Modeling GPS-Derived Orthometric Heights for a Small and Dense Network

Abstract

The Global Positioning System (GPS) relative carrier phase observations would provide a powerful and fast tool for obtaining an accurate relative three dimensional positioning of a point on the earth. However, the orthometric heights (elevations above geoid), which are the required values for most of surveying and engineering applications, are not directly provided by GPS observations. Instead, the ellipsoidal heights (elevations above ellipsoid) are derived from the processing of GPS observations. It follows that the separation between the ellipsoid and geoid (geoidal height) is an essential quantity in determining orthometric heights using GPS observations. This paper presents an accurate, relatively simple, and reliable technique to precisely model geoidal heights by combining both geopotential and regression surface fitting approaches utilizing least squares method for each one.For the purpose of this proposed approach, a dense and small test network was designed. Both precise leveling and GPS observations were carried out and adjusted for common stations to establish precise vertical control network. Then, the above mentioned technique was implemented and a geoidal model for the area was developed and tested. The results based on the developed model showed that GPS-derived orthometric heights were better than 1 cm, and a third order leveling specifications were achievable without differential leveling.