טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentMayas Nawatha
SubjectDetecting Gross Errors in GNSS Networks by Means
of Spanning Trees
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Professor Even-Tzur Gilad
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

A Gross Error is an observation, which has a random error in a different distribution apart from the observation set. Random errors are small and inconspicuous since they do not have large magnitudes. Gross error investigation is one of the first interest areas of statisticians and different approaches have been developed for this purpose so far.

With growing demands for precise geodetic measurements in general, and GNSS measurements in particular, there is a need for a precise and meticulous method for the detection and removal of gross errors from the measurements. In the literature, although many studies and experiments have already been made, there is not one method that is the best one overall to deal with gross errors in GNSS measurements.

This study aims at presenting a new perspective of GNSS networks based on principles from graph theory such as edges, nodes, loops and spanning trees.

By these principles, an effective and reliable method for detecting gross errors in GNSS measurements has been developed. The main idea of the method is to check for the cause of every unclosed loop, all loops are created from the branches and the chords of the spanning trees. The new method can be used without the need for using adjustment computations, regardless of the number of repeated vectors and number of known points taking part in the measured GNSS network.

The study examines the efficiency of the new method in detecting gross errors versus well-known classical methods. According to the classical methods, gross error detection is done by using Least Square adjustment with statistical tests of hypothesis (t, τ and w tests) and robust estimation methods (Andrews, Turkey, Danish and Huber) in addition to an extension of the Danish method, suitable for correlated observations. For an examination of the developed method and for testing it relative to the other methods, measurements from the 2002s G1 network were used. The Network is a supreme geodetic control network in Israel, and it is also used for Geo-Dynamics research.

The results of the various tests indicate the advantage of the new method in terms of accurate gross error detection. Even though tens of thousands of loops were calculated in the case studies, among all the tested methods, the new method was the most accurate one in detecting gross errors in the measured GPS network.