Weighting observations from multi-sensor coordinate measuring systems

In large scale coordinate metrology, estimates of target coordinates are determined from range and angle observations gathered by one or more laser trackers. In analysing such data, it is required to weight the range observations relative to the angle observations. While the system characterization will give a guide to the accuracy of these measurements, the actual behaviour will depend strongly on environmental effects, particularly those influencing the refractive index of the air. In this paper, we describe a general Bayesian approach to balancing sets of observational data in which the noise parameters are treated as unknowns but associated with prior distributions. Estimates of the appropriate weighting factors are derived from the posterior distributions for these noise parameters. We give examples of this general approach applied to the analysis of laser tracker data. (paper)