Geodetic Science Reports (School of Earth Sciences)

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    Reliability in Constrained Gauss-Markov Models: An Analytical and Differential Approach with Applications in Photogrammetry
    (Ohio State University. Division of Geodetic Science, 2005-02) Cothren, Jackson D.
    Reliability analysis explains the contribution of each observation in an estimation model to the overall redundancy of the model, taking into account the geometry of the network as well as the precision of the observations themselves. It is principally used to design networks resistant to outliers in the observations by making the outliers more detectible using standard statistical tests.It has been studied extensively, and principally, in Gauss- Markov models. We show how the same analysis may be extended to various constrained Gauss-Markov models and present preliminary work for its use in unconstrained Gauss-Helmert models. In particular, we analyze the prominent reliability matrix of the constrained model to separate the contribution of the constraints to the redundancy of the observations from the observations themselves. In addition, we make extensive use of matrix differential calculus to find the Jacobian of the reliability matrix with respect to the parameters that define the network through both the original design and constraint matrices. The resulting Jacobian matrix reveals the sensitivity of reliability matrix elements highlighting weak areas in the network where changes in observations may result in unreliable observations. We apply the analytical framework to photogrammetric networks in which exterior orientation parameters are directly observed by GPS/INS systems. Tie-point observations provide some redundancy and even a few collinear tie-point and tie-point distance constraints improve the reliability of these direct observations by as much as 33%. Using the same theory we compare networks in which tie-points are observed on multiple images (n-fold points) and tie-points are observed in photo pairs only (two-fold points). Apparently, the use of two-fold tiepoints does not significantly degrade the reliability of the direct exterior observation observations. Coplanarity constraints added to the common two-fold points do not add significantly to the reliability of the direct exterior orientation observations. The differential calculus results may also be used to provide a new measure of redundancy number stability in networks. We show that a typical photogrammetric network with n-fold tie-points was less stable with respect to at least some tie-point movement than an equivalent network with n-fold tie-points decomposed into many two-fold tie-points.
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    Local Geoid Determination from GRACE Mission
    (Ohio State University. Division of Geodetic Science, 2002-02) Garcia, Ramon V., 1966-
    An analysis is made about the feasibility of using in-situ GRACE measurements for local gravity field determination as an alternative to global solution methods, which yield solutions in terms of spherical harmonic coefficients. The method investigated is based on integral inversion aided with regularization techniques. The observables considered are potential differences (DT) and gravity disturbance differences (DGD). Both observables are affected by position, velocity and acceleration errors. With respect to position errors, the higher precision requirement is in relative position for DT, which requires about 1 cm of absolute positional accuracy to produce 0.01 m2/s2 error. For velocities, the higher precision requirement is in relative velocity for both DT and DGD. The observable DT required the higher precision 10−5 mgal in relative acceleration. The disturbing potential T at the Earth’s surface, assumed to be a sphere, can be obtained from values of DT and DGD given at satellite’s altitude. The process turns out to be ill-posed mainly due to gravity field attenuation at the operative altitude of the GRACE mission (300-500 km). Data error requirements are very demanding for downward continuation of both DT and DGD. The Tikhonov regularization method was applied for the following configuration: a grid of 0°.8 sampling interval for a 24° square area at 400 km altitude. Measurement errors smaller than 1x10−5 m2/s2 in DT are required to achieve solution errors of the level of 1 m2/s2 and with a relative error of about 10%. However, this increased to only 3 m2/s2 with 0.01 m2/s2 measurement error. It is found that model errors due to discrete and finite sampling cause large mean solution errors. The principal inversion methods employed were the Tikhonov, singular value decomposition, the conjugate gradient and the 1-D fast Fourier transform (FFT) method. Their performance was compared using simulations by employing three test areas with the same configuration described above, but different geographical location. The regularization methods were applied for both DT and DGD observables Overall, the Tikhonov method performed better than the other methods. For the above configuration, T was obtained with about 2.5 m2/s2 precision neglecting the mean error. In the search of the best regularization parameter (α ), the L-curve method, which can be applied to the Tikhonov, DSVD and the 1D-FFT, combined with Tikhonov, methods, was analyzed and yielded good results when considering only random errors in the iii measurements. However, when considering model errors, the method did not produce satisfactory results. A geometry adaptive method was formulated to find the best α . The method consists of determining a k factor that relates the residual norm related to the corner of the L-curve with the residual related to the best α . Finally, the Tikhonov regularization combined with B-spline smoothing was applied. The method yielded smaller solution errors using the above configuration. The solution errors obtained were about 1.2 and 1.1 m2/s2 for 1°.2 resolution using DT and DGD, respectively. The corresponding relative error was about 10%. This could potentially produce about 10 cm geoid for about 150 km resolution. All simulations were made using the geopotential model EGM96.
