Volume 16, Issue 4

In view of the defects of total station and laser tracker in the construction of three-dimensional control network, a construction method of three-dimensional control network is proposed by combining total station and laser tracker. Total stations and laser trackers are utilized separately to observe the control points according to the free-stationing method. In data processing, the weights of different types of observations of total station and laser tracker are reasonably determined based on the Helmert variance component estimation. The high-precision horizontal direction observations of total station, which are better than 0 . 5 ″ 0.{5^{\prime\prime }}, and the ultra-high-precision ranging observations of laser tracker, which are better than 10 μm, are effectively combined in order to obtain more precise adjustment results. The experimental results show that the positional precision of the combined adjustment is better than that of the adjustment results of a single measurement system, and the precision of three-dimensional control network can be further improved by employing Helmert variance component estimation to determine the weight reasonably.

Due to different structures of the Earth’s crust and mantle, there is a significant density contrast at their boundary, the Moho Density Contrast (or shortly MDC). Frequently one assumes that the MDC is about 600 kg/m 3 , but seismic and gravimetric data show a considerable variation from region to region, and today there are few such studies, and global models are utterly rare. This research determines a new global model, called MDC21, which is a weighted least-squares combination of three available MDC models, pixel by pixel at a resolution of 1° × 1°. For proper weighting among the models, the study starts by estimating lacking standard errors and (frequently high) correlations among them. The numerical investigation shows that MDC21 varies from 21 to 504 kg/m 3 in ocean areas and ranges from 132 to 629 kg/m 3 in continental regions. The global average is 335 kg/m 3 . The standard errors estimated in ocean regions are mostly less than 40 kg/m 3 , while for continental regions it grows to 80 kg/m 3 . Most standard errors are small, but they reach to notable values in some specific regions. The estimated MDCs (as well as Moho depths) at mid-ocean ridges are small but show significant variations and qualities.

When starting any GNSS measurements, there is a need to establish a survey plan with the required optimal baselines. The optimal GNSS baselines can be chosen by solving the geodetic second-order design (SOD). The particle swarm optimization PSO is used widely to solve geodetic design issues. This work employed the particle swarm optimization (PSO) algorithm, a stochastic global optimization method, to select the optimal GNSS baselines. The optimal baselines satisfy the set criterion matrix at a reasonable cost. The fundamentals of the algorithm are presented. The effectiveness and usefulness of the technique are then demonstrated using a Nile Delta GNSS network as an example. In some cases, we have to observe many GNSS benchmarks with limited instrumentations. PSO represents a powerful tool for optimizing baseline to get the required accuracy with limited capabilities (like limited receivers). The PSO algorithm, a stochastic global optimization approach, was used in this paper to find the best observation weights to measure in the field that will match the predetermined criterion matrix with a fair degree of precision. The method’s fundamentals are presented with an actual geodetic network over the Nile delta in Egypt. In the current work, two survey strategies were applied. One represents a case with 9 GNSS receivers (high capability), and another one represents the tested survey plan with limited GNSS receivers (3 receivers, low capability) after applying PSO. By comparing two survey strategies, applying the PSO algorithm to a real Nile delta geodetic network shows its effectiveness on the obtained coordinate accuracy. This obtained accuracy ranged from 2 mm to 3 mm in X, Y, Z, and 3 mm in height. Also, the linear closure error between known and estimated coordinates improved to be 1.4 cm after applying PSO.

The study of determining the accuracy of spatial vectors by the global navigation satellite system (GNSS) in real time (RTK) was conducted. The possibility of construction of precision geodetic networks by the combined method of static and RTK GNSS measurements which correspond to the set accuracy and reach the maximum economic efficiency is investigated. A technique providing the densification of GNSS network and the use of two simultaneously operating GNSS receivers (Rover) is proposed. The research was carried out at the points of the GNSS network of Dnister Pumped Storage Power Plant (PSPP) (Ukraine). As a result of comparison of reference and measured elements of vectors, it was found that the average absolute error in determining the spatial distance of 14 vectors was 5.3 mm. Rejection of vectors with a closed horizon reduced the error to 2.1 mm. The vectors are most accurately determined from two satellite systems (GPS, GLONASS) and from a single base station. The recommended distance to the base station is within one kilometer. Increasing the accuracy by 75 % in determining the vector by the proposed method in RTK mode is also shown. As a result of a posteriori optimization of combined GNSS networks, high accuracy on the reliability of vectors determined by the method in RTK mode was confirmed. The technique can be used to construct precision networks, to carry out repeated measurements for the monitoring of large engineering structures with an open horizon.

