Geodesy and Geomatics Engineering Technical Reports

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Canada’s unresolved Maritime boundaries
Canada’s unresolved Maritime boundaries
The resolution of offshores boundary disputes must first be attained before managed development of the offshore region under dispute may begin. Presently, Canada shares maritime boundaries with Denmark, France and the United States. An examination of these offshore boundaries shoes that only the maritime boundary between Denmark and Canada and the boundary off the Juan de Fuca Strait between Canada and the United States offer an area of little or no conflict. The other unresolved boundaries are disputed as the states concerned hold different position regarding the delimitation of the offshore boundary lines. A negotiation or adjudicated settlement to these boundaries must consider the history, the existing legal precedents for offshore boundary determination, the customary law involved and each state’s interests, however varied they may be. It is only after careful consideration of these facts that an equitable boundary solution will be found. Without drawing conclusions on what the final boundary will be in each instance, this paper presents an analysis on each of Canada’s unresolved boundaries. In addition to presenting the historical background on each boundary and arguments for certain boundary delimitation, the urgency attached to finding a boundary agreement is reviewed and a comparison attempted with the recent Gulf of Maine decision. Overall, the paper incorporates past and present events to give a detailed analysis of the situation regarding Canada’s unresolved offshore boundaries.
Carrier-Phase multipath mitigation in RTK-based GNSS dual-antenna systems
Carrier-Phase multipath mitigation in RTK-based GNSS dual-antenna systems
Carrier-phase multipath mitigation in GPS/GNSS real-time kinematic (RTK) mode has been studied for several years, at least since on-the-fly ambiguity resolution techniques were introduced, and receiver hardware improvements to the point that GNSS RTKbased systems provide position estimates at the mm to cm-level accuracy in real-time. This level of accuracy has heralded a new era of applications where the use of GNSS RTK-based techniques have become a very practical navigation tool, especially in the fields of machine automation, industrial metrology, control, and robotics. However, this incredible surge in accuracy tied with real-time capabilities comes with a cost: one must also ensure continuity, and integrity (safety). Typical users of these systems do not expect heavy machinery, guided and/or controlled by GNSS-based systems, to output erroneous solutions even in challenging multipath environments. In multipath-rich scenarios, phase-multipath reflections can seriously degrade the RTK solutions, and in worst scenarios, integer fixed solutions are no longer available. This dissertation intends to deal with these scenarios, where the rover algorithms should deal with multiple reflections and, in real-time, be able to ameliorate/mitigate their effect. GNSS-based heading/attitude is usually obtained combining the data from two or more antennas (also known as a moving baseline). Many companies provide commercial systems based on this technique, hence this dissertation finds its main applicability here. Typical heavy construction machinery includes dozers, motor-graders, excavators, scrappers, etc., which are being equipped more frequently with GNSS dual-antenna systems to provide positioning and orientation information to the operator. We have not used and collected data from one of these machines, although the author has worked extensively with such machinery and their GNSS-based systems. However, the theory developed throughout this dissertation and the proof of concept through controlled tests that mimic the machinery/installed GNSS dual-antenna systems, are the basis of this dissertation. Moreover the algorithms developed here are meant to be used independently from the receiver hardware, as well as from GNSS signals. Hence GLONASS, and/or Galileo signals can be processed too. This dissertation is based on the fundamental relationship between multiple multipath reflections from close-by strong reflections, and their effect on GNSS RTK-based dual-antenna systems. Two questions were answered: Firstly, is it possible to retrieve strong multipath reflectors in kinematic applications? Second, once these strong reflectors are correctly identified, how accurate/reliable are the corrections to the raw carrier-phase multipath, knowing that the host platform performs unpredictable manoeuvres? Based on the results, we can conclude that it is possible to estimate in real-time multipath parameters based on a strong effective reflector. In most of the tests it takes at least 2 minutes to obtain initial values (after Kalman filter convergence). Once they are determined, multipath corrections can be determined straightforwardly for each satellite being tracked, as long as there are no cycle-slips (mostly due to the combination of the machinery high dynamics, especially within the areas where antennas are located, and the machinery itself blocking momentarily satellite signals).