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    Geometric Constraints in Image Sequence and Neural Networks for Object Recognition
    (Ohio State University. Division of Geodetic Science, 1997-09) Li, Ron; Wang, Weian; Tseng, Hong-Zeng
    Spatially referenced mobile mapping image sequences contain rich information for applications such as transportation and utility management. Automatic object recognition and measurement from the images for reducing human operations and enhancing efficiency is a challenge in mobile mapping data processing. This report describes the research results of the project “Geometric Constrains in Image Sequences and Neural Networks for Object Recognition” supported by CFM/NASA (November 1996 – December 1997). Hopfield neural networks are applied to develop an algorithm for utility object recognition and photogrammetric measurements. Specifically, street light poles are modeled in the 3-D object space and compared with the corresponding features in the image sequences. The neurons of the net are formed by vector edge features from the model and images. The established Hopfield model is able to recognize light poles from a single image. It can also recognize and locate all light poles from the image sequences. It first recognizes all light pole features in the images. Secondly, corresponding light poles in stereo images are identified. Finally, the photogrammetric triangulation supplies 3-D positions of the poles in the object space. Such automation is particularly important for building special layers, for example traffic signs, fire hydrants, and road centerlines, to build GIS databases. The method developed has been successfully tested using mobile mapping image sequences. The major contributions of this research are · Establishment of a Hopfield neural network for object recognition from mobile mapping image sequences using 3-D object models and 2-D image features, · Application of the developed model to recognize and locate a specific light pole from a single image and from an image sequence, and to build a 3-D light pole database of all light poles, · Understanding of the behavior of individual parameters of the neural network and their impact on the recognition results, and · Development of the N2M2 system.
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    Satellite Geophysical Investigation of the Moon
    (Ohio State University. Division of Geodetic Science, 2000-12) Potts, Laramie V., 1961-
    Lunar mass variations for the region ± 64° latitude related to composition, structure, isostatic and tectonic development of the crust, mantle, and core were developed using gravity and topography from Lunar Prospector, Clementine, and earlier satellite observations. Computed terrain gravity effects were spectrally correlated with the free-air anomalies to differentiate the terrain-correlated and -decorrelated free-air components. Annihilating terrain gravity effects, obtained by subtracting the terrain-correlated anomalies from the terrain gravity effects, were used to estimate the lunar Moho and crustal thicknesses by least squares inversion assuming compensation by crustal thickness variations. Inversion of the terrain-correlated anomalies obtained a radial adjustment model of the Moho that equilibrates the lunar topography. Terrain-decorrelated anomalies were differentiated into crustal and subcrustal components based on their correlation spectrum with the free-air anomalies. Inversion ofthe terrain-decorrelated crustal maxima over central basins predicted mare fill thicknesses up to a few kilometers. Inversion of the subcrustal components inferred boundary undulations for the core-mantle, asthenosphere-lithosphere, and middle-upper mantle during bombardment time. Nearly all major nearside basins exhibit mascon gravity anomalies reflecting mass concentrations from superisostatic mantle plugs plus mare fill, while farside basins mostly involve maslite gravity anomalies from mass deficiencies due to subisostatic mantle plugs with marginal or no mare fill. The preponderance of farside maslites suggests a weaker nearside lithosphere due to higher thermal gradients from enhanced abundances of radioactive elements in the nearside mantle and crust than the farside. Comparing crustal thicknesses with transient cavity diameters suggests a critical crustal thickness of about 30 km presumably differentiated the development of superisostatic and subisostatic mantle plugs on the farside. Inferred subcrustal boundary undulations tend to support mantle convection on the nearside involving diapiric rise of magma, whereas viscous entrainment on the farside inhibited basalt flooding of basins. The elevated core-mantle boundary beneath the Procellarum-lmbrium basins is consistent with uplifting effects of the Imbrium impact involved with the "Great Lunar Hotspot". Comparison of the gravity and topography spectra of the terrestrial planets suggests the Moon has the lowest temperature gradient and hydrostatic equilibrium.
