Journal of Surveying Engineering

This paper presents a new method of estimating a shift between parameters of a functional model of observations. The method in question is based on the theory of $M_{\text{split}}$ estimation and assumes that design matrices of functional models may not have full column rank. Thus, this alternative method, which is called Shift-$M_{\text{split}}^{(+)}$ estimation, can be applied to analyze deformations of free geodetic networks. The shift of the parameters can then be regarded as a shift between the coordinates of the network points at two different measurement epochs. Such an application is illustrated using a numerical example, and the results are compared with the results of $R$-estimation and with a conventional free adjustment of the least squares. This paper presents the theory of Shift-$M_{\text{split}}^{(+)}$ estimators and ways to compute them. The procedures in question are based on the general principles of $M_{\text{split}}$ estimation and practical application of the Moore–Penrose inverses.

Taking advantage of numerical integration, we solve the direct and inverse geodetic problems on the ellipsoid. In general, the solutions are composed of a strict solution for the sphere plus a correction to the ellipsoid determined by numerical integration. Primarily the solutions are integrals along the geodesic with respect to the reduced latitude or azimuth, but these techniques either have problems when the integral passes a vertex (i.e., point with maximum/minimum latitude of the arc) or a singularity at the equator. These problems are eliminated when using Bessel’s idea of integration along the geocentric angle of the great circle of an auxiliary sphere. Hence, this is the preferred method. The solutions are validated by some numerical comparisons to Vincenty’s iterative formulas, showing agreements to within $2\times {10}^{-10}$ of geodesic length (or 3.1 mm) and $4\times {10}^{-5}$ as seconds of azimuth and position for baselines in the range of 19,000 km.

Ignoring the temporal correlations present within global navigation satellite systems (GNSS) observations can result in too much confidence being placed in the estimated positions. Temporally correlated errors occur when the magnitude of an error is similar over time. Treating temporally correlated GNSS errors as independent results in an overly optimistic variance-covariance (VCV) matrix, potentially resulting in an incorrect fix of the ambiguities and an overly optimistic estimated accuracy of the estimated positions. Unlike spatially correlated errors, temporally correlated errors are not mitigated or properly dealt with within most of today’s real-time kinematic (RTK) software. This paper reviews the theory of temporal correlations as well as previously developed solutions for obtaining more realistic position accuracies. A simulation is developed demonstrating the impact of neglecting temporal correlation. Using real data from five baselines up to 10 km in length, this paper then determines how long the L1 carrier phase observations remain correlated. By using the autocorrelation of the phase residuals, the L1 phase measurements are shown to be correlated for an average of 115 s. The length of temporal correlation varies according to receiver environment and satellite elevation angle. Trends in correlation time according to baseline length are also studied.

Determining the spatial relations between image and object spaces is an essential concern in photogrammetric applications. One such routine practice is to find the relative orientations between image pairs so that images acquired at a series of exposure stations can be properly aligned in a predefined reference frame. In a classic approach, this is typically done by the iterative least-squares estimation based on the collinearity condition. In this study, an analytical solution for the relative rotations between multiple images is derived utilizing the normal vectors of epipolar planes, which can be easily constructed by the coordinate vectors measured in conjugate images. This novel approach not only provides an effective geometric constraint between images but also makes possible a direct determination of the relative rotations without the need to carry out a tedious iterative computation. From the numerical test results, it is illustrated that the proposed approach is capable of providing a rotation solution at the same level of quality as the classic collinearity-based least-squares approach, but with an improved computational efficiency. Consequently, the cost of a photogrammetric analysis can be substantially reduced when the proposed approach is implemented in a real field application.

This paper presents a robust algorithm for the registration of building point clouds based on the planar features when there are no targets in the scanning process. First, obtaining the normal vectors of the planes that are fitted from the segmented point clouds in the overlapping areas is absolutely necessary to generate completed three-dimensional models. Then a mathematical model of registration can be established by using the character of the Rodriguez Matrix. Furthermore, the registration accuracy is analyzed and compared with the Iterative Closest Point (ICP) algorithm, and the results show that the algorithm is effective, and can get a satisfactory registration result.

The geomatics engineering contributions to continuous three-dimensional monitoring of ice sheet in a dam reservoir is presented in this paper. A total station robot was used to monitor the displacement of several probes placed on the surface of the ice sheet of a dam reservoir during winter seasons. Two prisms were mounted on each probe to take into account the deflection variation of the probe during a complete winter season. A similarity (Helmert) transformation was computed from measurements on control points to solve the problem of inconsistent observations. The results of the 2009 and 2010 winter campaigns at the Beaumont Dam are reported in this paper. We show that the horizontal displacements of the ice sheet, which can be as large as 20–30 cm, can vary quite differently from one winter season to another one, as a function of the temperature and its variation during winter. The horizontal displacements also depend on the probe's distance from the dam or from the reservoir banks. Vertical displacements of the ice sheet follow the reservoir water level fluctuations, especially for the probes far from the dam and reservoir banks. Three-dimensional displacements are explained by the gradual increase of the ice sheet’s thickness, the snowpack accumulation, and the local constraints (hinge effects) near the reservoir perimeter.