No abstract

Owing to the appearance of many global geopotential models, it is necessary to determine the most appropriate model for use in Egyptian territory. In this study, we aim to investigate three global models, namely EGM2008, EIGEN-6c4, and GECO. We use five mathematical transformation techniques, i.e., polynomial expression, exponential regression, least-squares collocation, multilayer feed forward neural network, and radial basis neural networks to make the conversion from regional geometrical geoid to global geoid models and vice versa. From a statistical comparison study based on quality indexes between previous transformation techniques, we confirm that the multilayer feed forward neural network with two neurons is the most accurate of the examined transformation technique, and based on the mean tide condition, EGM2008 represents the most suitable global geopotential model for use in Egyptian territory to date. The final product gained from this study was the corrector surface that was used to facilitate the transformation process between regional geometrical geoid model and the global geoid model.

Open global digital elevation models (GDEMs) represent a free and important source of information that is available to any country. Fusion processing between global and national digital elevation models is neither easy nor inexpensive. Hence, an alternative solution to fuse a GDEM (GTOPO30 or SRTM 1) with national GPS/levelling measurements is adopted. Herein, a transformation process between the GDEMs and national GPS/levelling measurements is applied using parametric and non-parametric equations. Two solutions are implemented before and after the filtration of raw data from outliers to assess the ability of the generated corrector surface model to absorb the effect of the outliers’ existence. In addition, a reliability analysis is conducted to select the most suitable transformation technique. We found that when both the fitting and prediction properties have equal priority, least-squares collocation integrated with a least-squares support vector machine inherited with a linear or polynomial kernel function exhibits the most accurate behavior. For the GTOPO30 model, before filtration of the raw data, there is an improvement in the mean and root mean square of errors by 39.31 % and 68.67 %, respectively. For the SRTM 1 model, the improvement in mean and root mean square values reached 86.88 % and 75.55 %, respectively. Subsequently, after the filtration process, these values became 3.48 % and 36.53 % for GTOPO30 and 85.18 % and 47.90 % for SRTM 1. Furthermore, it is found that using a suitable mathematical transformation technique can help increase the precision of classic GDEMs, such as GTOPO30, making them to be equal or more accurate than newer models, such as SRTM 1, which are supported by more advanced technologies. This can help overcome the limitation of shortage of technology or restricted data, particularly in developed countries. Henceforth, the proposed direct transformation technique represents an alternative faster and more economical way to utilize unfiltered measurements of GDEMs to estimate national digital elevations in areas with limited data.

Least-squares collocation (LSC) is a crucial mathematical tool for solving many geodetic problems. It has the capability to adjust, filter, and predict unknown quantities that affect many geodetic applications. Hence, this study aims to enhance the predictability property of LSC through applying soft computing techniques in the stage of describing the covariance function. Soft computing techniques include the support vector machine (SVM), least-squares-support vector machine (LS-SVM), and artificial neural network (ANN). A real geodetic case study is used to predict a national geoid from the EGM2008 global geoid model in Egypt. A comparison study between parametric and soft computing techniques was performed to assess the LSC predictability accuracy. We found that the predictability accuracy increased when using soft computing techniques in the range of 10.2 %–27.7 % and 8.2 %–29.8 % based on the mean square error and the mean error terms, respectively, compared with the parametric models. The LS-SVM achieved the highest accuracy among the soft computing techniques. In addition, we found that the integration between the LS-SVM with LSC exhibits an accuracy of 20 % and 25 % higher than using LS-SVM independently as a predicting tool, based on the mean square error and mean error terms, respectively. Consequently, the LS-SVM integrated with LSC is recommended for enhanced predictability in geodetic applications.

The demand for real-time high-precision positioning for global navigation satellite system applications is difficult to satisfy. In this regard, a single-frequency receiver is found to play an important role in overcoming this challenge, especially in developing countries where economic factors are a major restriction. Hence, the development of built-in models, such as the Klobuchar model, is an important objective for single-frequency users to mitigate the effect of ionospheric delay errors in real-time applications. Accordingly, this study aims to devise a new approach to enhance the behavior of the Klobuchar model and increase its efficiency in resolving the aforementioned problem. The new approach seeks to enhance the behavior of the Klobuchar model without refining or increasing its coefficients. To eliminate the ionospheric delay disturbance, the proposed methodology applies normalization and filtration processes to the raw ionospheric delay probability distribution estimated by the unified least squares technique. A final assessment of the new method for enhancing the Klobuchar behavior in predicting the precise position of a single-frequency static receiver under different weather conditions around the globe is presented in this paper.