On initial data in adjustments of the geometric levelling networks (on the mean of paired observations)

Abstract

There are many systematic errors in the precise levelling measurements. The most of them we have studied and their impact on the final accuracy of levelling is solved by appropriate corrections. The main objective of the current article is to reveal the greatest systematic error in the processing of levelling data, i.e., the use of only the averages of the fore and the back measurements of the elevations in levelling lines as initial data in the adjustment of the highest order levelling networks. Regardless of the type of distribution, simulations of random paired samples reveal that the averages of each pair only up to 33% of all cases are more closely located to the known theoretical expectation with respect to their parents. This fact implies that the collected data are not processed in the best way. In order not to lose information, we adjusted a reduced network of the Third Precise Levelling of Finland network in all possible combinations by the use of the fore, the back, and the mean of each line elevation. As a result, the final accuracy increases more than 10 times in comparison to an adjustment with the use of the averages only.