Journal of Surveying Engineering

This paper presents a partial total-least-squares adjustment method for condition equations (PTLSC) in which the observation vector and coefficient matrix contain linearly correlated errors. In the proposed method, the functionally independent variables in the observation vector and the coefficient matrix of the condition equations are abstracted to form a collected observation vector. The PTLSC method is formulated by minimizing the sum of the weighted squared errors of the collected observation vector by the use of a Lagrangian multiplier algorithm. The estimation of the covariance matrix based on linear approximation for the collected observation vector is also derived. The proposed PTLSC method was tested in an example of rectangular building adjustment in a geographical information system (GIS). The results indicate that the proposed PTLSC method can adjust the interior angles of the digitized buildings so they are right angles, and it can be used to maintain the correlations among the elements in the observation vector and the coefficient matrix.

The scaled unscented transformation (SUT) with scaled symmetric sampling strategy is introduced into Geomatics and expanded. Unlike the Taylor series expansion, this method treats nonlinear error propagation without a derivative calculation. The formula of variance estimated by the SUT is expanded to two types of second-order terms. Three new theorems are proposed to describe the accuracy of the variance estimated by the SUT under different conditions. The comparison of the SUT and the unscented transformation (UT) with symmetric sampling strategy is discussed. According to the ratio of disturbance defined in this paper, the SUT is found to be insensitive to different matrix decompositions. The effects of an inaccurate mean of a random variable on the mean and variance estimated by the SUT are expressed by second-order accurate formulas. The accuracy of variance estimated by the SUT is found to change according to the bias of change of the parameters. Based on theoretical analyses, a modified SUT algorithm and a systematized SUT algorithm are proposed to strengthen its practicability. Five examples are used to support the proposed theories and show the applicability of the SUT in statistics calculation and bias correction for nonlinear function of Geomatics.

To derive ellipsoid heights on passive marks with centimeter-level accuracy, many current specifications require the collection and adjustment of long-duration, static, postprocessed global navigation satellite system (GNSS) sessions. To increase efficiency, a campaign-style survey procedure that includes real-time kinematic (RTK) vectors from a real-time GNSS network was evaluated. Thirty different hybrid networks involving three to nine network RTK (NRTK) vectors per mark and some static GNSS vectors were developed from surveys completed in Oregon and South Carolina. The variance-covariance matrices of the static and kinematic vectors were scaled by variance-component estimation procedures to produce realistic error estimates for stochastic modeling. After least-squares adjustment and formal random-error propagation of the networks, the resulting ellipsoid heights on the passive marks had network accuracies ranging from 0.6 to 3.6 cm (95% confidence). These network accuracies reduced to < 2 cm when using six or more NRTK observations per mark. Further, the use of NRTK vectors obtained from observables of both the U.S. global positioning system (GPS) and Russia’s GNSS (GLONASS) were, on average, 19.2% more accurate vertically than vectors obtained solely from GPS observables.

Structural monitoring and engineering surveys that use the Global Positioning System (GPS) have traditionally performed using a so-called carrier-phase double-difference method in data processing. The method requires at least one reference GPS station to be continuously operated in the field during the monitoring period. The stability and data quality of the reference station would directly affect the accuracy of displacement measurements at the rover station. Furthermore, it becomes increasingly difficult to maintain “ideal” reference stations in urban environments. This article introduces a method for using stand-alone GPS units to conduct millimeter-accuracy structural deformation monitoring for poststudy or for near real-time structural health monitoring. Two years of continuous GPS observations obtained from two high-rise buildings in Beijing were used to depict the detailed method. The method comprises three steps: (1) solving GPS antenna positions with respect to a global reference frame (IGS08), (2) establishing a stable local reference frame and transforming the global positions into the local reference frame, and (3) deriving a regional seasonal model and correcting GPS-derived positional time series with the regional model. It is concluded that 2- to 3-mm horizontal accuracy and 5- to 7-mm vertical accuracy can be achieved for daily solutions with the proposed method in the Beijing metropolitan area. The key products from this study are the Stable Beijing Reference Frame (SBJRF) and the local seasonal model for GPS-derived (vertical) positional time series. SBJRF will be incrementally improved and periodically updated to synchronize with the update of the IGS reference frame. The general theory and method presented in this article could be applied to other urban areas for conducting structural health monitoring in near real time.

New high-resolution elevation models for Alaska have recently been released; they were created using interferometric synthetic aperture radar (IFSAR) and automated matching of high-resolution optical satellite stereo imagery (OSSI). These products promise to fill a void in available digital elevation models (DEMs) for the Arctic. However, the effective use of these models requires knowledge of their expected accuracy, and to date, a detailed analysis of these models in remote Arctic locations has not been undertaken. Expected accuracy is necessary to gauge the uncertainty of any scientific conclusions based upon analysis of these DEM sources. To that end, both aforementioned DEM techniques were compared to airborne LiDAR (light detection and ranging) in the area surrounding Sitka, Alaska. It was found that both the IFSAR and OSSI DEMs provide vertical accuracy at the 2–4-m level (1 σ) in flat and open terrain but perform significantly worse in areas of vegetation cover with standard deviations increasing to ∼7–12 m. The DEM errors were found to have a strong positive correlation with vegetation height, and the overall error pattern suggests that neither OSSI nor IFSAR accurately model either the ground or top of the tree canopy, instead representing a surface between the canopy and topographic elevation.

Active and passive rotations are used in many applied scientific fields, such as engineering, geodesy, and geophysics, just to name a few. However, a source of confusion could arise when both types of rotations are performed sequentially. The author is not aware of any publication where, in a tutorial manner, the relationship between active and passive rotations is coherently described, untangling in the process some of the most typical misconceptions. This technical note is a modest attempt to remedy this void by clarifying, as much as possible, some essential points that may help the understanding of these two varieties of commonly used rotations and how to properly apply them in some practical situations.