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Survey Review 49, No 357. November/December 2017

1. Tropospheric delay modelling for the EGNOS augmentation system
K. Kazmierski, M. Santos & J. Bosy

Tropospheric delay is one of the deleterious factors limiting the accuracy of the precise Global Navigation Satellite Systems positioning. The value of delay depends on the path through which a signal has to follow in the subsurface layers of the atmosphere. Tropospheric delay models are developed to overcome this limitation. Among them one can find UNB, TropGrid or IGGtrop models. In this paper, we adjusted the UNB3m model to the actual meteorological parameters from Europe. A new model was called UNBe.eu covering the EGNOS augmentation system area. The use of meteorological observations helped us to decrease the bias for more than 70% of reference radio sounding locations. Still, 30% of reference sites depicted a lack of any improvements of the ZTD estimation with regard to the newly established model. Therefore, this study puts forward a need for a deeper investigation of the discussed issue.

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2. Algebraic method to speed up robust algorithms: example of laser-scanned point clouds
B. Paláncz, J.L. Awange, T. Lovas, R. Lewis, B. Molnár, B. Heck & Y. Fukuda

Surface reconstruction from point clouds generated by laser scanning technology has become a fundamental task in many fields of geosciences, such as robotics, computer vision, digital photogrammetry, computational geometry, digital building modelling, forest planning and operational activities. Point clouds produced by laser scanning, however, are limited due to the occurrence of occlusions, multiple reflectance and noise, and off-surface points (outliers), thus necessitating the need for robust fitting techniques. In this contribution, a fast, non-iterative and data invariant algebraic algorithm with constant O(1) complexity that fits planes to point clouds in the total least squares sense using Gaussian-type error distribution is proposed. The maximum likelihood estimator method is used, resulting in a multivariate polynomial system that is solved in an algebraic way. It is shown that for plane fitting when datasets are affected heavily by outliers, the proposed algebraic method can be embedded into the framework of robust methods like the Danish or the RANdom SAmple Consensus methods and computed in parallel to provide rigorous algebraic fitting with significantly reduced running times. Compared to the embedded traditional singular value decomposition and principal component analysis approaches, the performance of the proposed algebraic algorithm demonstrated its efficiency on both synthetic data and real laser-scanned measurements. The evaluation of a symbolic algebraic formula is practically independent of the values of its coefficients; however, the computation of the coefficients depends on the complexity of the data. Since the main advantage of the symbolic solution is its non-requirement of numerical iteration, the data complexity will have weak influence on the speed-up. The novelty of the proposed method is the use of algebraic technique in a robust plane fitting algorithm that could be applied to remote sensing data analysis/delineation/classification. In general, the method could be applied to most plane fitting problems in the geoscience field.

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3. Robust wavelet-based inertial sensor error mitigation for tightly coupled GPS/BDS/INS integration during signal outages
Jian Wang, Houzeng Han, Xiaolin Meng, Lihui Yao & Zengke Li

This paper proposes a robust wavelet-based tightly coupled Global Positioning System (GPS)/ Beidou Navigation Satellite System (BDS)/Inertial Navigation System (INS) integration scheme aiming to improve the overall position accuracy during signal outages. A robust wavelet denoising model based on α-trimmed mean filter demonstrates its effectiveness on noise reduction and gross error elimination of inertial sensor raw data. Thereafter, a robust wavelet-based tightly coupled GPS/BDS/INS integration scheme is proposed, and GPS/BDS double-difference (DD) carrier-phase and pseudorange measurements are introduced to build a 27-state tightly coupled GPS/BDS/INS integration equation. The extended Kalman filter (EKF) has been designed for state estimation, and the inclusion of BDS enhances the satellite geometric strength of the whole navigation system. A field vehicle test indicates the position accuracy of five simulated GPS/BDS outages can be improved by about 7, 16, and 33% for north, east, and up components with the proposed scheme compared to standard integration scheme, and gross errors have been detected and eliminated with the new integration scheme. The authors also find that the BDS phase residual is larger than GPS and satellite dependent in the tightly coupled GPS/BDS/INS integrated navigation system.

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4. A modified sidereal filtering for mitigating the code measurement multipath effects of BeiDou GEO satellites
Xing Wang, Wenxiang Liu, Baiyu Li & Guangfu Sun

Multipath delay is one of major error sources which limit global navigation satellite systems positioning accuracy. Due to the orbit characteristics, multipath effects are more evident on the code range observables of BeiDou Navigation Satellite System (BDS) geostationary earth orbit (GEO) satellites. We employed zero-phase filter to extract the low-frequency components of multipath series with the definite cutoff frequency and pass-band gain, and introduced a modified sidereal filtering for mitigating the multipath effects on code measurements of GEO satellites. The applications of this modified sidereal filtering show that the corrections for the standard deviation of code observables residuals on BDS B1, B2, and B3 frequency have reached more than 30, 22, and 14%, respectively. After resolving the GEO satellites code measurement multipath effects, the precisions of code-only single-point positioning were also improved.

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5. On the need for pro-poor land administration in disaster risk management
E.-M. Unger, J. Zevenbergen & R. Bennett

There exists an intensifying and multifaceted relationship between rapid population growth, the increasing occurrence of natural disasters, and demands for land tenure security. Consequently, there is growing agreement on the need to adopt pro-poor land administration approaches, ones that better address the needs of the poor living in disaster prone contexts. Vulnerable communities and exposed lands could benefit from emerging pro-poor land administration, however, thus far, application of the pro-poor mind-set has gained minimal traction in the disaster risk management agenda. Using a research synthesis, existing evidence is analysed and consolidated, and a new inclusive conceptual framework is built; one that illustrates the underutilised potential for pro-poor land administration in disaster risk management. The developed framework explains the interactions between three identified and fundamental global change forces (people, land and disaster) and the three disaster risk drivers (vulnerability, exposure and hazard). The framework illustrates how pro-poor approaches can simultaneously have impacts on both land tenure security and disaster risk management. The conceptual framework is considered a first step toward an implementable strategy for applying pro-poor land administration technologies in the context of disaster risk management. Ultimately, pro-poor land administration should enable the poor to minimise vulnerabilities and disaster risks through an inclusive land tenure security approach to prevent, mitigate, prepare and respond to natural disasters.

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6. Erratum

Li, B., Wang, M., and Yang, Y., 2016. Multiple linear regression with correlated explanatory variables and responses. Survey Review.


When the above article was first published online, the article history dates were listed in error as Received 11 April 2013, Accepted 1 August 2013. This has now been corrected in both the print and online versions to Received 4 August 2014, Accepted 20 January 2015. Taylor & Francis apologises for this error.

