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2007 Abstracts
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Email: Jim Smith
The Top 10 Articles are available to download free from: http://maney.co.uk/top_articles/sre/. These are usually chosen annually by the Editor. To ascertain other articles which have been written
by a particular author:
Vol. 39, No. 306. October 2007 1. On the Positioning Enhancement of Digital Cadastral MapsYaron A. Felus In recent years, there is a renewed interest in the development and enhancement of legal digital cadastral databases. These databases usually are derived from paper parcel maps by manual or automatic conversion processes. Nevertheless, the converted cadastral data should be further processed to minimize inherent errors in the data conversion procedure, to resolve inaccuracies in the original parcel maps, and to fit them to the new GPS-based coordinate system with high precision. This paper describes a workflow of steps used to enhance and improve the spatial accuracy of digital cadastral maps. Every step in this workflow is analyzed and various problems are uniquely addressed. First, the problem of determining the correct coordinate transformation model is investigated using the Akaike's Information Criterion (AIC). Second, the problem of modifying boundary corners to fit existing ground features is solved by using a unique rubber sheeting procedure that takes into account linear features. Last, an adjustment with stochastic constraints is applied to include additional cadastral information and geometric conditions. The developed methodology KEYWORDS: Digital Cadastral Databases. Workflow. Coordinate Transformation. Rubber Sheet Method. Further information:
Continuous and reliable position determination is very important in any navigation application. Therefore a combination and integration of different location techniques and positioning sensors is required. In most navigation applications this integration is performed using a Kalman filter approach. In this paper a new approach which makes use of knowledge-based systems for preprocessing the sensor observations is presented. In the preprocessing step the quality and reliability of the sensor observations is tested and gross errors and outliers are detected and eliminated. Furthermore the preprocessing step is used to determine the weightings of the sensor observations in the stochastic model of the following central Kalman filter. The weightings of the sensor observations can then be adjusted in the filter depending on their availability and quality. This approach is developed in a research project at our University for a pedestrian navigation and guidance service. In this project different location techniques such as GNSS and indoor positioning are combined with dead reckoning sensors (e.g. digital compass for heading determination, accelerometers for measurement of travelled distance, barometric pressure sensor for altitude determination) for continuous position determination of a pedestrian user. The project takes a user case into account, i.e., the navigation and guidance of visitors of our university to certain offices and persons. Selected results of field tests using different sensors are also presented in the paper. From the tests it could be seen that such a service can achieve a high accuracy and reliability for continuous position determination of a pedestrian user. It can also be expected that the performance of the system can be increased using the new intelligent knowledge-based Kalman filter approach for the integration of all available sensor observations. KEYWORDS: Pedestrian Navigation. Kalman Filter. GNSS. Dead Reckoning. Further information:
Christopher Hansteen, professor of applied mathematics 1816-65 at the University of Oslo, and director of the Geographical Survey of Norway 1817-1872, renewed the national instrument collection and trained young officers in surveying fieldwork to establish a geodetic reference network for Norway. After 3 decades of national focus the opportunity to contribute internationally was initiated by F. G. W. Struve of Pulkova Observatory. The Russian-Scandinavian Meridian Arc project in Finnmark 1845-1850 was the first government sponsored international science project in Norway. We review Hansteen’s role and leadership from new archival source material. These sources have also lead to rediscovery of the universal instrument used by the Norwegian surveyors. We review and discuss the efforts of the key field observers. The precision of the measurements holds contemporary quality as judged by comparison with later observations. Although North Cape was initially planned as the northern terminal of the meridian arc, arguments were forwarded already in the reconnaissance report to replace it by Hammerfest. KEYWORDS: Astrogeodesy, Surveying, Geodetic Arc, Scientific Instruments, History of Science and Technology. Further information: Results of experiments with a laser reflectorless EDM instrument to test its tolerance are reported. Field distance measurements were simulated with measurements to >50 targets, identified with various surfaces, mostly not planar or normal to the sighting axis of instrument. Measured distances, covering the full nominal range of the instrument used, are characterized by systematic errors in the form of fluctuations with a maximum value up to 140mm at the distance of 20m, attenuating at longer distances. It was also found that the colour of target surfaces controls the maximum range of measurements, and some surface such as common mirror lead to erroneous results. Conclusions of our study are broadly consistent with conclusions of experiments with laser scanners. KEYWORDS Reflectorless EDM, Laser EDM. Tolerances of LRI EDM. Systematic errors. Further information: 5. Precise Real-time Positioning with a Low Cost GPS Engine
