Journal of Surveying Engineering

J. Badekas reinterpreted M. S. Molodensky’s three-dimensional similarity transformation as a vector solution using a centroid. The solution has since been (mis)interpreted by some others with inconsistent reference to the methods of both Molodensky and Badekas, principally relating to the translation vector and the stochastic model. This appears to have led to incorrect claims that the Molodensky–Badekas method is superior to the Helmert similarity and Burša–Wolf methods. This paper reviews the development and description of the original Badekas method, reconfirming its equivalence to the Burša–Wolf method in the forward direction, and provides an alternative solution that suits the same-formula reversal common in commercial surveying software. It is also demonstrated that the Molodensky–Badekas method has no inherent superiority over the Burša–Wolf method, has an ambiguous functional model, and nominally underestimates its parameter statistics when these are compared directly with those from the Burša–Wolf method.

Because of ill-posed problems, inverted parameters of ill-posed models always have large variances. The regularization method is widely used to solve this problem. Based on the mean square error (MSE) criterion, the regularization method reduces the parameter estimation variances through introducing biases. However, excessive biases will increase the MSE and the unreliability of the estimates. To improve this situation, this paper first analyzes the calculation of the MSE through the singular value decomposition (SVD) method and then proposes a bias reduction method. Based on this method, a bias-reduced regularization method is proposed to improve the MSE of regularized model parameter estimations. Simulation and practical examples are respectively displayed to demonstrate the effectiveness of the new method. In the simulation example, the root-mean-square error (RMSE) of the regularized model parameter estimates is reduced by 78%. In the polarimetric interferometric synthetic aperture radar (PolInSAR) surveying example, the RMSE of the inverted vegetation height is improved by 23%. Both examples clearly show the effectiveness of the new method.

Subdivision is a very important issue in land surveying and is characterized by the legal change of property boundaries in agreement with the local standards and regulations for maintaining the quality of the zone environment. It is the process of splitting a parcel or an allotment into smaller lots, each with its own separate title deed for the purpose of sale, residential development, and ownership transfer. Therefore, the act of partitioning has a significant role in the establishment of land-use activities. This research aims to introduce a simple and accurate algorithm to carry out land partitioning using a closed-form and direct solution procedure for any polygon-shaped parcel. The mathematical model is based on the coordinates of parcel vertices and some specified constraints to fulfill the site requirements and meet any regulations. The automation of this model was carried out in the Microsoft Visual Studio environment to handle the calculation of subdivision problems in accordance with some restrictions and conditions. In addition, to evaluate the performance of the proposed approach, numerical applications were performed. Furthermore, an appropriate technique is discussed to eliminate discrepancies in parcel areas between what is registered in the ownership document and that computed from the corner coordinates.

The multitemporal digital elevation model (DEM) of slopes constructed from three-dimensional (3D) point cloud data (PCD), which is obtained by terrestrial laser scanning (TLS), can realize the real-time monitoring and analysis of landslides. This paper proposes a new slope DEM construction method for the 3D ground PCD based on moving least square (MLS) theory. The proposed DEM construction method has three important components: MLS-based planar projection interpolation, self-adaptive hole-filling, and greedy projection triangulation (GPT) algorithms. On the basis of MLS theory, the planar projection interpolation algorithm can obtain interpolation-reconstructed points that maintain the important topographic features of slopes, and the self-adaptive hole-filling algorithm can identify hole-filling points from the interpolation-reconstructed 3D points and repair holes of the original 3D PCD. The modified GPT algorithm can efficiently construct more complete DEMs based on the hole-repaired 3D PCD with the support of the Delaunay criterion. The effectiveness of the proposed method is demonstrated with a case study. The DEMs constructed by the proposed method are continuous and can well simulate the topographic features of slopes. Thus, the new method can provide effective DEM data support in many fields, such as surveying and mapping, and geotechnical engineering.

Precise determination of the astronomical azimuth using the local hour angle (LHA) of Polaris is only applicable in northern middle latitudes. Therefore, to achieve fast and precise astronomical orientation in any part of the world, this study proposes continuous observations from the same station of multiple north stars and south stars at their culminating positions, thereby reducing the impact of errors in observation station longitude and time measurement. This method, which uses the regression model, determines the astronomical azimuth from the observation station to the ground target. Model validity is affected by various factors including sample size, data distribution, and data quality; therefore, suitable model conditions and individual characteristics of parametric and nonparametric regression are analyzed. Then, a two-step regression method comprising data binning followed by linear regression is proposed. Experimental data are subjected to direct linear regression, the summation of north and south star data followed by linear regression, nonparametric regression of summed data, and two-step regression of summed data. The two-step regression method produces the most accurate results that agree with those of the LHA method within a range of ±1.2120 × 10⁻⁶ rad (0.25″). Compared to the LHA method, the proposed method extends the geographical application range and eliminates the need for precise astronomical positioning prior to determining the orientation.