Survey Review 49, No 356. September/October 2017

1. A process to graphically demonstrate distance errors associated with local ground-based coordinate systems
P. D. Gibbings

This paper describes an empirical process for graphically illustrating, using any particular distance accuracy specification, boundaries where significant errors could be introduced in derived ground distances as a result of using local ground-based coordinate systems. The process involves selecting three-dimensional points across the project site, replacing their heights with combined scale factor corrections, and creating contours to represent potential distance errors. The resultant contour map shows potential distance errors in parts per million for comparison with accuracy specifications. The effectiveness will depend on the spacing of the selected points and the topography of the project site, but on most projects today closely spaced three dimensional points are readily available. The benefits were demonstrated on an example site, with the conclusion that the process is robust and effective, and will have applications on many large scale construction sites, residential estates, and other surveys where local ground-based coordinate systems may be used.

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2. Weighted coordinate transformation formulated by standard least-squares theory
D. Mihajlović & Ž. Cvijetinović

This paper presents a universal model of weighted coordinate transformation, i.e. transformation considering the errors of coordinates in both coordinate systems. It is intrinsically one of the typical examples of ‘error-in-variables’ (EIV) models. The proposed method of LS theory application on weighted coordinate transformation does not impose any constraints on the form of functional relationship among stochastic variables. Since the basic idea is to generalise Gauss–Markov model (GMM) by introduction of so-called ‘total residuals’, the proposed procedure is named ‘Generalised Gauss–Markov model’. Formulation of expressions for estimation of unknown transformation parameters is theoretically confirmed using the Gauss–Helmert model (GHM) and three different modifications of the GMM. The proposed procedure is in its essence a strict solution to total least-squares (unweighted) and weighted total least-squares problem in coordinate transformation. This thesis is experimentally confirmed by comparison of its results with those found in four characteristic examples from the literature.

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3. Efficient weighted total least-squares solution for partial errors-in-variables model
J. Zhao

Due to great computation burden of the original computational formula for partial errors-in-variables (EIV), an alternative formula for parameter estimation in the partial EIV model was proposed to promote computational efficiency. Unfortunately, more iteration is required for obtaining the weighted total least-squares (WTLS) solution of the partial EIV model with above two formulae. Consequently, those methods are not proper for larger data problem in terms of computational efficiency. To circumvent this difficulty, a new formula and the fast algorithm are proposed based on the Lagrange extreme value method. Through some numerical examples with coordinate transformation, it is illustrated that the new developed method is an effective strategy to conduct the WTLS adjustment for the partial EIV model. The computational efficiency is significantly improved at least 80%.

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4. Integrated geospatial evaluation of manual cadastral mapping: a case study of Pakistan
M. S. Ahsan, E. Hussain & Z. Ali

Cadastral mapping in Pakistan is often sketched on paper or cloth and generally falls below cartographic standards, lacking details on coordinate systems, datum and directional information of parcel lines. Survey numbers for parcel identification also lack digital interoperability. Parcel measurements and ownership information are manually recorded in multiple separate registers. The objective of this study is to leverage geospatial technology for automation, auditing and validation of present manual cadastral mapping in Pakistan. Only 62% of the parcel geometry could be automated due to irregular parcel shapes. However, the process revealed some interesting discrepancies in cadastral datasets. Geospatially calculated areas and rectangular base areas are approximately eight acres less than the officially notified estate areas recorded in the field book. This study advocates using geospatial technology to update manual cadastral mapping practices to help avoid such errors when validating existing datasets.

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5. Design and development of LADM-based infrastructure for Turkey
M. Alkan & Z. A. Polat

This paper investigates the adoption of ISO 19152, Geographic information — Land Administration Domain Model (LADM), for improvement of the current Turkey Land Information System (TLIS) data model and provides a brief overview of the current land information system in Turkey emphasising the main issues in creating the national information infrastructure. Then, the general concept of the country profile for Turkey with the adaptation of the LADM is described. In this context, the core data model of TLIS has been reviewed against the corresponding LADM basic classes. The proposed LADM for TLIS can be used to describe LA information in Turkey, although there are similarities, semantic differences and mismatches of classes and attributes between them. The results of study indicate that effective functioning of the information infrastructure requires proper integration of data, proceeded by analysing the contents of existing data sets, indicating key registers and defining a linkage system between them.

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6. Appraisal of the Hellenic Geodetic Reference System 1987 based on backward-transformed ITRF coordinates using a national velocity model
M. Chatzinikos & C. Kotsakis

The paper presents a detailed accuracy evaluation of the Hellenic Geodetic Reference System 1987 (HGRS87), a non-geocentric traditional local datum which was established thirty years ago and it is still used as the official coordinate system for surveying applications in Greece. This is the first time that a large-scale assessment of HGRS87 is performed, which aims to reveal its weakness by quantifying its consistency with a higher quality ITRF/GNSS-based frame over the entire country. A geodetic velocity model is employed in our analysis in an attempt to eliminate the accumulated geodynamical distortions of the (static) HGRS87 coordinates, and thus to provide a more judicious comparison between the underlying frames at a common epoch. Our results show that, even after removing the geodynamical distortions, the average accuracy of HGRS87 at national scale remains worse than 45 cm, yet significant variations exist in its regional accuracy level over different parts of Greece.

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Survey Review 49, No 355. July/August 2017

1. Characterizing noise in daily GPS position time series with overlapping Hadamard variance and maximum likelihood estimation
C. Xu & D. Yue

We assess the noise characteristics of daily position time series (Jet Propulsion Laboratory global solutions) from 12 International GNSS Service sites located in China, using both overlapping Hadamard variance (OHVAR) and maximum likelihood estimation (MLE). The result shows that OHVAR is computationally cheap, and the dominate power-law noise inferred is in good agreement with the ones inferred by comparing MLE values. However, OHVAR is insufficient to assess the long-period noise characteristics [e.g., random walk noise (RW)]. From the MLE analysis, the RW contribution is likely to be present in 14% of the time series, while the noise of most sites are characterized by a combination of white and flicker (or power law) noise (i.e., FL + WH or PL + WH). Moreover, sites near the northern crest of the equatorial ionization anomaly have larger amplitudes of WH in the vertical component, while no clear latitude dependency is observed in FL amplitudes.

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2. Mobile precise trigonometric levelling system based on land vehicle: an alternative method for precise levelling
J. Zou, Y. Zhu, Y. Xu, Q. Li, L. Meng & H. Li

The strict mathematical model of the mobile precise trigonometric levelling (MPTL) is deduced and its error sources are analysed in this paper. Some position sensors are added to instruments and observing reciprocal at the same time using two modified measuring robots so as to reduce the influence of atmospheric refraction, curvature of the earth and other factors. It is not necessary to measure the heights of instruments and targets by constructing the even numbers of observed edges to avoid errors of measuring heights. Experimental results indicate that MPTL has greatly increased the working efficiency and reduced the labour intensity compared with precise geometric levelling in the hills and mountains. A large number of experiments have proved that the standard deflection of measurement is less than ±1.0mm/√km and with an average speed of more than 7 kilometres per day in mountainous terrain.

