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This investigation introduces a rigorous mathematical transformation of variance--covariance matrices between a global geocentric frame and a plate-fixed geodetic frame. A practical example between the geocentric frame of International GNSS Service 2008 (IGS08) epoch 2005.00 and the geodetic frame North American Datum of 1983 (NAD 83) (2011) epoch 2010.00 was implemented. Although the theory is general, the transformation used here is controlled by the assumptions implicit in the definition of NAD 83. However, the same approach could be extended to future definitions of fixed-plate datums used by geodetic organizations for charting and mapping applications. Consequently, because the transformation between these two specific frames is assumed by definition to be a one-toone errorless transformation, the uncertainties for the 14 Helmert transformation parameters between the two frames are assumed to be zero. Nevertheless, the formulation is complete and applicable to other specific datum-transformation situations. [ABSTRACT FROM AUTHOR]

A study of deformations, which is based on the use of geodetic measurements, is usually performed by defining a kinematic model. Such a model, when used to describe a complex geophysical environment, can lead to a partial estimation of the deterministic dynamics, which characterize the entire network. Usually, in a case of deterministic nonlinear movements in the network, there is no possibility to determine a stable datum that may serve as a basis for deformation analysis. Today, the concept of stability in time ascribes rigidity to a congruent datum. This paper redefines the concept of the datum congruency and presents the development of a new dynamic datum, which more closely represents geophysical reality. The new datum changes the main characteristics of a traditional datum and successfully overcomes some of its inherent disadvantages. As an example, the proposed algorithm of the dynamic datum is applied to obtain a deformation analysis in the Carmel fault environs, one of the major geological structures in northern Israel. [ABSTRACT FROM AUTHOR]

Knowledge of the actual refraction coefficient is essential in leveling surveys and precise electromagnetic distance measurement reduction. The most common method followed by the surveyor for its determination is based on the use of simultaneous reciprocal zenith observations. The commonly used formula is only an approximation valid for approximately horizontal sightings, whereas the exact geometric solution turns out to be very complicated so that an iterative computation procedure is suggested instead. In the present paper, the goal is to derive a compact formula from the complete solution that is easy to implement and retains the necessary accuracy for horizontal and slanted sightings. In addition, the paper will also focus on the common situation for the surveyor where isolated observations have to be done and no partially compensating procedures-e.g., leap-frog or middle point-are possible. If temperature vertical profiles are unknown then the refraction coefficient cannot be reliably determined. Some surveyors may customarily use then an average value, e.g., , perhaps being unaware of the risks involved in such simplistic assumption. In the present paper, it is also a goal to present a useful and simple formula for approximately estimating the refraction coefficient in terms of easily accessible parameters to correct the bulk of the refraction effect in single observations, always bearing in mind that determination of the refraction coefficient by means of a model may turn out to be somewhat inaccurate, but still better than the blind use of a universal . [ABSTRACT FROM AUTHOR]

In geodetic networks, observations are measured repetitively, and the mean values of these observations are used for network adjustment, outlier detection, deformation analysis, etc. These repetitive observations are independent, and if one of them has outlier, the effect of the outlier decreases depending on the computed mean value. Also, the mean operator-a kind of least-squares estimation-smears the effects of the outlier over other observations. In this case, the detectability and reliability rates of the outlier detection method decrease. Moreover, the undetectable outliers spoil both of the estimated parameters and their standard deviations, causing incorrect results. To form a univariate sample, the same quantity must be measured at least twice for geodetic networks. The univariate case is simpler than the multivariate case, and if the repetitive observations may be analyzed as a univariate case, more reliable results can be obtained for outlier detection. In this study, the univariate analysis method was proposed for repetitive geodetic observations. The reliability of the univariate method was measured based on its mean success rate compared with the mean success rates of classical methods. The leveling network was simulated, and analyses were carried out. The results obtained from the univariate case are more reliable than those obtained from classical ones. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System (GNSS) surveys performed in critical environments (e.g., urban canyons, mountainous areas, or areas of dense vegetation) usually suffer from a lack of satellite coverage as a result of obstacles such as buildings and vegetation. GNSS mission-planning software provides an estimate of satellite visibility and dilution-of-precision (DOP) values along a planned trajectory to establish the best time frame over which to perform the survey. However, such an estimate is not reliable in a complex scenario because the surrounding environmental morphology is not considered. This paper introduces a new method to improve the prediction of GNSS satellite visibility. This method involves computing GNSS satellites position by means of the orbital parameters, as well as using three-dimensional digital surface models (DSMs) to develop a more reliable mission plan. The time evolution of key parameters describing the GNSS constellation is computed by means of a visibility georeferenced map for both dynamic and static surveys. [ABSTRACT FROM AUTHOR]

