Volume 14, Issue 1

Modelling the spatial variations of a specific Global Geopotential Model (GGM) over a spatial area is important to enhance its local performance in Global Navigation Satellite Systems (GNSS) surveying. This study aims to investigate the potential of utilizing some of Geographic Information Systems (GIS) geospatial analysis tools, particularly Geographically Weighted Regression (GWR), in geoid modelling for the first time in Egypt as a case study. Its main target is developing an optimum regression method to be applied in spatial modelling of the deviations of a specific GGM (e. g., PGM17). Using a precise local geodetic dataset of 803 GPS/levelling stations, PGM17 undulation differences have been modelled using different regression techniques to evaluate their precision and accuracy. Based on investigating 13 possible regression formulas of probable combinations of independent variables, results showed that the PGM17 discrepancies over Egypt depend mostly on the terrain heights and geoidal undulations. Over 80 checkpoints, the attained variations between the GWR model and known values varied from −0.574 m to 0.500 m, with a mean of 0.001 m and a standard deviation equals ±0.205 m. Based on available data, it has been found that GWR improved the PGM17 deviations by 9 % in terms of standard deviation and by 98 % in terms of the mean. Additionally, the study generates a reasonably innovative product for the local geodetic community by building an enhanced version of the PGM17. This surface will be a precious resource in GNSS surveying in Egypt for heights conversion, leading to considerable cost reduction in civil engineering works and mapping projects.

In this contribution, the minimum detectable bias (MDB) as well as the statistical tests to identify disturbed observations are introduced for the Gauss-Helmert model. Especially, if the observations are uncorrelated, these quantities will have the same structure as in the Gauss-Markov model, where the redundancy numbers play a key role. All the derivations are based on one-dimensional and additive observation errors respectively offsets which are modeled as additional parameters to be estimated. The formulas to compute these additional parameters with the corresponding variances are also derived in this contribution. The numerical examples of plane fitting and yaw computation show, that the MDB is also in the GHM an appropriate measure to analyze the ability of an implemented least-squares algorithm to detect if outliers are present. Two sources negatively influencing detectability are identified: columns close to the zero vector in the observation matrix B and sub-optimal configuration in the design matrix A . Even if these issues can be excluded, it can be difficult to identify the correct observation as being erroneous. Therefore, the correlation coefficients between two test values are derived and analyzed. Together with the MDB these correlation coefficients are an useful tool to assess the inner reliability – and therefore the detection and identification of outliers – in the Gauss-Helmert model.

Satellite navigation systems face different types of errors that affect the positioning accuracy. The tropospheric delay considers one of the major sources of error for the transmitted signal that could face a tropospheric delay of over 2 m at zenith and 20 m at lower satellite elevation angles. A positioning error of 10 m could result from inaccurate mitigation of the tropospheric delay. Two types of models are available; surface meteorological models and global empirical models. Surface meteorological models use surface meteorological data to give accurate mitigation while the global empirical models use global standard atmospheres. Global empirical models are favorable for satellite based augmentation systems such as EGNOS model for the EGNOS augmentation system. Several hybrid neutral atmosphere delay models have been developed (UNB1 through UNB4). The IGGtrop model is initially developed to provide tropospheric delay corrections for the users of Chinese BeiDou Navigation Satellite System (BDS) and its augmentation system. This paper presents an assessment study for the behaviour of IGGtrop model comparing with (EGNOS, UNB3M) models. The behavior of the three models is compared with IGS-tropospheric estimations for two different-latitude IGS stations; (bhr1 and eil1) in the northern hemisphere. This study recommends using IGGtrop model for estimating the zenith tropospheric delay correction for low-latitude regions in northern hemisphere for all seasons with an average zenith tropospheric difference of 0.75 cm. IGGtrop model is also recommended to be used for estimating the zenith tropospheric delay correction for high-latitude geographic regions in northern hemisphere during autumn and spring seasons with an average zenith tropospheric difference of 0.75 cm. While UNB3M model is the best choice for tropospheric delay correction for high-latitude geographic regions in northern hemisphere during winter and summer seasons with an average zenith tropospheric difference of 1.1 cm.