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3. Determining normal heights with the use of Precise Point Positioning
G. Krzan, K. Dawidowicz, K. Stępniak & K. Świątek

In this paper, the authors analysed the Precise Point Positioning (PPP) performance in determination of normal heights using observations from a test network consisting of ten sites. One-week observation interval was processed using standard PPP approach and Multi-Station PPP (MS-PPP) with ambiguity resolution using the NAvigation Package for Earth Observation Satellites v. 3.3.1 software. In post-processing corrections like the Earth rotation parameters, ocean loadings, antenna phase centre offsets and variations etc. needed to obtain the most accurate position were utilised. By processing the various lengths observing sessions (1 hour, 30 minutes, 15 minutes) the authors examined the degradation of the position determination precision with shortening the observation time. In the study both high-end receivers used most often at CORS, as well as commercial two-frequency receivers were utilised. Normal heights were obtained using PL–geoid–2011 model. The results of the research show that PPP is a viable alternative for Relative GNSS Positioning in the case of GNSS levelling.

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4. Periodic signals in a pseudo-kinematic GPS coordinate time series depending on the antenna phase centre model – TRM55971.00 TZGD antenna case study
K. Dawidowicz & G. Krzan

This study investigates the differences between position estimates obtained using individual and type-mean (igs08.atx) antenna calibration models in GPS pseudo-kinematic processing. We used 15-min observation windows to study the short-period oscillations. Continuous GPS observations from eight selected Polish EUREF Permanent Network stations with the same TRM55971.00 TZGD antenna were used. The results showed that the differences in the calibration models, directly propagate into the position domain, affecting sub-daily results and influencing periodic variations. The sub-daily variations have periods close to half a sidereal day with amplitudes of up to 10 mm in position components. It could also be demonstrated that the mean position offsets, resulting from the use of individual calibrations instead of type-mean igs08.atx calibrations, can reach up to 5 mm in the up component, while the offsets in the horizontal components generally remain below 1 mm.

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5. An iterative method for obtaining a mean 3D axis from a set of GNSS traces for use in positional controls
A. T. Mozas-Calvache & F. J. Ariza-López

This paper describes a new method of data mining for determining a 3D mean axis from a set of surveyed Global Navigation Satellite Systems traces. The purpose is to obtain a mean axis and its uncertainty in order for them to be used in line-based positional controls. The method is based on an iterative process of condensation. The final mean axis is selected when a determined level of accuracy is achieved. So the method provides a relative positional accuracy value of the final solution. The example developed in this study demonstrates the viability of this method and allows analysis of the initial size of the set needed in order to achieve a final accuracy. Using real data, the proposed methodology has also been compared with the K-means methodology in order to analyse its advantages and conditions of use. The results have demonstrated an improvement in accuracy and geometrical definition of the axis obtained.

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6. A new method for satellite selection with controllable weighted PDOP threshold
Z. Nie, Y. Gao, Z. Wang & S. Ji

With the development of multi-constellation Global Navigation Satellite Systems (GNSS), more and more navigation satellites are available for position determination. Although the increased number of visible satellites can improve the positioning performance, the computational load to track and process signals from all visible satellites will increase significantly. In practical applications particularly using mobile devices powered by batteries of limited capacity, it will be desirable to track and process only satellite signals that are necessary to meet given accuracy requirement. This requires the development of appropriate satellite selection algorithms. A new satellite selection algorithm with a controllable Weighted Positioning Dilution Of Precision (WPDOP) threshold is developed in this paper. The new approach can be used to select any number of visible satellites with respect to given positioning accuracy. Numerical computations with multi-constellation GNSS data were conducted to assess the performance of the proposed algorithm.

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7. Experiences with the QDaedalus system for astrogeodetic determination of deflections of the vertical
M. Hauk, C. Hirt & C. Ackermann

This paper explores the astrogeodetic deflection of the vertical (VD) determination with a light-weight tachymeter-based measurement system called ‘QDaedalus’ developed at ETH Zurich. A description of the relevant components of the system is given to show the set-up and operation. The measuring process including CCD-tachymeter calibration and the astronomical data processing are summarised. The paper then analyses the achievable accuracy of VDs based on new measurement data acquired in Bavaria over several nights. Our measurements were executed atop a pillar on the roof of the TUM and at six stations in the Bavarian Alps (Estergebirge) with highly accurate VDs from previous digital zenith camera measurements available. Our comparisons indicate an accuracy level of 0.15–0.20 arc-seconds for VDs measured with QDaedalus. As a conclusion, our results show that the QDaedalus system is a promising sensor for accurate local astronomical gravity field surveys when a zenith camera is not available.

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8. Learning effectiveness of virtual environments for 3D terrain interpretation and data acquisition
A. M. Perez-Romero, M. Castro-Garcia, M. J. Leon-Bonillo & F. Manzano-Agugliaro

The aim of this study is to assess the effectiveness of different learning strategies for 3D terrain interpretation and data acquisition by engineering students. According to the experimental design, students received homogeneous training, followed by differential training, which divided the students into three statistically homogeneous groups where each group was subject to a different learning process: (1) virtual environment learning; (2) learning using physical scale models; and (3) a theoretical class. Afterwards, the students were evaluated using two tests under real field conditions. Results were obtained for the following study variables: field-test scores and whether or not the student was repeating the course. The students who learned using physical scale models obtained the best scores; their scores were significantly higher than those of students using virtual environment or a theoretical class. These findings open up new perspectives on the teaching of surveying with respect to other teaching methods.

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9. Height uncertainty in digital terrain modelling with unmanned aircraft systems
S-G. Mårtensson & Y. Reshetyuk

The purpose of this paper is to investigate the height uncertainty of digital terrain models (DTMs) generated from unmanned aircraft system (UAS) surveys over different surface types – asphalt, gravel and grass. The data used in the study was acquired during two UAS flights performed in spring 2014 with a fixed wing aircraft and two different cameras, from the flying height of about 100 m, and it was processed in different software suites – Agisoft PhotoScan, RapidStation and RapidTerrain. The results show that it is possible to achieve the height uncertainty (expressed as a Root Mean Square Error) in a DTM of below 0.02 m on asphalt surfaces and below 0.04 m on gravel and grass surfaces, provided an overcast sky.

