A New Model for Spherical Instrument Measurement Uncertainty

Abstract

Monte Carlo uncertainty for spherical instruments (e.g. tracking interferometers, theodolites) using a spherical to cartesian coordinate transformation typically create 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 since the lateral uncertainty though an instrument is of the same order at all zenith angles. This paper looks at integrals over an instrument’s aperture and develops a new model for spherical instruments that can be applied to Monte Carlo and linear propagation of errors. Treating on-LOS and off-LOS rays differently, the latter accounting for measurement uncertainty across the aperture, results in spherically shaped uncertainty clouds at all angles. Examples of the two different models on uncertainty for both point-to-point and point-to-object geometries are shown.