Study on Standard Deviation of Leveling Observation

Abstract

　The standard deviation (SD) of leveling observation regulated by the public survey manual of Japan is calculated by the closing errors between fore and back. The closing errors are assumed to have no systematic error. The leveling observation data, however, show that the closing errors have the systematic error due to collimation change just after setting instrument or sinking staff. The Root Mean Square Error (RMSE) is more suitable for a measure of the leveling observation, because the RMSE estimates not only the variance by the random error but also the bias by the systematic error. The SD and the RMSE match under the condition that the systematic error itself becomes random.

　This paper insists that we should recognize the difference between the SD and the RMSE correctly, and that we should use “RMSE” instead of “SD” as a measure of the leveling observation.