Journal of Surveying Engineering

The weighted total least squares (WTLS) has been widely used in many geodetic problems to solve the error-in-variable (EIV) models in which both the observation vector and the design matrix contain random errors. This method is widely applied in its univariate form, where the observations and unknown coefficients appear in vector forms. However, in some geodetic problems, data sets appear in more than one dimension, and the vector representation of the univariate model may not be suitable to efficiently solve the problem. The observation and unknown parameter vectors can then be replaced with their counterparts in matrix representations in a multivariate model. In this paper, we propose a simple, fast, and flexible procedure for solving the multivariate WTLS (MWTLS) problem using the standard least squares theory. The method has the capability of applying to large-size and high-dimensional data sets. Our numerical experiments on both simulated and real datasets demonstrate the high performance of the proposed method for solving multivariate WTLS problems. In terms of computational complexity, our method outperforms the existing state-of-the-art methods, both numerically and analytically.

Methods for modeling the uncertainty in laser tracker angle measurements vary within the metrology industry, leading to confusion and questionable stochastic modeling for survey network adjustments and error propagation analysis. Interpreting the published laser tracker manufacturer performance specifications to determine an a priori sigma value for weighting azimuth and zenith angle measurements can be confusing and has led to differing implementations. This paper proposes a unique way to model survey network a priori laser tracker angular uncertainties based on laser tracker manufacturers’ published maximum permissible error (MPE) values referenced to current standards for weighting survey network measurements. This paper’s proposed model takes into account the disparate effects that pointing errors, target centering errors, and leveling errors have on azimuth and zenith angular uncertainties for measurements with steep sightings and at near ranges.

Astronomic positioning and orientation can be used to obtain the astronomic longitude and latitude of a station and the astronomic azimuth of a ground target by observing stars. The results of the positioning and orientation depend not only on the instrument, environment, and observed star, but also on the solution method. Due to atmospheric refraction and instrumentation, there is a systematic error in the zenith distance of observed starlight during astronomic measurements using theodolites. The existing methods either do not consider the systematic error of the zenith distance, or do not fully utilize all directional information of the star. Therefore, existing methods cannot simultaneously achieve high-accuracy astronomic positioning and orientation, particularly in the case of poor stellar distribution. To address this problem, an astronomic positioning and orientation method that considers the zenith distance system error is proposed. The experimental results showed that the proposed method had a higher positioning accuracy than the traditional astronomic positioning method. In addition, the new method showed significant advantages in instances of inhomogeneous distribution such as cloudy or daytime observation.

The capability of a commercial off-the-shelf amphibious bottom crawling robot is explored for surveying seamless topography and bathymetry across the beachface, surfzone, and very nearshore. A real-time-kinematic (RTK) antenna on a mast was added to the robotic platform, a Bayonet-350 (previously the C2i SeaOx). Data collected from the robot were compared with those collected by the Coastal Research Amphibious Buggy (CRAB) and the Lighter Amphibious Resupply Cargo (LARC), unique amphibious vessels capable of collecting seamless topography and bathymetry in use for decades at the US Army Engineer Research and Development Center’s Field Research Facility (FRF). Data were compared on five different days in a range of wave conditions ($H_s<1\mathrm{m}$ in 8-m depth) resulting in a root-mean square difference of 8.7 cm and bias of 2 cm for 24 different cross-shore profile comparisons. Additionally, a repeatability test was performed to asses measurement uncertainty. The repeatability test indicated a total vertical uncertainty (TVU) of 5.8 cm, with the highest spatial error at the shoreline.

Continuous seafloor transponder positioning with moored buoy observation system is an indispensable method for detecting seafloor crustal deformation. However, the between-buoy baseline information provided by the global navigation satellite system (GNSS) relative positioning, the precision of which can be up to centimeter level or even higher, is not introduced into the conventional joint adjustment method. The accuracy of seafloor transponder positioning might be improved if high-precision baseline information is taken into account. In this contribution, a joint adjustment (IJA) method with between-buoy baseline constraints is proposed for the GNSS acoustic (GNSS/A) underwater precise positioning system with moored buoy observation system. Specifically, the positions of both acoustic transducer and transponder are treated as unknown parameters, and the positions of the acoustic transducer provided by GNSS positioning are introduced as virtual observations. Between-buoy baseline information is also introduced to further improve the precision of underwater positioning. To verify the performance of the improved joint adjustment method, a series of simulation tests were carried out. Simulation results show that the positioning accuracy with the proposed method can be improved by about 24%–53% compared with the traditional method and 7%–44% compared with the joint adjustment method.

