Route Height Connection Across the Sea by Using the Vertical Deflections and Ellipsoidal Height Data

Distance between the main land and island is so long that it is very difficult to precisely connect the height datum across the sea with the traditional method like the trigonometric leveling, or it is very expensive and takes long time to implement the height transfer with the geopotential technique. We combine the data of GPS surveying, astro-geodesy and EGM2008 to precisely connect the orthometric height across the sea with the improved astronomical leveling method in the paper. The Qiongzhou Strait is selected as the test area for the height connection over the sea. We precisely determine the geodetic latitudes, longitudes, heights and deflections of the vertical for four points on both sides across the strait. Modeled deflections of the vertical along the height connecting routes over the sea are determined with EGM2008 model based on the geodetic positions and heights of the sea segmentation points from DNSC08MSS model. Differences of the measured and modeled deflections of the vertical are calculated at four points on both sides and linearly change along the route. So the deflections of the vertical along the route over the sea can be improved by the linear interpolation model. The results are also in accord with those of trigonometirc levelings. The practical case shows that we can precisely connect the orthometric height across the Qiongzhou Strait to satisfy the requirement of order 3 leveling network of China. The method is very efficient to precisely connect the height datum across the sea along the route up to 80 km.

Height connection across sea by using satellite altimetry data sets,ellipsoidal heights,astrogeodetic deflections of the vertical,and an Earth Gravity Model

Islands and the mainland are separated by seas,and the distances between them might be so long that the height on the mainland cannot be exactly translated to the islands,resulting in different height systems on the mainland and the islands.In this study,we used astrogeodetic deflections of the vertical and ellipsoidal heights of points on the mainland and island near their coastlines to implement height connection across sea areas.First,the modeled gravity and modeled astrogeodetic vertical deflections of segmentation points along connecting routes over the sea between the mainland and the island were determined by Earth Gravity Model(EGM),and the ellipsoidal heights of segmentation points were determined by the satellite altimetry data sets.Second,we used a linear interpolation model to increase the precision of the vertical deflections of segmentation points.Third,we computed the geopotential difference of points between the mainland and the island using a method derived from geopotential theory and the astronomical leveling principle.Finally,we estimated the normal height of the point on the island using the geopotential-difference iterative computation approach.Using observed data of normal heights,ellipsoidal heights,and astrogeodetic vertical deflections referring to height sites in Qingdao,Shandong Province,we conducted a numerical experiment involving the normal height connection across sea regions.We determined the data of the ellipsoidal heights and gravity of segmentation points along the connecting route across the water in the numerical experiment using DTU10.The distance of the height connection across the sea was approximately 10.5 km.According to China's official leveling specifications,the experimental results met the criterion of third-class leveling precision.

High Precision Vertical Deflection Over China Marginal Sea and Global Sea Derived from Multi-Satellite Altimeter

On the basis of gravity field model （EIGEN_CG01C）, together with multi-altimeter data, the improved deflection of the vertical gridded in 2＇×2＇ in China marginal sea and gridded in 5＇×5＇ in the global sea was determined by using the weighted method of along-track least squares, and the accuracy is better than 1.2^# in China marginal sea. As for the quality of the deflection of the vertical, it meets the challenge for the gravity field of high resolution and accuracy, it shows that, compared with the shipboard gravimetry in the sea, the accuracy of the gravity anomalies computed with the marine deflection of the vertical by inverse Vening-Meinesz formula is 7.75 m.s ^-2.

Bathymetry inversion using the deflection of the vertical:A case study in South China Sea

The deflection of the vertical is one of the essential products of altimetry.However,unlike gravity and vertical gravity gradients,it is seldom used in bathymetry inversion.In this study,an algorithm for bathymetry inversion using the deflection of the vertical is proposed.First,we separately derive the formulas for the bathymetry inversion from the north and east components of the vertical deflection and introduce the data processing.Then a local area in the South China Sea is selected as an example to test the method.The bathymetry inversion based on gravity anomaly is also conducted for comparison.Assuming the ship-borne depths are the true values,the error standard deviations(STDs)of the bathymetry derived by north and east components of the vertical deflection are 156.64 m and 165.57 m,respectively.It indicates that the north component has a better performance in bathymetry inversion than the east component.The inversion results from the combination of both components show a higher accuracy of bathymetry than that from a single component.The difference between the error STD of the combination results and that of the gravity anomaly is less than 0.2 m.The experiment’s results also show that the precision of the derived bathymetry can be improved if the parameters of linear regression are adjusted according to water depths.In summary,among the gravity field products used in this study,the gravity anomaly yielded the best performance in the bathymetry inversion.However,since additional data and computation time are required to derive gravity anomalies from altimetric observations,the vertical defections can still be used as supplements,especially in areas where accurate vertical deflections exist.

The ellipsoidal corrections for boundary value problems of deflection of the vertical with ellipsoid boundary

The boundary value problem of deflections of vertical with ellipsoid boundary is studied in the paper. Based on spherical harmonic series, the ellipsoidal corrections for the boundary value problem are derived so that it can be well solved. In addition, an imitation arithmetic is given for examining the accuracies of solutions for the boundary value problem as well as its spherical approximation problem, and the computational results illustrate that the boundary value problem has higher accuracy than its spherical approximation problem if deflection of the vertical are measured on geoid.

