Journal of Surveying Engineering

Accuracy and reliability are determining factors when selecting where to place a global navigation satellite system (GNSS) receiver for landslide monitoring and early warning in real time. Previous studies have revealed that surface occlusion models (SOMs) are beneficial to reduce the multipath error of satellite observation when the satellite line of sight is near the ground and improve the accuracy and reliability of GNSS monitoring. This paper investigates fitting functions to determine appropriate SOMs for GNSS stations located in different spatial environments. Based on their similarity to terrain patterns, Gaussian, Fourier, and sum of sine functions were chosen to build SOMs for the rover sites with different occlusions; the performance of fitting accuracy and application on the positioning were analyzed. The results indicate that the three functions present a similar performance considering the goodness of fit, but the Fourier and sum of sine functions can significantly improve the efficacy of SOMs and enhance performance in positioning for landslide monitoring. Therefore, these two functions can effectively support accurate and reliable GNSS landslide monitoring in real time.

Studies have suggested various solutions for determining the center coordinates and radius of a circle curve that are desired to pass through points whose coordinates are known. One solution is via adjustment according to the least-squares method based on the radius length. Another is based on the indirect measurement method, where the condition equation between the unknowns depends on the polar coordinate values of the points given in the radius equation. The center of the orthogonal coordinate system forms a triangle with the points that the circular curve is to pass through. Here, the distance between the center of the curve and the point where the circular curve is to be passed is the sought radius ($R$). From the points whose orthogonal coordinates are given, the approximate coordinates of the curve center can be calculated by the geodetic positioning method. In this case, the edge length between the center of the orthogonal coordinate system and the center of the curve and the point where the curve is to be passed is calculated. The break angle between the two sides is determined by means of the azimuth angles calculated according to the center of the Cartesian coordinate system of these two points. The radius $R$ can be calculated using the cosine theorem in plane trigonometry. If the number of points that the curve is desired to pass is more than three, the determination can also be performed through adjustment computation. In this study, how to apply the cosine theorem to determine the circular curve elements is first explained. Then, two new algorithms are presented based on the cosine theorem, being inspired from the proposals given in two previous works. Both algorithms were applied to the numerical data given in the previous works, and the results were given comparatively. Finally, a new numerical example was solved, and the findings were examined. Comparing the solution method according to the proposed alternative cosine theorem with the Ghilani & Wolf and Niemeier approaches for curves with a radius of 2 to 3 km, it is seen that the curve parameters difference is a few decimeters in the Gauss–Markov adjustment computation method, while it is a few centimeters in the Gauss–Helmert adjustment computation method. However, for 100 m radius of the curves, the differences were determined to be a few centimeters in both adjustment computation methods. The precision criterion for the parameters determined by the surveying engineers by calculation is determined in centimeter size independent from the radius size with the proposed cosine theorem solution, thus increasing the reliability of the parameters.

A major motivation of precise geoid computation is to adopt it as a national vertical datum or as an alternative vertical reference surface to aid surveyors in calculating physical heights using the Global Navigation Satellite System (GNSS). There exist several methods of geoid computation, and only one particular method is generally used to calculate the national geoid model irrespective of the size and topographical landforms of the country. The validation of the developed geoid models is done with the complete GNSS-leveling data set. In such a case, it is hard to claim the consistency in the precision of the developed geoid model throughout the country. This study aims to identify the consistency of the geoid models over India computed using the three approaches primarily followed in Curtin University of Technology (CUT), the University of New Brunswick (UNB), and the Royal Institute of Technology (KTH). Three analyses have been done on the calculated geoid models: (1) clusterwise validation with the GNSS-leveling data, (2) intermodel comparison for the whole study area, and (3) intermodel comparison for Indian states and Union Territories (UT) only. The GNSS-leveling validation results show that the standard deviations of differences for all the methods are within a range of $\pm 0.01\mathrm{m}$ with the exception of Uttar Pradesh West with the UNB method. However, inter-model comparison shows that the mean (meters) and standard deviation (meters) of the differences between the pairs (CUT-UNB), (CUT-KTH), and (KTH-UNB) are $0.241\pm 0.854$, $-0.133\pm 0.498$, and $0.374\pm 1.239$, respectively, with maximum difference sometimes exceeding 5 m. There is only one UT and four states for which the mean value is within ($-0.20\mathrm{m}$, 0.20 m) and standard deviation $\le \pm 0.05\mathrm{m}$ for all the three pairs. Therefore, the analysis shows that it is difficult to calculate a precise national geoid model using any one method alone and a strategy is required to merge various regional precise geoid models or methods to develop a consistently precise national geoid model.

