ROBUSTNESS ANALYSIS OF GEODETIC NETWORKS IN THE CASE OF CORRELATED OBSERVATIONS

Abstract

GPS (or GNSS) networks are invaluable tools for monitoring natural hazards such
as earthquakes. However, blunders in GPS observations may be mistakenly
interpreted as deformation. Therefore, robust networks are needed in deformation
monitoring using GPS networks. Robustness analysis is a natural merger of
reliability and strain and defined as the ability to resist deformations caused by the
maximum undetectable errors as determined from internal reliability analysis.
However, to obtain rigorously correct results; the correlations among the
observations must be considered while computing maximum undetectable errors.
Therefore, we propose to use the normalized reliability numbers instead of
redundancy numbers (Baarda’s approach) in robustness analysis of a GPS network.
A simple mathematical relation showing the ratio between uncorrelated and
correlated cases for maximum undetectable error is derived. The same ratio is also
valid for the displacements. Numerical results show that if correlations among
observations are ignored, dramatically different displacements can be obtained
depending on the size of multiple correlation coefficients. Furthermore, when 

normalized reliability numbers are small, displacements get large, i.e., observations
with low reliability numbers cause bigger displacements compared to observations
with high reliability numbers.