Journal of Surveying Engineering

Least-squares (LS) estimation is a standard tool for the optimal processing of geodetic and surveying observations. In many applications, additional nuisance parameters are frequently included within the LS adjustment process in order to account for unknown instrumental biases and other external disturbances that have affected the input data. Moreover, in view of the availability of more precise instruments and data sensors, the enhancement of the mathematical models with additional parameters is justified on the basis of detecting new higher-order systematic effects from the optimal inversion of progressively more accurate data sets. The objective of this paper is to expose an important trade off in the LS adjustment with linear models which are augmented with additional parameters in the presence of unknown systematic effects in the input data. In particular, a condition is derived that quantifies the necessary reduction in the data noise level which ensures the improvement in the estimation accuracy for the original model parameters, when a linear(-ized) model enhancement takes place.

A classic seven-parameter similarity transformation is typically applied in reference frame transformations. For modern day global applications with a higher accuracy requirement, this model is extended to accommodate time-dependent positional variations. The time-variant transformation, however, also brings a new problem—rank deficiency—while performing parameter estimations. In this paper, a stepwise parameter estimation approach is proposed to overcome this problem and give a reliable solution. It also enables one to investigate different types of transformation parameters independently. To prove its feasibility on present day global datum applications, this approach is applied to the reference frame transformation between ITRF2000 and ITRF97 at epoch 1997.0. In addition, a simulation test is performed to show the advantages of the proposed approach against other parameter estimation approaches currently in use, for its wider range of applications in science and engineering.

The rapid and precise determination of the azimuth information, purely based on the satellite positioning technology of global positioning system (GPS), is tested and evaluated by this paper. The main consideration of using GPS for the azimuth determination is expected to replace the traditional astronomical azimuth measurement, which is believed to be time-consuming and weather-dependent. A GPS approach is simply based on setting up the GPS receivers at the two ends of a baseline, recording and processing the phase observable, and converting its coordinate solution into an azimuth with the inverse geodetic formulas. This type of azimuth obtained by the GPS static solution has been assessed to be well consistent with the astronomical azimuth by a level of better than $\pm 1^{″}$ . The GPS kinematic mode of azimuth value, however, is biased from the standard value for a RMS error of $\pm 9^{″}$ . The correction of the deflection of the vertical, theoretically required by the geodetic and astronomical azimuth conversion, is also implemented and found to be only effective at the observation site where the $\eta \tan \phi$ value is higher than the estimation accuracy of the $\eta$ value provided by a gravimetric geoid model.

We consider a set of numbers independently drawn from a normal distribution. We investigate the statistical properties of the maximum, minimum, and range of this set. We find that the range is closely related to the standard deviation of the original population. In particular, we investigate the use of the online positioning user service (OPUS) global positioning system (GPS) precise position utility, which produces three estimates of each coordinate and reports the range of these three estimates. We find that the range divided by 1.6926 is an unbiased estimate of the standard deviation of a single coordinate estimate, and that the variance of this estimate is 0.2755 ${\sigma }^2$ . We compare this to the more conventional method of estimating the standard deviation of a single observation from the sum of squares of residuals, which is shown to have a variance 0.2275 ${\sigma }^2$ .

In this paper, we use geographic information system as a useful tool in compiling vertical crustal movement (VCM) over Eastern Canada. For modeling linear VCM, we employ tide gauge records and precise releveled segments, which reflect the glacial isostatic submergence of the coasts, as well as other global, regional, and local effects. The area of study is divided into two zones: Maritimes and South St. Lawrence zones. Piecewise polynomial surfaces of different orders are calculated by the method of least squares for each region to obtain representations of the recent vertical movements. This work provides the framework for multidisciplinary studies of geodynamics in the region, allowing different selection of zones for vertical crustal movements and simplifying the incorporation of more data in future investigations. We use ArcGIS to visualize the theoretical approaches, and to integrate and analyze different spatially distributed data. This powerful tool helps us to produce a more physically meaningful VCM map for the region. The map reflects the most significant geophysical phenomenon in the region, postglacial rebound, and it is in good agreement with the 2004 glacial isostatic adjustment model of Peltier [ICE-5G(VM2)].

After geodetic networks are established, relevant measurements are made and point coordinates are estimated by the least-squares method. However, the least-squares method does not give any information about the robustness of networks. To measure robustness of a network, the degree of deformation of individual points of the network is measured by strain. Furthermore, threshold values are needed to evaluate networks. These threshold values will enable us to evaluate the robustness of the network. If the displacements of individual points of the network are worse than the threshold values, we must redesign the network by changing the configuration or improving the measurements until we obtain a network of acceptable robustness. This paper describes how to obtain the displacements at individual points of a network, employs the specifications of the Geodetic Survey Division, and shows the power of the technique on different geodetic networks.