Application of fuzzy logic theory to geoid height determination

Abstract

Today, because satellite based positioning techniques such as GPS and GLONASS has a wide range use in practical geodetic applications, precise geoid determination became a major issue of geodesy. The reason for this, heights obtained with satellite measurements and conventional way are determined according to different referents surfaces. Ellipsoidal height can be determined with satellite measurements easily. However, in many geodetic applications instead of ellipsoidal heights, orthometric heights, reckoned from geoid, are required. Because orthometric and ellipsoidal heights are determined according to different surfaces, these two height systems are not collided each other and the difference between the systems are called geoid height or geoid undulation and geoid height is a transformation parameter used between the two systems. If geoid height could be determined precisely, orthometric heights can be obtained from ellipsoidal heights easily. Therefore, instead of conventional way of leveling, heights can be obtained with GPS measurements by saving time and money. In this study, geoid heights were determined by polynomial coefficients and Fuzzy logic (both Mamdani and Sugeno Fuzzy model) using data in Istanbul and effect of calculation methods of geoid height were examined.