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That can represent a tremendous amount of computation, or, as some have characterized least squares, “mathematics that no mortal could do by hand.” Indeed, it was not until powerful personal computing became inexpensive and readily available that least squares landed in the toolbox of many surveyors. Basically, it’s a way to find a “best fit” of correlated measurements where the minimum sum of the squares of their errors may be determined. It provides statistically the most-likely location of multiple measured points, with the option of varying the “weight” of selected measurements. “Least squares” is a broad term for an array of methods that take the concept of error distribution and apply it across many correlated measurements, even those evaluated in a complex network. The concept was refined by others and adapted for use beyond astronomy geodesy and surveying are but two of the many uses.
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The term “Gaussian distribution,” that might be familiar to surveyors as the “normal distribution” bell curve of statistical uncertainty fundamental to the evaluation of surveying measurements, owes its name to Gauss. Least squares grew out of the field of astronomy, and it is widely accepted that Carl Gauss first proposed it more than two centuries ago. When it comes to evaluating surveying and geodesy measurements, many people rely on the mathematical sophistication and primacy of least squares network analysis and adjustment to provide the “final answer.” While a few surveyors may be confident in the tightness of the solutions produced by their instrumentation and view this idea of adjusting survey networks as unnecessary, a growing number of surveyors consider it so critical in their work that they apply least squares to every survey.