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Survey Review 49, No 354. May/June 2017

1. An improved regional ionospheric model for single-frequency GNSS users
M. Abdelazeem, R. N. Çelik & A. El-Rabbany

In this study, we develop a regional ionospheric model for single-frequency precise point positioning (PPP) users in Europe. GNSS observations from 60 IGS and EUREF reference stations are processed using the PPP module in the Bernese software to estimate the vertical total electron contents. The developed model has spatial and temporal resolutions of 1° × 1° and 15 minutes, respectively. The resulting model is validated for PPP applications using GNSS observations from another set of stations in three different days. The single-frequency PPP accuracy and convergence time obtained through the developed model are assessed and compared with those obtained through the international GNSS service global ionospheric maps (IGS-GIM). The dual-frequency ionosphere-free PPP is used as a reference. It is shown that the model improves the PPP accuracy and convergence time by about 20, 45 and 45% for the 2D, height and 3D components, respectively, in comparison with the IGS-GIM model.

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2. A novel approach to design measurement models of single-frequency GPS receivers for cost-effective structural monitoring networks
H. Lee, J.-O. Lee, T. A. Musa & H.-Y. Chen

The global positioning system (GPS) has become an effective tool for measuring the dynamics of engineering structures from their absolute displacements. Although dual-frequency GPS receivers are widely adopted for structural monitoring applications to guarantee coordinate accuracy of the order of a few centimetres, the associated cost is too high to place larger number of these sensors. It has been recently recognised that single-frequency GPS receivers have great potential to be the smart sensors for measuring structural displacement due to their low-cost, small form-factor and low power consumption. Hence, the structural monitoring using single-frequency GPS receivers provides a much more cost-effective and compact tool for these applications; however, it remains a challenge to resolve the ambiguities rapidly and reliably. To address such a technical issue, this research focuses on design of GPS measurement models that can be effectively implemented in the structural monitoring networks. The main feature of these models is that they simultaneously model all available observables within the network, including not only GPS satellite ranging signals but also some dynamic constraints of structural monitoring networks, such as nominal coordinates and baselines of the target antennas. A series of tests has been carried out, using simulated satellite geometries and measurements, to assess impact of the proposed models on kinematic positioning performance. The results indicate that overall performance of the models that employ the single-frequency GPS observables and the dynamic constraints can be significantly improved by employing the redundant measurements.

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3. Solution for rank-defect EIV model based on TLS estimation
J. Yang, Y.-J. Wang, Q.-X. Wang & Y.-Q. Tao

Coefficient matrix of mathematical model is rank defect because of lacking essential observation data, traditional method of solving this kind of problem is to supplement constraint condition and compute parameters of model under least squares estimation. However, when elements of coefficient matrix are also made up of observation data as observation vector, error in variables model (EIV model) exists while the model is rank defect. In the contribution, EIV model with rank defect problem is talked about. After proposing this problem, the character of rank defect model is analysed under total least squares estimation. Solution for rank defect model based on TLS is presented, and iterative algorithm is established based on Lagrange function in the contribution. Coordinate transformation model with big rotation angle is taken as an example to prove the feasibility and performance of the presented solution. Based on numerical results of the instance, some conclusions are drawn at last of the contribution.

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4. A robust weighted total least-squares solution with Lagrange multipliers
X. Gong & Z. Li

Weighted total least-squares (WTLS) is becoming popular for parameter estimations in geodesy and surveying. However, it does not take into consideration the possible gross errors in observations, which may lead to a reduction in the robustness and reliability of parameter estimations. In order to solve this problem, in this study, Lagrange multipliers (LM) are employed to make WTLS solution rigorous and the IGG (Institute of Geodesy and Geophysics) weight function is employed to make WTLS solution more robust and reliable, resulting in a new robust WTLS solution (RWTLS-LM-IGG). A comparison with existing WTLS and robust WTLS solutions is conducted for linear regression and coordinate transformation, through experimental evaluation with simulation data sets (with different numbers and magnitudes of gross errors) and two sets of real-life data. The results of simulation experiments show that the variance component and the mean square error of estimated parameter vector obtained by using the existing methods increase almost linearly with an increase in the numbers and magnitudes of gross errors, but these values obtained by using the proposed method are almost stable, which means an effective reduction of the influence of the gross errors by the proposed method as compared with the existing methods. It is also found that the larger the numbers and magnitudes of gross errors, the more obvious such a reduction. Furthermore, the experiment results with two sets of real-life data are consistent with the results of simulation experiments.

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5. Assessing the performance of multi-GNSS precise point positioning in Asia-Pacific region
X. Zhao, S. Wang, C. Liu, J. Ou & X. Yu

Multi-Global Navigation Satellite System (GNSS) integration can effectively improve the satellite geometry strength, and certain effect on the precise point positioning (PPP) accuracy and convergence speed. Taking the system difference into account, this paper deduces the unified GNSS observation model, which is extended to the multi-GNSS PPP functional model. Meanwhile, the stochastic model used in Kalman filter parameter estimation is presented in the paper. Furthermore, to evaluate the performance of the multi-GNSS PPP in Asia-Pacific region, observed data from the International GNSS Service reference stations are analysed using the self-developed software. In detail, the results from Global Positioning System (GPS)-, GLObal NAvigation Satellite System (GLONASS)- and BeiDou Navigation Satellite System (BDS)-only PPP, double combined PPP and GPS/GLONASS/BDS combined PPP under the different observation duration and cut-off elevation angles are analysed. Results demonstrate: (1) compared with the single system PPP, the convergence speed of the multi-GNSS PPP is improved while the accuracy is not significantly improved after processing the 24-h data set; (2) when the observation duration is short, such as 0.5 h, the mean convergence percentage of the BDS combined with GPS and GLONASS PPP increases by an average of 49.6% compared with the single individual systems except for BDS, respectively, under the cut-off angle of 5° and (3) when PPP positioning with high cut-off elevation angles, and at the point of centimetre-level positioning, the GPS/GLONASS/BDS combined PPP has a better performance on the convergence percentage and convergence speed. For example, the percentages of the position biases within 0–5 cm for GPS/GLONASS/BDS are increased by 7.2 and 4.5% in North and East direction compared with GPS/GLONASS under the cut-off angle of 35°, more than any other. And the mean convergence time is only 14.5 min.

