Utilizing the adopted average topographic density of 2670 kg/m3 in the reduction of gravity anomalies introduces errors attributed to topographic density variations, which consequently affect geoid ...modeling accuracy. Furthermore, the mean gravity along the plumbline within the topography in the definition of Helmert orthometric heights is computed approximately by applying the Poincaré-Prey gravity reduction where the topographic density variations are disregarded. The Helmert orthometric heights of benchmarks are then affected by errors. These errors could be random or systematic depending on the specific geological setting of the region where the leveling network is physically established and/or the geoid model is determined. An example of systematic errors in orthometric heights can be given for large regions characterized by sediment or volcanic deposits, the density of which is substantially lower than the adopted topographic density used in Helmert's definition of heights. The same applies to geoid modeling errors. In this study, we investigate these errors in the Hong Kong territory, where topographic density is about 20% lower than the density of 2670 kg/m3. We use the digital rock density model to estimate the effect of topographic density variations on the geoid and orthometric heights. Our results show that this effect on the geoid and Helmert orthometric heights reach maxima of about 2.1 and 0.5 cm, respectively. Both results provide clear evidence that rock density models are essential in physical geodesy applications involving gravimetric geoid modeling and orthometric height determination despite some criticism that could be raised regarding the reliability of these density models. However, in regions dominated by sedimentary and igneous rocks, the geological information is essential in these applications because topographic densities are substantially lower than the average density of 2670 kg/m3, thus introducing large systematic errors in geoid and orthometric heights.
•Correction of geometric geoid using B-spline method, a smooth spline surface in the least squares sense.•The capability of approximating a 2D surface from irregularly distributed data.•The corrector ...surface development along with the elimination of biases.•Providing reliable results regarding the corrector surface against the raw data set.
The performance of the gravimetric geoid models is usually evaluated by comparison of geoid heights with the GNSS/levelling derived geoid. But the GNSS/levelling network can be infected by significant systematic biases and random errors, especially in large and uneven areas. This contribution addresses the challenging problem of the corrector surface development along with the elimination of biases. To this end, fitting an appropriate geometric surface to the GNSS/levelling geoid heights is required, which is accomplished by applying the least squares B-spline approximation theory to the GNSS/levelling data. In addition, the 3D affine transformation is used to detect systematic effects of the GNSS/levelling network compared to a global geoid model. This strategy is applied to the adjustment of the Iranian GNSS/levelling network. A significant tilt is observed across the country ranging from −0.35 m to 0.04 m. The entire study area is divided into four zones and the corrector surfaces are obtained in each zone. The accuracy of three global geoid models, EGM2008, EIGEN-6C4 and SGG-UGM-1, along with that of the Iranian regional geoid model IRG2016, are then investigated based on the raw GNSS/levelling heights and the corrector surfaces. The evaluations show the reliable results regarding the corrector surfaces against the raw data set. All geoid models show their maximum RMSE values of discrepancies in the mountainous zones and their minimum RMSEs in the zones having lower variety in topography. This indicates that the irregular topographies are not well detected by the global models over the study area.
The most common approaches for assigning weights to observations in minimum L1-norm (ML1) is to introduce weights of
or
,
being the weights vector of observations given by the inverse of variances. ...Hence, they do not take covariances into consideration, being appropriated only to independent observations. To work around this limitation, methods for decorrelation/unit-weight reduction of observations originally developed in the context of least squares (LS) have been applied for ML1, although this adaptation still requires further investigations. In this article, we presented a deeper investigation into the mentioned adaptation and proposed the new ML1 expressions that introduce weights for both independent and correlated observations; and compared their results with the usual approaches that ignore covariances. Experiments were performed in a leveling network geometry by means of Monte Carlo simulations considering three different scenarios: independent observations, observations with “weak” correlations, and observations with “strong” correlations. The main conclusions are: (1) in ML1 adjustment of independent observations, adaptation of LS techniques introduces weights proportional to
(but not
); (2) proposed formulations allowed covariances to influence parameters estimation, which is unfeasible with usual ML1 formulations; (3) introducing weighs of
provided the closest ML1 parameters estimation compared to that of LS in networks free of outliers; (4) weighs of
provided the highest successful rate in outlier identification with ML1. Conclusions (3) and (4) imply that introducing covariances in ML1 may adversely affect its performance in these two practical applications.
