PDF Evaluation of Elliptically Contoured GNSS Integer Ambiguity Residuals

Abstract

In this contribution we will present and evaluate the joint probability density function (PDF) of the multivariate integer GNSS carrier phase ambiguity residuals, thereby assuming that the GNSS data belong to the very general class of elliptically contoured (EC) distributions. Examples of distributions belonging to this class are the multivariate normal distribution, the t-distribution and the contaminated normal distribution. Since the residuals and their properties depend on the integer estimation principle used, we will present the PDF of the ambiguity residuals for the whole class of admissible integer estimators. This includes the estimation principles of integer rounding, integer bootstrapping, and integer least squares. The probabilistic properties of these estimators vary with the distributions from the EC-class. In order to get a better understanding of the various features of the joint PDF of the ambiguity residuals we will use a step-by-step construction aided by graphical means.