Least squares variance component estimation for surveying network adjustment

Abstract

The stochastic model of least squares adjustment plays an essential role in geodetic network data processing because the model describes the accuracy of the measurements and their correlation with each other. Knowledge of weights of the observables is necessary to provide a better understanding of the sources of errors and to model the error, hence the weights need to be determined correctly. For geodetic applications, it is crucial to have knowledge about covariance matrix of the observables since variance components are most commonly used to determine a realistic precision. This study focuses on the estimation of variance components from different types of data for geodetic applications, which include deformation survey and cadastral survey. Least Squares Variance Component Estimation (LS-VCE) method was used in this study because the method is simple, flexible and attractive due to the precision of variance estimators that can be directly obtained. For deformation monitoring network, simulations of geodetic and Kenyir dam networks data were performed. Meanwhile, for cadastral observation data from several types of instruments such as chain measurement, Electronic Distance Measurement and total station were utilized. The results revealed that the estimated variance components for distance scale error ap seem to become unrealistic for each data tested as the baseline of the networks was not long enough. In addition, it was found that the traverse network which included chain survey, showed insignificant result to the precision of station coordinates when the measurements were combined. The distance-dependent model was selected as the best model for Kenyir dam network since W-test values of Epoch 1 and 2 were 0.30 and 0.50, where the expectation and the variance of W-test values were 0 and 1, respectively. The findings showed that LS-VCE method was very reliable in various geodetic applications. In conclusion, the program developed is valuable for professional groups which include surveyors and engineers, as well as geophysics and geologists.