The mean and the variance matrix of the ‘fixed’ GPS baseline.

Abstract

In this contribution we determine the first two moments of the 'fixed' GPS baseline. The first two moments of the 'float' solution are well-known. They follow from standard adjustment theory. In order to determine the corresponding moments of the 'fixed' solution, the probabilistic characteristics of the integer least-squares ambiguities need to be taken into account. It is shown that the 'fixed' GPS baseline estimator is unbiased in case the probability density function of the real-valued least-squares ambiguity vector is symmetric about its integer mean. We also determine the variance matrix of the 'fixed' GPS baseline. This matrix differs from the one which is usually used in practice. The difference between the two matrices is made up of the precision contribution of the integer least-squares ambiguities.