Geodesy and Geomatics Engineering Technical Reports
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Development of the automatic data management and the analysis of integrated deformation measurements

The monitoring of deformations and the analysis of deformation measurements have recently evolved to the limit that technology can provide. Traditionally, geotechnical measurements have been perform and analysed separately from geodetic surveys (angles, distances, and high differences). It is now possible to deal with them together in an integrated analysis, largely due to the University of New Brunswick (UNB) Generalized Method for the analysis of deformation measurements. Current microcomputer technology allows for the collection and onsite analysis of measurements. The automation, or computer control, of data collection, processing, and analysis has decided advantages over manual methods, particularly concerning data integrity and the handling of large volumes of repeated measurements.
A system, “DAMADA”, for the management of data for deformation analysis, from the time of sensing to the depiction of the deformation, was developed to facilitate the implementation of integrated analyses using the UNB Generalized Method. In doing so, it makes the collection, processing and analysis of both geotechnical and geodetic data as automated as would be practical.
DAMADA has been successfully applied at a hydroelectric power generating station. The experiences of that application have led to several conclusions. The testing and calibration of instrumentation can improve the reliability and fidelity of the data, especially over long term repeated use in monitoring. DAMADA automatically accounts for routine testing and calibration as an integral part of the observation regimen. Three dimensional coordination of all observation points, geotechnical as well as geodetic, can facilitate the trend analysis, modelling, and depiction of the deformation of a structure. DAMADA can run on a modest microcomputer (80287) under DOS and is limited only by the storage capacity of the computer’s hard drive. Although it currently considers horizontal and vertical geodetic observations separately, DAMADA is flexible enough that it could accommodate the simultaneous three dimensional monitoring of a structure.


Diagramatic approach to solve leastsquares adjustment and collocation problems

The standard method of obtaining the solution to the leastsquares adjustment problems lacks objectivity and can not readily be interpreted geometrically. Thus far, one approach has been made to interpret the adjustment solution geometrically, using Hilbert space technique.
This thesis is still another effort in this respect; it illustrates the important advantage of considering the parallelism between the concept of a metric tensor and a covariance matrix. By splitting the linear mathematical models in the leastsquares adjustment (parametric, conditional and combined models) into dual covariant and contravariant spaces, this method produces diagrams for the leastsquares adjustment and collocation, from which the necessary equations may be obtained.
Theories and equations from functional analysis and tensor calculus, necessary for the analysis of this approach, are described. Also the standard method used in the leastsquares adjustment and the leastsquares collocation are reviewed. In addition, the geometrical interpretation of a singular weight matrix is presented.


Differential Global Positioning System navigation

This thesis examines and evaluates some geometrical aspects of a method called "differential navigation", which is used as a means of real time calibration for a navigation system. Particularly, the evaluation and analysis is applied to a new satellitebased radionavigation system, known as NAVSTARGPS (NAVigation Satellite Timing And Ranging systemGlobal Positioning System).
The NAVSTARGPS, being developed by the United States Department of Defense, is scheduled to be fully operational by the end of the decade and is capable of providing realtime continuous positions accurate to 10 meters. Field test results using some of the current prototype GPS satellites have manifested these capabilities.
These early results and other studies led the United States, for national security reasons, to intentionally curtail the GPS capabilities to the general public and provide accuracies of the order of 200 meters.
The need for better accuracies required by a large class of "unauthorized users" prompted us to extend the conventional performance capability of the GPS to the differential one. Differential GPS navigation provides an opportunity to thousands of unauthorized users, unable to gain the full benefit of the GPS system, to effectively make use of the system under intentionally degraded conditions and retrieve the original signals.
Under certain assumptions and through a simulation computer program, this study evaluated and demonstrated the validity and feasibility of the above concept, with main emphasis on the investigation of various geometrical aspects related to the differential operation. Inferences correspond only to marine applications (two dimensional) of the GPS 18satellite constellation considering hypothetical intentional degradations.
Recommendations for the continuation of this research are also given.


