Journal of Surveying Engineering

We have established a stable regional geodetic reference frame, designated as SChina20, using approximately 10-year observations (2010–2019) at 40 Global Navigation Satellite System (GNSS) sites in South China. The regional reference frame is tied to the International GNSS Service (IGS) Reference Frame 2014 (IGS14) at epoch 2020.0. The primary products from this study are seven parameters for transforming the positional time series from IGS14 to SChina20 and a seasonal model for predicting vertical land surface displacements in South China. The frame stability of SChina20 is $0.4\mathrm{mm}/\mathrm{year}$ in all three directions. We suggest that the scope of usage of SChina20 is spatially limited to the South China region and temporally limited to the 25-year time window from 2000 to 2025. We have also established a local-scale reference frame for the Hong Kong–Zhuhai–Macau (HZM) area, designated as HZM20. Applications of SChina20 in delineating urban subsidence and landslide are demonstrated in this article. SChina20 will be updated every few years to mitigate degradation of the frame stability over time and to synchronize with future updates of the IGS reference frame.

This paper examines the reliability criteria in sequential least-squares adjustment. Sequential least-squares techniques are widely implemented to effectively use adjustment processes. We use the reliability concept to quantify the potential for detecting blunders and to estimate their impact on the adjusted parameters. To gain additional insight into sequential least squares, we address internal and external reliability for recursive least squares (RLS) and two-step least squares (TSLS). After a short introduction to RLS, TSLS, and the concept of reliability, the paper describes the theoretical tools we developed to exploit the benefits of reliability criteria in sequential least-squares adjustment. Finally, the paper presents the results of a of two numerical example, indicating that the reliability can also be used effectively in sequential least-squares adjustment.

Image-assisted total stations (IATSs) have extensive application prospects in astronomic surveys, deformation monitoring, precision engineering surveying, and topographic mapping. During image processing of data, the angle measured by the total station must be analyzed together with the image information, and therefore, camera system errors must be considered in addition to the systematic errors of the total station. Systematic errors of total stations can be eliminated or reduced by calibration. However, there is a lack of effective methods for the correction of the camera system errors. We analyzed the mounting error sources of the camera systems of IATS, constructed a model for the conversion between pixel coordinates and the angle measurements of the total station as well as an error correction model, and analyzed the effects of system mounting errors on the angle measurements. We also determined the effects of camera system mounting errors on the angle measurements using celestial objects. The results show that if both the horizontal and vertical components of the coaxiality error are assumed to be 2″ and the elevation angle is 50°, the errors of the horizontal and vertical angles can reach 3·0″ and 2·0″, respectively. These errors must be corrected for on-ground precision measurements of the astronomical longitude, latitude, and orientation, which require a precision of 0.1″.

Global navigation satellite system interferometric reflectometry (GNSS-IR) is a new remote sensing method that has shown great potential for estimating soil moisture variation and vegetation growth in the vicinity of GNSS sites. Various retrieval methods have been proposed, and the accuracy of the retrieval results are continually improving. However, few experiments have comprehensively evaluated the potential of the BeiDou Navigation Satellite System (BDS) to retrieve soil moisture and vegetation growth in a farmland environment, especially the vegetation height. In this study, volumetric soil moisture (VSM) variation and wheat growth were retrieved from BDS B1/B2/B3 and Global Positioning System (GPS) L1/L2 signal-to-noise ratio (SNR) data collected from a wheat farm in Zhangxizhuang, Beijing, and evaluated by comparison with in situ observations. VSM was retrieved before significant wheat growth and after wheat harvest, wheat growth was retrieved in the remaining period, and traditional, empirical mode decomposition (EMD), and wavelet algorithms were used to estimate the optimal wheat height change process. The experimental results show that the root-mean-square error (RMSE) between GPS L1/L2 and BDS B1/B2/B3 frequencies in VSM retrieval and in situ VSM is 0.039 and 0.035 and 0.027, 0.022, and $0.021{\mathrm{m}}^3·{\mathrm{m}}^{-3}$, respectively. Moreover, the negative normalized amplitude exhibits a good correlation with the normalized difference vegetation index (NDVI) during high wheat coverage ($\mathrm{R}=0.67$). The GNSS-derived wheat height is consistent with the in situ wheat height change, and the retrieval value perfectly reflects the process of the wheat crop height changing rapidly to relatively stable and then to harvest. Thus, GNSS-IR technology has excellent capability and potential for monitoring farmland VSM and vegetation growth.