using Neural Networks Position information obtained from standard GPS receivers has time variant errors. To make effective use of GPS information in a navigation system, it is essential to model these errors. In this paper, a new approach is presented for improvement of positioning accuracy using MLP, RBF, and RNN neural networks (NNs). The NNs estimate position errors that are used as Differential GPS (DGPS) corrections in real time positioning. Method validity is verified with experimental data from an actual data collection, before and after Selective Availability (SA) error. The result is a highly effective estimation technique for accurate positioning, so that positioning accuracy is drastically improved to less than 1.10 meters with SA on and 0.70 with SA off. The experimental tests results with real data emphasize that total performance of RNN is better than RBF and MLP considering trade off between accuracy and speed for DGPS corrections prediction. KEYWORDS: DGPS, Error Prediction, Neural Networks, SA Error. Further information:
Geospatial Data Infrastructure (GDI) is a concept that is a reality in most developed countries today. This concept is however only just beginning to take a foothold in most developing countries. This paper reports on a study to access Kenya's preparedness for GDI take off by evaluating the achievements made thus far in the basic components of GDI: data, technology, policies, institutional framework and people. It is observed that the relatively lukewarm political support and absence of a long-term strategic vision are serious constraints to GDI diffusion. Similarly, the lack of sustainable funding policies and strategies, coupled with the absence of a concise implementation strategy greatly undermine the development of GDI in Kenya. Most geospatial data sets are still in analogue form, are not regularly updated, and their consistency across organizations still needs to be verified. In addition, the absence of an active GIS professional organization greatly handicaps GDI development in Kenya. Nevertheless, despite this largely negative picture, the GDI status in Kenya compares well with those of most other African countries. KEYWORDS: Geospatial Data Infrastructure. Sustainable funding. Implementation strategy. Further information:
The GPS antenna is the connecting component between the GPS satellite
and the GPS receiver. Its function is to transfer the satellite
signal propagation to the receiver with minimum interruption. A
satisfactory process is expected to result in an accurate and reliable
performance of the GPS receiver. KEYWORDS: GPS Antenna. Multipath Errors. Pseudo-range. Signal Processing. Further information:
Vol. 39, No. 305. July 2007 1. Evaluation of Global Geopotential Models in Determining
the Quasi-Geoid for Southern Africa Precise geoid models are needed to enable GPS-derived heights to be converted to the local height datum. A major component of these models is a global geopotential model. Several candidate models are assessed in the context of forming the basis for a regional quasi-geoid for Southern Africa. These candidates include the EGM96 and models based upon data from the GRACE satellite mission. EGM96 is particularly unreliable in areas where no terrestrial gravity data exist. The GRACE models perform best when only medium (up to degree 120) harmonic expansions are used, minimising the contribution of predicted gravity anomalies. Comparisons with 62 GPS/levelling data points in the western part of South Africa indicate a RMS fit of 13cm for the best combination. This fit can be improved to 4cm if the quasi-geoid model is allowed to tilt in two directions. KEYWORDS: Geopotential model. Quasi-geoid. Southern Africa. GPS heights Further information:
Piling engineering is the first step in the construction of bridges
and offshore platforms. However, limitations in the real-time determination
of the positions of piling pickets exist. For instance, requirement
of line of sight, lack of real-time positioning capability and fragility
to the hostile observation environment are typical problems for
