“Real-World” Instrument Uncertainties

As mentioned earlier, instrument uncertainty values as published by the manufacturer are a good way to compare different measurement systems, but they are a poor way to predict real-world measurement uncertainty. A number of factors, such as the calibration / performance of an individual instrument, the technique of the operator, and the measurement environment have significant effects on uncertainty.

Each instrument in SA has associated with it Instrument Uncertainty Variables. These can be found in the Instrument Properties window. Uncertainty variables are used to model an individual instrument’s uncertainty characteristics.

If you look at the uncertainty variables for a laser tracker or total station, four values are provided (see image). These values together dictate the uncertainties for the horizontal angle, vertical angle, and distance components for an instrument. They are used in concert with a measurement’s relative position from the instrument to determine the uncertainty of the individual measurement.

By default, the values assigned to uncertainty variables are experimentally determined, conservative values for a given class of instrument. In other words, they generally give a result that is “in the ball- park”, but are probably a bit worse (higher uncertainty) than can truly be achieved with the instrument. This is done to a) err on the safe side, b) avoid conflict with instrument manufacturers, and c) avoid the need to continually update data as instruments evolve, which could be a time-consuming task.

In order to get the most realistic uncertainties for measurements and USMN, it is necessary to use uncertainty variable values that closely match the individual instrument, operator, and measurement environment characteristics. But how is this done? Manufacturers don’t (and can’t possibly) publish these values, and they differ from one instrument to the next and (to a lesser extent) from one operator/ measurement situation to the next.

USMN itself can be used to determine the most accurate values for these variables. This is done by setting up a set of monuments, and then moving an instrument around through the workspace, measuring each of those monuments in turn.

Consider a situation in which an instrument, its operator, and the environment is perfect (and therefore would have zero uncertainty). A perfect instrument, after having measured all monuments from different positions, would see a given monument in the exact same location in space. When fit together (using a traditional best-fit), there would be zero error. The observations would lie on top of each other perfectly. USMN would see this “perfection” and would report uncertainty variables of zero (no error).

Of course, in reality this never happens. In the real world, an instrument can measure a monument two different times and “see” it in a slightly different place. By analyzing the error between measurements of a common point from the same instrument, in different positions, USMN can perform a complex calculation and determine the real-world uncertainty variables for a given measurement situation.