Measurement Uncertainty Evaluation of Object Coordinates by the Goniometric Method

The features of the uncertainty evaluation of measuring the coordinates of an object by the goniometric method (theta-theta position fixing) are discussed. Measurement models are presented that relate its coordinates in the local rectangular coordinate system with the spherical coordinates of the object found using goniometers. The model includes corrections for determining the location of base stations, corrections for determining elevation angles due to inaccuracies in leveling the station platform and azimuth, and corrections associated with inaccuracies in the location of stations to the north. Uncertainty budgets for measurements of rectangular coordinates are given, which can be the basis for creating software for automating the calculation of measurement uncertainties. The estimates of the expanded uncertainties are found by the kurtosis method.

I. Introduction

The problem of an object spatial coordinates determining is widely used in geodesy, radio navigation, radio-, optical and acoustic locations [1] –[4]. Depending on the number of reference stations (RS) used in this case (radar, optoelectronic or acoustic) and their capabilities, this problem is solved by various methods.