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    INS, GPS, and Photogrammetry Integration for Vector Gravimetry Estimation
    (Ohio State University. Division of Geodetic Science, 1998) Dwaik, Fathi Y., 1964-
    Vector gravimetry using Inertial Navigation System (INS) in semi-kinematic mode has been successfully applied. The integration of INS with other sensors, Global Positioning System (GPS) or Gradiometer, for instance, has been under investigation for many years. This dissertation examines the effect of photogrammetric derived orientation on the INS sensor’s calibration and estimation of the gravity vector. The capability of such integration in estimating the INS biases and drifts is studied. The underlying principle, mathematical models, and error sources are presented and analyzed. The estimation process utilizes the measurements of the Litton LN-100 inertial system, Trimble 4000 SSI GPS dual frequency receiver, and metric frame camera. An optimal filtering technique is used to integrate both GPS and INS on the level of raw measurement for both systems. Introducing accurate and independent orientation parameters, e.g., the photogrammetric source in this study, is demonstrated to enable calibration of inertial gyros and bounding of their drift errors. This leads to improvement in the horizontal components of the gravity vector estimation. The estimability and improvement of the deflection of the vertical components are tested using flight test data over Oakland, California, and a set of photogrammetric images simulated along the flight trajectory. The error statistics of the orientation measurement are modeled on the basis of the variance-covariance matrix of a photogrammetric bundle adjustment of all photos. With just a few ground control points at the beginning of the trajectory, the orientation measurement errors along the trajectory are correlated significantly from epoch to epoch, thus reducing the information content of the external orientation estimates. The horizontal gravity component estimation is tested with respect to its sensitivity to the variance of the orientation measurement errors, to its auto-correlation in time, to the cross-correlation between angles, and to the amount of available ground control. Although photogrammetric measurements, if uncorrelated, control orientation errors as well as better than achievable with aircraft maneuvers, the inherent correlation with a very limited amount of ground control provides only a small improvement. On the basis of the simulation parameters, the gravity estimation error was reduced from 20 mgal (GPS/INS only) to about 9 mgal (best uncorrelated control) versus 17 mgal (correlated control).
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    GRACE Time-Variable Gravity Field Recovery Using an Improved Energy Balance Formalism
    (Ohio State University. Division of Geodetic Science, 2015-08) Shang, Kun
    Earth’s gravity is continuously varying with respect to time due primarily to mass transports within the Earth system and external gravitational forcing. A new formalism based on energy conservation principle for time-variable gravity field recovery using satellite gravimetry has been developed and yields more accurate estimation of in-situ geopotential difference observables using K-Band Ranging (KBR) measurements from the Gravity Recovery and Climate Experiment (GRACE) twin-satellite mission. The new approach can preserve more time-variable gravity information sensed by KBR range-rate measurements and reduce orbit error as compared to previous energy balance studies. Results based on analysis of more than 10 years of GRACE data indicate that the estimated geopotential differences agree well with the predicted values from official Level 2 solutions: with much higher correlation of 0.9, as compared to 0.5–0.8 reported by previous energy balance studies. This study demonstrates that the new approach is more flexible for both global and regional temporal gravity recovery, leading to the first independent GRACE monthly solution series based on energy conservation principle, which is comparable to the results from different approach. The developed formalism is applicable to the general case of low-low satellite-to-satellite radiometric or laser interferometric tracking measurements, such as GRACE Follow-on or other Next Generation Gravity Field missions, for efficient retrieval and studies of Earth’s mass transport evolutions. The regional gravity analysis over Greenland reveals that a substantially higher temporal resolution is achievable at 10 or 11-day interval from GRACE data, as compared to the official monthly solutions, but without the compromise of spatial resolution, nor the need to use regularization or post-processing. Studies of the terrestrial and ground water storage change over North China Plain show high correlation in sub-monthly scale, among the 11-day time-variable gravity solutions from this study, in-situ data, and hydrologic and atmospheric models. The 11-day solutions with 1-day step successfully capture the surface mass change caused by the rapid snow and ice accumulation and melting during the extreme weather event of 2008 Southeast China snow and ice storm. These results demonstrated that sub-monthly solutions from GRACE can provide an additional constraint to understand the rapid mass transport and the dynamic processes for both extreme weather events and short-time surface and ground water monitoring, which may potentially improve our understanding of various mass transports within the Earth system, and applicable to societal services such as disaster response or mitigation, and water resources management.