Computing Local Geoid Model Using DTM and GPS Geodetic Points.Case Study:Mejez El Bab-Tunisia

Different methods have been deployed to compute the geoid, the altimetry reference for surveying applications. One of their main goals is to allow the use of GPS (Global Positioning System) or GNSS heights, which are related to an ellipsoid and therefore must be corrected. Some of these methods are accurate but quite heavy as developed by [1], but one of them is easy to use while giving very good results in a local system: some mm for a 10 × 10 km2 area developed by [2] [3]. In our study, we have used software called “Géoide Program”, previously used at the CERN in Switzerland and set up by [4], which they complete this software allowing a parameterization of general data to provide results in a general system. Then, tests have shown the way to optimize computations without any loss of accuracy. For our computations we use gridded of geodetic heights, from Lambert or WGS 84 datum’s, DTM (Digital Terrain Model) and leveled GPS points. To obtain these results, components of the vertical deflection are computed for every point on the grid, deduced from the attraction exerted by the mass Model. Then, geodetic heights are computed by an incremental way from an arbitrary reference. Once the calculation is performed, the geodetic height of any point located in the modelled area can be interpolated. The variations of parameters (mainly size and increments of the DTM and of the modeled area, and ground density) have shown that they do not play a significant role although DTM must be large enough to take into account an important area around a selected zone. However, the choice of the levelled GPS points is primordial. We have performed tests with real data concerning Mejez El Bab zone, in north of Tunisia. Nevertheless, for a few hundreds of square kilometers area, and just by using a DTM and a few levelled GPS points, this method provides results that look extremely promising, at least for surveying activities, as it shows a good possibility to use GPS for coarse precision levelling, and as DTM are now widely available in many countries.

Prediction of Gravity Anomalies Over the South China and Philippine Seas from Multi-satellite Altimeter Sea Surface Heights

t Gravity anomalies on a2.5 ×2.5 arc-minute grid in a non-tidal system were derived over the South China and Philippine Seas from multi-satellite altimetry data. North and east components of deflections of the vertical were computed from altimeter-derived sea surface heights at crossover locations, and gridded onto a 2.5 × 2.5 arc-minute resolution grid. EGM96-derived components of deflections of the vertical and gravity anomalies gridded into 2.5 × 2.5 arc-minute resolutions were then used as reference global geopotential model quantities in a remove-restore procedure to implement the Inverse Vening Meinesz formula via the 1D-FFT technique to predict the gravity anomalies over the South China and Philippine Seas from the gridded altimeter-derived components of deflections of the vertical. Statistical comparisons between the altimeter-derived and the shipboard gravity anomalies showed that there is a root-mean-square agreement of 5.7 mgals between them.

Determination of Geoid over South China Sea and Philippine Sea from Multi-satellite Altimetry Data

A new computational procedure for derivation of marine geoid on a 2.5′×2.5′grid in a non-tidal system over the South China Sea and the Philippine Sea from multi-satellite altimeter sea surface heights is discussed. Single-and dual-satellite crossovers were performed, and components of deflections of the vertical were determined at the crossover positions using Sand-well's computational theory, and gridded onto a 2.5′×2.5′resolution grid by employing the Shepard's interpolation procedure. 2.5′×2.5′grid of EGM96-derived components of deflections of the vertical and geoid heights were then used as reference global geopotential model quantities in a remove-restore procedure to implement the Molodensky-like formula via 1D-FFT technique to predict the geoid heights over the South China Sea and the Philippine Sea from the gridded altimeter-derived components of deflec-tions of the vertical. Statistical comparisons between the altimeter-and the EGM96- derived geoid heights showed that there was a root-mean-square agreement of ±0.35 m between them in a region of less tectonically active geological structures. However, over areas of tectonically active structures such as the Philippine trench, differences of about -19.9 m were obtained.

Comprehensive compensation method for the influence of disturbing gravity field on long-range rocket guidance computing

With the improvement of the accuracy of the inertial system,the influence of the disturbing gravity field on the accuracy of long-range rocket has become increasingly prominent.However,in actual engineering,there are problems of low accuracy and being time-consuming for disturbing gravity field compensation.In view of this,this paper proposes a set of online comprehensive solutions combining disturbing gravity reconstruction and stellar correction.According to the pre-launch binding parameters,the net function assignment method is used in the navigation system to calculate disturbing gravity in the boost phase online.In the guidance system,a closed-loop guidance online compensation method is proposed based on the state-space perturbation method for the disturbing gravity in the coast phase.At the same time,the vertical deflection can also be corrected by stellar guidance.The calculation results are simulated and verified under different circumstances.Simulation results show that the proposed online compensation algorithm has an accuracy improvement compared with the element compensation algorithm on ground.And the stellar guidance algorithm can further correct the impact deviation.The impact deviation after comprehensive compensation does not exceed 50 m,and the compensation percentage is greater than 65%.