This paper presents a method for the surveying and reliable processing of Global Navigation Satellite System (GNSS) observations in rapid and ultrarapid static surveying for determination of control-point coordinates. The presented technique allows for reliable determination of coordinates, even in the case of highly difficult observation conditions (e.g., for control points situated along forest edges or entirely in the forest, near buildings, or in the vicinity of power-transmission lines). The paper also analyzes different projects of the global positioning system (GPS/GLONASS) networks from the perspective of their credibility and reliability. The control-point coordinates are determined by three GNSS receivers positioned in line on a special base, providing a credible control of GNSS baselines during rapid and ultrarapid static surveys. The GNSS receivers are separated by the distance of 0.5 m. Given the gross errors in baseline coordinates determined that happen in practice, simultaneous use of three receivers for position determination of a control point allows reliable determination of the coordinates even under significantly obstructed access to satellites. The practical surveys were conducted using Topcon and Trimble receivers using real and virtual reference stations. The presented survey and GNSS data-processing methodology allow obtaining centimeter-level accuracy in a few minutes of GPS/GLONASS observations for control points located in obstructed conditions. [ABSTRACT FROM AUTHOR]

Geodetic network design and optimization is a very well-known concept in geodesy. However, in many cases, the available geodetic network configuration with respect to the estimation model is insufficient because of the physical and financial limitations. For the case of estimating the datum transformation parameters between two datums, the colocated points are only an unevenly and inhomogenously distributed subset of the available national/regional networks. Because the transformation parameters are defined with respect to an earth-centered, earth-fixed (ECEF) frame, very limited geographic coverage of the national/regional networks often leads to a weakly multicollinear estimation problem. Such limited geographical coverage is often coupled with the intrinsic geometrical distortions as well as the relatively lower precision of the observations, in particular, when transforming a terrestrial network into a space-based network. In such cases, the individual parameters become highly correlated and oversensitive to the network configuration, and the individual transformation parameters cannot be estimated reliably. In this study, the concept of an idealized three-dimensional (3D) regional network geometry is introduced, its inverse cofactor matrix is analytically derived, and a regularized estimation method based on the inverse cofactor matrix of an ideal network distribution is presented to deal with the weakly multicollinear datum transformation problem. The efficiency of the proposed method is shown in three realistically simulated networks. The proposed method outperforms the standard least squares in terms of mean square error (MSE) and reduces the correlations among the parameters. [ABSTRACT FROM AUTHOR]

This contribution reviews a few basic concepts of optimization and design of a geodetic network. Proper assessment and analysis of networks is an important task in many geodetic-surveying projects. Appropriate quality-control measures should be defined, and an optimal design should be sought. The quality of a geodetic network is characterized by precision, reliability, and cost. The aim is to present a few case studies that have been designed to meet optimal precision and reliability criteria. Though the case studies may be of interest to the geodetic community in their own right, the aim is to gain insight into the general optimization problem of a geodetic network. This is also potentially of interest for educational purposes. The case studies include a zeroth-order design to improve the precision of the network points in a traverse network and a first-order design to meet the high reliability and maximum precision criteria in a geodetic network. It is shown that not only the configuration of the network but also the type of the observations used can affect the design criteria. For example, the case studies presented show that the optimal shape of the trilateration network (intersection with distances) can result in a weak network in the sense of reliability and precision if the observations are replaced by angles rather than distances (triangulation network). In close relation to the optimization problem of a geodetic network, the global positioning system satellite configuration is also optimized for a particular case that provides the minimum value of the geometric dilution of precision. [ABSTRACT FROM AUTHOR]