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    Source Parameters Inversion for Recent Large Undersea Earthquakes from GRACE Data
    (Ohio State University. Division of Geodetic Science, 2015-08) Dai, Chunli
    The north component of gravity and gravity gradient changes from the Gravity Recovery And Climate Experiment (GRACE) are used to study the coseismic gravity change for five earthquakes over the last decade: the 2004 Sumatra-Andaman earthquake, the 2007 Bengkulu earthquake, the 2010 Maule, Chile earthquake, the 2011 Tohoku earthquake, and the 2012 Indian Ocean earthquakes. We demonstrate the advantage of these north components to reduce north-south stripes and preserve higher spatial resolution signal in GRACE Level 2 (L2) monthly Stokes Coefficients data products. By using the high spherical harmonic degree (up to degree 96) data products and the innovative GRACE data processing approach developed in this study, the retrieved gravity change is up to – 34±1.4 μGal for the 2004 Sumatra and 2005 Nias earthquakes, which is by far the highest coseismic signal retrieved among published studies. Our study reveals the detectability of earthquakes as small as Mw 8.5 (i.e., the 2007 Bengkulu earthquake) from GRACE data. The localized spectral analysis is applied as an efficient method to determine the practical spherical harmonic truncation degree leading to acceptable signal-to-noise ratio, and to evaluate the noise level for each component of gravity and gravity gradient change of the seismic deformations. By establishing the linear algorithm of gravity and gravity gradient change with respect to the double-couple moment tensor, the point source parameters are estimated through the least squares adjustment combined with the simulated annealing algorithm. The GRACE-inverted source parameters generally agree well with the slip models estimated using other data sets, including seismic, GPS, or combined data. For the 2004 Sumatra- Andaman and 2005 Nias earthquakes, GRACE data produce a shallower centroid depth (9.1 km) compared to the depth (28.3 km) from GPS data, which may be explained by the closer-to-trench centroid location and by the aseismic slip over the shallow region. For the 2011 Tohoku earthquake, the inversions from two different GRACE data products and two different forward modeling produce similar source characteristics, with the centroid location southwest of and the slip azimuth 10° larger than the GPS/seismic solutions. The GRACE-estimated dip angles are larger than that from GPS/seismic data for the 2004 Sumatra-Andaman and 2005 Nias earthquakes, the 2010 Maule, Chile earthquake, and the 2007 Bengkulu earthquake. These differences potentially show the additional offshore constraint from GRACE data, compared to GPS/seismic data. With more accurate and higher spatial resolution measurements anticipated from the GRACE Follow-on mission, with a scheduled launch date in 2017, we anticipate the data will be sensitive to even smaller earthquake signals. Therefore, GRACE type observations will hopefully become a more viable measurement to further constrain earthquake focal mechanisms.
