Proceedings of the Korean Institute of Navigation and Port Research Conference (한국항해항만학회:학술대회논문집)
- Volume 2
- /
- Pages.101-106
- /
- 2006
Two Layer Multiquadric-Biharmonic Artificial Neural Network for Area Quasigeoid Surface Approximation with GPS-Levelling Data
- Deng, Xingsheng (School of Geodesy & Geomatics, Wuhan University) ;
- Wang, Xinzhou (Research Center for Hazard Monitoring and Prevention, Wuhan University)
- Published : 2006.10.18
Abstract
The geoidal undulations are needed for determining the orthometric heights from the Global Positioning System GPS-derived ellipsoidal heights. There are several methods for geoidal undulation determination. The paper presents a method employing a simple architecture Two Layer Multiquadric-Biharmonic Artificial Neural Network (TLMB-ANN) to approximate an area of 4200 square kilometres quasigeoid surface with GPS-levelling data. Hardy’s Multiquadric-Biharmonic functions is used as the hidden layer neurons’ activation function and Levenberg-Marquardt algorithm is used to train the artificial neural network. In numerical examples five surfaces were compared: the gravimetric geometry hybrid quasigeoid, Support Vector Machine (SVM) model, Hybrid Fuzzy Neural Network (HFNN) model, Traditional Three Layer Artificial Neural Network (ANN) with tanh activation function and TLMB-ANN surface approximation. The effectiveness of TLMB-ANN surface approximation depends on the number of control points. If the number of well-distributed control points is sufficiently large, the results are similar with those obtained by gravity and geometry hybrid method. Importantly, TLMB-ANN surface approximation model possesses good extrapolation performance with high precision.
Keywords
- Two Layer Multiquadric-Biharmonic Artificial Neural Network (TLMB-ANN);
- quasigeoid;
- Hardy’s Multiquadric-Biharmonic functions;
- Levenberg-Marquardt algorithm