In 1986, Canada, Greenland, and the United States adopted the North American Datum of 1983 (NAD 83) to replace the North American Datum of 1927 as their official spatial reference system for geometric positioning. The rigor of the original NAD 83 realization benefited from the extensive use of electronic distance measuring instrumentation and from the use of both TRANSIT Doppler observations and very long baseline interferometry observations. However, the original NAD 83 realization predated the widespread use of the global positioning system and the use of continuously operating reference stations. Consequently, NAD 83 has evolved significantly in the United States since 1986 to embrace these technological advances, as well as to accommodate improvements in the understanding of crustal motion. This paper traces this evolution from what started as essentially a two-dimensional (2D) reference frame and has been progressing toward a four-dimensional (4D) frame. In anticipation of future geodetic advances, the U.S. National Geodetic Survey is planning to replace NAD 83 about a decade from now with a newer, more geocentric spatial reference system for geometric positioning. [ABSTRACT FROM AUTHOR]

The subtle curves of the masterpiece of ancient Greece, the Athenian Parthenon, have been the object of many investigations of scientists of various disciplines. A lot of discussion has centered on the shape of the monument's curved stylobate surface and the kind of mathematical curve that best describes it. This paper presents a new approximation of the stylobate's curves using the Parthenon's transverse and longitudinal inclinations estimated from the measured uneven heights of the lowermost drums of its peristasis columns. This study uses least squares techniques and their appropriateness checked through their correlation coefficients to estimate two kinds of conic sections: a circle and a parabolic curve. Finally, the minimum detectable constructional inaccuracy is estimated. [ABSTRACT FROM AUTHOR]

The least-squares estimation exhibits a poor performance in the presence of gross errors. One of the typical approaches to control the influence of outliers is to use robust estimation techniques. The well-established geodetic reliability theory is comprised of two main components: internal and external reliability. Both reliability measures are important diagnostic tools for inferring the strength of the model validation. To gain further insight into robust M-estimation performance, the variation characteristics of internal and external reliability measures are addressed for a particular robust estimator. Theoretical analyses show that, during the iterative reweighting procedure for uncorrelated observations, the internal reliability measures as represented by minimal detectable bias become larger and larger. For purpose of illustration, a numerical example associated with a simulated geodetic leveling network is provided. As expected, for the outlying observations, their corresponding external reliability measures get smaller and smaller when the iteratively reweighted least-squares method is implemented. [ABSTRACT FROM AUTHOR]

A new geodetic method for accurate determination of nearshore wave characteristics is proposed. This method is based on a robotic total station set on stable position on the coast and aiming at a passive reflector mounted on a buoy, usually at a distance of a few hundred meters. This method permits the identification of the changing three-dimensional coordinates of the reflector/buoy in a selected, fixed coordinate system independent of the buoy with centimeter accuracy, and a rate of up to 6 Hz, and it can even determine very precisely waveforms, including those with steep sides. The effectiveness of the method is demonstrated on the basis of results of two cases studies. While this method provides exceptional quality results for small waves, it can also be used for large waves as well, and especially to calibrate other wave measurement techniques. Techniques to avoid clipping effects usually affecting the wave measurements and the possibility to measure the wave and current direction are also discussed. [ABSTRACT FROM AUTHOR]

This article deals with the characteristics of deformation of a body or a figure represented by discrete points of geodetic network. In each point of geodetic network kinematic quantities are considered normal strain, shear strain, and rotation. They are computed from strain and rotation tensors represented by displacement gradient matrix on the basis of known point displacement vector. Deformation analysis requires the appropriate treatment of kinematic quantities. Thus statistical properties of each quantity in a single point of geodetic network have to be known. Empirical results have shown that statistical properties are strongly related to the orientation in single point and local geometry of the geodetic network. Based on the known probability distribution of kinematic quantities the confidence areas for each quantity in a certain point can be defined. Based on this we can carry out appropriate statistical testing and decide whether the deformation of network in each point is statistically significant or not. On the other hand, we are able to ascertain the quality of the geometry of the geodetic network. The known characteristics of the probability distributions of two strain parameters and rotation in each point can serve as useful tools in the procedures of optimizing the geometry of the geodetic networks. [ABSTRACT FROM AUTHOR]

