New Method of Getting Position of Instrument Station Based on Two Known Points and The Law of Cosines

Abstract

Getting the position of the instrument in starting traverse and staking out surveying can be very helpful for the surveyors. The most common method is the placement of the instrument on the known point, then those surveys are possible to be accomplished. This research is aimed to develop a new method and procedure to get x, y, and z values of the unknown position of the instrument based on two known points and the law of cosines. The method of this research is the implementation of the law of cosines and Euclidean Norm in solving the problem of getting the coordinate of instrument position. The innovation of this procedure has not been used yet in survey practice and has not been accommodated in electronic distance measuring (EDM) based survey instruments such as Total Station. The experiment of measurement to test the procedure is conducted virtually using the total station of SimusurveyX 1.0.7. The total measurement of ten random triangles is 60 times, where each triangle is measured 6 times. The result of measurement is close to the ground truth, and it can be repeatable. The implication of this research is enabling the surveyors to shortcut traverse measurement by locating Total Station in the first unknown point of the traverse.

Keywords

• law of cosines
• traverse measurement
• position
• coordinate
• simulation
• precision
• accuracy