This study proposed classifying and weighting the coordinate components to improve the precision of the coordinate transformation. A coordinate transformation model should avoid the participation of angle parameters to reduce the error caused by the linearization process when describing the rotation matrix. Based on Rodrigues’ formula, the coordinate transformation model and the calculation method for the initial values of the parameters were given. It is difficult to reasonably determine the pretest information for robust estimation, so the median function was used to classify and estimate the error in the coordinate components to determine the threshold value of the weight function in each direction. The third scheme of the Institute of Geodesy and Geophysics (IGG3) weight function was used as the equivalent weight function. The parametric adjustment method with additional constraints was adopted to solve the transformation parameters. The simulation test and case analysis were conducted using the tunnel control network of particle accelerator engineering as an example. The results show that the method in this study is not affected by empirical parameters when determining the weight, its robustness is stronger than the traditional robust estimation method, and the coordinate transformation precision is higher.

Since 2014, China has embarked on the process of building its own national continuously operating reference system (CORS), called the ground-based augmentation system (GAS), as one of the seven planning services of the BeiDou global navigation satellite system (BDS-3). The performance specifications for GAS were released, and the system has begun to render open services formally in May 2021. This paper involves a comprehensive introduction to GAS, from the aspects of its system composition, reference time system, and coordinate reference frame. The performance specifications and service products of GAS are presented and discussed. Performance tests of GAS services including wide-area and regional real-time augmentation positioning service and postprocessing data service were been carried out. The results show that wide-area real-time augmentation positioning service can realize meter-level to decimeter-level positioning for pseudo-range and carrier-phase positioning, respectively, while for regional real-time service, it can provide centimeter-level positioning within seconds, for postprocessing data service, it can realize millimeter-level positioning in mainland China. Overall, the performance test results of GAS service show that the service performance can well meet the design requirements and indicate the broad application prospects of GAS in the future.

This study presents the results of an astrogeodetic survey campaign conducted in the mountainous terrain of the Surses region in Switzerland. In our third astrogeodetic campaign using the QDaedalus system, we observed new deflections of the vertical (DoV) using three astrogeodetic systems. These observations were used to validate DoV data derived from the Global Gravity Model GGMplus and the Swiss Geoid model CHGeo2004. Astrogeodetic observations were conducted at 15 benchmarks (BMs) along the astrogeodetic profile over five nights in June 2021 at elevations ranging from 1,185 to 1,800 m and a station spacing of about 1 km. This is the first time two TS60 total station-based QDaedalus systems and one zenith telescope-based COmpact DIgital Astrometric Camera (CODIAC) system were used together for an astrogeodetic observation campaign. The standard deviations (SDs) of the QDaedalus system data for each session were 0.04″–0.22″ and 0.01″–0.20″ for the N–S and E–W components, respectively, while the SDs of the CODIAC system for each session were 0.02″ for both components. These high quality data were compared to DoV data derived from GGMplus and CHGeo2004. The N–S components from GGMplus exhibited large residuals ranging from $-{2.31}^{″}$ to 1.75″, while the E–W component residuals are from $-{0.27}^{″}$ to 1.80″. The residuals from CHGeo2004 range from $-0.60$ to 1.21 for the N–S components and $-1.01$ to 0.32 for the E–W components. These results show that the derived DoV data from CHGeo2004 are closer to the observed DoV and more accurate than the global GGMplus model that does not incorporate local gravity field data. The first and second astrogeodetic observation campaigns were conducted in the coastal terrain of Istanbul, Turkey and in the flat terrain in the Munich region, Germany, respectively. In this study, we provide an overall comparison of these previous results to the GGMplus residuals. Our latest results show that the GGMplus model is of higher quality in the Surses mountainous terrain than in the coastal terrain of Istanbul, while it is of lower quality than in the flat terrain of the Munich region.