Comparison of measurements in co-ordinate metrology

The primary output from a co-ordinate metrology system is a set of measured co-ordinates representing the locations of targets. This paper is concerned with the following issues: (a) how do we express the uncertainty associated with a set of measured co-ordinates and how can we summarise the uncertainty characteristics of a co-ordinate measuring system, (b) if two co-ordinate measuring systems measure the same set of targets, how do we assess whether the two sets of measured co-ordinates are consistent with each other, and (c) given two sets of measurements of the same set of targets, how can we obtain a combined estimate of the target locations. Any concept of traceability of co-ordinate measurements will need to provide a way of answering these questions. We show that multivariate probabilistic techniques, multivariate counterparts to those described in the Guide to the Expression of Uncertainty in Measurement, can give useful answers to these questions. We illustrate their application to laser tracker and theodolite systems.