Differential distortions in photogrammetric block adjustment

The selfcalibrating photogrammetric bundleblock ad adjustment program UNBASC2 is revised. Its design matrices rederived to account for the additional parameters being a function of the radial distance of image points. The revision improved the adjusted image coordinates by up to two micrometers. Similar revisions were made to the program GEBAT.
With improved mathematical modelling, further differential increase in the precision of photogrammetric densification may be achieved by improving the weighting scheme. Ignoring correlation in the weight matrices of observations and known parameters can lead to differential distortions.
Weights for observed image coordinates and for known coordinates of ground control points are examined. It is shown that in the presence of additional parameters, image weights transformed from the observation space to the model space will always be correlated. A test adjustment shoes the maximum correlation to be 2.5%, resulting in changes to the adjusted coordinates of not more than 0.5 micrometers. A similar improvement is obtained with the proper weighting of the ground control points in UNBASC2.
Although many bundle adjustment programs can treat ground control points as stochastic, they are not designed to accept their full covariance matric event though there can be very high correlations. Evidence of highly correlated covariance matrices of the adjusted coordinates from weighted station adjustments of control networks are presented. It is shown that similar high correlation patterns can also occur in photogrammetric densification adjustments.
The implications of the high correlation on geodetic densification are illustrated by the global ripple effects and the importance of relative precision. Alternative apriori covariance matrices are proposed. Although these are not suitable for rigorous statistical assessment, they produce coordinates with acceptable distortions.
When a matrix inverse is involved, the effects of a distortion on the least squares solution may not be readily apparent. Therefore, the method of differential distortion analysis is developed to clarify the effects of each distorting variable.


Displacement monitoring by integrating online photogrammetric observations with dynamic information

Data collection and – processing in photogrammetric monitoring are thoroughly investigated.
The determination of displacements by photogrammetry requires multiple photographic campaigns and therefore photomeasurements on multitemporal photographs. An online semiautomatic photogrammetric system for targeted and natural object points using the analytical stereoplotter has been developed. In the case of targeted points, the analytical plotter has been utilized as an online monocomparator with the measuring mark driven automatically to predetermined photolocations. For natural points an integrated “crossidentification” and measuring procedure has been designed and implemented. The combination of comparator/stereoplotter mode allows the pointtransfer operation to be done “digitally”. In both cases image positioning is performed under computer control, and online editing capabilities are provided.
A combined sequential photogrammetric approach was developed for data processing. The dynamic characteristics of the object position vectors are introduced in both the functional and stochastic models. This, the single epoch static photogrammetric model has been extended to incorporate the additional object information where the object parameter vector is updated not only as new observations become available but also as a function of time.
Examples with real and simulated data are given which demonstrate the usefulness of the newly developed methodologies. That is, a) the time required for the photomeasurements is significantly reduced while their accuracy is improved, and b) the integration of photogrammetric and dynamic information provides better estimation or the location and accuracy of the unknown parameters.


Doppler satellite control

The application of the Transit Doppler satellite system to geodetic positioning, is investigated, using the operational ephemeris for satellite coordinates, and navigationtype receivers to track the satellites. A set of test data from eight stations in Atlantic Canada is analyzed. Four a priori decisions were to use the shortest possible integration interval (4.6 seconds); to use the technique of translocation to reduce the effect of ephemeris and refraction errors to allow the satellite trajectory to relax parallel to itself during the adjustment; and to process the data completely automatically.
Transit mathematical models are related to the basic principles of electromagnetic metrology. The assumptions involved in Transit mathematical models are analyzed in detail.
The least squares approximation, least squares spectral analysis and least squares estimation algorithms used here are related to the basic principles of Hilbert space optimization.
The accuracy of the operational ephemeris is investigated by comparing it to the NWI, precise ephemeris; by comparison between stale and fresh ephemerides during injection passes; and Guier plane navigation. The operational ephemeris errors are found to be well represented by biases in the along track, radial, and cross track directions which have standard deviations (from pass to pass) of 26, 5 and 10 m respectively.
The shape of the operational ephemeris is investigated by a comparison between Transit and Keplerian orbit elements; time series analysis of Transit variable orbit parameters; and least squares approximation of the Transit variable orbit parameters. The shape of each of the variable orbit parameters ∆E, ∆a, ɳ is well approximated by the base functions ɸ = {1, cos2nt, sin2nt, t} where n is the satellite mean motion and t is time.
The measurement variances of three models of Transi navigation receiver are found to be 1.5, 4.0 and 10.0 counts [subscript 2] respectively for the ITT 5001, Marconi 722 and Magnavox 702.
The internal consistency of multipass point positioning station coordinates is found to be 1.3 m. However this is found to be optimistic, since the orbit was held fixed for these computations. The internal consistency of adjusted network coordinates is less than one metre, but again this is found to be optimistic.
The index of external consistency (rms value of ∆/σ [subscript ∆]) between independent point positioning solutions at one station are found to be 2.4 to 4.0 for point positioning when the orbit is fixed and 1.2 to 1.5 when the orbit is relaxed. The external consistency between two sets of point positioning solutions using data one year apart is 4.7, attributed principally to uncorrected pole motion effects. The external consistency between an adjusted Transit network and a terrestrial network is 1.6.


