Uncertainty in two-stage measurement: Explanation using simulation studies

Abstract

In geodesy we often estimate coordinates of a two-dimensional point in a model of two-stage measurements. The points from the national trigonometric network have different accuracy, and independence is not met. We encounter situations where we cannot get quality results even by repeating measurements. The dependency among old points and their accuracy may have a considerable impact on the estimated coordinates of new points. To examine the impact, this paper presents simulation methods describing the uncertainty of estimated points. The main goal of this paper is to study the uncertainty of Least Squares Estimators in one surveying problem. This is a situation where an object should be very precisely connected to the government network. We draw attention to the fact that the Least Squares Method can give non-admissible geometric representation of an object's estimated coordinates. The main objective is to compare outputs from the two-stage regression model and from simulation studies.