Robustness Analysis of Geodetic Networks

Abstract

ABSTRACT: Geodetic control networks established for engineering construction (e.g., highways, railways, bridges, dams) typically have coordinates estimated by the method of least-squares and the 'goodness' of the network is measured by a precision analysis based upon the covariance matrix of the estimated parameters. When such a network is designed, traditionally this again is based upon measures derived from the covariance matrix of the estimated parameters. This traditional approach is based upon propagation of random errors. In addition to this precision analysis, reliability (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 the statistical test then those observations are removed, the network 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. Robustness analysis is a natural merger of reliability and strain and is defined as the ability to resist deformations induced by the smallest detectable outliers as determined from internal reliability analysis. This paper addresses the consequences of when outliers are not detected by Baarda's test. This may happen for two reasons (i) the observation is not sufficiently checked by other independent observations and (ii) the test does not recognize the gross 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