Dynamic monitoring with video systems

While close range photogrammetry has been widely applied for static deformation analysis, video cameras have many characteristics that make them the senors of choice for dynamic analysis of rapidly changing situations. The also have limitations.
This study explores the potential of a video system for monitoring dynamic objects. The system consists of two camcorders, VCR and PC with frame grabber. To analyze the characteristics of the camcorders, the preliminary tests were conducted with still and moving targets. Then, to estimate the performance of this system for vibrations, a car was imaged covering several phases when starting to drive. The sequential images of a moving car were recorded on VCR. 15 images per seconds were digitized in an offline mode by frame grabber. The image coordinates of targets attached to the rear bumper of a car were acquired by IDRISI, and the object coordinates were derived based on DLT.
This study suggests that home video cameras, PC, and photogrammetric principles are promising tools for monitoring of moving objects and vibrations as well as other time dependent situations.


Early results towards the Canadian geoid in the threespace scenario

The three space StokesHelmert scheme of the precise gravimetric geoid determination has been theoretically developed and numerically realized in UNB. A transformation of observed values of terrestrial gravity in Real space, from No topography space into Helmert space on geoid surface, is accomplished by a series of gravity reductions and corrections. Helmert cogeoid can be decomposed into two parts: the lowfrequency part, called reference cogeoid is determined from satellite data directly; the highfrequency part, called residual cogeoid is determined by the solution of geodetic boundary value problem using derived terrestrial gravity. The cogeoid is transformed to the geoid by correcting from the primary indirect effects.
The final Canadian geoid has been compared with GPS/Leveling data. Difference due to the long wavelength part of the differences is obvious and other systematic errors, such as the bias and vertical deflection between the geometric geoid model and gravimetric geoid model, definitely exist.


Enhanced Gaussian background modelling algorithm and implementation in FPGA for realtime moving object detection in surveillance video

A realtime solution of moving object detection (MOD) in surveillance video was explored in this work motivated by the practical need of realtime automated video analysis system. The core element of a moving object detection process is its background modeling algorithm in the content of surveillance and road monitoring applications. By reviewing and analyzing previous works, single Gaussian (SG) background modeling algorithm was selected and enhanced. Then a circuit that performs MOD with enhanced SG algorithm was designed and implemented in a Virtex6 FPGA of a ML605 evaluation board with other hardware components. The experiment results showed that the proposed MOD system could perform realtime MOD in a video of 1280×720p@30fps. It outperforms the software experiments/implementations and the stateofart FPGAbased implementations.


Error distribution and accuracy measure in navigation

The present report contains a description of some statistical terms associate with the accuracy of a position fix in navigation. It summarizes the principal results of a series of statistical studies related to error distributions and accuracy measure in navigation.
The material breaks up into four main parts. The first part provides an introduction to the problems associated with the need for statistical data analysis in navigation. The second section is devoted to error distributions. The distributions considered include the Normal, the Exponential, the twoparameter Gamma, the Double Exponential, the Compound and Composite distributions, the Rayleigh etc. Sections 2.1 to 2.9 introduce a few definitions of probability density functions, while the last section presents the application of these distributions to navigational problems. The third part bring in an exposition of the various accuracy measures which characterize uncertainty in navigation. These measures include the ellipsoids, the ellipses, the radial errors and some of the onedimensional accuracy measure. Finally, the report concludes with some suggestions for the future.
The purpose of this presentation is to collect, under one cover, most of the essential aspects of the available literature devoted to error distributions and accuracy measures in navigation.