This study selected five indexes to determine the relationship between data quality and positioning precision. These indexes are multipath on L1, multipath on L2, observations by cycle slips, clock offset, and clock stability. To reduce the number of common errors, six types of global positioning system (GPS) receivers are selected and set up in an Ultra-Short Distance Network at the National Measurement Laboratory, Taiwan, for 3 days. The first three indicators are calculated with the Teqc software, and the last two indicators are computed using the Bernese software. Moreover, the observations from three GPS tracking stations, namely, short baseline (about 25 km), middle baseline (about 150 km), and long baseline (around 2000 km), were downloaded from the Internet and processed using Bernese software. Analytical results indicate that clock stability and observations divided by cycle slips are found to be very important positioning factors. Clock offset and multipath effects do not significantly affect the GPS results. [ABSTRACT FROM AUTHOR]

Surveying technology as regards total stations (TS) has changed in the last fifty years. The original idea of measuring and storing polar coordinates has been progressively revolutionized by means of reflectorless distance measuring capabilities, as well as steer measurements, robotic, camera, and scanning functions. This enables the so-called intelligent tacheometry which is explained in detail herein, relying on the instruments capability to react autonomously on the object due to the reflectorless measuring device and eventually with image assistance and in interaction with the robotic drive. This paper revises thoroughly the evolution of conventional TS as figured out in the sixties until the promising image assisted scanning total station that are starting to come out with many surveying capabilities, but half way of what it might be an image assisted photogrammetric scanning TS (IAPSTS) with full photogrammetric functionalities. Following the writers’ opinions, the IAPSTS might surprisingly change the way both field surveying and processing are carried out in scenarios such as documentation of cultural heritage and industrial factory measurements. [ABSTRACT FROM AUTHOR]

The observations of geodetic very long baseline interferometry (VLBI) measurements refer to an invariant point of the radio telescope. This point is often called the reference point. For the interpretation of VLBI results it is necessary to know the position of this invariant point and its possible variation with time. Only the knowledge of the reference point makes it possible to combine VLBI results with results from other colocated techniques and in the framework of the global geodetic observing system (GGOS). Within the GGOS an automated monitoring of the reference points and therefore of the local-tie vectors at colocation stations is discussed earlier in other studies. In this paper a new mathematical model is described to allow such an automated monitoring of the reference point of an azimuth-elevation type radio telescope. [ABSTRACT FROM AUTHOR]

The detection of the discordant points, i.e., outliers, in linear regression models is a problem, which has been studied extensively. Huber’s M-estimation is recommended not only for robust regression but also for detecting outliers. However, M-estimation does not show high performance in detecting outliers for some cases. The aim of this paper is to propose a new method for improving the ability of M-estimation in outlier detection. It consists of the iterative combination of the M-estimator along with a scheme of reducing weights in some observations at random. The theorems proving contribution of the proposed algorithms have also been included. A series of Monte Carlo simulation experiments show that the performance of the new algorithm in the presence of outliers is better than M-estimation alone. By using the new method, the results, on average, improved by about 7%. [ABSTRACT FROM AUTHOR]

By applying integrated least-squares adjustment of multicampaigns geographic positioning system (GPS) measurements, the velocity of any GPS monument can be obtained. The resulting velocities are used to estimate the strain rate tensors and their variances under infinitesimal strain assumption in a discrete triangle. In this paper, the GPS measurements of five campaigns, which were carried out in Shanghai City from 2002 to 2005, are used to determine the velocity of each GPS monument. Then the horizontal strain rate tensors are calculated with the relative velocities of the sites obtained. The analysis of these principal strain rates together with a comparison of the geological information is performed. The patterns of the principal strain rates show a significant northwest to southeast extension zone in the southwestern part of Shanghai, which agrees well with the neo-tectonic activity of an existing geological fault, the so-called “Dachang–Zhoupu” fault. [ABSTRACT FROM AUTHOR]