The Fisher Information Matrix (FIM) determinant and the precision of the circle parameters are derived for generic configurations with $n$ data points. The conditions for maximizing the FIM determinant are examined, and analysis shows that an infinite number of point configurations exist to maximize the FIM determinant. A collinear point configuration is proposed to obtain the highest precision of the radius, as do the configurations with the maximum FIM determinant. Moreover, theoretical analysis and the Monte Carlo method are employed to reveal that the highest precision of the parameter estimation is achieved synchronously with the maximum FIM determinant. When points are limited along an arc, the distribution ratio sequence (DRS) is designed to describe point configurations. Experiments show that the DRS of the maximum FIM determinant generally outperforms other arbitrary ones when points are limited along a certain arc.

A least-squares solution for (a)symmetric nine-parameter three-dimensional affine coordinate transformation based on quaternions is presented. Retrieval of the nine transformation parameters (three translations, three scale factors, and three Euler rotation angles) and their covariance matrix from the quaternion-based estimates is given in detail. The proposed method can successfully handle all the cases regardless of the magnitude of the parameters and full covariance matrices of the control points. Efficiency and consistency of the solution are discussed within five different case studies consisting of many numerical examples.

Aiming at the low efficiency of precise geodetic leveling in tough terrain, we propose a precise trigonometric leveling (PTL) method to replace first-order Class II leveling. First, we analyze the errors of unidirectional trigonometric leveling and list corresponding ways to reduce those errors. Then, the practical formula of PTL is introduced that combines the simultaneous reciprocal observation with the leap-frog method to reduce the effect of atmospheric refraction. Besides, the PTL method uses two robotic total stations to perform an even number of reciprocal observations to avoid measuring the heights of instruments. Finally, two experiments are conducted using the PTL method; one is river-crossing precise leveling, and the other is highland precise leveling. Compared with the precise geometric leveling in the 25 km of the leveling circuit, the result shows that the standard deviation per kilometer of PTL is $\pm 0.9\mathrm{mm}/\sqrt{\mathrm{km}}$, which is less than $\pm 1\mathrm{mm}/\sqrt{\mathrm{km}}$ and proves that PTL can achieve first-order Class II leveling precision to some degree conditions.

The technology of integer ambiguity resolution-enabled precise-point-positioning (also referred to as PPP-AR) has been proven capable of providing comparable accuracy, efficiency, and productivity to long-baseline real-time kinematic positioning (RTK) during the last decade. Commercial PPP-AR services have been provided by different institutions and companies and have been widely used in geodetic missions. However, the usage and research of the PPP-AR mostly concentrated on nonaviation applications, e.g., vehicle navigation, surveying, and mapping, and monitoring crustal motions. Few of them focused on fixing the ambiguities during an aircraft flight. In this contribution, we implemented the PPP-AR technique for the first time in an airplane flight test to investigate how much the fixed ambiguities could contribute to airplane positioning solutions in challenging circumstances, including high velocity and severe maneuvers. We first looked into the influences of the tropospheric delay on the positioning and ambiguity solutions because the height of the airplane may dramatically change within a narrow time span, and thus, a proper constraint of this parameter was crucial for the computation of the tropospheric effects. Then, how to fix the ambiguities successfully and reliably in challenging circumstances was discussed. Finally, the airplane data was processed in 15 and $1s$ intervals with ambiguity float and fixed solutions under different configurations to illustrate in which condition and to what extent the fixed ambiguities can improve the airplane positioning accuracy.

