Improving telescope mechanical error estimates using pointing data

A procedure was developed to make precise estimates of mechanical errors in telescopes using observed pointing error data. A kinematic model was used to relate pointing errors to mechanical errors and the parameters of the kinematic model were estimated with a statistical model fit using data from four large astronomical telescopes as well as simulated data containing known errors. Modified ordinary least squares regression provided a baseline solution that was found to yield mechanical error estimates with relatively large standard errors due to correlation among the terms. The baseline results were comparable to those typically obtained on large research telescopes.; Bootstrapping, ridge regression, and Bayesian regression were each investigated as methods to improve the estimated parameter precision. Bootstrapping estimates of parameters associated with uncorrelated errors were more precise than the baseline model but the parameter estimates related to the correlated errors were not improved. Bootstrapping, however, allowed the form of the distribution of each mechanical error estimate to be studied in addition to allowing its parameters to be quantified.; Ridge regression yielded more precise parameter estimates than the baseline model and the proper selection of the ridge parameter was found to have only a week dependence on the specific data. This is a useful property because it eliminates much of the judgement associated with employing ridge regression for telescope mount modeling.; Bayesian regression produced the greatest improvement in precision over the baseline results. The Bayesian regression error estimates were precise enough to be of practical use in designing, operating and maintaining large telescopes and related equipment. The method provides a way to estimate geometric errors with greater precision than they can be measured using current approaches.; The improvement in precision of the model parameters also lead to better telescope pointing. Predictions from the model showed that the Bayesian regression results will produce pointing errors on large telescopes that are approximately 15% less than typical errors using current techniques.