the traditional surveying techniques. KEYWORDS: RTK GPS, Sea piling engineering, Coordinate transformation. China. Further information: 3. Automatic Multi total station monitoring of a tunnel A tunnel has been under construction for the Lisbon Metro network on the muddy bed of river Tagus. An incident during the jet-grouting for the muddy soil treatment led to flooding of a specific sector of the tunnel and to the need for repair works. Consequently, a decision has been made to monitor with a short time resolution the movements of that sector before, during and after reparation works. This includes the period in which the tunnel will be in use for its regular operation, with commuters using the subway. Given these general conditions with severe inter-visibility limitations, as well as the cost restraints, an automatic monitoring system has been designed and put in place, resorting to four LEICA TC2003 motorised total stations and to the available commercial software, LEICA GeoMoS. The computational procedure of the mentioned software implies a network configuration, in which every total station set up needs a cluster of control points associated with that particular setup in order to perform a space resection. However, it is often difficult to find stable points inside a tunnel under monitoring let alone during repair works. Therefore, to overcome this difficulty, adjustment software - EpochSuite – has been integrated into the monitoring system. Since it runs after the collection of data, the adjustment software makes it possible to perform a more robust and accurate computation of displacement vectors of signalised object points, which represent the tunnel under study. EpochSuite uses a database management approach that is particularly useful in handling many monitoring epochs and uses automatic outlier detection tools. This paper reports on the network configuration, the instrumental setup and the software framework in which the automatic monitoring system actually operates. KEYWORDS: Automatic monitoring. Metro tunnel. Total station. Adjustment software. Further information:
In continuation of earlier work on the geoid of Eastern Africa [8] a further study has been undertaken to determine the geoid of Tanzania, bounded by latitude –12* * * * -1°, longitude 29* * ? * 40*. The geoid was determined at a resolution grid of 5 minutes of arc. The Geodetic Reference System 1980 (GRS80) was used. The data used included the EIGEN-GRACE02S geopotential model to degree and order 120, a recent terrestrial gravity data anomaly set, marine (ship track) gravity and satellite radar altimetry data. A digital terrain model derived from the Shuttle Radar Topography Mission (SRTM) was also used to compute topographical effects. The spherical one-dimensional fast Fourier transform (FFT) method was used to compute the geoid heights residual to the geopotential model. Internal error propagation was used to get a pessimistic accuracy estimate of 30cm, and comparisons are made with heights derived from Transit Doppler observations co-located with trigonometrically determined heights. Gravimetric geoid height differences were compared with corresponding astrogeodetic geoid height differences provided by a 970 km geoidal section. KEYWORDS: Geoid. East Africa. EIGEN-GRACE02S. Geopotential model. Shuttle Mission. Further information: 5. Use of Bloom’s taxonomic complexity in online
multiple choice tests in geomatics education Tests are the most common method to evaluate teaching effectiveness throughout the period of instruction (formative) and assess student learning outcomes at the end of the instruction period (summative). Teaching geomatics is not an exception to this rule. The recent proliferation of computer hardware and software technologies now makes Multiple Choice (MC) type assessment methods more attractive. MC tests provide more objective measures on assessing student learning with efficiency over the Internet. In this study we show, using in-house software, that multiple choice tests when combined with technology, especially multimedia, can be flexible and easy to use. The interface has two unique features: 1) it accommodates questions of various multimedia formats, diagrams, tables, images, or equations that can be conveniently incorporated into the examination; 2) it tracks the students’ time spent on each question during the examination. We found that 79 percent of the variation in the average time students spent on each question can be explained by Bloom’s taxonomy (with a correlation coefficient on 0.89. Hence by grouping exam questions at Bloom’s taxonomic levels we can detect student learning difficulties effectively within each level. KEYWORDS: Bloom’s taxonomy. Education. Multiple-choice. Online tests. Further information: 6. The impact of the ionospheric correction latency on
