Journal of Surveying Engineering

Estimating the accuracy of source geometry parameters is helpful for understanding error propagation in a nonlinear inversion. To date, no studies have estimated the nonlinear inversion accuracy of source geometry parameters. Multipeak particle swarm optimization (MPSO) is used to invert source geometry parameters, providing them good reliability as is shown by Monte Carlo analysis. Also, Sterling interpolation is introduced to estimate the accuracy of nonlinear inversion of parameters in earthquakes. The square roots of variance in the source geometry parameters are obtained by the displacements and the corresponding errors. A simulation experiment illustrates that changing the number of observation points does not affect the accuracy of the seven source geometry parameters. When the number of observation points is constant, the square roots of variance in the source geometry parameters increase with an increase in noise in the observations. Finally, Sterling interpolation accuracy estimation as proposed is applied to the Lushan and L’Aquila earthquakes. We find that the random noise in the observation data affects the inversion results. The applicability and feasibility of the proposed method are verified.

Optimization of a geodetic network is a process in which a specific stage (or stages) is designed in such a way that the obtained result meets the assumed (optimum) design requirements. The goal of this article is to present a new method for designing observation plans first-order design (FOD) that aims at maximally reducing the number of observations (the cost criterion) while maintaining the a priori established quality criteria (accuracy and reliability). To achieve this goal, a categorization of points was introduced and the criteria were arranged into a hierarchy. Because the method uses computer simulation, sequential estimation was also used to speed up the computational process. The cost model is a general model defined as minimization of the number of observations in the network, regardless of their weight. The study was carried out using the example of a geodetic network designed for the National Stadium in Warsaw. The results bear out the effectiveness of reduction of observations and show the impact that strict criteria have on the scale of this reduction.

Photogrammetry using structure from motion (SfM) and multiview stereopsis (MVS) techniques can recover three-dimensional (3D) structure from a set of overlapping, unoriented, and uncalibrated images captured by nonmetric digital cameras. It is possible to generate accurate reconstructions of sparse points using mathematically robust bundle adjustment procedures together with accurate surveying control data. However, MVS, which recovers the dense geometry by matching and expanding between sparse points, is prone to additional error. Miscellaneous constituents such as sensor specifications, data collection, and site conditions can introduce random noise or artifacts that locally degrade the accuracy of the dense point cloud. This paper proposes seven indexes, named dense point cloud quality factors (DPQFs), as proxy indicators of image-based dense reconstruction accuracy. DPQFs include proximity to keypoint features, distance to GCPs, angle of incidence, camera stand-off distances, number of overlapping images, brightness index, and darkness index. The correlation between the DPQFs and the 3D error was investigated in simulated and empirical experiments scenarios with varying factors. The results of this study showed that the DPQFs provide proxy indications for accuracy when the error estimation for the dense point clouds is more challenging than error propagation computations in bundle adjustment (BA). The DPQFs can be defined solely using the SfM-MVS data, without prior knowledge about the error. Inclusion of the factors as additional fields of information and their visualization provide tangible intuitions regarding the factors that influence the accuracy of image-based 3D reconstruction.

This paper discusses the possibility of replacing the commonly used clothoid transition curve on a railroad route with a new transition curve adapted to railway operational requirements. The new transition curve is similar to the clothoid in its initial section, but it differs significantly over its extent, especially in the final section, where it provides a smooth entry from the transition curve into the circular curve. The subject of this study is the consideration of two key aspects of transition curves: the dynamic properties of the proposed geometric solution and the conditions related to the replacement of the existing clothoid transition curve. The dynamic analysis carried out confirmed that from an operational point of view the new transition curve is more favorable in the initial section than in the clothoid, while in the final section it has a definite advantage. In the final section the superiority of the new transition curve over the Bloss curve (representing S-shaped transition curves) is demonstrated. In our analysis of technical conditions related to the replacement of the clothoid with a new transition curve, it was shown that this operation does not require large lateral shifts of the railway track, and the values of the shifts depend mainly on the extent of the transition curves and the angle of shift of the main directions of the route. In the most unfavorable cases (large turn angle, considerable extent of transition curve) the situation can be significantly improved by a relatively small reduction in the radius of the circular curve.