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6. Performance evaluation of single-frequency point positioning with GPS, GLONASS, BeiDou and Galileo
L. Pan, C. Cai, R. Santerre & X. Zhang

The single point positioning (SPP) mode has been widely used in many fields such as vehicle navigation, Geographic Information System and land surveying. For a long period, the SPP technology mainly relies on GPS system. With the recent revitalisation of the GLONASS constellation and two newly emerging constellations of BeiDou and Galileo, it is now feasible to investigate the performance of quad-constellation integrated SPP (QISPP) with GPS, GLONASS, BeiDou and Galileo measurements. As a satellite-based positioning technology, the QISPP is expected to improve the accuracy and availability of positioning solutions due to the increased number of visible satellites and the improved satellite sky distribution. In this study, a QISPP model is presented to simultaneously process observations from all four Global Navigation Satellite System (GNSS) constellations. Datasets collected at 47 globally distributed Multi-GNSS Experiment (MGEX) stations on two consecutive days and a kinematic experimental dataset are employed to fully assess the QISPP performance in terms of positioning accuracy and availability. Given that most navigation users are using single-frequency receivers, only the observations on a single frequency are utilised. The results indicate that the QISPP improves the positioning accuracy by an average of 16, 13 and 12% using the MGEX datasets, and 43, 31 and 51% using the kinematic experimental dataset over the GPS-only case in the east, north and up components, respectively. The availability of the QISPP solutions remains 100% even for a mask elevation angle of 40°, whereas it is only 37% for the GPS-only case. All these results are achieved using geodetic-type receivers and they are possibly optimistic for users who use navigation-type receivers.

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7. TotalStation/GNSS/EGM integrated geocentric positioning method
E. Osada, M. Owczarek-Wesołowska, M. Ficner & G. Kurpiński

In this study, we have investigated the use of the plumb line direction from Global Gravity Earth Model EGM2008 in the 3D integrated TotalStation/GNSS positioning. Our study shows that measurements along a total station traverse provides more accurate positioning results if the vertical deflection of plumb line is retrieved from EGM2008, than positioning with unknown deflection. The use of EGM2008 model improves the 3D coordinates accuracy to the level of precise GNSS measurements, while lack of this data introduce spatial displacements of the measured points, up to 26 cm. Hence our method can be useful for building precise 3D models of terrestrial objects in the GRS80 geocentric coordinate system.

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8. A method of GPS/BDS/GLONASS combined RTK positioning for middle-long baseline with partial ambiguity resolution
W. Gao, C. Gao & S. Pan

As China's BeiDou Navigation Satellite System (BDS) has become operational in the Asia-Pacific region, it is important to demonstrate the capabilities that a combination of GPS, BDS and GLONASS to high-precision positioning. Multi-constellation combination increases the available satellites and thus improves the positioning reliability. However at the same time, it will bring some challenges to the high-dimension ambiguity resolution (AR). In this contribution, a GPS/BDS/GLONASS combined real time kinematic (RTK) positioning method for middle-long baseline is proposed. In order to reduce the influence of troposphere and ionosphere delays on AR, a two-step AR strategy is adopted, where wide-lane and ionosphere-free observation model are used respectively. In the integer ambiguity search process, a partial ambiguity resolution (PAR) method is proposed to improve the AR performance. In the PAR method, satellite cutoff elevation, satellite number, AR success rate and ratio are used together to determine the ambiguity subset, which can be fixed reliably. A set of baselines ranging from about 30 to 60 km, which all contain GPS/BDS/GLONASS observations, are used to test RTK positioning performance. Experiment results demonstrate that GPS/BDS/GLONASS combined RTK positioning with partial ambiguity resolution can get much improved performance for middle-long baseline both in positioning speed and accuracy, as within about 20 s and 5 cm, respectively.

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9. Theory and method of hypothetical test for nonparameters in linear semiparametric model
S. Ding, J. Shi & W. Jiang

The linear semiparametric regression model is a combination of the linear parametric model and nonparametric model. Based on the penalised least squares theory for the semiparametric model, this paper presents a detailed discussion on the theory and method of the hypothetical test for the non-parameter in the semiparametric model. The hypothetical statistics are derived and the corresponding property is proved. The proposed theory and method of the hypothesis test are confirmed by simulated experiments.

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10. Optimal conformal map projections in harmonic polynomials in terms of Gauss-Schreiber coordinates
S. Orihuela

The Gauss–Schreiber projection generates a kind of rectangular isometric coordinates that allow to represent, in a continuous form, a terrestrial sector in NS extension including the poles. When they are applied in harmonic polynomials, they enable the optimal mapping of regions that are impracticable for other variables commonly used, e.g. Mercator or stereographic. In this paper, we present the detailed development of the polynomial in Gauss–Schreiber coordinates and an algorithm for map projection optimisation according to the Chebyshev–Gravé's thesis. The result is practical and allows the use of stereographic polar coordinates to be replaced.

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11. Book Review: GPS Satellite Surveying, fourth edition
Martin Schaefer

‘GPS Satellite Surveying’ by Leick, Rapoport and Tatarnikov is an excellent up-to-date reference book for GNSS experts and industry professionals. It covers in detail all aspects of GNSS surveying at a highly technical level, this edition having added chapters on least-squares adjustments and receiver antennas, for instance. In addition other material has been updated for this edition to match the progress of technology. The book covers all existing systems (GPS, GLONASS) and systems in development (BEIDOU, Galileo), with some reference to regional systems, such as the Japanese QZSS or Indian IRNSS. The topics covered range from geodesy via positioning and RTK to troposphere and ionosphere interactions and much more.

This book will require a priori knowledge of basic principles of GPS and an interest in processing GNSS signals, with a good understanding of mathematical functions. For the non-specialist end-user of GNSS this book will be quite technical and it should not be seen as an introductory book; it is rather aimed at engineers, specialist software designers and geodetic scientists. It is also not a guide to setting up and performing a GNSS survey as the title might imply.

Following a brief introductory chapter there is a chapter on least-square adjustment which discusses the various models used and ending with a section on Kalman filtering. The next chapter addresses recursive least squares. The following chapter covers basic geodesy, including the International Reference Frame, the International Celestial Reference System, datum, 3D geodetic models, ellipsoidal models and conformal mapping model.

Having covered the basic mathematics and geodetic material, the book then goes on in chapter 5 to discuss satellite systems, including the various factors impacting on a satellites orbit and brief introductions to the different satellite positioning systems. The next chapter discusses the various approaches to GNSS positioning, including the various factors, such as cycle slips and antenna calibration that can affect the results. It also discusses relative positioning, ambiguity fixing and network-supported positioning, such as PPP, CORS and PPP-RTK.

The next chapter looks at various approaches to real-time kinematic relative positioning, including for long and short baselines. There follows a chapter on tropospheric and ionospheric effects and the various ionospheric models. The final chapter covers GNSS receiver antennas. There then follow nine appendices, the first three fairly substantial, a general background covering spherical trigonometry, rotational matrices, linear algebra, linearisation and statistics, an appendix on the ellipsoid and one on conformal mapping. The final six appendices cover ‘vector calculus and delta function’, some basic electromagnetic theory, ‘diffraction over half-plane’, ‘single cavity mode approximation with patch antenna analysis’, ‘patch antennas with artificial dielectric substrates’ and ‘cover patch array geodetic antenna’. There follow 21 pages of references, and author and subject indexes.

