June 17, 2021

Surveying & The Least Squares Method

1 min read

Most surveyors know, from study and training if not personal experience, that “least squares” are important. That might be the extent of what they know though. Important, yes, but why? And what exactly is least squares adjustment? What exactly does it do for land surveyors and other geospatial professionals?

Least squares adjustment can be defined, as “a model for the solution of an overdetermined system of equations based on the principle of least squares of observation residuals.” For surveyors, “overdetermined systems” are the networks of related coordinates used to establish boundaries, locate points on Earth, facilitate large construction projects, etc.

These networks are usually “overdetermined” in a mathematical sense because of varying randomness in observation technologies and measuring equipment. Usefully analyzing all this randomness to improve network accuracy and integrity requires a set of powerful mathematical techniques (including matrix algebra) that are collectively termed least squares adjustment.

This is an over-simplified explanation, of course, but perhaps establishes that least squares adjustment plays an important role in any surveying practice that uses or creates coordinate networks. That is to say, all surveying practices.

How can surveyors apply least squares adjustment efficiently? After all, even though surveyors tend to be extremely intelligent and well educated, they often aren’t comfortable using some of these types of advanced mathematics on a daily basis.

Fortunately, as computing power became widely available, practical least squares adjustment was one of the first applications to be developed specifically for land surveyors. One such program, MicroSurvey’s STAR*NET, has been around since the mid-1980s, and has been used by thousands of surveying firms in many different workflows.

Least Squares can be complicated when trying to understand how to really works, but it is however the recommended method for adjustments in the field of Land Surveying.


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