Kinematic laser scanning is widely used for the fast and accurate acquisition of road corridors. In this context, road monitoring is a crucial application, since deficiencies of the road surface due to non-planarity and subsidence put traffic at risk. In recent years, a Mobile Mapping System (MMS) has been developed at the University of Bonn, consisting of a GNSS/IMU unit and a 2D laser scanner. The goal of this paper is to evaluate the accuracy and precision of this MMS, where the height component is of main interest. Following this, the applicability of the MMS for monitoring the planarity and subsidence of road surfaces is analyzed. The test area for this study is a 6 km long section of the A44n motorway in Germany. For the evaluation of the MMS, leveled control points along the motorway as well as point cloud comparisons of repeated passes were used. In order to transform the ellipsoidal heights of the MMS into the physical height system of the control points, undulations were utilized. In this respect, a local tilt correction for the geoid model was determined based on GNSS baselines and leveling, leading to a physical height accuracy of the MMS of < 10 mm (RMS). The related height precision has a standard deviation of about 5 mm. Hence, a potential subsidence of the road surface in the order of a few cm is detectable. In addition, the point clouds were used to analyze the planarity of the road surface. In the course of this, the cross fall of the road was estimated with a standard deviation of < 0.07 %. Yet, no deficiencies of the road surface in the form of significant rut depths or fictive water depths were detected, indicating the proper condition of the A44n motorway. According to our tests, the MMS is appropriate for road monitoring.

Based on deeply analysis for optimization process of basic fruit fly optimization algorithm (FOA), a new improved FOA (IFOA) method is proposed, which modifies random search direction, increases the adjustment coefficient of search radius, and establishes a multi-sub-population solution mechanism. The proposed method can process the nonlinear objective function that has non-zero and non-negative extreme points. In the paper, IFOA method is applied to ill-conditioned problem solution in the field of surveying data processing. Application of the proposed method on two practical examples show that solution accuracy of IFOA is superior to that of three well-known intelligent optimization algorithms and two existing improved FOA methods, and it is also better than truncated singular value decomposition method and ridge estimation method. In addition, compared with intelligent search method represented by particle swarm optimization algorithm, The IFOA method has the advantages of less parameter settings, simple optimization process and easy program implementation. So, IFOA method is feasible, effective and practical in solving ill-conditioned problems.

The evaluation of geoscience data is a far-reaching topic which cannot be systematically covered. The purpose of inferential statistics is to harness useful information from data for making decisions. This paper conducts in-depth statistical study for the Bursa-Wolf and Molodensky Badekas models of the three-dimensional transformation parameters. We also considered the combined and observation equations scenarios of these methods for the comparative study. Four key indicators are conducted to evaluate the performance of the two transformation models according to the residual results. These include root mean square error (RMSE), paired t-test, Wilcoxon signed-rank test and the Cohen’s d effect size measure. RMSE evaluation is based on the mean difference between model estimates and observed values. The correlations in the model results is investigated based on paired t-test. Wilcoxon signed-rank test assesses the statistical significance of the model’s paired differences. To estimate the effect size of the performance differences, Cohen’s d measures are computed. Further, the residuals of the estimated parameters are plotted according to their respective control points. The inference results of these tests generally show that Badekas transformation approach is more precise than Bursa-Wolf. Specifically, Badekas combined case is the most precise, followed by its observation case, then Bursa-Wolf combined and finally its observation case is the least performing model. The application of various data analysis and statistical verifications make the task of data interpretation and best model selection easier.