For the researcher or expert user of GNSS much of the material in the book will be familiar, but it will be very useful to have it all brought together for easy reference in a single volume.

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Survey Review 48, No 347. March/April 2016

1. Real time monitoring ground motion using GPS with real time corrections
R. Tu, L. Wang & Z. Liu

The high rate GPS velocity determination technology which is based on the broadcast ephemeris and epoch differenced model can retrieve displacement of ground motion with the precision of a few centimetres to decimetres in real time. Moreover, the precision of the recovered displacement can be improved if the un-modelled errors such as broadcast ephemeris residuals, atmospheric residuals, multipath effects and high frequency noise are tackled more accurately. In this paper, we propose a method to improve the precision of the recovered displacement by appropriately making use of reference station corrections. For the reference stations, the coordinates are highly constrained to extract the error corrections that are to be broadcast via a communication link to the rover. After correcting the rover’s observations, some errors such as ephemeris residuals and atmospheric residuals are effectively eliminated or at least reduced. This improves the accuracy of the observations and thus enhances the reliability of the velocity estimation. The displacement can be recovered by integrating the estimated velocity after de-trending using a linear trend that is caused by the un-corrected residuals. The series of validation results in the experiment have shown that the displacement of the simulated motion can be real time recovered with a precision of 1–2 cm, and is thus applicable for real time monitoring of the ground motion.

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2. Geodetic and fibre optic measurements of a full-scale bi-axial compressional test
S. Lackner, W. Lienhart, G. Supp & R. Marte

Earth filled dams are commonly used as flood prevention dams and for hydroelectric power plants. Their stability is critical for an uninterrupted operation and a reliable protection from catastrophic incidents. During the operation, dams are subjected to lateral loading by hydrostatic pressure. In order to predict the deformation behaviour the material parameters have to be known accurately. Therefore, Graz University of Technology carried out a series of life-size experiments to determine the material parameters of an earth filled dam. Controlled vertical load was applied in these experiments and the resulting deformations were measured with geodetic and fibre optic methods. Single points on the slope were continuously tracked with robotic total stations. In addition, the whole dam surface was monitored using a scanning total station. Finally, relative movements between points on the dam were measured with fibre optic sensors based on fibre Bragg gratings. The achievable measurement precision and the relation between acting load and resulting deformation is investigated in detail for every measurement technique. The authors show in their evaluation that absolute deformations can reliably be detected with the geodetic methods. However, individual loading steps cannot be resolved because of the limited precision of the geodetic measurements. Our results demonstrate that the sensitivity of the monitoring system can be significantly increased with the fibre optic sensors and the scanning data also contribute to assess the stability of the experiment set-up.

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3. Impact of coseismic deformation fields with different time scales on finite fault modelling in 2010 California Baja Earthquake
J. Niu, C. Xu, Q. Fan & Z. Yin

In this study, the static coseismic deformations with different time scales in the target event are extracted from the long term and short term solutions of continuous GPS and the epoch-by-epoch solution of high rate GPS respectively. The mean discrepancies among these deformations are less than 1 cm. The earthquake source parameters are inverted in the layered inhomogeneous half-space under the static dislocation theory from the static coseismic displacements with different time scales. It can be concluded that the time scale of the static coseismic displacement shows a relatively small impact on the source parameters in this moderate earthquake. The disturbances on the fault slips are less than 20 cm, and less than 0·1 on the moment magnitudes. As the time scale grows, the postseismic deformation in the static coseismic displacement from the short term solution increases, which indicates that apparent early postseismic displacements exist on the day after the termination of the earthquake.

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4. Determination and testing of strain parameters in landslide region of Koyulhisar, Turkey
F. Poyraz

Koyulhisar in Turkey is in danger of landslides, and to determine the risk of landslides in this area, many projects and studies are currently being conducted. Between 2007 and 2008, global navigation satellite system measurements were made, providing data on seasonal effects. The displacements, and also the forces behind these displacements, need to be studied. These forces may be determined using various methods. One method is the determination of strain parameters. With regard to the maximum and minimum principal strain parameters obtained (λ1 = 56·3433 μs, λ2 = −35·4642 μs) from the city centre measurements, there is statistically significant stress accumulation in the Koyulhisar region. Furthermore, for the compression and contraction directions obtained in the city centre, compression was obtained in the north–south direction and contraction movement was obtained in the east–west direction. These movement directions show that the tectonic movements in the region have an effect on the landslide.

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5. Registration of foundation properties – cultural asset on behalf of their own fused foundations
Y. E. Çoruhlu

The Convention Concerning the Protection of the World Cultural and Natural Heritage for protecting cultural assets and handing them down to future generations was adopted in 1972 by United Nations Educational, Scientific and Cultural Organization (UNESCO). This convention was adopted by Turkey in 1983. This regulation has a noteworthy principle, which states that the cultural assets are not only the properties of the countries in which they are located in but also of mankind. The regulation stipulates national/international protection of cultural assets and handing them down to future generations. For this purpose, law 2863 was enacted in 1983. In Turkey, there are 96 000 registered cultural assets, 19 825 of which are managed by the General Directorate of Foundations (GDF). The GDF conducts restoration of cultural assets and handing them down to future generations in a very efficient way. Today, there are more than 40 000 fused (mazbut in Turkish) foundations and around 80 000 foundation properties in Turkey, 19 825 of which are foundation cultural assets. It became possible to increase the number of these foundation cultural assets by article 30 of Foundations Law 5737, which came into force in 2008. In other words, this article allows properties, which were first built by foundations, registered as cultural assets, and came into the possession of the Treasury, Municipality, Special Administration or Village Legal Entities to be registered at fused foundations. The aim of this study was to reveal reregistration process of properties, which are protected by national and international legislation and registered as cultural assets, in order to protect, utilise and improve them in the name of the foundations. In this study, the subject will be explored by describing the process steps, providing workflow diagrams using current applications, and giving examples from original documents.