Claiming a juridical continental shelf under Article 76 of the United Nations convention on law of the sea (UNCLOS)
Claiming a juridical continental shelf under Article 76 of the United Nations convention on law of the sea (UNCLOS)
The United Nations Convention on Law of the Sea (UNCLOS) divides the sea floors into zones, one of which, the (juridical) Continental Shelf, only comes into existence if it is claimed by a Coastal State. Article 76 of UNCLOS defines the Continental Shelf in a complex and possible contradictory manner, one that seemingly requires a great deal of data and scientific analysis. UNCLOS establishes the Commission on the Limits of the Continental Shelf (CLCS) to who claim are to be submitted for comment. The CLCS has issued Guidelines detailing the types and format of evidence they will consider. This thesis analyses Article 76 and the Guidelines and creates a model of a process that can be followed by a Coastal State to prepare a Continental Shelf claim that will meet both requirements.
Combination of geodetic networks
Combination of geodetic networks
The rigorous combination of terrestrial satellite geodetic networks is not easily accomplished. There are many factors to be considered. The more important are how to deal with terrestrial networks that are separated into horizontal and vertical components which are not usually coincident; the relation of each component to a different datum; and the existence of unmodeled systematic errors in terrestrial observables. Satellite networks are inherently three-dimensional and are relatively free of systematic errors. In view of these facts, and with present practical considerations in mind, fourteen alternate mathematical models for the combination of terrestrial and satellite geodetic networks are investigated, catalogued and categorized in this report. To understand the reasoning behind the formulation of the models presented and the interpretation of the results obtained, some basic definitions and properties of datums, and satellite and terrestrial networks are presented. Based on previous investigation and the authors interpretation of the problem of combining geodetic networks, the models under study are split into two major groups. The first group treats datum transformation parameters as known. While the second includes them as unknowns to be estimated in the combination procedure. Each model is investigated in terms of its dimensionality, unknown parameters to be estimated, observables, and the estimation procedure utilized. The group of three-dimensional models that treat the datum transformation parameters as unknowns to be estimated are themselves separated into two parts. The Bursa, Molodensky, and Veis models contain only one set of the rotation parameters each, while the Hotline, Krakisky-Thomson, and Vanicek-Wells models each contain two sets of unknown rotations. For the combination of terrestrial and satellite networks, the latter three models represent physical reality. The models that are not three-dimensional do not take advantage of the inherent tri-dimensionality of satellite networks. Thus, when the satellite network data is split into horizontal and vertical components for combination with terrestrial data, the covariance between the components is omitted. Even though the use of two and one-dimensional combination models are required at present due to the sparseness of adequate terrestrial data and the need for the solution of practical problems, it is not recommended for the future. The Bursa model is recommended for the combination of two or more satellite networks. However, when combining terrestrial and satellite networks, when datum transformation parameters are unknown, none of the Bursa, Molodensky, or Vies models are adequate. In this case, the Hotline or Krakiwsky-Thomson model which parametrize the lower order systematic errors in the terrestrial network, should be used. The combination of the Krakiwsky-Thomson and Vanicek –Wells models is seen to be the best, from a theoretical point of view, for the combination of a satellite and several terrestrial networks. Such a solution will yield the datum transformation parameters between each of the datums involved, the orientation of each datum with respect to the Average Terrestrial coordinate system, and parameters representing the overall systematic orientation and scale errors of each terrestrial network. No substantiative conclusions could be given based on the numerical testing carried out. A sparseness of adequate data prevented this. The numerical testing has not been wasted, however. The type and quality of data required for several models has been demonstrated. Further, the available data was utilized to substantiate the fact that the proposed solution of the Krakiwsky-Thomson model is possible.
