Least Squares - History - Context

Context

The method of least squares grew out of the fields of astronomy and geodesy as scientists and mathematicians sought to provide solutions to the challenges of navigating the Earth's oceans during the Age of Exploration. The accurate description of the behavior of celestial bodies was the key to enabling ships to sail in open seas where before sailors had relied on land sightings to determine the positions of their ships.

The method was the culmination of several advances that took place during the course of the eighteenth century:

• The combination of different observations taken under the same conditions contrary to simply trying one's best to observe and record a single observation accurately. This approach was notably used by Tobias Mayer while studying the librations of the moon.
• The combination of different observations as being the best estimate of the true value; errors decrease with aggregation rather than increase, perhaps first expressed by Roger Cotes.
• The combination of different observations taken under different conditions as notably performed by Roger Joseph Boscovich in his work on the shape of the earth and Pierre-Simon Laplace in his work in explaining the differences in motion of Jupiter and Saturn.
• The development of a criterion that can be evaluated to determine when the solution with the minimum error has been achieved, developed by Laplace in his Method of Least Squares.