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6. The use of laser scanning as a method for measuring stairways following an accident
M. Eyre, P. J. Foster, K. Hallas & R. Shaw

Stairs present significant potential for harm to their users. A fall on stairs, particularly in descent, often leads to serious injury or even death. The authors have been involved in the investigation of many workplace stair accidents. Proper forensic investigation into the cause of a stair accident has often found the incident to be wholly or partly caused by poor stair design. In order to establish the relationship between the stair design and a given fall, an onsite survey has to be conducted, determining the rises and goings along with other key dimensions. The Health and Safety Laboratory (HSL), Buxton, UK, regularly undertake this type of survey using a digital inclinometer, a steel rule and a tape measure. Laser scanning is an emerging technique that is now accessible to the surveyor to complement or replace traditional approaches. The laser scanner and associated software produces a dense point survey in 3D, allowing dimensional analysis of the features. The authors used both traditional and laser scanning techniques to study the scenes of two fatal stair falls. The analysis presented allows the suitability of laser scanning for stair-fall investigation to be considered. Identification and classification of errors are needed in order to consider if the error is acceptable or can be mitigated. Laser scanners are impressive instruments providing data from which can be used to create a virtual 3D environment that can be used to reconstruct and explain an event and contributing factors. The use of both survey methods currently provides the investigator with complimentary data that allows accurate measurements to be presented in the context of the three-dimensional environment.

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7. Predicting ionospheric critical frequency of the F2 layer over Lycksele using the neural network improved by error compensation technology
D. Zheng, W. Hu & P. Li

In this contribution, according to the critical frequency of the F2 layer (foF2) from the ionosonde station and the International Reference Ionosphere 2012 (IRI2012) model [the International Radio Consultative Committee (CCIR) coefficient], a single station model (called the Fusion model) for predicting the hourly value of foF2 over Lycksele (64.69°N, 18.80°E) is developed by the back-propagation neural network (BPNN) technology compensated for the model-deviation of the IRI2012 model. The input parameters of this BPNN-based foF2 prediction model include day number (day of the year), universal time, solar zenith angle, solar cycle information, geomagnetic activity (a 3-day running mean of the 3-h planetary magnetic index Ap and Kp) and the foF2 values from the IRI2012 model; the output parameter is the model-deviation. The data sets employed in this model are obtained from the National Geophysical Data Centre and National Aeronautics and Space Administration (NASA), about 215 614 sets, which are derived during the period from January 1958 to December 1984 (1960s data is missing). The data sets from 1971 to 1984 are selected for validation instead of for training use. Prediction values from the Fusion model, the General BPNN and IRI2012 models are each compared with the observed data. The results indicate that the proposed model is superior to the other models for hourly value of foF2 prediction over Lycksele. According to the statistical analysis of average root mean square error, the proposed model offers an improvement of 19.11% over the IRI2012 model.

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8. Investigation of long-range dependencies in the stochastic part of daily GPS solutions
J. Bogusz, A. Klos, M. Figurski & M. Kujawa

The long-range dependence (LRD) of the stochastic part of GPS-derived topocentric coordinates change (North, East, Up) results with relatively high autocorrelation values with a focus on self-similarity. One of the reasons for such self-similarity in the GPS time series are noises that are commonly recognised to prevail in the form of the flicker noise model. To prove the self-similarity of the stochastic part of GPS time series we used more than 130 ASG-EUPOS (active geodetic network EUPOS) stations from an area of Poland with a 5-year span of the daily topocentric coordinate changes. The deterministic part of time series was removed by means of the least-squares (LS) method, median absolute deviation (MAD) criterion and the sequential t-test algorithm, respectively. Then the self-similarity of the residue was proved by the results of the Ljung–Box test, whose values close to zero showed the dependence of the stochastic part of the GPS time series. The residue was analysed by means of the rescaled range (R/S) method with the H (Hurst) parameter and the detrended fluctuation analysis (DFA) with the scaling exponent α. Both H and α values ranged within assumed LRD limits of 0.5 and 1. This analysis was followed by noise investigation with a maximum likelihood estimation (MLE). The white plus the power-law noise models were assumed a priori, which gave us a spectral indices κ between − 0.4 and − 1.2 for all of the time series. It proved that fractional white noise outweighs other types of noises in GPS time series. Authors found here, that the LRD methods by omitting the noise amplitude data led to an underestimation of H values and their misinterpretation. The larger the omitted amplitude is, the greater the difference between the noise characters estimated with R/S values in comparison to the reference values of κ are. Some of these differences exceed even the value of 0.6, which may result in the estimation of false noise character in GPS data thus eliciting wrong conclusions.

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9. Climate change, land use and land surveyors
P. van der Molen & D. Mitchell

Research reveals that the land sector is a major emitter of greenhouse gases. But the land sector has also potential to reduce emissions. Different from other emission sectors like energy and transport, the land sector (in particular the rural area including forests) has the potential to also remove greenhouse gases from the atmosphere through sequestration and storage. This requires land use, land use change and forestry to be managed with respect to climate change goals. Carbon storage has the potential to generate carbon credits, which according to the Kyoto Protocol are exchangeable in a market environment. But is the market secure enough? This paper aims primary at presenting the subject matter as a synthesis of extant literature. Secondary, the paper shows interfaces with the land surveyor's profession namely land management and land administration.

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Survey Review 48, No 346. January/February 2016

1. Structural integrity verification of cable stayed footbridge based on FEM analyses and geodetic surveying techniques
V. Gikas, P. Karydakis, T. Mpimis, G. Piniotis & H. Perakis

This paper presents the mathematical models developed for the design of a pedestrian, cable stayed bridge, the geodetic monitoring procedures and their detailed cross-comparisons and analyses undertaken during the phases of construction and at commissioning stage. Because of the asymmetric design, the relative flexibility of the pylons, the eccentric positioning of the central joint and the off-plane low angles of the cables, a multi-sensor, event based geodetic monitoring scheme was adopted to assess the structural integrity of the bridge. During construction, the bridge kinematics were measured along both sides of the deck and at selected points on the pylon facades using a digital level and a high accuracy total station used in metrology respectively. At a commissioning stage, a number of load test series were undertaken using conventional geodetic techniques and a tactical grade Inertial Measurement Unit (IMU). Analysis confirmed the overall mathematical modelling assumptions made for the individual stages of construction and for the completed structure. However, analysis also revealed the increased structural rigidity of the structure. This particularly applies for the torsional stiffness of the deck that exhibits low (by a factor of 0·5) rotation angles compared to those obtained from the analytical models.

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2. Fit-for-purpose land administration: lessons from urban and rural Ethiopia
R. M. Bennett & B. K. Alemie

Lessons for designing fit-for-purpose land administration and land management activities, where the stated purposes are poverty alleviation, food security, and good governance, are provided. Contemporary developments from urban and rural Ethiopia provide the empirical basis: data is synthesised from fieldwork and other research activities undertaken between 2011 and 2013. With its large population and important geopolitical location, Ethiopia will continue to act as a yardstick for measuring the success of the global development agenda, particularly in Eastern Africa. Observations from training sessions conducted with cadastral and urban planning experts in Addis Ababa reveal challenges and opportunities regarding capacity development for urban land administration, urban land markets, and state land management. From the city of Bahir Dar, an alternative perspective of urban land administration is provided: the presented results shed light on the varying quality of cadastral development, but also the positive and negative impacts of cadastral implementation. Meanwhile, results from Dilla Town reveal the opportunity to link cadastral development to other infrastructure development activities (e.g. road construction and upgrade). The case also reveals the ongoing tension between ensuring adequate compensation payments relating to land acquisition, whilst also delivering a broader community benefit. Outputs from exploratory design work on the potential for land consolidation in the Amhara region are also articulated. The status of cadastral development in rural areas is revealed, along with future challenges for using cadastral data in land consolidation activities. Overall, the synthesised studies expose how fit-for-purpose ideologies are increasingly informing Ethiopian cadastral design, and under what conditions these designs can support poverty alleviation, food security, and good governance.