To address the problem of inaccurate mixed additive and multiplicative random error stochastic model weighting, we apply the minimum norm quadratic unbiased estimator (MINQUE) to a mixed additive and multiplicative random error model (TMAMM). Then we construct the corresponding calculation formula and iterative algorithm. Based on the formula and algorithm, we estimate the corresponding additive error variance and multiplicative error variance components. The MINQUE variance component estimation (VCE) method is based on (1) invariance, (2) unbiasedness, and (3) minimum normality. Therefore, the variance component estimates derived from the MINQUE method for the mixed additive and multiplicative random error stochastic model also have unbiased and least norm properties. The mixed additive and multiplicative random error stochastic model is modified based on an estimated variance component valuation to obtain a more reasonable parameter valuation. Numerical simulation experiments, digital terrain model (DTM) experiments, and side net measurement are used to verify the effectiveness of the proposed method.

In this manuscript, a novel time-frequency approach based on noise characterization is proposed for Structural Health Monitoring (SHM) using Global Navigation Satellite System (GNSS) observations. The Allan variance (AVAR) is used to conduct a thorough analysis of GNSS observations, offering greater insight into the noise properties of the system. The results of this noise analysis are utilized to assess bridge movements and enhance the precision of the SHM system. The primary focus of the manuscript is the application of AVAR in GNSS-based SHM, and the results demonstrate the proposed approach’s efficacy in accurately assessing bridge movements. The AVAR analysis revealed that GNSS measurements are contaminated with quantization, white, flicker, and random walk noises, with white and flicker as the dominant noises and the others as secondary. The application of the Kalman Filter reduced the magnitude of white and flicker noise in measurements by an average of 69.3% and 62.6%, respectively. The dominant periods of dynamic movements, determined from the Least Squares Harmonic Estimation (LS-HE) analysis, were found to be within the range of 68.53–179.75 min. The findings of the proposed approach indicate that bridge movement changes amount to 11.48 cm, which is within the permissible design limits. This novel time–frequency approach, based on noise characterization using AVAR, holds significant potential for designing and implementing GNSS-based SHM systems.

Estimating horizontal alignment using discretized roadway data points, such as GIS maps, is complicated because the number of curved and tangent segments and their start and end points are not known a priori. This study proposes a two-step approach: The first step estimates the number and type of segments and their start and end points using an artificial neural network (ANN)-based approach. The second step estimates the segment-related attributes such as radii and length by circular curve-fitting. The novelty of this study lies in the simplicity of the input vector to the ANN model, which contains only the latitude and longitude readings of a point and those of its neighboring points. Training and test data were comprised of points extracted from curved and tangent segments of random horizontal alignments, generated synthetically using a computer programming code. The proposed approach was evaluated and compared with other available methods presented in the literature using real roadway horizontal alignment data from one freeway and one rural roadway with a total length of 47 km and 65 curved segments. The analysis results indicated that the proposed approach outperforms other approaches in terms of estimation performance, particularly when the roadway follows a winding alignment.

The goal of this paper was to perform an exhaustive search regarding which combination of minimum L1-norm (MinL1) criteria is a better option for outlier identification. By means of Monte Carlo simulations (MCS), we compared the mean success rate (MSR) of combinations of three approaches for weight matrix $\times$ two approaches for test statistics $\times$ and two approaches for method of solution = 12 combinations of criteria for outlier identification with MinL1, in six geodetic network configurations. Six of them had never been evaluated via MCS, and four had never been tested in the literature. In general, the optimal combination was the adjustment with the same weights for the observations, normalized residual as the test statistic, and simplex method of solution (MinL1S - $w_i$ - simplex). In each case, we also computed the MSR of the iterative data-snooping (IDS) for reference. IDS presented MSR higher than all 12 MinL1 combinations in the four geodetic networks with mean redundancy numbers greater than or equal to 0.5. However, the MSR of the MinL1 optimal combination were 1.62 and 2.65 times higher than those of the IDS for the leveling and the global navigation satellite system (GNSS) networks with mean redundancy numbers less than 0.5, respectively. These results provide strong evidence that MinL1 with such criteria combinations has the potential to be the new state-of-the-art method for outlier identification in low redundancy GNSS and leveling networks.

A test application of a height transfer method employing quasi-geoid undulation extrapolation using vertical deflection (VD) measurements obtained by the digital zenith camera VESTA (VErtical by STArs) is described. This method in combination with ellipsoidal height measurements by global navigation satellite system (GNSS) may provide a cheaper and more convenient alternative to classical geometrical leveling, particularly for long distances and/or when natural or administrative obstacles are present. VD measurements were taken along a 4.5-km traverse of the first-order leveling points located at both ends and in the middle, with GNSS measurements taken at the first-order leveling points. The height transfer results were then compared to the existing network data from the national database. The agreement between the height transfer results and the leveling network data was within the expected deviations. Possible error sources were evaluated, and requirements for VD measurement point selection were formulated.

