitational wave data analysis.

## Contribution

The paper presents a novel, stable ellipsoid fitting algorithm that works with minimal data points and accurately retrieves shape and orientation parameters.

## Key findings

- Effective on simulated data sets
- Applicable to highly elongated and arbitrarily oriented ellipsoids
- Potential use in gravitational wave data analysis

## Abstract

We describe a generalised method for ellipsoid fitting against a minimum set of data points. The proposed method is numerically stable and applies to a wide range of ellipsoidal shapes, including highly elongated and arbitrarily oriented ellipsoids. This new method also provides for the retrieval of rotational angle and length of semi-axes of the fitted ellipsoids accurately. We demonstrate the efficacy of this algorithm on simulated data sets and also indicate its potential use in gravitational wave data analysis.