Journal of Surveying Engineering

The World Geodetic System 1984 (WGS84) has been consistent with the International Terrestrial Reference Frame (ITRF) since 1994. After the original release of WGS84 in 1987 by the Defense Mapping Agency (since superseded by the National Geospatial-Intelligence Agency, NGA), there have been six subsequent realizations of the frame, designated WGS84 (G730), WGS84 (G873), WGS84 (G1150), WGS84 (G1674), WGS84 (G1762), and WGS84 (G2139). Users of WGS84 often fail to document metadata indicating the realization and epoch related to their data collections. As a result, when transforming between realizations or between other reference frames, the transformation can lead to incorrect results. We aim to bring awareness to the nature of WGS84 and the ambiguity in how it is defined. An internally consistent set of transformation parameters is derived that allows for transformation between the WGS84 realizations and other global reference frames while accounting for nuances and inconsistencies in the published literature. The derivations are based on existing (though not easily discoverable) information. Transformation accuracy is evaluated through comparison to other software and NGA-published GPS tracking station coordinates. After accounting for plate tectonic motion, the estimated uncertainties average $\pm 0.03\mathrm{m}$ horizontally and $\pm 0.08\mathrm{m}$ vertically for transformations involving all realizations other than the original WGS84. Uncertainties are at the meter level for transformations that include the original WGS84. If plate motion is ignored, the horizontal uncertainties can increase by several decimeters, depending on location within a plate.

Variance component estimation (VCE), herein called joint inversion, is a widely used approach to weigh the contributions of different data sets. Traditionally, the random errors of observations in VCE are modeled as Gaussian. However, in many geodetic measurements and sensor technologies, the observation data are non-Gaussian; therefore, the joint inversion with a more general heavy-tailed error model is preferred. Another issue is that the VCE deduced from the existing approaches may be not an interior solution, which means that the estimates may lie outside of the parameter space. Although there are some works on VCE in the Gaussian error model with equality or inequality constraints to mitigate this effect, to the best of our knowledge, there does not exist any work addressing the interior solutions of variance components for the heavy-tailed error model. In this article, we consider these issues for the first time and describe the behavior of multiple data sets using the joint functional model, which allows for the nonlinear modeling through nonlinear (differentiable) observation functions, where the random errors are modeled as Student’s $t$-distributed. To address the estimation problem, an iteratively reweighted least squares (LS) approach to self-tuning robust estimation of joint functional model parameters, the variance components, and the degree of freedom ($df$) of the Student’s $t$-distribution is derived based on a variational generalized expectation-maximization (GEM) algorithm. The proposed algorithm is computationally cheap and easy to implement. The performance of the algorithm is evaluated by means of Monte Carlo simulations of the joint volcano source model. Furthermore, the suitability of the research model and the proposed variational GEM algorithm is investigated within a numerical experiment involving the multisource modeling and adjustment of real data sets of the 2015 Calbuco volcano eruption.

More and more global digital bathymetric models (DBMs) have been developed using different kinds of data and have played a great role in navigation, national military defenses, tsunami predictions, marine resource developments, and so on. In order to select appropriate DBMs for usage in different ocean areas, it is necessary to verify their accuracies. In this study, the accuracy of four recent global DBMs, i.e., DTU18BAT, ETOPO1, GEBCO_2020Grid, and SRTM15 + V2.0, are evaluated by shipborne bathymetry data. By setting the shipborne depths data as true values, the error statistics and spatial distribution of the models are firstly analyzed both in spatial and frequency domains. The results show that SRTM15 + V2.0 has the highest accuracy. After removing gross errors, the error standard deviations of SRTM15 + V2.0 are smaller than 50 m, and 90% of the evaluation points have errors smaller than 100 m except in the Indian Ocean. The four models were fused together to obtain a new DBM with higher accuracy. This was done using a weighted combination algorithm based on iterative search to determine the combination parameters. The results showed that compared with the initial four models, the new model has an improved standard deviation of 2.816 m. Also, in a $10°\times 10°$ area in the Indian Ocean where initial mean error and error standard deviation were, respectively, $-10.688$ and 94.041 m, the average error has decreased by 8.527 m, and the error standard deviation has decreased by 13.528 m. The results of this study can provide a reference for the selection and optimization of the seabed topography model.

Vertical curve fitting is important both for road safety management and railway maintenance. Different parameterizations were proposed to specify a vertical curve satisfying the constraint of continuity between its components. The vertical curve-fitting model was developed to explore the effects of different parameter sets on the fitting performance for a vertical curve. The steepest descent (SD), Gauss-Newton (GN), and Levenberg-Marquardt (LM) algorithms were used to search for the optimum solution. Experiments showed that the different parameterizations have different effects on the performance of the three algorithms. For one parameter set, the three algorithms converged to different solutions. For the other, the three algorithms converged to the same optimal solution. The two parameterizations responded differently to initial values, which were illustrated visually. From six different initial values, the LM algorithm converged to different solutions for one parameterization, but to the same optimum for the other. The condition number (CN), an index for evaluating the extent of ill-posed problems as well as correlations between parameter pairs, was examined to interpret the reasons of one parameterization outperformed the other in both robustness and effectiveness. Results also showed that the LM algorithm outperformed the GN algorithm in robustness and outperformed the SD algorithm in efficiency.

In 1967, as directed by the Oregon Beach Bill, the Oregon State Highway Department undertook a survey of the entire coast to delineate the shore zone boundary. Survey control points and photo control were established for an aerial survey that same year, but only hardcopy records currently exist. If the 1967 survey coordinates can be accurately updated, the aerial imagery can be processed in modern photogrammetric software to produce digital elevation models of the entire coast, which will enable volumetric coastal change analysis over a period of half a century. The goal of this study was to develop and test a procedure for combining historic and current horizontal traverse survey data to update the 2D control survey coordinates (with the intent to add leveling data and extend the procedures to obtain 3D coordinates in a later study). First, a custom workflow and algorithms were developed to convert the historical survey records to machine-readable format. GNSS data—both static postprocessed and real-time network (RTN)—were then acquired for recoverable marks. An adjustment of the traverse data constrained to RTN coordinates was compared against an independent adjustment of the static GNSS data performed in the National Geodetic Survey OPUS-Projects software. The results show that the methods can produce updated horizontal coordinates for the 1967 survey accurate to within two centimeters.