Journal of Surveying Engineering

The existing theory of the total least squares (TLS) accuracy estimation contains the following problems: (1) the approximation function method based on the Taylor series expansion cannot avoid the derivative operation; (2) the selection of the number of simulations for the Monte Carlo method is subjective; and (3) the adaptive Monte Carlo algorithm is complex. Aiming at these problems, we introduce the adaptive two-stage Monte Carlo (ATMC) algorithm into the theory of accuracy estimation of the TLS. In order to consider the biases of estimation for parameters, residuals, and the estimation of the variance of unit weight, the computing process for accuracy estimation of the TLS contains bias estimation and accuracy estimation, and the algorithm is provided. In addition, based on the quasi-Monte Carlo method, an adaptive two-stage quasi-Monte Carlo (ATQMC) algorithm is proposed for the calculation of the expected bias in parameter estimates, and the algorithm flow is given. The experimental results verified the effectiveness of the ATMC and ATQMC algorithms. Compared with the ATMC algorithm, the ATQMC algorithm proposed in this paper is more efficient in the calculation of the expected bias in parameter estimates.

Based on the standard of precise multisystem orbit and clock offset, the evaluation methods of satellite orbit, satellite clock offset and the signal-in-space range error (SISRE) from broadcast ephemeris were given in this study. The SISRE was used as a key performance index to compare the global BeiDou navigation satellite system (BDS-3) with the regional navigation satellite system (BDS-2), Global Positioning System (GPS), Galileo, Globalnaya Navigazionnaya Sputnikovaya Sistema (GLONASS), and Quasi-Zenith Satellite System (QZSS). Through the combination of domestic tracking stations and inter satellite links, the orbit determination accuracy of BDS-3 has been significantly improved. The radial (R), tangential (T) and normal (N) direction orbit accuracies of BDS-3 medium Earth orbit (MEO) satellites were 0.08, 0.37, and 0.34 m, respectively, which were considerably better than those of other satellite navigation systems. The R-, T-, and N-direction orbit accuracies of BDS-3 inclined geosynchronous orbit (IGSO) satellites were 0.17, 0.59, and 0.56 m, respectively, which were better than those of QZSS IGSO satellites. The R-, T-, and N-direction orbit accuracies of BDS-3 geostationary earth orbit (GEO) satellites were 0.27, 3.42, and 1.29 m, respectively, revealing considerable accuracy advantages in the R and N directions compared with QZSS GEO, although performance in the T direction was inferior. For the clock offset, the BDS-3 MEO satellites had an accuracy of 1.83 ns, which was noticeably superior, similar, slightly inferior, and superior to those of BDS-2, GPS, Galileo, and GLONASS. The clock offset accuracies of BDS-3 IGSO and GEO satellites were 3.13 and 3.17 ns, respectively, which were slightly better than those of QZSS IGSO and GEO satellites but did not have an obvious advantage over BDS-2. The primary reason could be that the launch time of the two types of BDS-3 satellites was close to the analysis period, and therefore, the clocks may be still in the aging process. Considering only orbit error, the average SISRE (orb) of BDS-3 MEO, Galileo, GPS, and GLONASS was 0.10, 0.28, 0.57, and 1.03 m, respectively. The SISRE (orb) of BDS-3 IGSO was 0.19 m, which was marginally greater than that of BDS-3 MEO but smaller than those of the other systems and considerably smaller than that (0.90 m) of QZSS IGSO. The SISRE (orb) of BDS-3 GEO was 0.60 m, which was comparable to that of GPS (0.59 m) and considerably smaller than that of QZSS GEO (0.91 m) satellites. Considering both orbit and clock offset error, the SISRE of BDS-3 MEO satellites was 0.52 m, which was slightly greater than that of Galileo (0.40 m), marginally smaller than that of GPS (0.59 m), and considerably smaller than that of GLONASS (2.33 m). The BDS-3 IGSO satellites had a SISRE of 0.90 m, which was greater than those of GPS and Galileo but comparable to that of QZSS IGSO (0.92 m). The average SISRE of BDS-3 GEO satellites was 1.15 m, which was greater than those of GPS and Galileo and slightly greater than that of QZSS0.95 m GEO satellites, but smaller than that of GLONASS.

