Robust Conicoid Fitting in Converting GPS Height

Abstract

Height difference between GPS height and normal height is called height anomaly. If height anomaly for a point can be estimated, GPS height above the surface of the WGS-84 ellipsoid can be converted into normal height, which is used in engineering applications. A new robust procedure by using the conicoid fitting method (CFM) with the Huber M-estimation was proposed, to convert GPS height to normal height using some survey marks of a GPS control net where both normal height and GPS height are known. The robust CFM was presented on the example of a B-order GPS control net. The accuracy was analyzed and the results are promising. The impact of survey marks distribution and density on fitting accuracy was also discussed. In flat areas, converting GPS height to normal height by using CFM arrives at sub-centimeter level accuracy under some conditions. Geometric leveling has employed geodesy and survey engineering for many years. In this time a constant advancement of the instrument and survey methods took place (1). The Global Positioning System (GPS) has been widely used in engineering recently. It is well known that the horizontal accuracy of GPS is better than the vertical one. Moreover, the adjusted GPS height is the height above the surface of WGS-84 ellipsoid, which is not consistent with leveled heights above the mean sea level used in engineering applications. Thus, it is necessary to convert GPS height into normal height or orthometric height. If accurate normal height can be achieved by adjusting and converting GPS height, it can be used to replace laborious geodetic leveling work (2). Many attempts have employed to improve the accuracy of GPS-derived elevations by applying geoid and mathematical models. Hu et al (2) have compared the conicoid fitting method (CFM), neural network method (NNM), and CFM & NNM in converting GPS height, and they suggested that CFM & NNM produces more accurate results than CFM and NNM. Zhang et al (3) have discussed the accuracy of GPS height transformation based on GPS leveling data with model EIGENCG01C. They found the accuracy with the proposed model is closed to 0.7 meter in the west part of China for the region of 2000 km × 2000 km at the interval of 100 km, and about 0.13 m, 0.05 m and 0.06 m for three cases in the middle and east of China respectively, and all of the results are better than that with model EGM96. Ilija Grgiet al (1) have adopted GPS leveling measurements with the use of local geoid model to transmit the height from mainland to the island Rab in the Republic of Croatia. It is shown that the GPS leveling with the use of HRG2000 is exact and reliable, and better than it is generally acknowledged. Featherstone and Sproule (4) propose a model of the Australian Height Datum (AHD) instead of the classical geoid (AUSGeoid98) to provide a more direct transformation of GPS ellipsoidal heights to the AHD. Kuroishi et al (5) propose a new hybrid geoid model GSIGEO2000 for Japan. In addition, Mathematical models are also used in converting GPS height when the local geoid is unavailable. Gao and Xu (6) have proposed a new method for sub-regional fitting and transforming GPS height into normal height by applying bicubic splines and the bicubic surface function. Lin (7) has proposed algorithms of applying a back- propagation artificial neural network (BPANN) to develop a regional grid-based geoid model using GPS data and orthometric height. In the paper, 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 cm.