Establishment and maintenance of a new geospatial frame for TanzaniaTZRF10

Tanzania like most of the African countries has an old and conventional Geodetic Network. This network was established and computed by the Directorate of Overseas Surveys (DOS) of Great Britain in the 1950’s. The present network is based on the 30th arcmeridian of the Clarke 1880 modified ellipsoid with its origin at BuffelsfonteinCape Town in the Republic of South Africa. The present network does not satisfy the overgrowing mapping requirements of the country as well as other Georelated information requirements. They include homogeneous cross border mapping activities (most of the international boundaries have not been physically defined), smooth land regularization projects in new urban areas, production and update of large scale topographical maps in urban areas and homogenous spatial mapping as well as the studies of crustal dynamics as related to plate tectonics and natural hazards associated with seismic or volcanic activities.
The Survey and Mapping Division of Tanzania (SMD) has realized the values of high precision and geocentric dynamic spatial frame in facilitating the geodetic positioning (coordinates and velocities in the geocentric coordinate system), navigation and general purpose spatial referencing to date as the most versatile, accurate and economical way of addressing the above issues. In view of those values and strong capabilities of modern dynamic geodetic frames, Tanzania has been collaborating with other African countries to establish a unified African Geodetic Reference Frame (AFREF). However, lack of appropriate expertise, proper awareness of the concept amongst most of the national mapping organizations and differences in economic levels in the African countries have always been the limiting factors.
In view those limitations, the primary objective of this thesis is to provide the basis for the establishment and maintenance of a 3dimensional dynamic reference frame for Tanzania in the ITRF system with optimum accuracy requirement in an economic way. The new frame will be compatible to satellite position techniques and would consider the advancement in the communication technology and the increased capacity of the internet applications real time geodetic applications that has been illustrated by Weber [2002] and Weber et al. [2003].
To achieve the research objectives a conceptual plan to realize a new spatial framework in Tanzania (TZRF10) has been developed, using the leastsquares covariance analysis technique as a tool to evaluate for its geometrical consistency. A case study on reference frame maintenance using the BerneseV5.0 scientific software; has been developed and evaluated for its performance based on NAD83 (CSRS) data from the Geodetic Survey Division of Natural Resources of Canada NRCan.
The present advancement in communication technologies and increased capacity of internet–based real time geodetic applications has been illustrated through implementation of a case study and evaluated for its performance using a developed matlab software code.


Estimation of gravity tilt response to atmospheric phenomena at the Fredericton tiltmetric station using a least squares response method

Variations in apparent direction of gravity, with respect to the tiliting bedrock, at the Fredericton tilitmetric station have been observed, although somewhat intermittently, since 1974. Gaps in these observations account for over half of their overall time span. These tilt observations contain, among others, variations due to atmospheric pressure and surface temperature induced tilts. This work is concerned with modelling the response of the observed tilt, both for purposes of noise reduction and for understanding the phenomena themselves, to the atmospheric pressure and surface temperature variations, which are also observed at this station.
As a preliminary evaluation of the collected tilt data, tidal analyses were performed for the purpose of estimating M[subscript 2] diminishing factors and testing ocean loading models which were supplied by Beaumont [1980]. This analysis also provided a means for testing the general performance of the Fredericton station and revealed a backlash effect of the recording apparatus on the recorded tilt.
Being confronted with the problem of estimating the response of an observed phenomenon to other observed phenomena, for the case of gappy and noise data, directed this research estimation method capable of handling such data. An evaluation of the existing techniques of cross spectral analysis and time domain convolution (see Appendix III) shows that these techniques are inadequate for our purposes. This least squares response method, developed in Chapter 4, has its basis in least squares spectral analysis [Vanicek, 1971] which is reviewed also in Chapter 4. A statistical test of significance of peaks in the least squares spectrum was also derived during this work.
Application of the least squares response method to the Fredericton station data is discussed and summarized in Chapter 5. The results of this analysis indicates that more study is required in interpreting the response estimates in physical terms. However, apparently valid results for tilt response to surface temperature and atmospheric pressure are generated by the least squares response method from the very noisy data of the Fredericton station. In particular it is shown that atmospheric pressure induced tilts have magnitudes in excess of tidal tilts. Recommendations regarding future work at the Fredericton station are made.
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