Quality Control Of Geodetic Networks Through Robustness Analysis
Abstract
After geodetic networks (e.g., horizontal control, leveling, GPS etc.) are monumented, relevant measurements are made and point coordinates for the control points are estimated by the method of least-squares, and the `goodness' of the network is measured by a precision analysis making use of the covariance matrix of the estimated parameters. When such a network is designed, traditionally this again uses measures derived from the covariance matrix of the estimated parameters. This traditional approach is based upon propagation of random errors. Reliability of geodetic control networks (the detection of outliers/gross errors/blunders among the observations) has been measured using a technique pioneered by the geodesist Baarda. In Baarda's method a statistical test (data-snooping) is used to detect outliers. What happens if one or more observations are burdened with an outlier? It is clear that these outliers will affect the observations and produce incorrect estimates of the parameters. If the outliers are detected by a statistical test then those contaminated observations are removed, the network is re-adjusted, and we obtain the final results. In the approach described here, traditional reliability analysis (Baarda's approach) has been augmented with geometrical strength analysis using strain in a technique called robustness analysis. In statistical literature robustness is insensitivity to outliers in the data. Robustness analysis is a natural merger of reliability and strain and is defined as the ability to resist deformations induced by the largest undetectable outliers as determined from internal reliability analysis. This paper addresses the consequences of outliers not being detected by Baarda's test. This failure may happen for two reasons (i) the observation is not sufficiently checked by other independent observations or (ii) the test does not recognize the gross error (type II error). By how much can these undetected errors influence the network? If the influence of the undetected errors is small the network is called robust; if it is not it is called a weak network. In this study, the computational process to determine threshold values for robustness primitives is discussed and some results are presented.
- Publication:
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AGU Spring Meeting Abstracts
- Pub Date:
- May 2004
- Bibcode:
- 2004AGUSM.G43A..01B
- Keywords:
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- 1299 General or miscellaneous