long-baseline instantaneous kinematic GPS positioning The primary objective of this paper is to estimate the influence of the double-difference (DD) ionospheric corrections latency on the instantaneous (one-epoch) ambiguity resolution (AR) in long-range RTK under typical ionospheric conditions. The key to the success in integer AR rests mainly in the mitigation of the atmospheric errors, i.e., the ionospheric and tropospheric delays. Between these two, the former has the greatest influence on the AR, since both ambiguities and ionospheric delay are frequency-dependent. Instantaneous RTK is presently one of the most challenging topics in precise GPS applications. The research presented here addresses this topic through the development and testing of a multiple reference station approach implemented in the MPGPS™ (Multi Purpose GPS Processing Software) software. Atmospheric corrections are used in order to obtain a high quality RTK position over long distances. In our approach, DD ionospheric correction prediction derived from the previous correctly resolved epoch is applied. Yet, at the beginning of the session, a short initialization period is still required in order to produce the initial prediction. After the initialization the method is based on single epoch solution. This method assures a high success rate of the instantaneous AR for long baselines (over 100 km). Since the previous-epoch ionospheric delay is used, and instantaneous mode is applied in the algorithm, the proposed method is robust against cycle slips and data gaps, and still capable of producing centimetre-level RTK positions. The RTK solution was simulated in the post-processing mode. Namely, different DD ionospheric delay correction latencies were simulated in 10 s increments and sent to the (simulated) rover in order to test the AR performance. The AR results were compared and analyzed, and the performance of the RTK positioning was assessed based on the static true solution. Several hours of GPS data, collected by the State of Israel permanently tracking network, were processed. The analyses show that about 90s latency may exist while the instantaneous ambiguities could still be resolved correctly. The numerical tests presented in this study show the centimetre-level positioning results for mobile receiver. KEYWORDS: Ionospheric correction. Long-baseline. Kinematic GPS. Positioning. Further information: 7. Geodetic Monitoring of a Landslide USING Conventional
surveys and GPS techniques Many landslides occurred along Amman-Jerash-Irbid Highway in Jordan during its construction in 1991 and 1992. Geological and geotechnical studies were curried out at that time to analyse the problem. This work presents geodetic monitoring of a major landslide on the highway, 6 km to the north of Amman. The importance of this study comes from the need to protect and guarantee the continuity of a major, active highway, which connects the north of the Kingdom to its capital Amman and passes through an unstable and landslide-prone area. For monitoring the landslides in this area we designed a geodetic network, which consists of fifty-six points. Measurements were carried out over a two years period (2002-2004), and GPS receivers and total stations of high precision were used. The measurements were performed annually at two different times, before and after the rainy season. The observations adjustment and the deformation analysis were executed using locally developed computer programs. The study enabled us to determine a value of 0.5 m/year as an average movement of the landslide-prone area. KEYWORDS: Geodetic monitoring. Landslide. Conventional surveys. GPS. Further information:
Vol. 39, No. 304. April 2007 1. The Snake projection: a customised grid for rail projects. Surveying on large engineering projects such as railway routes presents particular problems in terms of the coordinate system to be used, since they generally extend beyond the limit of an acceptable site grid. This paper presents a method for tailoring a projection in such a way that the scale factor is always close to unity within a few kilometres of a very long but gently sinuous construction project. It also corrects for height scale factor, and the result is that engineers using automated techniques can effectively ignore scale factor and height above sea level corrections when working on the project. This is now used by Network Rail contractors on the East Coast and West Coast main lines, where the scale factor on the track has been kept within ± 20 ppm of unity along a route of several hundred kilometres. The software has been developed to be applied to any railway project, but also has potential to be used on projects of similar geometry, such as major pipeline routes. KEYWORDS: Railways. Construction. Projection. Scale Factor. Coordinates. Further information:
Resultant approach is here employed to optimize the dimensionless space angles to solve in a closed form the over-determined three-dimensional intersection problem. The advantages of the resultant optimization approach are the non-requirement of the approximate initial starting values, non iterative and does not rely on linearization during its operation, save for the nonlinear variance-covariance/error propagation to generate the weight matrix. Resultant method, a branch of abstract algebra, is employed to compute the combinatorial scatters, which are then optimized to offer a closed form solution. Using the test network Stuttgart Central as an example, it is demonstrated that the resultant optimization approach can be applied as an alternative approach to conventional methods such as least squares for point positioning within the over-determined intersection framework, especially when the approximate starting values for linearization and iterative approaches are not known as may happen in Photogrammetry, Machine Vision or in Robotics.
