Least Squares Analysis and Positional Tolerance Explained

Least squares analysis, except for positional tolerance requirements, is not required for most survey work and thus tends to fit a niche group of land surveyors. Improvements in data collection and office software have made it so it is as efficient to perform least squares as easily as any other processing technique.

This seminar focuses on how a surveyor can use least squares to optimize their field survey data, creating networks that optimize field work efficiency, and quickly validate lack of blunders and quality of the information. General terms and concepts will be presented and how a surveyor can quickly evaluate the survey information. Field techniques that optimize checks will be presented. Total station, GNSS vectors, and combined total station/GNSS surveys will be presented. The presentation will be field system and office system independent utilizing generic formats and public domain software.

Searching for an exacting definition of positional tolerance in survey literature can be a frustrating endeavor even though ALTA standards for it have existed for a long time. This seminar intends to illustrate what the presenter feels positional tolerance is in terms of product of least squares analysis utilizing public domain software. The differences between absolute vs. relative positional tolerance along with post-adjustment standard deviations of bearings and distances on our products will be presented. Differences in “opinions” of what multipliers should be used to obtain positional tolerance quantities at the usual standard of 95% confidence will be presented.

The concept of survey network design as a tool for pre-analysis of predicting success in passing a positional tolerance standard completes the presentation.