A New Model for Spherical Instrument Measurement Uncertainty

Publication Details

Abstract

Modeling uncertainty as point clouds is a good method for visualizing measurement uncertainties. Monte Carlo methods are often used to generate these point clouds by adding errors to a measurement and then iterating through tens or hundreds of measurement cycles. The result, when plotted, appears as a cloud of points surrounding the point of interest. In some cases, the uncertainties can be rather complicated when combining measurement uncertainties from multiple instruments. Monte Carlo uncertainty for spherical instruments (e.g., tracking interferometers or theodolites) using a spherical-to-cartesian coordinate transformation typically have point clouds that change from spheres at the equator to disks as the point clouds approach zenith and nadir. This does not comport with reality, because the lateral measurement uncertainty though an instrument is of the same order at all zenith angles. This article investigates this phenomenon and proposes an uncertainty model resulting in spherical uncertainty clouds at all angles.