Online global positioning system (GPS) processing services have provided users with the opportunity to obtain freely high precision coordinates in a recognized datum. However, all services are dependent on the quality of the data and the length of data span supplied to them by the user. This study aims to assess the four globally available online GPS processing services from the point of view of a user wishing to take advantage of such a service for datum realization. Data from eight selected international GNSS service stations have been processed by each service and the results have allowed a statistically significant comparison analysis to be performed. Although users can expect a variability of results from different services when processing identical data, solutions with 24 h data are generally repeatable at the 1–2 cm level and accurate in terms of international terrestrial reference frame coordinate recovery at the 3–4 cm level. Such differences are accentuated as observation time decreases. Finally, postprocessing kinematic data, currently performed by only one online service, is a valid option for users provided they ensure data quality. [ABSTRACT FROM AUTHOR]

The National Oceanic and Atmospheric Administration’s National Geodetic Survey (NGS) manages the National Continuously Operating Reference Station (CORS) system that comprises a network of over 1,350 sites, each containing a geodetic quality Global Navigation Satellite System receiver. This network is currently growing at a rate of about 15 sites per month. NGS collects, processes, and distributes data from these sites in support of high-accuracy three-dimensional positioning activities throughout the United States, its territories, and a few foreign countries. CORS data are also used by geophysicists, meteorologists, atmospheric and ionospheric scientists, and others in support of a wide variety of applications. This paper addresses the history of the CORS network, some of its applications, and plans for enhancing it within the next few years. [ABSTRACT FROM AUTHOR]

Terrestrial network solutions prepared by different institutes and/or at different epochs imply different reference frame definitions, since various reference stations and processing strategies may be involved. A combination procedure, utilizing a time-variant similarity transformation model, enables a geometric integration of multiple solutions into a common reference frame definition. Additional benefits, including an elimination of systematic bias and a cross check on the quality of each individual network solution, could also be achieved. In this study, a combination approach which takes into account complete geometric interrelations between multiple solutions is developed. With the observable dependency analysis procedure, the proposed approach guarantees a self-consistent, more meaningful, combination solution regardless of the choice of a reference solution. Numerical tests have been performed on actual International Global Navigation Satellite System (GNNS) Service (IGS) and National Geodetic Survey (NGS) solutions using the Geodetic Network Analysis Tool software developed along with this study. Results reveal potential problems if the proposed analysis procedure is not implemented in a combination solution. [ABSTRACT FROM AUTHOR]

Robust estimation yields more accurate results than least-squares estimation in the presence of undesirable errors. It has been recently applied to the process of GNSS differential positioning in the standard fashion of iteratively reweighted least squares. We propose an improvement of the technique, based on a previous result by which robust estimation is truly robust only if considered as a global optimization problem. Robust estimation by global optimization techniques will prove to be an even more powerful method, capable of solving problematic baselines that are nonsolvable by classic methods. [ABSTRACT FROM AUTHOR]

The estimation of the atmospheric refraction coefficient by conducting simultaneous and mutual zenith observations is a well-known geodetic procedure. The respective mathematical model is based on certain assumptions regarding the actual path followed by the optical ray while propagating in the atmosphere (spherical symmetric model). Starting from this model an approximate solution can be derived, which is generally accepted in the literature on the subject. The present paper examines the mathematical model of this geodetic technique in a rigorous manner, which results in an exact solution for the computation of the atmospheric refraction coefficient or equivalent for the zenith angle correction that is due to the effect of the atmospheric refraction. As the direct computation of the exact solution is rather complicated, an iterative way of computing the same quantity is derived, which can be realized easily on any pocket calculator. In order to assess the derived formulas we investigate the applicability of the exact, the convergence rate of the iterative and the errors introduced by the approximate formulas, by conducting a representative series of synthetic numerical experiments. The overall discussion aims to provide a helpful insight into the geometric and theoretical features of this traditional geodetic method. To practitioners that attempt to apply the standard correction formulas to zenith observations in order to compensate the effect of atmospheric refraction in the frame of typical surveying applications, such as trigonometric leveling, the paper also points out possible numerical errors introduced by the traditional approximate formulas. [ABSTRACT FROM AUTHOR]

