Graph Theory Applications to GPS Networks

This paper aims at presenting a new perspective of GPS networks, based on principles from graph theory, which are used to describe some connectivity properties of GPS networks. This is possible using a directed, connected graph and an incidence matrix. As the incidence matrix maintains information about the GPS graphy, the fundamental set of independent loops in the GPS network can be read from the incidence matrix. A spanning tree serves as a primary tool in locating the independent loops. According to the loop law the coordinate differences around loops sum up to zero. The measured vectors contain random and gross errors. Hence, if the entire independent loops sums are less than a certain threshold in three components, we can guarantee that there are no gross errors in the observations. The fundamental set of independent loops, based on different spanning trees, is used to detect gross errors in the observations without using adjustment computation. We use a small, simulated network containing gross errors to demonstrate the proposed algorithm. © 2001 John Wiley & Sons, Inc.