Applications of Graph Theory to Gross Error Detection for GPS Geodetic Control Networks

摘要

This paper describes a broad perspective of the application of graph theory to establishment of GPS control networks whereby the GPS network is considered as a connected and directed graph with three components. In this algorithm the gross error detection is undertaken through loops of different spanning trees using the "Loop Law" in which the individual components ΔX, ΔY and ΔZ sum up to zero. If the sum of the respective vector components ΣX, ΣY and ΣZ in a loop is not zero and if the error is beyond the tolerable limit (ε>w),it indicates the existence of gross errors in one of the baselines in the loop and therefore the baseline must be removed or re-observed. After successful screening of errors by graph theory, network adjustment can be carried out. In this paper, the GPS data from the control network established as reference system for the HP Dam at Baishan county in Liaoning province is presented to illustrate the algorithm.