A multistart Nelder–Mead neural network algorithm (multi NM-NNA) is presented, the purpose of which is to solve the problem that the existing nonlinear search algorithms are unstable when inversing earthquake source parameters with GPS data. Multi NM-NNA uses the nonuniform sampling strategy to generate the initial starting points to reduce manual intervention, and the Nelder–Mead simplex algorithm is used to optimize the local optimization capability of the NNA. Different GPS stations and fault types are simulated, and the NNA, hybrid particle swarm optimization (PSO)/simplex algorithm [multipeaks particle swarm optimization (MPSO)], and NM-NNA are used to perform earthquake source parameter inversion, respectively. The simulation experiment results show that the calculation precision of the NM-NNA is not affected by the number of stations, and it has better stability in the inversion of different fault types. Compared with the NNA and MPSO, the NM-NNA is more suitable for earthquake source parameter inversion, and the computational efficiency is higher than the NNA. The NNA, MPSO, NM-NNA, and multi NM-NNA are used to invert the earthquake source parameters of the Bodrum–Kos earthquake and carry out the precision estimation of the parameters. Experimental results show that the parameter estimates inverted by the multi NM-NNA are closer to the existing research results and have smaller standard deviation. It is shown that inversion uncertainty of the multi NM-NNA is lower, the calculation results are more stable, and the computational efficiency of the multi NM-NNA is higher than NNA. In the complex and changeable earthquake environment, the multi NM-NNA has greater application potential.

This paper describes research carried out both to obtain the location and identify possible vestiges of the old geodetic benchmarks used by the expedition formed by French geodesists Arago and Biot and Spanish geodesists Chaix and Rodríguez, to carry out the prolongation of the meridian arc of the Paris Observatory in the Valencian Community in the early 19th century in order to define the meter as the base unit of length of the International System of Units. Geodetic, historical, and field work methodologies were integrated in the study to obtain scientifically sound results, which include the determination of coordinates of the original geodetic benchmarks and the successful identification of several remains. An outstanding typical error of 0.4″ for the old angular measurements can also be deduced from the analysis. Conversely, several old altitudes were found to have errors or considerably lower accuracies than those expected, around 1 m.

Interferometric synthetic aperture radar (InSAR) is a cost-effective method for displacement measurement at dams and reservoir banks, and is especially relevant for structures without embedded equipment or rarely monitored. However, the lack of redundant observations prevents the determination of a posteriori variances for InSAR measurements, which limits the uptake of the InSAR technology for structure monitoring. This paper presents a methodology for the integration of persistent scatterer interferometry (PSI) and Global Navigation Satellite System (GNSS) displacement measurements. Double differences between PSI and GNSS data are used as observations in a redundant network connecting the points of interest, with GNSS data used to constrain PSI measurements. This procedure allows the determination of adjusted displacements and a posteriori variances at all network points. Maximum uncertainty of 3 mm was achieved for displacements along the SAR sensor line-of-sight at both the dam and its surrounding slopes. The proposed method is of interest for monitoring purposes, because it allows displacement measurement at both the structure and its surroundings, together with the displacement uncertainty, which aids decision makers in the planning of maintenance operations for the whole area influenced by the dam.

The article describes selected case studies of the trilateration network design. The analyzed case studies may be of interest to the geodetic community but may also be potentially interesting for educational purposes. The reference system of the trilateration network in all analyzed variants defined two fixed points. The aim of this article is to assess the impact of network geometry on reliability measures. To investigate this impact, seven criteria for assessing network geometry were defined. Four criteria relate to the shape of the network, whereas the other three describe the location of two fixed points (reference system) relative to the other network points. The subject of the research were correlations between the values of the adopted criteria for assessing the network geometry and the values of reliability measures that were obtained in individual analyzed variants of the network. Based on these studies, appropriate conclusions were formulated regarding the impact of the network geometry on the values of reliability measures in relation to the tested network examples.