以自適應法優化大地起伏模型於工程上之應用

Abstract

由於測量、建設、製圖等方面的需求不斷增加，並隨著城市的快速發展，目前空間資訊的趨勢已從早期的二維資訊轉變為三維資訊。如何確定高程基準是相當重要的一項議題。在現代測量中，大地起伏扮演著重要角色，能將GNSS獲得的橢球高轉換為工程應用的正高。因此，建構高精度的大地起伏模型則至關重要。在本研究中，提出了一種自適應法應用於提升區域大地起伏模型，包含重力法大地起伏模型以及EGM2008大地起伏模型。該演算法在大地起伏趨勢估計的過程中，能自動選擇最適應的候選點，識別出屬於同一簇(cluster)的點，並能有效剔除不適合的點。此外，嚴格的序列式最小二乘法結合可調整之門檻值用於識別適合的觀測量，以便能自動生成優化模型以滿足使用者預設之精度品質。依據數值驗證成果，本研究方法可用於獲得精度在±14 mm/√km左右的城市尺度(25平方公里)之大地起伏模型。在一般工程應用中，應用大地起伏模型於GNSS之高程轉換，能有效率且較經濟地獲取高精度之正高。

Due to the increasing demand in surveying, construction, and mapping, with the rapid development of the city, the current trend in spatial information has changed from the earlier two-dimensional information to three-dimensional information. How to determine the height datum is quite important. In modern surveying, geoid undulation plays an important role in converting the ellipsoidal height obtained by GNSS into the orthometric height for engineering applications. Therefore, an accurate geoid undulation model for Taiwan has become paramount. In this study, an adaptive approach algorithm for improving the regional geoid undulation model based on the gravimetric geoid model and EGM2008 geoid is presented. The algorithm automatically selects the most adaptive candidate points in the process of geodetic level undulation trend estimation, identifies the points belonging to the same cluster, and effectively eliminates unsuitable points. Furthermore, a rigorous sequential least square combined with tunable criteria are used to identify appropriate observables so that optimized models can be automatically generated to satisfy the level of quality predefined by the user. Finally, based on the numerical validation, the proposed approach can be applied to obtain the urban-scale (25 square kilometers) geoid undulation model with a quality level around ± 14 mm/√km. The high accuracy orthometric heights can be efficiently and economically achieved in general engineering applications using GNSS in combination with the geoid undulation model.