Global Navigation Satellite System (GNSS) and remote sensing Digital Elevation Models (DEMs) represent earth’s surface elevation with reference to ellipsoid and orthometric heights. Proper estimation of the geoid (difference of ellipsoid and orthometric heights) is necessary before comparing data referenced to the different vertical datum. In this paper, an error in estimating EGM96 orthometric height is highlighted, verified by NGA/NASA developed model and MATLAB®. A significant error was found in the ArcGIS derived EGM96 orthometric heights range between ±6.9 meters. In addition, interpolation of low-resolution geoid data also produces significant biases depending on geographic location and the number of the interpolation data point. The bias was maximum negative in the central part of Tibetan Plateau and Himalaya. Therefore, estimation of orthometric height similar to NGA/NASA model precision is necessary for comparison of DEMs for natural resources management, 3D modelling and glaciers mass balance mainly in the mountainous regions.

Combining multi-source measurements can improve the accuracy and the spatial resolution of the three-dimensional (3-D) displacements field. Few researches have been conducted to integrate InSAR, GPS and leveling data of Tianjin in the recent three years to get the 3-D large displacement velocity field. How to effectively combine multi-source measurements and obtain the accurate 3-D large displacement field in high spatial resolution is worth studying. In this paper, the optimal method for acquiring 3-D displacement field by combining InSAR, leveling and GPS measurements is obtained by comparing the different methods. Then we realize the combining InSAR, leveling and GPS measurements to obtain the high-precision 3-D displacement field in Tianjin (China) from 2016 to 2018. Compared with different methods, we integrate InSAR, GPS and leveling measurements and use the weighted least squares method to estimate the 3-D displacement field with the highest accuracy. Although the accuracy of the horizontal displacement field obtained by this method has not been greatly improved, the vertical accuracy is obviously better than the other methods. The introduction of leveling measurements is beneficial to improve the accuracy of the vertical displacement field. Compared with independent GPS measurements, the standard deviations of 3-D displacements velocity field estimated by optimal solution method is 2.6 mm/yr, 2.1 mm/yr and 2.7 mm/yr in the vertical, eastern and northern directions, respectively. These results indicate that this method effectively utilizes the advantages of GPS, InSAR and leveling measurements, and extends the limitations of a single technical in describing surface-time scale applications. And the 3-D displacements information with a large spatial scale and high spatial resolution provides a reliable data basis for studying the crustal movement and its dynamic mechanism in China.

GNSS has limitations or cannot be applied in specific environments with poor geometry like city streets, tunnels, bridges, quarries, mines, ports or in indoor environment in general. In 2003 Locata Corporation from Australia began with the development of a new, completely independent technology called Locata, which was designed to overcome the limitations of GNSS. Within the project “Wearable Outdoor Augmented Reality System for the Enrichment of Touristic Content” Locata system was implemented for the first time in the Republic of Croatia. The quality of the established LocataNet network and the quality of the Locata positioning are presented in this paper as the basis for future research of possibilities to use Locata in displacement measurement. Achieved positioning precision is in a range of few mm in the horizontal direction and up to a couple of cm in the vertical direction. Although high level of precision is achieved, the accuracy, i. e. the errors of positioning solutions are up to several cm. Among other things, the research presented in this paper is focused on the reasons for achieved lower accuracy that probably have their roots in the instability of the LocataLite transmitting antennas in the established LocataNet. They namely affect the estimated float ambiguities of carrier phase measurements. Potential of relative positioning is another topic of this research, because it could allow the fixing of ambiguities to integer values and result in increase of accuracy and precision of positioning.

Post Processed Static (PPS) and Precise Point Positioning (PPP) techniques are not new; however, they have been refined over the decades. As such, today these techniques are offered online via GPS (Global Positioning System) data processing services. In this study, one Post Processed Static (OPUS) and one Precise Point Positioning (CSRS-PPP) technique is used to process 24 h GPS data for a CORS (Continuously Operating Reference Stations) station (P565) duration of year 2016. By analyzing the results sent by these two online services, subsidence is determined for the location of CORS station, P565, as 3–4 cm for the entire year of 2016. In addition, precision of these two techniques is determined as ∼2 cm. Accuracy of PPS and PPP results is 0.46 cm and 1.21 cm, respectively. Additionally, these two techniques are compared and variations between them is determined as 2.5 cm.