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    Heights, the Geopotential, and Vertical Datums
    (Ohio State University. Division of Geodetic Science, 2000-11) Jekeli, Christopher
    This report reviews the fundamental definitions of heights and vertical datums, specifically motivated by the modern technique of determining heights using accurate satellite vertical positioning in combination with an accurate model for the geopotential. It is shown that the determination of heights in such a manner requires knowledge of the potential value of the vertical datum (as opposed to leveling procedures that do not require this). Furthermore, to determine the potential of a vertical datum ideally requires normal heights (defined at the origin point of the datum, or determined elsewhere by leveling) rather than orthometric heights, as this avoids the complication of assuming a density model for the crust. The models associated with these procedures are also developed within the context of the temporally varying field of the tidal potential, which leads to a more fundamental distinction between a vertical datum (local geoid) and the global geoid. That is, the global geoid, by definition, has always the same potential value but its surface varies (varying geoid undulation); while the vertical datum has an origin changing only because of crustal deformation and the potential varies due to the direct and indirect tidal effects. The models thus developed also form the basis for monitoring the stability of vertical datums under the influence of geodynamic vertical crustal deformations, such as caused by post-glacial rebound. This has obvious implications in the monitoring of lake levels that are tied to a particular vertical datum. Preliminary models and procedures are indicated.
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    Applications of Parameter Estimation and Hypothesis Testing to GPS Network Adjustments
    (Ohio State University. Division of Geodetic Science, 2002-12) Snow, Kyle Brian
    It is common in geodetic and surveying network adjustments to treat the rank deficient normal equations in a way that produces zero variances for the so–called "control" points. This is often done by placing constraints on a minimum number of the unknown parameters, typically by assigning a zero variance to the a priori values of these parameters (coordinates). This approach may require the geodetic engineer or analyst to make an arbitrary decision about which parameters to constrain, which may have undesirable effects, such as parameter error ellipses that grow with distance from the constrained point. Constraining parameters to a priori values is only one way of overcoming the rank deficiency inherent in geodetic and surveying networks. There are more preferable ways, which this thesis presents, namely Minimum Norm Least–Squares Solution (MINOLESS) and Best Linear Minimum Partial Bias Estimation (BLIMPBE). MINOLESS not only minimizes the weighted norm of the observation error vector but also minimizes the norm of the parameter vector, while BLIMPBE minimizes the bias for a subset of the parameters. In this thesis, these techniques are applied to a geodetic network that serves as a datum access for GPS–buoy work in Lake Michigan. The GPS–buoy has been used extensively in recent years by NOAA, The Ohio State University (OSU), and other organizations to determine lake and ocean surface heights for marine navigation and scientific studies. The work presented in this paper includes 1) parameter estimation using (Weighted) MINOLESS and hypothesis testing for the purpose of determining if recent observations are consistent with published coordinates at an earlier epoch; 2) a discussion of the BLIMPBE estimation technique for three new points to be used as GPS–buoy fiducial stations and a comparison of this technique to the "Adjustment with Stochastic Constraints" method; 3) usage of standardized reliability numbers for correlated observations; 4) a proposal for outlier detection and minimum outlier computation at the GPS–baseline level. The work may also be used as an example to follow for establishing new fiducial points with respect to a geodetic reference frame using observed GPS baseline vectors. The results of this work lead to the following conclusions: 1) MINOLESS is the parameter estimation techniques of choice when it is required that changes to all a priori coordinates be minimized while performing a minimally constrained adjustment; 2) BLIMPBE appears to be an attractive alternative for selecting subsets of the parameter vector to adjust. BLIMPBE solutions using various selection–matrix types are worthy of further investigation; 3) outlier detection at the GPS–baseline level permits the entire observed baseline to be evaluated at once, rather than making decisions regarding the ii hypothesis at the baseline–component level. It is shown that the two approaches can yield different results.