Complex crustal strain approximation
Complex crustal strain approximation
The analysis of repeated geodetic observations has become an important tool for the investigation of the kinematics of tectonic plate boundary zones. The most appropriate analytical method for such investigations of contemporary crustal deformation is the strain analysis, a method of differential geometry. In attempting to find an elegant mathematical formulation to describe plane strain, the use of complex analysis proves to be very advantageous. The analytical modeling of spatially and temporally continuous and discontinuous displacement fields is developed using least-squares approximation of generalized polynomials. Algebraic polynomials are proposed for the continuous approximation, whereas specifically designed step functions are used to model the discontinuities in space and time. A mathematical model of simultaneous network adjustment and strain approximation is elaborated. It yields a general analytical method which enables strain-rates, or accumulated strain and fault-slip, to be determined from various types of geodetic measurements. In contrast to the widely used observation method (Frank’s method), this approach does not rely on repeated observations of the same observables. Repeatedly observed networks of non-identical design can be analyzed. The constraints incorporated by the approximation model allow strain estimation even when the network of some observation epochs suffer from formulation or configuration defects with respect to positions. Experiments with various graphical representations of strain are carried out. Strain pedal-curves and shear-rosettes expressing extension and shear in a given direction, plotted at equally spaced grid points, provide a comprehensive display of non-homogenous strain-fields in space. Confidence regions associated with extension and shear in a given direction are plotted together with these strain figures. A software package ‘CRUSTRAIN’ is developed for the simultaneous adjustment and strain approximation and for the display of the estimated strain parameters. The method is first tested with synthetic data and then with a real kinematic network. The method is applied to the 1970-80 Hollister network, which had been observed by the U.S. Geological Survey. This applications reveals the strength as well as the limitations of the proposed technique. An approximation model is evaluated which incorporates third-degree complex algebraic polynomials with three episodic terms in time. This approximation estimates co-seismic fault-slip and strain release associated with three moderate earthquakes which occurred in the Hollister area within the time interval in question.
Computational and geometrical aspects of on-the-fly ambiguity resolution
Computational and geometrical aspects of on-the-fly ambiguity resolution
Precise (centimetre level accuracy) kinematic differential positioning using GPS (Global Positioning System) requires the use of carrier phase observations with correctly resolved integer ambiguities. On-the-fly ambiguity resolution, i.e., ambiguity resolution while the receiver is in motion, is desirable, since it increases the flexibility and reliability of kinematic positioning. On-the-fly ambiguity resolution, however, is not an easy task. A lot of factors can be categorized into three broader groups, namely the ambiguity resolution technique, the effects of the observation errors and biases, and the observation geometry, i.e.., the geometry between the satellites, the monitor station(s), and the user. In this research, the possibility of performing reliable and fast on-the-fly ambiguity resolution of GPS carrier phase signals is studied. An integrated on-the-fly ambiguity resolution technique was developed for this research. This technique was designed to work with either single-frequency, codeless, or dual-frequency GPS data from a minimum of five observed satellites, and it accommodates the use of more than one monitor station. The validity of the technique has been verified using static, simulated kinematic, and kinematic GPS data. The technique has been shown to be capable of resolving initial integer ambiguities on-the-fly reliable and quickly, even instantaneously under certain conditions. Geometrical and computational aspects of on-the-fly ambiguity resolution have also been studied in this research, particularly related to their effects on the performance of on-the-fly ambiguity resolution. The geometrical aspects studied involve the following geometrical parameters: the wavelength of the signal, selection of primary satellites, number of satellites, observation differencing strategy, location of satellites available, data rate, number of secondary monitor stations, and location of secondary monitor stations. The computational aspects studied involve the ambiguity searching space construction and the process of identifying the correct ambiguities.