Experience with surveying practices has shown that correlated observations are very often encountered, especially in preprocessed observations. Hence, it is not only of theoretical interest, but also of practical interest, to investigate the detection of outliers for correlated observations. The so-called quasi-accurate detection (QUAD) of outliers for correlated observations is developed. The corresponding computation principle and its implementation are investigated in detail. The key of QUAD is how to select the quasi-accurate observations (QAO) reasonably. A new, distinctive sensitivity-analysis based method is proposed for selecting the QAO. For illustrative purposes, an application to global positioning system network adjustment is analyzed. The numerical results demonstrate that more than one outlier can be correctly identified and localized by using the proposed procedure. [ABSTRACT FROM AUTHOR]

Robust estimation has proved to be a valuable approach to adjust a surveying network when there are systematic or gross errors in the observations or systematic errors in the functional model. In the present paper we propose to solve robust estimation as a global optimization problem. In particular, we will apply the simulated annealing method and genetic algorithms. The usual strategy of iteratively reweighed least squares is analyzed versus the global optimization approach. Results show that in problematic cases robust estimation is not truly robust unless performed by a global optimization method. [ABSTRACT FROM AUTHOR]

With the development of space-based systems, the results of various applications are generally provided in an earth-centered and earth-fixed global coordinate frame. However, many times it is necessary to transform those results, together with their errors, into local geodetic frames for physical modeling and geometrical interpretation of results as well as to combine them with terrestrial observations. Although it is common practice to transform errors using the full matrix error propagation law, results of many studies in global Cartesian frames are published in compact form without attaching the necessary variance–covariance parameters, therefore preventing a consistent transformation of covariances into a local geodetic frame. This is especially true for coordinates released as time series of sequential epochs. Examination of coordinate/velocity correlations in a global Cartesian frame (GCF) and a local geodetic frame (LGF) reveals that the transformation matrix from GCF into LGF (which depends on the position and origin of LGF) decorrelates the covariance matrix in the GCF up to 90%, depending on design matrix, a priori weights, and constraints. In this study, utilizing the error decorrelation in the LGF, analytical, transformation equations were inverted for correlation parameters in GCF so as to reconstruct the approximate covariance matrix in GCF from a diagonal matrix of variances. Variances in the LGF were then obtained by a basis change through singular value decomposition. Results show that the new semianalytical expressions could be used successfully to transform variances in GCF into LGF especially in the absence of covariance terms. [ABSTRACT FROM AUTHOR]

In the computation of a geodetic network, it is well known that the least-squares adjustment may not be the ideal solution when gross errors appear. In general there are two fundamental approaches to determining gross errors: the application of the detection tests (Baarda’s data snooping, Pope’s τ test, etc.) over the least-squares solution, and the use of robust estimation methods. It has been shown that in the case of more than one gross error, these detection tests become inefficient. Moreover, even for the case of single error detection, these tests may be questionable. Hence, data snooping relies on a good a priori precision estimation, and, regarding Pope’s τ test, it is the purpose of this paper to analyze the limitations in its use with correlated observations, even for a single gross error detection. Conclusions will be drawn by means of a generalization of a result mentioned in Pope’s work (originally restricted to the case of uncorrelated data) and then applied in an example. [ABSTRACT FROM AUTHOR]

Accurate global positioning system (GPS) vector determination is now one of the major applications in modern geodesy. Most of the errors are modeled either to smooth atmospheric effects or to remove biases, such as clock offsets. The network design criteria and the vector processing solutions are based in distances to the reference stations and in the time span of the vectors involved in the sessions. Thus, the final solutions are computed accurately and the residuals show the quality of the computations. What is not usually taken into account in the final vector computation is the bearing of the vector to be processed, as the cutoff angle is considered fixed. This note deals with the variation on the final solution due to different cutoff angles, and still more importantly to the bearing of the vector in high- precision GPS vector determination. If in the future, the International Global Navigation Satellite System Service starts to distribute orbits that are created using the ANTEX file, this elevation-angle dependency should diminish. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