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    Linear Features in Photogrammetry
    (Ohio State University. Division of Geodetic Science, 2000-01) Habib, Ayman; Asmamaw, Andinet; Kelley, Devin; May, Manja
    This research addresses the task of including points as well as linear features in photogrammetric applications. Straight lines in object space can be utilized to perform aerial triangulation. Irregular linear features (natural lines) in object space can be utilized to perform single photo resection and automatic relative orientation. When working with primitives, it is important to develop appropriate representations in image and object space. These representations must accommodate for the perspective projection relating the two spaces. There are various options for representing linear features in the above applications. These options have been explored, and an optimal representation has been chosen. An aerial triangulation technique that utilizes points and straight lines for frame and linear array scanners has been implemented. For this task, the MSAT (Multi Sensor Aerial Triangulation) software, developed at the Ohio State University, has been extended to handle straight lines. The MSAT software accommodates for frame and linear array scanners. In this research, natural lines were utilized to perform single photo resection and automatic relative orientation. In single photo resection, the problem is approached with no knowledge of the correspondence of natural lines between image space and object space. In automatic relative orientation, the problem is approached without knowledge of conjugate linear features in the overlap of the stereopair. The matching problem and the appropriate parameters are determined by use of the modified generalized Hough transform. These techniques were tested using simulated and real data sets for frame imagery.
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    Airborne Vector Gravimetry Using GPS/INS
    (Ohio State University. Division of Geodetic Science, 2000-04) Kwon, Jay Hyoun, 1967-
    Compared to the conventional ground measurement of gravity, airborne gravimetry is relatively efficient and cost-effective. Especially, the combination of GPS and INS is known to show very good performances in the range of medium frequencies (1-100 km) for recovering the gravity signal. Conventionally, gravity estimation using GPS/INS was analyzed through the estimation of INS system errors using GPS position and velocity updates. In this case, the complex navigation equations must be integrated to obtain the INS position, and the gravity field must be stochastically modeled as a part of the state vector. The vertical component of the gravity vector is not estimable in this case because of the instability of the vertical channel in the solution of the inertial navigation equations. In this study, a new algorithm using acceleration updates instead of position/velocity updates has been developed. Because we are seeking the gravitational field, that is, accelerations, the new approach is conceptually simpler and more straightforward. In addition, it is computationally less expensive since the navigation equations do not have to be integrated. It is more objective, since the gravity disturbance field does not have to be explicitly modeled as state parameters. An application to real test flight data as well as an intensive simulation study has been performed to test the validity of the new algorithm. The results from the real flight data show very good accuracy in determining the down component, with accuracy better than ±5 mGal. Also, a comparable result was obtained for the horizontal components with accuracy of ±6 to ±8 mGal. The resolution of the final result is about 10 km due to the attenuation with altitude. The inclusion of a parametric gravity model into the new algorithm is also investigated for theoretical reasons. The gravity estimates from this filter showed strong dependencies on the model and required extensive computation with no improvement over the approach without parametric gravity model.
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    Geophysical Investigations on Gravity Gradiometry and Magnetic Data over the Wichita Uplift Region, Southwestern Oklahoma
    (Ohio State University. Division of Geodetic Science, 2015-04) Erkan, Kamil
    The Wichita uplift in southwestern Oklahoma is a unique region that shows strong gravity and magnetic field anomalies. Detailed geologic data as well as structural cross sections are also available for the region. This report includes a qualitative geophysical analysis of the airborne gravity gradiometer profiles, and a quantitative analysis of an airborne magnetic field data collected in the region. Two datasets were analyzed independently. Firstly, an effort has been made by comparative analyses of different gravity gradient components with the gravity field from EGM2008 side by side in order to understand the nature of the subsurface structural setting. Secondly, a spectral analysis of magnetic field has been applied using the well-known power-law behavior of the magnetic field. The resulting source intensity map delineates the areas with high magnetic sources, and also is in agreement with the geologic findings in the region.
