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.