Having available reference networks close to working areas minimizes error propagation and reduces costs to society when surveying or setting out engineering projects. The densification of reference networks using the Global Navigation Satellite System resulted in a more agile and cost-effective process. However, in locations with a signal obstruction or multipath—typical of urbanized areas—the solution is still to densify through direction and distance observations with total station. Traverse is the most widely applied among the conventional methods, although it has a higher error propagation. Triangulateration, in turn, is a method with higher redundancy and, therefore, less error propagation, but is also less productive, especially in urbanized areas. In this study, we present a new method for the densification of horizontal reference networks through multiple free stations, eliminating centering errors and allowing for unique and simultaneous adjustment of network points. To conduct an a priori quality analysis, the proposed method was compared with triangulateration and traverse methods considering the absolute confidence ellipses of network points; the relative confidence ellipses of the alignments; and the redundancy numbers of the observations in a simulated horizontal network. Although the redundancy of triangulateration guarantees higher reliability, the experiments showed that the multiple free stations method is more productive than traverse and triangulateration as it does not require the target points to be occupied. Besides that, it also provides better precision, that is, smaller confidence ellipses due to centering error elimination.

Abstract

Carrier-phase smoothing code (CPSC) is a code-smoothing technology that uses carrier-phase changes to reduce code noise in Global Navigation Satellite System (GNSS) appliances. Although CPSC performs well in reducing noise and is easy to implement, it is a trade-off between the reduction of noise and the increase of the variation of ionospheric errors. The width of the smoothing window needs to be large to reduce noise. However, a wider smoothing window increases the variation of ionospheric errors. To circumvent this dilemma, the grid ionospheric model (GIM) was used to estimate the variation of ionospheric errors between consecutive epochs, and a noise estimation method is proposed for low-cost single-frequency receivers. Furthermore, an optimal carrier phase smoothing code (OCPSC) algorithm with an adaptive width smoothing window is proposed to reduce the noise of Global Positioning System (GPS) data. We found that the OCPSC is more robust and its positioning performance is better overall for low-cost single-frequency receivers than is the traditional CPSC. In a static mode, when applying the OCPSC algorithm, the positioning accuracy can be improved by 0.15 m (6%) and 0.06 m (6%) in the horizontal and vertical directions, respectively. These improvements are 0.08 (3%) m and 0.06 m (1%) when a kinematic mode is applied.

Practical Applications

The research presented here demonstrates that the OCPSC algorithm effectively addresses the trade-off between the reduction of noise and the increase of the variation of ionospheric errors. In the OCPSC algorithm, the grid ionospheric model is used to estimate the variation of ionospheric errors between consecutive epochs, and a noise estimation method is used to estimate noise for low-cost single-frequency receivers. The OCPSC algorithm was applied to static and dynamic experiments. All results in this paper show that, compared with traditional CPSC, the OCPSC algorithm provides more-accurate positioning results for low-cost single-frequency receivers. Because future smartphones will integrate GNSS chips, the proposed OCPSC algorithm has great potential to be applied widely to the market of multiconstellation single-frequency Precise Point Positioning with low-cost smartphones.

$M_{\mathrm{split}}$ estimation is a modern estimation method that has found various applications in processing geodetic data. Its basic variants were not meant to be robust against outliers; however, the practical applications showed that the method could be used in such a context. Therefore, there is a need to describe the robustness of different $M_{\mathrm{split}}$ estimation variants. The paper uses the global breakdown point in an extended interval (GBdP-$e$) but also introduces the tolerance for growing errors of observations (TGE) to perform such an examination. It presents such measures obtained for the absolute $M_{\mathrm{split}}$ estimation and robust $M_{\mathrm{split}}$ estimation variants, which have not been shown before. The results prove that the absolute $M_{\mathrm{split}}$ estimation predominates the squared $M_{\mathrm{split}}$ estimation in such a context. Furthermore, the robust variants are much less sensitive to outliers than both basic variants mentioned. TGE not only describes how the method tolerates outliers but could also be applied to assume the most appropriate values of the steering parameters, which seems essential. The paper shows the theoretical relationship between basic $M_{\mathrm{split}}$ estimation variants and respective $M$-estimation methods. It is a basis for introducing and deriving GBdP-$e$ and also TGE for $M$-estimation. The paper shows that both measures are equivalent in the case of $M$-estimation. TGE could provide information about that estimation type’s sensitivity to growing errors of observations (also robustness to outliers) that is unavailable by applying other measures, including classical breakdown points, influence functions, rejection points, or mean success rate. TGE presents the robustness potential of the $M$-estimation variants in a rather vivid and straightforward way, even for methods not classified as robust against outliers, e.g., the least-squares estimation.