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    Gravity Recovery Using COSMIC GPS Data: Application of Orbital Perturbation Theory
    (Ohio State University. Division of Geodetic Science, 1998-10) Hwang, Cheinway
    COSMIC is a joint Taiwan-US mission to study atmosphere using GPS occultation. Its GPS data for precise orbit determination can be used for gravity recovery. In this report a kinematic approach was employed which assumes the positional data can be derived from the GPS data of COSMIC in the operational phase. Using the geometric relationship between the positional variations of orbit and the variations in the six Keplerian elements, improved formulae for the radial, along-track and cross-track perturbations were derived. Based on a comparison with true perturbations from numerical integrations, these formulae are more accurate than the commonly used order-zero formulae. The improved formulae were used to simulate gravity recovery using the COSMIC data. In one simulation with the OSU91A model to degree 50 as the a priori geopotential model, it is demonstrated that the EGM96 model can be improved up to degree 26 using one year of COSMIC data. A significant effort was devoted to the recovery of temporal gravity variation using COSMIC data. Sea level anomaly (SLA) was first generated using the Cycle 196 TOPEX/POSEIDON altimeter data. The steric anomaly due to thermal expansion was created using temperature data at 14 oceanic layers. The steric anomaly-corrected SLA was used to generate harmonic coefficients of temporal gravity variation. With a 3-cm noise at a one-minute sampling interval in the COSMIC data, the gravity variation cannot be perfectly reproduced, but the recovered field clearly shows the gravity signature due to mass movement in an El Niño. With a 0.1-cm noise, the temporal gravity variation up to harmonic degree 10 is almost exactly recovered and this prompts the need of a better processing technique and a sophisticated GPS receiver technology.
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    Static and Kinematic Absolute GPS Positioning and Satellite Clock Error Estimation
    (Ohio State University. Division of Geodetic Science, 2000-04) Han, Shin-Chan, 1975-
    This study presents the results of investigations to determine accurate position coordinates using the Global Positioning System in the absolute (point) positioning mode. The most common method to obtain accurate positions with GPS is to apply doubledifferencing procedures whereby GPS satellite signals are differenced at a station and these differences are again differenced with analogous differences at other stations. The differencing between satellites eliminates the receiver clock errors, while the betweenstation differences eliminate the satellite clock errors (as well as other errors, such as orbit error). However, only coordinate differences can be determined in this way and the accuracy depends on the baseline length between cooperating stations. The strategy with accurate point positioning is to estimate GPS satellite clock errors independently, thus obviating the between-station differencing. The clock error estimates are then used in an application of a single-difference (between-satellite) positioning algorithm at any site to determine the coordinates without reference to any other site. Using IGS (International GPS Service) orbits and station coordinates, the GPS clock errors were estimated at 30- second intervals and these estimates were compared to values determined by JPL (Zumberge et al., 1998). The agreement was at the level of about 0.1 nsec (3 cm). The absolute positioning technique was tested in an application of a single-differenced (between-satellite) positioning algorithm in static and kinematic modes. For the static case, an IGS station was selected and the coordinates were estimated. The estimated absolute position coordinates and the published values had a mean difference of up to 18 cm with standard deviation less than 2 cm. For the kinematic case, data (every second) obtained from a GPS buoy were tested and the result from the absolute positioning was compared to a DGPS solution. The mean difference between the two algorithms is less than 40 cm and the standard deviation is less than 23 cm. It was proved that a higher rate (less than 30 sec.) of satellite clock determination and a good tropospheric delay model are required to do absolute kinematic positioning to better than 10 cm accuracy.
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    Static Calibration of Tactical Grade Inertial Measurement Units
    (Ohio State University. Division of Geodetic Science, 2010-09) Hayal, Adem G.
    The demand for precise positioning grows up parallel to the advances in production of the geolocation instruments. Today, the Global Positioning System (GPS) is the most common positioning system in use because of its being very precise, convenient and cheap. However, when working in such areas that the external references (e.g. GPS satellites) are not available, a system that does not require information from any external source of information is required. Especially, these kinds of systems necessitate in detection of unexploded ordnances (UXO) buried in forestry areas, where precise position information is vital for removing them. The Inertial Navigation System (INS) operates in any environment and does not depended on any external source of information. It can operate alone or as an integrated system with GPS. However, the Inertial Measurement Unit (IMU) sensor outputs include some errors which can cause very large positioning errors. These errors can significantly be reduced by using calibration methods. The most accurate calibration methods are performed in laboratories and they require very precise instruments. However, the most significant IMU errors, biases and scale factor errors, change from turn on to turn on of the IMU and therefore they need to be estimated before every mission. The Multi-Position Calibration Method developed by Shin (2002) is a good example which is cost efficient and it can be applied in the field without use of any external calibration instrument. The method requires numerous IMU attitude measurements and use the gravity magnitude and Earth rotation rate as reference for calibration. The performance of the Multi-Position Calibration Method was tested by using a cart based geolocation system which includes 2 tactical grade IMUs, Honeywell HG1700 and HG1900. The calibration test was conducted in a parking lot of Ohio State University on 06 June 2010. The calibration estimations have shown that the navigation accuracy could be improved by up to 19.8% for the HG1700 and 17.8% for the HG1900. However, the results were not consistent among each other and in some cases decrease in the positioning accuracy was yielded.
