A study of the optimization problem for calibrating a Lacoste and Romberg G gravity meter to determine circular errors

This report discusses how the circular errors of a gravity meter could be effectively calibrated in a laboratory. Minimization of the trace of the variance-covariance matrix of adjusted parameters, is adopted as the criterion for the optimization. The mathematical analysis of the trace is made in the case of one wavelength in order to find the best distribution of observations, as well as the worst. For several wavelengths, a number of simulative computations are carried out for finding effective distribution of observations and the best and worst weights. A set of numerical solutions for the equations over a certain range of observations is obtained. Based on the simulative studies, the concepts of phase distribution and effectiveness of observations in the periodic error calibration are presented and so a design for the most effective distribution of observations is introduced. For the calibration of periodic errors with several wavelengths, it is preferable to select two weights that can be mutually compensated in fitting them with all involved periods. An attempt is made to answer how many observations should be made for determining the periodic screw errors with reasonable accuracy.