In classical two-dimensional (2D) geodetic networks, reducing slope distances to horizontal ones is an important task for engineers. These horizontal distances along with horizontal directions are used in 2D geodetic adjustment. The common practice for this reduction is the use of vertical angles to reduce distances using trigonometric rules. However, one faces systematic effects when using vertical angles. These effects are mainly due to refraction, deflection of the vertical (DOV), and the geometric effect of the reference surface (sphere or ellipsoid). To mitigate refraction and DOV effects, one can choose to observe the vertical angles reciprocally if the baseline points’ elevation difference is small. This paper quantifies these effects and proposes a proper solution to eliminate the effects in small-scale geodetic networks (where the longest distances are less than 5 km). The goal is to calculate slope distances into horizontal ones appropriately. For this purpose, we used the SWEN17_RH2000 quasigeoid model (in Sweden) to study the impact of the DOV applying different baseline lengths, azimuths, and vertical angles. Finally, we propose an approach to study the impact of the geometric effect on vertical angles. We illustrate that the DOV and the geometric effects on vertical angles measured reciprocally are significant if the height difference of the start point and endpoint in the baseline is large. Geometric correction should be considered for the measured vertical angles to calculate horizontal distances correctly if the network points are not on the same elevation, even if the vertical angles are measured reciprocally.

In existing roads, the geometrical parameters of the alignment are the primary input for safety or geometrical improvement studies. However, the as-built drawings are not always available to obtain geometrical parameters, whereby they must be back-calculated from surveying data. The procedures to back-calculate geometrical parameters of existing roads and fit profile data use parametric methods such as polynomials or explicit functions and nonparametric methods such as splines or smoothers. In smoother-based methods, a usual computing decision is to consider a fixed spacing, one smoothing algorithm, and one set of smoothing parameters to obtain a single set of curvature, deflection, and length (KAL) parameters of vertical curves. Therefore, different values of KAL parameters will be obtained depending on the choice of spacing, smoothing algorithm, and smoothing parameters. This paper aims to study the relative effect in the variability of KAL parameters of a vertical curve, introduced by several spacing combinations, smoothers, and parameters, using data obtained with an unmanned aerial vehicle (UAV). Elevation and slope data were obtained from a digital elevation model every 2, 5, and 10 m. The slope-horizontal distance diagrams were smoothed using single, double, and triple exponential smoothing for different levels, trends, and season parameters. The KAL parameters were back-calculated for each slope-horizontal distance diagram, and the variability analysis was undertaken with boosting regression, multiple analysis of variance, and $k$-nearest neighbor algorithm and tested using receiver operating characteristics (ROC) curves. Results show that the smoothing algorithm and parameters choice affected mainly the $K$ parameter and that the single exponential smoothing algorithm is more suitable than double and triple exponential smoothing algorithms to estimate the KAL parameters.

Given the problem that the relative weights of multitype data sets are not considered in the current studies of Bayesian von Karman regularized slip distribution inversion, we propose to add hyperparameters that control the variance-covariance information of different data sets within the Bayesian framework, present a detailed and complete theoretical method, and successfully apply it to the earthquake that occurred in Norcia, Italy, in 2016. Synthetic tests show that compared with the Bayesian von Karman regularization method with equal weights for different data, the improved Bayesian von Karman regularization method can more effectively invert the real slip distribution of this dip-slip earthquake, its inversion results are more stable, and the data fitting accuracy is higher, thus verifying the advantages of the improved method. In the slip inversion of the Norcia earthquake, the hyperparameters of the global navigation satellite system (GNSS) and interferometric synthetic aperture radar (InSAR) data sets converged to different values, which shows it is indeed necessary to determine different relative weights of different data sets. Moreover, the inversion results show that this earthquake ruptured to the surface, the fault slip region was mainly concentrated in a depth range of 0–6 km, the maximum slip was 3.87 m, and the released coseismic seismic moment was $8.95\times {10}^{18}\mathrm{Nm}$, corresponding to a moment magnitude of $M_{\mathrm{W}}=6.60$. These results are consistent with the existing research, thus verifying the practicability of the improved method.