To evaluate the posterior precision of weighted total least-squares (WTLS) estimates in an errors-in-variables model, first-order approximate precision estimation (FOA) methods are usually used. However, FOAs might not be valid if the underlying assumption is invalid, and this assumption has not been sufficiently proven. Therefore, this paper investigates the validity of the latent assumption and proposes a new first-order approximate (NFOA) precision estimation method to avoid the underlying assumption and design a corresponding algorithm. The difference between NFOA and FOA is formulated and analyzed. The proposed NFOA method is tested by a simulated classic straight-line fitting example with six scenarios and a simulated three-dimensional (3D) affine transformation experiment with four scenarios, and the mean values of the standard deviation of true errors (MSDTE) and FOA are also calculated for comparison. The results numerically indicate that NFOA works better than FOA and is close to the MSDTE, which means that NFOA can evaluate the precision of estimated parameters more reasonably and accurately.

Several least-squares adjustment techniques were tested for dam deformation analysis. Deformation monitoring had only been studied horizontally. Simulated observations were first performed to compare the three methods of least-squares: observations with their initial weight, observations with the estimated variance component, and the regularization method. The best scenario was adopted for the real network. The results demonstrated that a more accurate outcome is possible by least-square variance component estimation (LS-VCE). Comparison of the estimated and simulated displacements in the LS-VCE method indicated that the difference for the two east–west and north–south components is 0.05 and 0.08 mm, while this difference in the other two modes is 1.02 and 0.67 mm for observations with their initial weight, and 0.64 and 0.16 mm for the Tikhonov regularization method, respectively. In the best method, an improvement was found in the standard deviation of the east–west, south–north components, the estimation of the major axis of the error ellipse, and the trace of the variance–covariance matrix of unknowns, in comparison with the other methods.

This study investigates the effect of stochastic model errors on the significance test for velocities in the analysis of a global positioning system (GPS) position time series. This effect is studied by considering the estimated probabilities of type I and type II errors occurring in the hypothesis testing. For this purpose, synthetic daily time series with 3-, 7-, and 10-year periods are considered. Many random samples are simulated for each series such that they include white noise (WN), flicker noise (FN), and random walk noise (RWN) with specified magnitudes. First, it is shown that an incorrect WN-only stochastic model almost always yields false-positive decisions in testing the velocities. Later on, noise magnitudes in the series are obtained through the least-squares variance components estimation (LS-VCE) method. Confidence interval estimates depict that the estimated velocity uncertainties may be biased because of estimation errors of variance components. However, the type I and type II error probabilities in testing the velocities do not change significantly for most of the series samples with WN and FN. For the time series consisting of WN, FN, and RWN, the error in estimating the RWN magnitude causes more effect on the uncertainty of velocity. In this case, type I error relating to the velocity estimation may, on average, be increased by 9.4% while type II error remains the same.

This work deals with the estimation of the variance–covariance matrix of the parameters of a fitted ellipse and an ellipsoid by a direct and an indirect procedure. In the direct approach, the Cartesian equation of an ellipsoid was expressed in terms of the coordinates of the ellipsoid center, the three ellipsoid semiaxes, and the three rotation angles. The general least-squares method was applied to estimate these parameters and their variance–covariance matrix. In the indirect approach, the Cartesian equation of an ellipsoid was expressed as a polynomial. The coefficients of this polynomial equation and their variance–covariance matrix were estimated using the general least-squares method. Then these coefficients were transformed into the parameters of the ellipsoid through an analytical diagonalization of a suitable matrix. The variance–covariance matrix of these parameters was estimated applying the law of propagation of variances. Both approaches are applied to the special case of an ellipse. The numerical examples in both cases indicated that the two procedures produce almost identical results.

This case study examines two essential aspects of mobile terrestrial laser scanning (MTLS). First, it provides results of an investigation into key data management issues experienced by a fairly large producer/consumer of MTLS data. Second, it documents the requirements, design, and implementation of a software tool for automated metadata cataloging of MTLS data and projects. This tool, known as LidarCrawl, was developed to directly address data management issues encountered in the distribution and reuse of MTLS data. This tool enables a geospatial-enabled web-based portal to view MTLS data availability and improves data discovery and usage for all MTLS user levels. While the current case study focuses on the management of MTLS data for the Department of Transportation, the tool provides a means for automated metadata cataloging for general geospatial data in various domains.

