Application of a Back-Propagation Artificial Neural Network to Regional Grid-Based Geoid Model Generation Using GPS and Leveling Data

The height difference between the ellipsoidal height $h$ and the orthometric height $H$ is called undulation $N$ . The key issue in transforming the global positioning system (GPS)-derived ellipsoidal height to the orthometric height is to determine the undulation value accurately. If the undulation $N$ for a point whose position is determined by a GPS receiver can be estimated in the field, then the GPS-derived three-dimensional geocentric coordinate in WGS-84 can be transformed into a local coordinate system and the orthometric height in real-time. In this paper, algorithms of applying a back-propagation artificial neural network (BP ANN) to develop a regional grid-based geoid model using GPS data (e.g., ellipsoidal height) and geodetic leveling data (e.g., orthometric height) are proposed. In brief, the proposed algorithms include the following steps: (1) establish the functional relationship between the point’s plane coordinates and its undulation using the BP ANN according to the measured GPS data and leveling data; (2) develop a regional grid-based geoid model using the imaginary grid plane coordinates with a fixed grid interval and the trained BP ANN; (3) develop an undulation interpolation algorithm to estimate a specific point’s undulation using the generated grid-based geoid model; and (4) estimate the point’s undulation in the field and transform the GPS ellipsoidal height into the orthometric height in real-time. Three data sets from the Taiwan region are used to test the proposed algorithms. The test results show that the undulation interpolation estimation accuracy using the generated grid-based geoid is in the order of $2–4\mathrm{cm}$ . The proposed algorithms and the detailed test results are presented in this paper.