Last Squares Adjusment – Revisited

I received an email today stating that they had run across my post on least squares adjustment while looking for a practical example and found none. (Not even at my site). He said that he had found many definitions and theories, but no actual examples.

That is true. The reason is that anything other than a trivial example is beyond the mathematical abilities of perhaps 95% of the practicing surveyors, including me. That fact is also the reason that so many surveyors are unwilling to accept the technique. Contrast that though with the willingness to accept an adjustment done by a data collector, simply by pushing the adjust button.

A least squares adjustment may be hard to program and compute, but it is very easy to understand what it does. Very simply, when presented with the equipment specifications, error estimates on centering accuracy, and field personnel techniques and abilities, the adjustment produces a result where no distance, no angle, or no control point varies from the field measured values more than the error associated with that measurement.

Contrast that with the typical traverse adjustment. We first check the angular closure and find out that to balance, 2 seconds must be added to each angle. Is this reasonable? Some traverse legs are long, some are sort. Shouldn’t more error be associated with angles where one or both legs are short? But how much more? And why should we assume that all angular error was in one direction? Common sense tells us that this is not likely. Angular error, if it is random, should be such so that some angles are greater and some are less than the true value. (just like tossing a coin and getting either heads or tails, not just heads).

Then after angle adjustment, we calculate the traverse, determine the closure, and again distribute the error of closure by prorating it to the latitudes and departures by ratio usually by either the transit or compass rule.

Check the correlation between adjusted measurements and your field measurements by inversing and computing the angle between legs and the length of each leg from your final computed coordinates. How do these compare with measured values? I would bet that there is no correlation. If you had to justify your procedure in court, could you prove you met ALTA standards?

I have used StarNet least squares adjustment software for many years, and wouldn’t do an ALTA survey or the boundary of a tract to be subdivided without it. And as I pointed out in a previous post, the ALTA standards practically mandate it. (Call Ron Sawyer of StarPlus Software at 510-653-4836 for a demo) StarPlus Software does not have a website.

Other companies also provide least squares programs for survey data.

One is Best Fit Computing. An excellent discussion of least squares may be found on their website at http://www.bestfit.com/prac_outliers.shtml

A free demo of Columbus, their least squares adjustment program that has all the functionality of the full release (up to 12 stations and no limit on the number of observations).can be downloaded at: http://www.bestfit.com/freedemo.shtml

Modules are also available in Ashtech Solutions, Trimble Office and Autodesk products. Find something you like and begin using it. I don’t think you will ever go back to other means of adjustment.