The adjustment of laser tracker network measurements for large-scale metrology applications has unique considerations not commonly encountered in the network adjustment approaches generally used in either standard metrology or in traditional geodetic surveying. Many applications that require the measurement accuracy of a laser tracker are confined to small working areas to measure the dimensional quality of manufactured parts. Large-scale metrology applications require the same high measurement accuracy, but over a comparatively larger working area. This paper describes a unified least-squares approach to adjust three-dimensional survey network measurements that takes into account the unique considerations of large-scale metrology networks. The impetus for these unique considerations arises from an application that falls neatly between the disciplines of metrology and geodesy—resembling a mixture of the conditions and requirements from both. This paper will also describe a case study of a large-scale metrology survey network used to align the particle accelerator at Michigan State University’s Facility for Rare Isotope Beams (FRIB).

An $n$-station continuously operated global navigation satellite system (GNSS) network contains $n\text{-}1$ independent baselines. Baseline structure is critical to positioning accuracy, and the final result is dependent on the baseline selection strategies. The baseline length and amount of common observations are the primary principles for baseline selection. However, there are few discussions about the optimal strategy to determine the independent baseline of a huge GNSS network. To enhance the performance of the multibaseline solution, a comparison is drawn between the conventional method and a weighting strategy. Observations from continuous stations distributed globally within the International GNSS Service (IGS) are explored. At first, two conventional principles for baseline selection are tested. Subsequently, a weighting scheme is developed to exploit these two strategies. The enhanced method improves nearly 10% external accuracy compared with the classical methods, which can be verified from the experiment on January 1, 2012. Lastly, the network experiment is extended to the whole year of 2012 to increase statistical significance. It is therefore revealed that the novel weighting strategy (WEIGHT), with an equal chance of two conventional strategies, mitigates 0.4%–3.0% three-dimensional (3D) coordinate error of the whole year. Also, an analysis of the probability of gross errors indicates that WEIGHT exhibits better performance. Unlike the conventional view, it is shown that a proper weight of OBS-MAX and SHORTEST could form a better coordinate calculation result and a lower gross error rate. In conclusion, these experiments suggest a proposed method that synthetically considers the length of total stations and the total number of observations, and it is verified that WEIGHT is a better choice for searching independent baselines.

This paper investigates the usability of Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) methods, traditional PPP with a float-ambiguity solution and with ambiguity resolution (PPP-AR), in structural health monitoring applications based on experimental tests using a single-axis shake table. To evaluate the performance of the PPP methodologies, harmonic oscillations of the motion table with amplitudes ranging from 5 to 10 mm and frequency between 0.1 and 3 Hz were generated representing a wide range of possible structural motions. In addition, ground motion similar to those experienced during a real earthquake, the 1995 Kobe earthquake, and step motions were generated on the shake table. GNSS PPP–derived positioning results at 20 Hz were compared, in both of the frequency and time domains, with reference data comprising LVDT data and relative positioning data. Results show that both PPP methods’ measurements can be used in the computation of harmonic oscillation frequencies compared to the LVDT and relative positioning values. The observed amplitudes of the harmonic oscillations are slightly different from the LVDT values on the order of millimeters. The results of a step motion experiment demonstrated that PPP-AR is better than traditional PPP in exhibiting quasi-static or static displacement. Moreover, the capabilities of traditional PPP and PPP-AR methods are evaluated with respect to the natural frequency of a small-scale structural model excited on the shake table. The frequency spectrum of this small-scale structural model derived from the PPP methods is consistent with finite-element model (FEM)–predicted values and relative positioning. The research presented here demonstrates the potential of the high-rate GNSS PPP and PPP-AR methods to reliably monitor structural and earthquake-induced vibration frequencies and amplitudes for both structural and seismological applications. Specifically, all results reveal that high-rate PPP-AR is more accurate than traditional PPP for both dynamic and static displacement detection.