8. Minimizing Random Errors

Using appropriate equipment under favorable conditions by an experienced field crew and repeating measurements is the best way to minimize random errors. This is why we spend so much time familiarizing ourselves with our equipment and measuring so many times.

An example of angle measurement standards are the precise traverse theodolite and angle specifications in the FGCS Standards and Specifications for Geodetic Control Networks. These are summarized in Tables F-1 and F-2.

Table F-1

Table F-2


Both tables demonstrate that to achieve higher accuracy, finer resolution equipment is needed along with additional measurements. The general relationship of random error magnitude and number of measurements is shown in Figure F-7.


Repeating a measurement several times can result in a larger initial random error reduction. Adding more measurements further reduces error.

Eventually a point of diminishing returns is reached: additional measurements don't appreciably lower the error. It's up to the surveyor to determine when that point is reached based on the job and equipment available.

This relationship is non-linear so doubling measurements doesn't cut error in half. Plus the graph never reaches 0 error because there is always some error present.

Figure F-7
Repeated Measurements and Error