Robustness analysis of geodetic networks in the case of correlated observations

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 undetecle 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

DESIGN OF GEODETIC NETWORKS BASED ON OUTLIER IDENTIFICATION CRITERIA: AN EXAMPLE APPLIED TO THE LEVELING NETWORK

We present a numerical simulation method for designing geodetic networks. The quality criterion considered is based on the power of the test of data snooping testing procedure. This criterion expresses the probability of the data snooping to identify correctly an outlier. In general, the power of the test is defined theoretically. However, with the advent of the fast computers and large data storage systems, it can be estimated using numerical simulation. Here, the number of experiments in which the data snooping procedure identifies the outlier correctly is counted using Monte Carlos simulations. If the network configuration does not meet the reliability criterion at some part, then it can be improved by adding required observation to the surveying plan. The method does not use real observations. Thus, it depends on the geometrical configuration of the network; the uncertainty of the observations; and the size of outlier. The proposed method is demonstrated by practical application of one simulated leveling network. Results showed the needs of five additional observations between adjacent stations. The addition of these new observations improved the internal reliability of approximately 18%. Therefore, the final designed network must be able to identify and resist against the undetectable outliers – according to the probability levels