Astronomical positioning can determine the astronomical longitude and latitude of a station based on observations of celestial bodies. The accuracy of astronomical positioning depends on the observation instruments, surveying environment, and geometric distribution of stellar observations. For astronomical theodolite, existing theories support that the best positioning accuracy can only be obtained with uniformly distributed stars on an equal-altitude circle. In fact, inhomogeneous distribution can also obtain the best positioning accuracy. To illustrate this problem, a quantitative index to determine the optimum geometric distribution of stellar observations by introducing the mean resultant length of vectors in directional statistics is proposed, providing a theoretical basis for studying high-precision astronomical positioning and automated star selection algorithms. Multiple optimum distributions of observations with constant numbers of stars during simulation experiments using the equal-altitude method have been demonstrated. Regarding the approximate equal-altitude method, the inhomogeneous distribution of stars guided by the conclusion described in this paper was also optimum. It could achieve the same accuracy as the uniform distribution. These results can aid in overcoming the limitations of the existing uniform distribution theory for astronomical positioning and provide a theoretical basis for achieving high-precision and high-efficiency astronomical positioning by inhomogeneous distribution stellar observations, especially when only a small number of stars can be observed.

Seasonal ground movements, particularly subsidence and heave, present a great challenge for the design of roadways, parking lots, underground utility lines, and buried culverts. The US Geological Survey has been operating 13 deep borehole extensometers in Houston, Texas, for land subsidence monitoring since the 1970s and the early 1980s. The half-century extensometer datasets provide direct and continuous measurements of seasonal ground movements in the vertical direction. The Houston global positioning system (GPS) network (HoustonNet) provides independent measures for the timely evaluation of extensometer data. According to this study, shallow expansive soils can induce up to 4 cm (peak-to-trough) seasonal subsidence and heave, and deep sediments can further produce up to 2 cm seasonal subsidence and heave. The latter is primarily caused by the seasonal fluctuations of hydraulic heads in the lower Chicot and upper-Evangeline aquifers, varying considerably over time and space. The results from this study are important for determining potential vertical movement (PVM) for the design of pavements and shallow foundations and for the optimization of groundwater management in the Houston region.

Precise navigation, as a method for guiding vehicles from one point to another, is an important subject these days especially in navigation of aircraft. Global navigation satellite systems (GNSSs) are capable tools for such a purpose. Any intentional or unintentional interference in satellite signals may cause risks of deadly accidents. Therefore, it is tremendously important to control airports or harbors and locate any existing radio frequency interference device. This localization can be done based on measuring time of arrival (TOA), angle of arrival (AOA), or time difference of arrival (TDOA) of signals from the device to sensors or receivers at some basepoints. In this article, a method is proposed based on these arrivals for optimizing the configuration created by these basepoints from a large grid of points covering a control area. Furthermore, a simulation test was performed to verify the theory, and after that a control network was designed and optimized for the international Landvetter Airport of Sweden. Our simulation studies show that when the AOA is used, our optimization is more robust with respect to the control grid resolution. In addition, optimization based on the TDOA improves the coverage over the control area with a significant reduction of error of control points, but because of the special geometric shape of the Landvetter Airport, such an optimization was not successful.

In the development of neural networks, many realizations are performed to decide which solution provides the smallest prediction error. Due to the inevitable random errors associated with the data and the randomness related to the network (e.g., initialization of the weight and initial conditions linked to the learning procedure), there is usually not an optimal solution. However, we can advantage of the idea of making several realizations based on resampling methods. Resampling methods are often used to replace theoretical assumptions by repeatedly resampling the original data and making inferences from the resampling. Resampling methods provide us the opportunity to do the interval prediction instead of only one point prediction. Following this idea, we introduce three resampling methods in neural networks, namely Delete-d Jackknife Trials, Delete-1 Jackknife Trials, and Hold-Out Trials. They are discussed and applied to a real coordinate transformation problem. Although the Delete-1 Jackknife Trials offer better results, the choice of resampling method will depend on the dimension of the problem at hand.