International standards establish strict criteria for the measurement of railway track geometric parameters by track inspection trolleys. In the case of the rails’ internal geometry, the values of some parameters (such as track gauge and cant) must be determined directly by a set of high-resolution and high-precision sensors. To ensure the quality of the data (or detect any mechanical misalignment), prior to the observation program the instrument needs to undergo a simple but rigorous check, a procedure the authors argue the regulations fail to properly define. A simple but rigorous routine validation procedure is put forward with which to check the correct functioning of the measurement process by providing estimates for the expected error and variance of the measured parameters. A methodological proposal for in-field observations and error analysis is described in depth. A practical application is described as applied to a track section of the Madrid–Extremadura–Portuguese Border (Spain) high-speed line, which is currently under construction, analyzing the experimental data for the parameters track gauge and cant.

High-accuracy and homogeneously distributed dense terrestrial gravity observations are essential data for detailed analysis of the Earth gravity field as well as for precise modeling of the geoid, which is a natural datum for point heights in geodetic and surveying applications. Precise modeling of the regional geoid and the related quality assessments of the terrestrial data are still substantial issues in many countries. The terrestrial gravity measurements in Turkey have been carried out by different institutions; therefore, the collected data have different qualities and standards. For this reason, detailed analysis of the archival data quality and datum consistency is required for regional geoid modeling using these data. In this article, the accuracy of a gridded gravity anomaly dataset was validated using pointwise gravity values with known accuracy in a limited area in northwest Turkey. Hence, this study aimed to test the contribution of the regridded gravity anomalies in combination with two different gravity datasets to determine a precise geoid model for the region. The assessments showed that the accuracy of the grid gravity anomaly dataset was approximately 5.0 mGal in the study area. Although the pointwise data used as control data in this study have high accuracy (∼3.0 mGal), they exhibit nonhomogeneous and striped distribution in the area, which is not appropriate for geoid modeling purposes. The calculations using regridded data with a combination of the two datasets resulted in a geoid model accuracy of 9.4 cm. The calculated accuracy was compared with the official Turkey Geoid model (TG) and Earth Gravitational Model 2008 (EGM2008) in its full spectrum, and the improvements were reported.

Continuously operating reference station (CORS) networks, as one of the fundamental segments of the precise global navigation satellite systems (GNSSs) positioning techniques, have been undergoing rapid development and growth in the last two decades. The existing and newly created CORS networks coincide with both the services provided and the covered area. This is the situation in Poland, where there are five nation-wide and local networks that have in total over 500 stations and provide access to similar GNSS data, real time kinematic (RTK), and network real time kinematic (NRTK) services. This paper presents one of the most comprehensive tests conducted to evaluate the quality of network-based GNSS positioning services performance provided by all CORS networks available in Poland. The test was performed in November 2017 and included the analysis of accuracy and reliability of positioning performance, time to first fix (TTFF), an average age of correction as well as the compliance of the reference frame realization. The test data were obtained from the field measurements of consecutive RTK/NRTK services and simultaneous continuous measurements carried out at 20 reference points of the first-order geodetic network, evenly distributed throughout Poland. Obtained results allowed to estimate the positioning performance accuracy and reliability for all tested streams and their mutual comparison of quality along with the analysis of the reference frame realization compliance implemented by all networks. In most cases, the results confirm the nominal accuracy of positioning (at 68% confidence level) based on tested streams of 1 cm for horizontal and 2 cm for vertical components. However, it was also found that for some networks and streams the obtained accuracy was twice lower (reaching up to 4 cm for the height component), and compliance with the vertical reference frame is lower.

${\mathit{M}}_{\mathrm{split}(\mathit{q})}$ estimation allows us to estimate competitive parameters, namely different versions of the parameter vector within the split functional model. In the univariate model, such parameters can be regarded as location parameters for different observation aggregations. The whole observation set might be an unrecognized mixture of observations that belong to such aggregations. There are two main variants of ${\mathit{M}}_{\mathrm{split}(\mathit{q})}$ estimation: the squared and absolute ${\mathit{M}}_{\mathrm{split}(\mathit{q})}$ estimations, which differ from each other in objective functions. The estimation process is always an iterative one, irrespective of the estimation variant. This paper addresses the main practical problem in such a context, namely the choice of the starting point and its possible influence on the estimation results. The paper shows that this issue is important; it also proposes the best choice that guarantees the correct solutions of the optimization problem. The authors also consider two types of iterative processes and conclude that the traditional iterative process is recommended for squared ${\mathit{M}}_{\mathrm{split}(\mathit{q})}$ estimation, whereas the parallel process is suitable for absolute ${\mathit{M}}_{\mathrm{split}(\mathit{q})}$ estimation.