This blog post is about the Linear Least Squares Problem. This method is credited back to Legendre and Gauss, some of my favorite mathematicians. Why are they such inspiring people? Here is a passage from a post that goes into more depth about Gauss's application of least squares:
The 24-year-old Gauss tackled the orbit problem, assuming only Kepler’s three laws of planetary motion, with his newly discovered error distributions and his method of least squares for three months. He spent over 100 hours performing intensive calculations by hand without any mistakes (and without the luxury of today’s computers!). He had to estimate the six parameters of the orbit (as shown in Figure 7) from only 19 data points, subject to random measurement errors. He even invented new techniques such as the Fast Fourier Transform for interpolating trigonometric series, which produced efficient numerical approximations o