State geodetic network Kyrgyz Republic Sharsheev, Ermek Sabyrovich; Belek uulu, Esenbek; Konurbaeva, Gulzat Ularbekovna ...
BIO web of conferences,
01/2024, Letnik:
83
Journal Article
Recenzirano
Odprti dostop
This article describes the creation and development of GPS networks on the territory of the Kyrgyz Republic. The state geodetic GPS network consists of three levels: 0-order GPS network, 1st order ...GPS network and 2nd order GPS network. GPS points are combined with GGS points (State Geodetic Network). The adjusted coordinates of GPS points are obtained in the ITRF system for the epoch of 2005 (ITRF 2005).
Examination of possibilities in using geodetic (survey) instruments of the same specifications, but different technical performances is always an interesting geodetic topic. The main purpose of this ...research is to analyze the accuracy of special purposes leveling networks where height differences were measured with Koni 007 CZJ and Leica DNA 03 levels. Obtained results showed that both leveling results fulfill the required conditions of precision leveling, but the preference is given to level DNA 03.
The paper deals with some problems when applying a correction to reduce the effect of vertical refraction in precise leveling observation. An example for calculating the refraction correction for one ...first order leveling line with length of 109 km in Bulgaria is given. Comparison between the obtained errors before and after applying refraction correction has been made. The results show that is important to measure the temperatures simultaneously with the leveling by aspiration thermometer with an accuracy of ±0.1 °C. It is recommended to make experimental research and to adopt appropriate for Bulgaria model for taking into account the influence of vertical refraction.
Latvian National First Order Levelling Network consist of 15 polygons and 51 lines and was re-established in 2011. From 1
st
of December of year 2014 in Latvia Republic is new Latvian normal height ...system at epoch 2000, 5. Normal heights are widely used in origination and application of geospatial data in civil engineering and quasigeoid computation etc. The main objective of this work is to describe 2
nd
order leveling network development idea, purpose and process. Essential of work is option, check, used and analyze historical height data, which has all Eastern European countries, and newly measured height data.
We compared the method of least squares (LS), Pope’s iterative data snooping (IDS) and Huber’s M-estimator (HU) in realistic leveling networks, for which the heights or the vertical displacements of ...points are known. The study was conducted using the Monte Carlo simulation, in which one repeatedly generates sets of observations related to the measurement data, then calculates values of the estimators and, finally, assesses it with respect to the real coordinates. To simulate outliers we used popular mixture models with two or more normal distributions. It is shown that for small, strong networks robust methods IDS and HU are more accurate than LS, but for large, weak networks occurring in practice there is no significant difference between the considered methods in the accuracy of the solution.
In a complicated leveling-network, it was often simple to write manually the equations to express all the condition that must be met for a conditional adjustment. Therefore conditional adjustment ...which was straightforward and regularity in its development and solution.was early becoming very popular . But with the advent of the computer technology, it was gradually reducing its effects which was not well suited to computers for its equations not unique and shapes diversity. Based on this, an available leveling-network conditional adjustment program was developed to solve the problem of conditional diversity. By aid of transferring matrix, the program design scheme of the conditional adjustment was proposed by means of visual basic language platform. The coefficient matrix of the conditional equations was written out based on transferring vectors and arithmetic rules. The normal equations were solved by method from Guassian main column eliminated. The Residuals and the measuring precision was achieved by the results from the normal equation back substituted to conditional equation. The application shows that conditional adjustment by transmitting matrix can simplify procedure of writing the conditional equations, and easily program for conditional adjustment.
PDF