Based on multidimensional equivalent water height (EWH) time series in the Qinghai-Tibetan Plateau recovered from GRACE data, rotated multi-channel singular spectrum analysis (RMSSA) was employed to separate and reconstruct its more accurate local mode of inter-annual oscillations of terrestrial water storage (TWS). The results show that RMSSA could effectively suppress the mode mixture of MSSA, and improve the physical interpretation of the inter-annual oscillations of TWS. Three significant inter-annual oscillations with periods of 6.1a, 3.4a, and 2.5a have been found in the multidimensional EWH series in the Qinghai-Tibetan Plateau (QTP), which account for 38.5 %, 23.5 %, and 16.7 % of the total variance, respectively (after the seasonal and long term have been deducted). The spatial patterns and propagation paths of these three inter-annual oscillations are different and exhibit their own independent local characteristics. Based on the analysis of multi-source GRACE GSM data, the results show that the data solution errors have little influence on the extraction of inter-annual oscillations of TWS. The significant 6.4a, 3.5a, and 2.5a inter-annual oscillations are also found in CPC hydrologic model in the QTP using RMSSA, which account for 22.9, 29.9, and 19.3 % of the total variance, respectively. Three inter-annual oscillations separated from GRACE and CPC show similar spatial patterns and significant cross-correlations, respectively. The maximum cross-correlation coefficients are above 0.5 at the 95 % confidence level over 42, 71, and 75 % of the grids in the QTP, respectively. The results indicate that the soil moisture and terrestrial water storage from GRACE have common inter-annual oscillations and corresponding driving factors in the QTP. We conclude that these three inter-annual oscillations of TWS can be explained by the influence of the Arctic oscillation, oceanic Niña, and Indian Ocean dipole.

In the current study, the accuracy of airborne gravity data is evaluated based on the most recent Global Geopotential Models (GGM) and terrestrial gravity data to find out to what extent these data are acceptable to be used in multi-applications (e. g., geodesy and geophysics). To achieve this goal, the remove-compute-restore (RCR) scheme, upward, and downward continuation operational methods (least square collocation and fast Fourier transform procedures) are applied. The airborne gravity data had been acquired by the Egyptian Nuclear Material Authority (ENMA) in the central-western desert for geological applications. Firstly, three GGMs models (EGM2008, EIGEN-6C4 and XGM2019e up to various degrees) are used to compare with the free-air airborne gravity anomaly, The EGM2008 model up to degree 720 produces the smallest mean and STD difference values with 2.59 and 3.07 mGal, respectively. The terrestrial gravity data are compared with the airborne gravity anomaly at both flight and ground levels. In-flight level, the terrestrial gravity data are upward continued to the flight level and compared with the airborne gravity anomaly. The statistical results show that the mean and STD differences are about 4.2 and 0.75 mGal, respectively. While in-ground level evaluation, two operational techniques are used to downward continue the airborne gravity data (Fast Fourier Transform (FFT) and Least Squares Collocation (LSC)). The combined Satellite model EGM2008 up to degree 720 and SRTM 30 m are used to remove and restore the long and short-wavelength information. It is observed that the collocation gives better statistical results than FFT with mean and STD difference values are about 3.13 and 1.13 and mGal, respectively.

It is well-known that the solution domain has a discrete character in precise satellite positioning because of the integer nature of ambiguities. Therefore, in addition to the classic least squares estimation, the search procedure has to be employed in the computation process to obtain the so-called ‘fixed solution.’ The article’s subject is to improve the search procedure conducted in the coordinate domain. The reduction process is to transform the original math model into an equivalent one in the sense of obtaining the same solution. The reduction aims to increase the efficiency of searching for some parameters, i. e., integer ambiguities. The article presents the concept of employing the reduction procedure to the computation process of precise positioning based on the ambiguity function. The transformation matrix for the reduction is based on the well-known integer decorrelation procedure. Numerical experiment results display a positive impact of the reduction process on the search procedure efficiency. This positive impact is manifested by a dramatic decrease in the number of candidates needed to test all admissible solutions inside the search region. The percentage decrease in that magnitude is at least 50 % for all session lengths and achieves a maximum value of over 75 % for the 10-minute session. Computational time decreases by over 40 % while short sessions are processed. There is no improvement for sessions longer than 15 minutes, but, as explained in the paper, there is no need to improve that magnitude in such cases.

Determining a precise local geoid is particularly important for converting the Global Navigation Satellite System (GNSS) heights to orthometric heights. The geometric method for computing the geoid has been extensively used for a comparatively small region, which, in some points, interpolates geoid heights based on GNSS-derived heights and levelling heights. Several considerations should be considered when using the geometric method to increase the accuracy of a local geoid. Kuwait is used as a test area in this paper to investigate several features of the geometric method. The achievable precision is one of these aspects, the role of the interpolation method, global geopotential models, and the influence of the topographic effect. The accuracy of the local geoid can be substantially enhanced by integrating a geopotential model with a digital terrain model of the research region. It is possible to get a precision of 2–3 cm.

The Hong Kong Principal Datum (HKPD) is the currently adopted official geodetic vertical datum at the Hong Kong territories. The HKPD is practically realized by heights of levelling benchmarks. The HKPD heights are, however, neither normal nor orthometric. The reason is that heights of levelling benchmarks were determined from precise levelling measurements, but without involving gravity observations along levelling lines. To reduce systematic errors due to disregarding the gravity information along levelling lines, we used terrestrial and marine gravity data to interpolate gravity values at levelling benchmarks in order to compute and apply the orthometric correction to measured levelling height differences. Our results demonstrate the importance of incorporating the gravity information even for a relatively small region but characterized by a rough topography with heights of levelling benchmarks exceeding several hundreds of meters. According to our estimates, the orthometric correction reaches (and even slightly exceeds) ±2 cm, with maxima along levelling lines crossing mountain chains.