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  • Author or Editor: R. Kiamehr x
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A new geoid model for Iran (IRG04) was computed based on the least squares modification of the Stokes formula. IRG04 was derived from the most recent gravity anomaly database, SRTM high resolution Digital Elevation Model (DEM) and GRACE GGM02 global geopotential model. In order to define a new height datum for Iran, we attempted to combine this high resolution gravimetric geoid model with GPS/levelling data using the corrective surface approach. The corrective surface was constructed from 224 GPS/levelling points and then evaluated with 35 independent points. Different interpolation techniques were tested for the creation of the corrective surface; among them the Kriging method was selected as it gave the smallest RMS and ‘noise level’ at the comparisons with GPS/levelling data. The RMS fit of the new combined geoid model versus the independent GPS/levelling data is 0.09 m, it is near four times better compared to the original gravimetric geoid model. The combined model should be more convenient and useful in definition of the new height reference surface, specifically in engineering and GPS/levelling projects.

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In this article, we propose a technique for the precise cleaning of the gravity anomaly database based on the cross validation approach. The terrestrial gravity anomalies were compared versus a global geopotential model and take into account the effect of topography in this comparison. The efficiency of the cross-validation technique is illustrated in outlier detection as well as in choosing the proper gridding technique as a case study in construction of the Iranian new gravity database. In order to reduce the effect of topography and the discretisation error, a special interpolation scheme is used for gridding of the free-air gravity anomalies. The final grid file was created based on the Kriging method with 80″ × 90″ block resolution. The overall accuracy for the new Iranian gravity database is estimated in the order of 10 mGal.

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There are different criteria for designing a geodetic network in an optimal way. An optimum network can be regarded as a network having high precision, reliability and low cost. Accordingly, corresponding to these criteria different single-objective models can be defined. Each one can be subjected to two other criteria as constraints. Sometimes the constraints can be contradictory so that some of the constraints are violated. In this contribution, these models are mathematically reviewed. It is numerically shown how to prepare these mathematical models for optimization process through a simulated network. We found that the reliability model yields small position changes between those obtained using precision respectively. Elimination of some observations may happen using precision and cost model while the reliability model tries to save number of observations. In our numerical studies, no contradictions can be seen in reliability model and this model seems to be more suitable for designing of the geodetic and deformation networks.

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The modification of Stokes’ formula allows the user to compensate the lack of a global coverage of gravity data by a combination of terrestrial gravity and a global geopotential model. The minimization of the errors of truncation gravity data and potential coefficients could be treated in a least-squares sense as is the basic ingredient in the Royal Institute of Technology (KTH) approach as proposed by Sjöberg in 1984. This article presents the results from a joint project between KTH and the National Land Survey of Sweden, whose main purpose is to evaluate the KTH approach numerically and to compute a gravimetric geoid model for Sweden. The new geoid model (KTH06) was computed based on the least-squares modification of Stokes’ formula, the GRACE global geopotential model, a high-resolution digital terrain model and the NKG gravity anomaly database. The KTH06 was fitted to 1162 GPS/levelling points by a 7-parameter transformation, yielding an all-over fit of 19 mm and 0.17 ppm. The fit is even smaller than the estimated internal accuracy for the geoid model (28 mm). If we assume that the accuracy of the GPS and levelling heights are 10 mm and 5 mm, respectively, it follows that the accuracy of the expected gravimetric geoid heights are of the order of 11 mm. Also, we found a significant expected difference between the KTH06 and NKG2004 models in rough topographic areas (up to 36 cm). As the major ground data and global geopotential model were almost same in the two models, we believe that there are different reasons that come into play for interpreting the discrepancies between them, as the method for eliminating outliers from the gravity database, the interpolated denser gravity observations using the high-resolution digital elevation model before Stokes’ integration, the potential of the LSM kernel, which matches the errors of the terrestrial gravity data, GGM and the truncation error in an optimum way, and the effect of applying more precise correction terms in the KTH approach compared to the remove-compute-restore method. It is concluded that the least-squares modification method with additive corrections is a very promising alternative for geoid computation.

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The problem of handling outliers in a deformation monitoring network is of special importance, because the existence of outliers may lead to false deformation parameters. One of the approaches to detect the outliers is to use robust estimators. In this case the network points are computed by such a robust method, implying that the adjustment result is resisting systematic observation errors, and, in particular, it is insensitive to gross errors and even blunders. Since there are different approaches to robust estimation, the resulting estimated networks may differ. In this article, different robust estimation methods, such as the M-estimation of Huber, the “Danish”, and the L 1 -norm estimation methods, are reviewed and compared with the standard least squares method to view their potentials to detect outliers in the Tehran Milad tower deformation network. The numerical studies show that the L 1 -norm is able to detect and down-weight the outliers best, so it is selected as the favourable approach, but there is a lack of uniqueness. For comparison, Baarda’s method “data snooping” can achieve similar results when the outlier magnitude of an outlier is large enough to be detected; but robust methods are faster than the sequential data snooping process.

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