Computational methods for the discrete downward continuation of the earth gravity and effects of lateral topographical mass density variation on gravity and the geoid
Computational methods for the discrete downward continuation of the earth gravity and effects of lateral topographical mass density variation on gravity and the geoid
In this thesis, computational methods for the discrete Poisson downward continuation of the Earth gravity are studied. In addition, the effect of the lateral topographical mass density variation on gravity and the geoid is systematically investigated. A solution in the spherical harmonic form for the Poisson integral equation is derived. It is pointed out that the solution of the discrete inverse Poisson problem exists, but may not be unique and stable. For a small input error, a larger error is introduced. It is in this sense that the inverse Poisson problem is said to be an ill-posed problem. It is found that the modified spheroidal Poisson kernel reduces the ‘real’ far-zone contribution with respect to using the spheroidal Poisson kernel significantly, but it cannot perform better than the standard Poisson kernel in reducing it. A fast algorithm is developed for the evaluation of the far-zone contribution. Heiskanen and Moritz’s (1967) radius condition gives a critical radius of the near-zone cap that is too small for the determination of the em-geoid, while Martinee’s (1996) condition gives an unnecessarily large radius. It is proposed that the critical near-zone radius be determine as a function of the accuracy of the global geopotential model from which the far-zone contribution is evaluated. The combined iterative method is proposed to speed up the convergence of the solution of the discrete inverse Poisson problem. The truncated singular value decomposition method is introduced to solve the discrete Poisson integral equation that may be ill-conditioned for a small discrete step. The three discrete models for the Poisson integral, namely the point-point, point-mean and mean-mean models are assessed against synthetic data. It is shown that the mean-mean model can produce a sufficiently accurate solution when the so called ‘averaging error’ is properly corrected for. A block-wise technique is developed to solve the discrete Poisson integral equation efficiently with a compressed storage technique for the coefficient matrix. The package DOWN97 is developed to evaluate the discrete Poisson downward continuation. The analytical downward continuation is compared to the Poisson one by using synthetic data and Helmert gravity anomalies. It is shown that the analytical downward continuation agrees with the discrete Poisson’s within 10% of the total downward continuation effect. A fast algorithm is developed to evaluate the analytical downward continuation with its implementation in software. A ultra-high degree synthetic global geopotential model conforming to the Kaula-type degree variance models is too smooth to simulate the Helmert gravity anomalies, especially in mountainous regions. An approach for evaluating the effect of the lateral topographical mass density variation on gravity and the geoid is proposed. Formulae for evaluating the standard deviation of the primary indirect topographical mass density effect (PIDE), the direct topographical mass density effect (DDE) and the secondary topographical mass density effect (SIDE) are derived. The effect of the lateral topographical mass density variation on the geoid height ranges from -7.0cm to 2.8 cm by using a 30” X 30” DTM (Digital Topographic Model). The software for evaluating the PIDE, DDE and SIDE is described.
Conceptual framework modelling and analysing periurban land problems in southern Africa
Conceptual framework modelling and analysing periurban land problems in southern Africa
Customary periurban environments in southern Africa are facing many challenges, as can be seen in most countries in the region especially Botswana, Malawi and South Africa. The periurban land problems have continued to exist despite many land tenure and land administration attempts aimed at resolving the customary periurban land problems. There is a need to better understand customary periurban land problems in order to design improved intervention strategies to meet effectively the land tenure and land administration requirements in southern Africa. This research developed a soft systems-based analytical framework to guide the analysis, modelling, and design of land tenure and land administration options as well as the implementation to meet land tenure and land administration requirements in periurban areas of southern Africa. A problem highlighted in the study of periurban land problems is the lack of understanding of the real issues, and the belief expressed in the literature that the periurban land problems can be resolved by merely replacing customary tenure with a western-based statutory tenure system. The primary objective of this research is to help clarify and deepen understanding of periurban land problems often exacerbated by the misconceptions surrounding customary tenure. This was achieved by developing a non-prescriptive and intuitive soft systems-based analytical framework for analysing, identifying and designing strategies for meeting the land tenure and land administration requirements for periurban areas in southern Africa. The major conclusion is that a soft systems approach that incorporates different worldviews, goals, norms, cultures and interests of local communities, can structure thinking about the periurban land problems. The soft systems-based conceptual framework is developed by integrating concepts and theories from anthropology, cadastral studies/geomatics engineering, urban land economics and planning, and soft systems engineering. The conceptual framework analyses the periurban land problems in three major phases: the institutional/cultural systems analysis phase, the operational systems analysis phase and the monitoring and control systems phase. Conceptual models are then developed from the issues identified in the institutional/cultural analysis phase. The comparisons of conceptual models with the real world situations stimulate debate about why the differences exist, and leads to the identification and evaluation of desirable and feasible strategies for meeting land tenure and land administration requirements in periurban environments. The soft systems-based conceptual framework is tested by applying it to the periurban situation of Botswana in southern Africa. Comparisons are also made with periurban environments of Malawi and South Africa.

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