Gross-Error Detection in GNSS Networks Using Spanning Trees

Abstract

Many methods and techniques have been developed to detect gross errors in geodetic measurements, but none seems to have prevailed. Statistical tests and robust methods are the most common approaches for detecting outliers in geodetic measurements. Least-squares adjustment and iterative attitudes are the essence of those methods. In this paper, closing loops in Global Navigation Satellite System (GNSS) networks are used to detect gross errors. Spanning trees are used to define a set of independent loops in the network. Careful examination of the misclosure of loops assists in defining the faulty vectors. The method is very effective and delivers another alternative for outlier detection without using adjustment computation and statistical tests. The method of outlier detection by means of spanning trees is presented and tested against well-known methods like convectional statistical tests (w-test, τ-test, and t-test) and robust M-estimation methods (Andrews, Huber, and Danish). A number of tests were performed on a GNSS network that contains 115 points and 917 vectors to detect gross errors in different scenarios, and the results are presented in the paper. Based on the results of the presented tests, it is seen that the w-test and the M-estimation methods correctly detect all outliers in the GNSS network, whereas τ-tests and t-tests do not always detect the correct errors. The new method for detection of gross errors by means of spanning trees performs quite well and can correctly exclude all outliers with only one iteration.