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    Direct Sensor Orientation in Airborne and Land-based Mapping Applications
    (Ohio State University. Division of Geodetic Science, 2001-06) Grejner-Brzezinska, Dorota A.
    Since the early 1990s, the concept of Mobile Mapping Systems (MMS) has evolved from rather simple land-based systems to more sophisticated, real-time multi-tasking and multi-sensor systems, operational in land and airborne environments. Mobile Mapping technology has made a remarkable progress, notably expanding its use in remote sensing, and surveying and mapping markets. New systems are being developed and built for specialized applications, in support of land-based and airborne imaging sensors, aimed at automatic data acquisition for GIS databases. The major objective of this report is to review the concept of Mobile Mapping System and GPS/INS supported direct platform orientation (DPO) in particular, as well as their evolution since early 1990s, with a special emphasis on the research and development carried out in this area at the Ohio State University. A short review of the inertial navigation concept is given, and a notion of GPS/INS (inertial navigation system) integration is also presented. The concept of direct georeferencing is also explained and compared to the traditional aerotriangulation (AT) method of image geo-registration, and the importance of multi-sensor system calibration is discussed, including its impact on the positioning accuracy. Some examples of currently attainable navigation performance, based on the OSU-developed Airborne Integrated Mapping System (AIMS) and the land-based system for highway mapping are discussed, and future perspectives of MMS are presented. Although MMS may be, in general, associated with land-based applications, the concept of airborne mapping (remote sensing) based on DPO is also discussed here, primarily due to the fact that airborne positioning and orientation systems based on GPS/INS integration are based on similar hardware and software designs, and clearly evolved from the traditional airborne mapping as a consequence of the advent of a high-accuracy GPS/INS systems. Thus, the DPO facilitated through GPS/INS fusion is a common denominator for the modern land-based and airborne mapping, which often times involves multiple imaging sensors to achieve higher accuracy, and data complementarity and redundancy.
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    Object Recognition from AIMS Data Using Neural Networks
    (Ohio State University. Division of Geodetic Science, 1998-12) Li, Ron; Ma, Fei; Tu, Zhuowen
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    Coastal Altimetry and Applications
    (Ohio State University. Division of Geodetic Science, 1999-01) Anzenhofer, Michael; Shum, C. K.; Rentsh, Mathias
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    Spline Representations of Functions on a Sphere for Geopotential Modeling
    (Ohio State University. Division of Geodetic Science, 2005-03) Jekeli, Christopher
    Three types of spherical splines are presented as developed in the recent literature on constructive approximation, with a particular view towards global (and local) geopotential modeling. These are the tensor-product splines formed from polynomial and trigonometric B-splines, the spherical splines constructed from radial basis functions, and the spherical splines based on homogeneous Bernstein-Bézier (BB) polynomials. The spline representation, in general, may be considered as a suitable alternative to the usual spherical harmonic model, where the essential benefit is the local support of the spline basis functions, as opposed to the global support of the spherical harmonics. Within this group of splines each has distinguishing characteristics that affect their utility for modeling the Earth’s gravitational field. Tensor-product splines are most straightforwardly constructed, but require data on a grid of latitude and longitude coordinate lines. The radial-basis splines resemble the collocation solution in physical geodesy and are most easily extended to three-dimensional space according to potential theory. The BB polynomial splines apply more generally to any sphere-like surface (e.g., the geoid or the Earth’s surface) and have a strong theoretical legacy in the field of spline approximations. This report provides a review of these three types of splines, their application to the geodetic boundary-value problem, and formal expressions for determining the model coefficients using data with observational errors.