Volume 7, Issue 2

The Carmel Fault is one of the major geological structures of northern Israel. It is the northwestern part of Carmel-Tirtza Fault System and a northwestern branch of the Dead Sea Fault. The Carmel Fault region is covered by a monitoring geodetic network consisting of 23 sites, which were measured four times between 1999 and 2010 by means of GPS. The site velocities can be estimated only if the datum of the network has not been changed between measurement epochs. The GPS vectors must be adjusted so that the datum will remain undisturbed throughout the measurement campaigns. Usually we assume that GPS vectors define the network datum components of orientation and scale. Fluctuations in the GPS orbits could affect the orientation and scale between monitoring campaigns and therefore, in this study, we assume that GPS vectors are not immune to changes in their datum content. An appropriate approach is taken to prevent the inclusion of these components in the adjustment of a 4D network. If not, the result will be an inevitable mixture between the deformation parameters and the datum components of the GPS vectors. In this study the GPS vectors from each campaign are stripped from their datum content using the extended free network adjustment constraints. The datumless measurements are used to define the datum by preliminary coordinates and linear constraints, which remain constant for all monitoring campaigns, as well as to define the position of the network points and their velocities. Later on, the variations across the network geometry can be modeled by means of a physical model.

In this study, some stochastic and deterministic models have been proposed for the assessment of the regularity and isotropy of geodetic point patterns. These models utilized realized point configurations within a rectangular window, leaning on stochastic geometry. As an illustrative example, the geographical extent of the Egyptian Territory was selected as a test window. The proposed models have agreed with the visual and qualitative characteristics of the investigated patterns. Also, it has been found that the stochastic and deterministic models for regularity and isotropy have very strong mutual correlation coefficients. Furthermore, the proposed models were applied to some geoid interpolation algorithms. In particular, the relationships among the data/check point distributions and the geoid interpolation accuracies, were investigated. Finally, a closed expression was proposed, which efficiently describes the relations among such features. So, it is recommended to use such approach for the pre-analysis and planning of the geographic distributions of point patterns in similar and other geodetic applications.

Levellings are performed to observe height changes of different epochs at discrete surveying points. A reliable estimation of surface deformations by a bivariate polynomial needs a sufficient configuration of the underlying network. Because the spacial distribution of the surveying points is not homogeneous in the discussed regions, the network configuration has to be optimized. This study proposes an optimization procedure that estimates the optimal number and position of the surveying points considered for a reliable analysis. Furthermore, the already existing observations are accepted or rejected due to the network’s geometry. Therefore, two different approaches are combined. First, the sampling theorem from time series analysis is used to estimate the number and position of the surveying points. Second, the partial redundancies from statistics take the reliability into account. Applying the optimization procedure to several test regions, the benefit of the optimized network configurations is discussed.

The robust estimation by the expectation maximization (EM) algorithm is derived for the variance-inflation model in addition to the known estimation for the mean-shift model. To compare these methods with the τ - test, Huber’s robust M-estimation and the multiple outlier test, a random linear model and laser scans for fitting a plane are generated by Monte Carlo methods. It turns out that the results for detecting outliers by the EM algorithms for the mean-shift and variance-inflation model approximately agree although the numbers of convergences are different. The results are superior to the ones of the methods with which they are compared. In case of the generated laser scans, the maximum number of outliers, which can be detected, is approximately identified.

In many cases, the uncertainty of output quantities may be computed by assuming that the distribution represented by the result of measurement and its associated standard uncertainty is a Gaussian. This assumption may be unjustified and the uncertainty of the output quantities determined in this way may be incorrect. One tool to deal with different distribution functions of the input parameters and the resulting mixed-distribution of the output quantities is given through the Monte Carlo techniques. The resulting empirical distribution can be used to approximate the theoretical distribution of the output quantities. All required moments of different orders can then be numerically determined. To evaluate the procedure of derivation and evaluation of output parameter uncertainties outlined in this paper, a case study of kinematic terrestrial laserscanning (k-TLS) will be discussed. This study deals with two main topics: the refined simulation of different configurations by taking different input parameters with diverse probability functions for the uncertainty model into account, and the statistical analysis of the real data in order to improve the physical observation models in case of k-TLS. The solution of both problems is essential for the highly sensitive and physically meaningful application of k-TLS techniques for monitoring of, e. g., large structures such as bridges.

This paper presents an investigation on the efficacy of particle swarm optimization (PSO) and genetic algorithm (GA), two popular global optimization algorithms to solve complex optimization problems, for the second order design (SOD) - a process of selecting optimal baseline configuration, in a GPS network while satisfying the desired precision criteria at minimal cost. The algorithms are tested on a six-point GPS network established within IIT Kanpur campus. The results have shown that the PSO has yielded better results than the GA in solving the SOD problem.