The Effect of Critical Distance in Digital Levelling

Abstract

Critical distance concerns precise digital levelling, which has inaccurate results at a certain sighting distance. The influence of critical distance on a measured height difference has been confirmed by calibrating certain digital levels and their appropriate code devices on a vertical comparator under laboratory conditions. The paper aims to explore the influence of critical distance on height differences obtained by precise digital levels of Leica NA3003 and DNA03 by experimental measurements realised in situ. The processing of the measurement results consisted of defining a random error on a station by using parameter estimation of an error model to specify a partial error on a station dependent on sighting distance. Then the processing phase continues with the finding of the relation between the sighting distance and the dispersion of height differences acquired by digital levelling under terrain conditions. The theoretical part involves the development of levelling accuracy theories that vary over time by view on random and systematic error propagation. The numerical and graphical solution of the experimental measurements involves ordering the height differences into sighting groups according to the sighting distance. The standard deviation computed in each sighting group represents a measure of the dispersion of height differences. Suppose the standard deviation in the sighting group in both independent experimental locations K1 and K2 exceeds twice the total standard deviation. In that case, it is most likely considered to be the influence of the critical distance, which is then compared with values obtained by laboratory calibration of the same digital levels.