Applications of Least Squares to find optimal solutions to real world problems involving circle regression.

Abstract

The Least Squares Method is a mathematical technique that helps to estimate parameters using a regression analysis approach based on minimizing residuals, which is the difference between data (an observed value) and a computed value. Most popular estimations include linear, quadratic, polynomial fits to approximate the given data. The best fit to the data using these functions are determined through the respective correlation coefficients. However, there are applications when all these well-known fits do not give good approximations, such as when the data is in the form of a circle; in which case, a different regression approach is required. Real-world data that arise from applications don’t necessarily exhibit trends that can be captured by standard regression algorithms, for example predicting the diameter of the head of a baby through ultrasound data to predicting optimal location of an aircraft from satellite stations at different locations. In this work, one formulates this circle regression problem using a matrix approach to find the optimal solution. Using a matrix approach, we expand the circle regression approach to finding the most accurate location of an aircraft. Our results suggest that the proposed method is reliable and robust and can be used for other related real world applications.