Stake measurement is a significant ground-observation method used to monitor glacier dynamics in the cryosphere and validate the reliability of remotely sensed investigations. However, some stake observation records obtained by total stations have not been efficiently utilized via the classic forward intersection method. The forward intersection method requires a pair of cognominal observation records and cannot function if stakes are only observed from one control point at a stake measurement, which commonly occurs in measurements. Therefore, we propose an improved intersection method that combines stake trajectories and sightlines, the trajectory-sightline intersection method, which requires only a single observation record. In the processing of stake identification, location and elevation from the trajectory-sightline intersection method are constrained by the velocity and surface altitude of the glacier. Then, the trajectory-sightline intersection method is applied to the stake measurement of Dalk Glacier in East Antarctica. The results show that the trajectory-sightline intersection method extracted an additional 44 intersections, thus increasing the data utilization ratio by 20.35%. Moreover, leave-p-out cross-validation indicated that the trajectory-sightline intersection method, with an average offset of $0.88\pm 0.54\mathrm{m}$ in the horizontal position and $0.26\pm 0.12\mathrm{m}$ at the elevation, has similar accuracy to the differential global positioning system (DGPS) applied to Livingston Island. The ice flow velocities of Dalk Glacier calculated from trajectory-sightline intersections agree with those from forward intersections (the mean velocity difference is ${0.47\mathrm{m}·\mathrm{year}}^{-1}$). Therefore, the trajectory-sightline intersection method is an effective method for improving data utilization and obtaining stake locations and glacier velocities.

Commercially available global navigation satellite system (GNSS) processing software is user-friendly and can be used in a wide variety of positioning applications from establishing geodetic control over large regions to deformation monitoring on a local scale. It is important to study the accuracy of positioning from commercial software for presurvey planning. Previously, this was done in several studies; however, none of them focused on the effect of large height differences in positioning solutions. It is known in the literature that large height differences on a baseline degrade GNSS solutions. In this study, we investigate the effect using TOPCON MAGNET v 4.0.1 through analysis of continuously operating reference stations (CORS) in California, US. Because the effect of height differences on global positioning system (GPS) baseline components has not yet been properly quantified, the positioning accuracy standards given in the surveying guidelines may not be appropriate and are often overoptimistic. When the height difference was less than about 300 m, the root mean square error was about 2–3 mm for the horizontal components and about 20 mm for the vertical component for baseline lengths of 10–20 km. However, for a height difference of 1,500 m, the error became 5–8 mm for the horizontal and 70 mm for the vertical components. In all cases, the vertical error was greater than the horizontal by a factor of 5–9, which is much greater than the expected 2–4 for GNSS. These results are likely only applicable to the version of the MAGNET software used in this study.

GNSS_Vel_95CI.py is an open-source Python-3 module for calculating the 95% confidence interval (95% CI) for the site velocity derived from global navigation satellite systems (GNSS) daily positions, which are often affected by time-correlated noises. The detailed methodology for calculating the 95% CI is documented in a recent article (Wang 2022) and initially programmed in Fortran. However, few young researchers (e.g., graduate students) are familiar with Fortran now. In an effort to support a broader user community, we have realized the method in the Python programming language, which has been commonly taught in current college curriculums. Through the use of this module, researchers and engineers can focus on the applications of GNSS time series, rather than on coding and data processing. In particular, the module has the option to output the autocorrelation function (ACF) and the GNSS time-series decomposition results: the linear, nonlinear, seasonal, and residual components, which allow students and researchers having little coding experience to conduct advanced GNSS time-series analysis. The module is versatile, easy to install through the pip installer and GitHub, and simple to use. An example Python program is provided to illustrate the use of this module.