One of the possible uses of the global positioning satellite permanent stations is to use them as a datum reference when a new base station is established in a geodetic or surveying project. However, the actual procedure is not always obvious. Combining a number of permanent stations in the process involves important decisions that the analyst must make, which can alternate the results dramatically. Important network design aspects that must be addressed are, for example, how many permanent stations should be involved in the process; how long should the session duration be; how should one constrain the permanent stations in the adjustment procedure; and so forth. This paper suggests an algorithm based on multibaseline processing, minimum constraints, and free net adjustment concepts, in order to produce a base station with reliable coordinates and realistic accuracy, while using one or more permanent stations. In order to demonstrate the algorithm and to support the conclusions, it presents numerical examples from the Permanent Stations Array in the State of Israel, processed at the Technion—Israel Institute of Technology, using GAMIT software. [ABSTRACT FROM AUTHOR]

In terms of computer algebra systems, an inverse problem of a meridian arc is discussed in two somewhat different ways in this paper. One is the conventional power series method and the other is a Hermite interpolation. The research in the paper shows that the derived new solutions are concise in form and high in accuracy. The paper also shows that a computer algebra system is a powerful tool to solve some mathematical derivations in geodesy, surveying, and cartography. [ABSTRACT FROM AUTHOR]

A robust strategy for controlling the influence of outliers on model parameters and variance components is proposed based on the principle of robust M estimation. The robust estimators for parameters and variance components are derived. A practical robust estimator similar to Helmert’s one for maximum likelihood estimation is obtained. The robustness and efficiency of the new robust estimation procedure is demonstrated and compared with those of the classical least squares method by applying a practical global positioning system network in China. [ABSTRACT FROM AUTHOR]

Vincenty’s (1975) formulas for the direct and inverse geodetic problems (i.e., in relation to the geodesic) have been verified by comparing them with a new formula developed by adapting a fourth-order Runge-Kutta scheme for the numerical solution of ordinary differential equations, advancing the work presented by Kivioja in 1971. A total of 3,801 lines of varying distances (10 to 18,000 km) and azimuths (0 to 90°, because of symmetry) were used to compare these two very different techniques for computing geodesics. In every case, the geodesic distances agreed to within 0.115 mm, and the forward and reverse azimuths agreed to within 5×10-6 seconds of arc, thus verifying Vincenty’s formula. If one wishes to plot the trajectory of the geodesic, however, the fourth-order Runge-Kutta extension of Kivioja’s formula is recommended as a numerically efficient and convenient approach. [ABSTRACT FROM AUTHOR]

Analysis of an exceptionally long and homogeneous geodetic monitoring record of a deep-seated, slow (15 cm/year) moving landslide indicates that changes in the distance between a survey point lying on stable ground and several control points lying on slipping ground have effectively and accurately detected and recorded dislocations of the control points exceeding the value of a few millimeters; a result confirmed by independent, submillimeter-accuracy spirit leveling data. Landslide monitoring based on radial length changes permits estimation of the velocity and of the acceleration of the landslide movement, and is free of various disadvantages characterizing other geodetic techniques (delayed results, high cost, need for accessibility of control points, etc.). This method can therefore be used to provide near-real time, efficient, low cost, and reliable monitoring for many landslides and other deforming bodies at a few millimeter accuracy. It may also be combined with modern telemetric or robotic survey systems to provide real-time and automated deformation monitoring. [ABSTRACT FROM AUTHOR]

This paper reconsiders the two-step analysis method in an attempt to show how correct processing of both steps will ensure results identical to those obtained when using the one-step method and moreover may result in improved variance-covariance estimation of the deformation parameters. The approach for solving a vector of parameters indirectly from the measurement vector by using a vector of pseudomeasurements is referred to as a two-step analysis. In deformation networks, the first step is processing the geodetic measurements sequentially without modeling the variation in the network geometry. The results of this first step are sets of network point coordinates pertaining to the specific epochs of the measurements. In the second step the variation in network geometry is modeled. The result of this step is a set of deformation model parameters. It is argued that a proper processing of the two-step method will ensure a correct estimation of the variance-covariance matrix of the deformation parameters, which is a critical value in the overall deformation analysis scheme. [ABSTRACT FROM AUTHOR]