Further information:
The Mw 9.3 mega-thrust earthquake on December 26th, 2004 off the coast of North Sumatra, Indonesia has resulted in large co- and post-seismic motions throughout SE Asia. As a result, the geodetic network of Thailand has been deformed. The THAICA network has been regularly observed with GPS since 1994. Therefore the continuous tectonic motions in Thailand, which is located on the Sundaland block are well known. The last GPS campaign prior to the mega-thrust earthquake took place in October 2004 as part of the EU-ASEAN funded SEAMERGES project. Shortly after the earthquake, the GPS campaigns were repeated in January 2005 and February 2005 to determine the displacements. The GPS data in Thailand were processed, using the Precise Point Positioning strategy of the GIPSY software package. Data from the International GPS Service (IGS) were included, to obtain the positions and velocities of the Thai GPS sites in the International Terrestrial Reference Frame (ITRF) solution of 2000. Since the coordinate time series of the Thai geodetic network spanning up to a decade are available, the absolute steady-state velocities prior to the earthquake are known with uncertainties below 1 mm/yr. Results obtained from the latest campaign indicated that the earthquake has resulted in the horizontal displacements, ranging from 33 cm in the south, 9 cm in the centre, to about 3 cm in the north and east of Thailand. In addition, it was found that the post-seismic motion due to the earthquake has increased further the displacement at the PHUK station. KEYWORDS: Earthquake. Deformation measurement. Thailand. Horizontal displacements. Further information:
Many studies, involving Earth's science, made by geodesists and geometers revealed the great importance of the two remarkably influential geodetic curves, which are known as geodesic and loxodrome. The most recent observations assembled from artificial satellites paid a great attention to the ellipticity of the Earth’s equator. The biaxial ellipsoidal model was always manipulated as a simulate representation in favour of the triaxial model of the earth. Because the triaxial ellipsoidal surface has a changing curvature along the curve of constant latitude, the mathematical manipulation becomes complex and the computations are labour intensive. Also because the conformal map is flat or spherical in any sense, the formulae of spherical or plane trigonometry are applied. Unfortunately, the mathematics in the development of a geodesic on the ellipsoid and its image on the map are fairly complex, requiring advanced mathematics. Constructive geometry of the earth's surface has for a long time been devoted to the spherical model. The present paper offers the geometric model by which the constructive transformation of some ellipsoidal curves can be facilitated. The conformal transformation from/onto the ellipsoid and a spherical surface is utilized to set up the equations of the loxodrome on the ellipsoidal surface and the inverse of the geodesic curve from the ellipsoid to the conformal sphere. The procedure is illustrated and its merits are introduced by means of some practical geodetic problems. KEYWORDS: Conformal Projection. Triaxial Ellipsoid. Conformal Sphere. Geodesic. Loxodrome. Further information:
Repeated gravity measurements in the tectonically active Mygdonian basin, close to Thessaloniki - North Greece, showed gravity changes ranging from 420 to 810 nm s?2, within a period of 20 years. These gravity changes, which were interpreted as local vertical crustal movements, using the free-air relation, correspond to changes from -26 to 13 cm. The rate of the gravity (and correspondingly height) change is higher in the rebound period, after the 1978 seismic sequence near Thessaloniki. The rate of the vertical changes estimated from the gravimetric observations was compared with corresponding rate estimated from GPS measurements. Conclusions were drawn, concerning the fault system of the region. KEYWORDS: Crustal movement. Gravity. GPS. Earthquake. Thessaloniki. Further information:
Two new cylindrical map projections of the reference ellipsoid have been developed. The first cylindrical map projection possesses the property of preserving the areas of ellipsoidal surfaces. In other words, it is an “equal area cylindrical map projection of the reference ellipsoid”. The origin of this map projection system can be placed at any point on the surface of the reference ellipsoid and as such the map projection could be ideal for localized applications, where minimum distortion is required. This map projection is recommended for implementation in Land Information Systems and/or cadastres, where the area of the land has to be preserved on the mapping surface. The second cylindrical map projection is conformal but, like the first map projection has the property that its origin can be placed at the point of interest. This property, which is common in both map projection systems, makes it possible that the centre of the map projection system be placed at the middle of geographical area of interest to minimize the distortion at that specific area. Besides, since the map projections have been developed for the reference ellipsoid it is possible to directly transfer the GPS coordinates into the mapping surface, which adds to the practical applications of the two map projections systems. KEYWORDS: Cylindrical Projection. Equal Area Projection. Conformal Projection. Reference Ellipsoid. Land Information System. Cadastre. Further information: 7. The virtual reference station concept in Finland –
a case study The quality and performance of the Virtual Reference Station (VRS)
concept was studied in conditions that are typical of northern latitudes
and Finland. The practical study consists of two major parts. The
objective of the first part was to find the accuracy and initialization
times and how they are affected by different factors. The factors
that were studied are the baseline length, rover position within
the network, number of satellites, satellite geometry, influence
of obstructions and temporal variation of accuracy during the fixed
solution. KEYWORDS: Virtual Reference Station. RTK. North Finland. Accuracy. Initialisation Times. Further information: 8. Accuracy analysis of relative positions of permanent
GPS stations in the Marmara region, Turkey The accuracy of GPS (Global Positioning System) derived relative positions of stations depends on several factors. Besides the baseline length and duration of observation session, the methodology and the software used influence the results. In this paper, the observations made in the Marmara Continuous GPS Network (MAGNET) have been analysed to determine how the accuracy of derived relative positions of GPS stations depends on the baseline length and the duration of the observing session. Seven days of GPS observations in the MAGNET collected in 2002 were processed in the ITRF 2000 reference frame using Bernese 4.2 software. The baseline length varies between 6 km and 340 km, the session duration varies between 4h and 24h. The independent baseline components have been analysed. KEYWORDS: Relative Positions. GPS Stations. Turkey. Tectonic Zone. Baselines. Further information: 9. A Performance Evaluation on the Internet Based Static
GPS Computation Services In conventional relative GPS surveying, users must use at least
two sets of GPS receivers, as well as the associated processing
software packages. This is not only a hardware or software constraint,
but also a logistical problem. Furthermore, in many instances the
data processing steps may be more difficult for users with limited
experience in GPS technology. These problems can be resolved with
an Internet GPS Service, whereby the user can finish all of the
processes with only one GPS receiver without the need to use a base-station
or to buy and maintain any data processing software. KEYWORDS: Static GPS. Internet service. Errors. Computational services. Systems comparisons Further information:
Vol.39, No. 303. January 2007 1. The impact of Land market processes on the poor in rural
Vietnam This paper examines the link between formal land tenure and poverty
alleviation in the context of rural Vietnam. It assesses the relevance
of the ideas of Hernando de Soto through the documentation of both
formal and informal land market processes in order to identify efficiencies. Further information: 2. Determination of North-East Asia’s highest peak
(Mt Jade) by direct levelling. Further information: 3. A simulation of the effect of GPS pseudolite observations
on the obstructed sky view GPS has been being used in positioning and navigation for decades. However, there are still many unsolved problems existing, for instance the degradation of positioning precision when the view of sky is obstructed. Pseudolite, a ground-based GPS satellite-like signal transmitter, can provide extra measurements in order to improve the positioning precision of GPS system alone in the obstructed areas. In this study, pseudolite data were collected to tackle the obstruction of GPS satellite signals, and to evaluate the effectiveness of the GPS pseudolite. The results of this study demonstrated that the pseudolite observations improved the dilution of precision (DOP) by more than 35% and positioning precision by 40%, and with the addition of extra measurements it made 1cm positioning possible even in the obstructed areas. Further information:
4. Performance analysis of the real time kinematic GPS
(RTK GPS) technique in a highway project (stake-out). RTK GPS has seen great technological advances over the past few
years and is now routinely used in a wide variety of engineering
type applications. RTK GPS provides centimetre level position in
seconds, allowing workers to get the precision. One GPS receiver
is placed in a control point (named the reference station) with
known coordinates. RTK system combine GPS information and data radio
communication with advanced algorithms to calculate precise position
of the projects, such as highway and bridge, GIS project. Further information: 5. The use of GPSSIT (GPS virtual station technique) with
total station for the measurement of details in residential areas GPS become one of the most important tools used in several surveying
missions during last one and half decade. It is confidently and
intensively used in several surveying tasks from establishment of
precise geodetic control networks to the measurement of features
and details on land. To fulfill those tasks, there are several techniques
that GPS suggests and are available to be used according to the
required precision and the requirements of special applications.
Under this concept, these GPS techniques can be stated as static,
kinematic, semi-kinematic and on the other hand, with respect to
the special precision requirements of different applications, they
can also be stated as relative, absolute and DGPS techniques. Even
if GPS ease the surveying processes for these applications when
we use GPS, GPS can some times put forward some limitations. Therefore,
it can be said here that GPS has still some difficulties and limitations
especially when GPS signals are blocked by some obstacles such as
buildings in urban areas. Therefore, one can experience with those
cases frequently during the detail measurements in an urban area.
Tall buildings, trees and etc in an urban environment can be the
main constraints that can cause those GPS signal blockages. Here
in this paper, it is argued if a technique is available and allows
us to use GPS even for measuring those urban details without worrying
about GPS signal blockages. Further information: 6. Total least squares solution of coordinate transformation Coordinate transformation is one of the most commonly used processes in geodesy and surveying. Coordinates of points in one coordinate system are to be obtained in another coordinate system. To this end, the transformation parameters between two individual coordinate systems are calculated from the identical points, coordinates of which are known in both systems. This is achieved by the least-squares (LS) estimation. LS estimation is the classical approach in adjustment computations. It consists of a functional model that depicts the functional relation between the unknowns and the observations, and a stochastic model that represents the relative accuracies between the observations. In some cases, such as coordinate transformation, errors occur both in the observation vector and the design matrix. In classical approach, this is usually ignored and this ignorance remains as an uncertainty in the solution results. One way to take these errors in design matrix into account is to use Total Least Squares (TLS) estimation, which is quite new not only in surveying but also in mathematical sciences. By using TLS, one can take both the observations and all or a part of the design matrix as stochastic components. Therefore, more realistic values for the unknown parameters can be estimated. In this study, TLS technique was used to estimate the transformation parameters between two coordinate systems. The results are compared to the classical LS solution. TLS is able to handle the uncertainty and the results are more realistic than the classical approach. Further information: 7. Precise determination of the Clairaut constant in ellipsoidal
geodesy The Clairaut constant, the cosine of the maximum latitude of the geodesic, is used in a number of applications in ellipsoidal geodesy. This study provides formulas to precisely determine the Clairaut constant from the coordinates of two given points on the geodesic. Further information:
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