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3. Investigating efficacy of robust M-estimation of deformation from observation differences
K. Nowel

Generalized robust M-estimation of deformation from observation differences (GREDOD) is a robust method for deformation analysis of geodetic control networks. This method has been developed based on the well known robust Iterative weighted similarity transformation (IWST) method. Hence, in the GREDOD method, as in the IWST method, the L1-norm weight function is the weight function for the displacement vector and the displacement vector components are the weight function variables. The L1-norm weight function for variables in the form of the displacement vector components is the simplest and most natural solution, but it is not known whether this is the most efficacious solution for the GREDOD method. To assess this, the current study used different robust weight functions which were tested for variables in the widely used form of the displacement vector components and for variables in the form of displacement lengths. All solutions were tested on the basis of the simulated two-epoch observations of the absolute control network of the Montsalvens dam in Switzerland. The efficacy measure for individual solutions was the mean success rate (MSR).

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4. Creation of land fund for the purpose of land management in the Republic of Serbia
J. P. Gučević, D. M. Milićević, O. P. Vasović & V. A. Djokić

This paper presents the activities carried out by the authorities of the Republic of Serbia in order to properly manage agricultural land. It is well known that land, as a scarce resource in any country, must be managed in a proper way. The government is in charge of land management, land legislation and land policies that have a major influence on land development. The Republic of Serbia is currently in transition from fully state owned land to private ownership, but this path is fraught with numerous obstacles. While the experiences of other countries may help avoid some common pitfalls, each country faces a unique set of challenges not found elsewhere. To be able to properly choose the right direction of land management, it is essential to consider multiple potential scenarios of good land stewardship. A land fund is an example of a good international practice that countries like Serbia should follow, implement and adapt in a way which reflects its national heritage and current circumstances. The real estate market is turbulent and changes over time, but it must be and remain transparent, open and without restrictions in order to assure the wellbeing of future generations and development of the country.

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5. External error modelling with combined model in terrestrial laser scanning
J. Wang, H. Kutterer & X. Fang

Terrestrial laser scanning (TLS) is a promising tool in geodetic applications. Data quality of outdoor TLS measurements is considerably limited by external errors caused by atmospheric variations and object related factors. In this study, external models related to atmospheric refraction, beam wander and incidence angle were introduced and integrated into a seven-parameter similarity transformation (7PST) model to compose a combined model. The combined model was rigorously adjusted by an iterative Gauss–Helmert (GH) model primarily to estimate external calibration parameters and transformation parameters simultaneously. In the application on a dam surface, a t-test showed that a significant external calibration parameter was the range scale, which mainly corresponded with the incidence angle model. The precision of estimated representative points was improved by approximately 50% with the proposed method. The presented models show a great potential for detecting external errors and registering multiple scans in outdoor applications.

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6. Property, human rights law and land surveyors
P. van der Molen

Land surveyors have a lot to do with property rights. This paper presents an inventory of international human rights law regarding property rights, relevant for land surveyors. It addresses the history and current status of international law and case law, and it reflects on the aspects that shape the human right to property as a controversial human right. The paper includes a consideration on related rights, such as the human right to housing and to food. The paper concludes that human rights form an important context for the land surveyor's profession and ends with describing interfaces between the human rights to property and the profession.

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7. Static GNSS precise point positioning using free online services for Africa
A. Abdallah & V. Schwieger

The GNSS precise point positioning (PPP) technique has been extensively covered in recent research. In this study, six International global navigation satellite system (GNSS) Service (IGS) stations defined by 4-digits code in Africa were selected to be processed. The stations cover different climates in Africa. HARB, SUTH and WIND stations cover the mid-latitude area and NKLG, NURK and MAL2 are located in the equatorial region. Two data sessions were selected in processing to cover the winter and summer seasons: the first session of 3 days [01–03 January 2013 (DOY: 001–003/2013)] and the second session of 3 days [01–03 July 2013 (DOY: 182–184/2013)]. This paper aims to evaluate the accuracy of static PPP coordinate solution in Africa for different convergence times using free online services: Canadian Spatial Reference System (CSRS)-PPP, Automatic Precise Point Service (APPS)-PPP and GPS Analysis and Positioning Software (GAPS)-PPP. The stations’ observation times were divided into different observation times (1, 2, 4, 8, 12, and 24 h).The PPP coordinate solution was compared to the reference solution of those stations. The investigation is continued by estimating the PPP total tropospheric zenith delay (TZD) parameters, which were obtained by the different online services. These parameters were compared to the published parameters from IGS. The comparison between the different online services shows that the CSRS-PPP provides the best solution after 4 and 8 h. The APPS-PPP and CSRS-PPP provides the same solution in millimeters level after 12 h. In the equatorial region, the PPP coordinate solution is significantly improved between 12 and 24 h. Moreover, GAPS-PPP is not recommended to be used in the equatorial stations, where it shows a high error compared to CSRS-PPP and APPS-PPP even after 24 h. The mid-latitude stations show a better PPP coordinate solution in the winter than in the summer, but the equatorial stations present a low accuracy for the two sessions. Regarding the PPP tropospheric delay estimation, an additional station (HNUS) is used in the mid-latitude area, which has a low ellipsoidal height. APPS-PPP shows the best solution in the TZD estimation. The GAPS-PPP online service shows a systemic error in estimation and a high RMS relative to the TZD values known from IGS. The ellipsoidal height for antenna indicates a negative correlation to the estimated tropospheric values, but there is no effect for the variation of the ellipsoidal height in the estimated RMS. The estimated tropospheric parameters are correlated with the PPP coordinate estimation, where the GAPS-PPP service provides the worst PPP coordinate solution and at the same time, it shows the worst accuracy for tropospheric parameters estimation. Moreover, the estimated tropospheric parameters for the mid-latitude stations in the summer season show a higher RMS than in the winter season, which matches the same sequence of the PPP coordinates. The NKLG and NURK stations present a low accuracy for the tropospheric estimation, which is matching to the low accuracy of the PPP coordinates obtained from the different online services.

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