GPS高程拟合方法及其拟合精度对比

利用已有的包头至集宁GPS C级网测量的控制测量成果的GPS实测数据和几何水准资料作为已知数据,利用线性拟合法、曲面拟合法对GPS高程拟合,通过与水准高程的精度对比分析,论述该等级网GPS拟合高程可以达到四等几何水准测量的精度。     

关于GPS高程测量精度的分析比较

通过对联测了２５个四等水准的ＧＰＳ点,分别用平面拟合模型和曲面拟合模型解算各点的正常与四等水准结果比较,得出一些有益的结论,对ＧＰＳ的实际生产具有一「一的指导意义。     

GPS水准高程拟合与精度分析

本文根据常用的GPS水准高程拟合模型,利用测区的已知数据进行试算,并根据试验结果,从拟合的似大地水准面,已知点高程精度和GPS点大地高三方面,分析了GPS水准高程拟合精度,总结了提高拟合精度一些方法     

阜新市区似大地水准面拟合研究

基于GPS水准的阜新市区似大地水准面拟合问题,对获得的高程异常数据采用Huber抗差估计方法剔除粗差,并运用逐点剔除法选取GPS水准拟合的已知点,提高似大地水准面的拟合精度;通过对GPS水准中5种模型的试验比较,得到建立该地区似大地水准面的最佳方案—多面函数法。经闭合差检核,精度可达到四等水准的要求。     

高程拟合点的分布对GPS点的高程精度影响分析

以衡阳市四等GPS控制测量为数据来源,通过比较点位水准高程与GPS拟合高程的差值变化规律,分析水准高程拟合点的分布对GPS网点的高程精度影响,同时,验证GPS拟合高程的可靠性.根据互差的变化规律,可以更好地为水准路线的布设提供依据.     

两种常用的GPS高程拟合模型拟合精度研究

通过利用金塘大桥海中一级加密网这一成果对GPS高程异常拟合模型精度进行研究,分别用平面拟合模型和多项式曲面拟合模型解算出各点的正常高并与四等水准结果比较,得出一些有益的结论,对GPS的实际应用具有一定的指导意义.     

矿区似大地水准面拟合模型适用性分析

为提高GPS/水准数据拟合高程异常的逼近精度,利用某矿区控制网观测的GPS/水准数据,计算控制点高程异常值,分别用加权平均法、Shepard插值、多项式曲面拟合和多面函数法4种方法对矿区似大地水准面进行拟合。对各种拟合模型的原理和拟合精度进行比较分析。在此基础上,根据似大地水准面物理和几何特性,采用组合拟合的方法进一步改善似大地水准面的拟合精度,利用该模型内插高程异常值与实测GPS/水准点的高程异常值比较,其均方根误差不超过0.02 m,结合GPS观测成果可以取代四等及以下几何水准测量。     

GPS高程拟合的应用

在GPS水准拟合原理的基础上,介绍了确定似大地水准面的原理与方法,分析了用数学模型法和少量GPS与水准重合点,将GPS大地高直接转换为具有厘米级正常高的实现方法。实验结合玉铁铁路某段GPS控制网,应用二次曲面法、移动曲面法和多面函数法进行拟合,得到相应的正常高,并根据已知水准高程进行精度分析和比较,探讨各模型的适用性。     

GPS水准面拟合方法研究

研究用较多已测点的原始数据,分别采用GPS水准的六参数法、多面函数法、移动曲面拟合法、有限元法逼近GPS网中较少检核点的高程异常值;再用较少已测点的原始数据,逼近GPS水准网中较多检核点的高程异常值.通过对实测数据的计算分析可发现,具有分区拟合性质的移动曲面拟合法与有限元法较优,使用较少的拟合点时,实测三等水准联合GPS高程观测可取代四等水准测量.     

拟合点独立解算的GPS水准拟合探究

传统的GPS水准拟合主要是应用某一种拟合模型对拟合点群进行拟合,未能考虑到不同拟合点对同一拟合模型具有不同适应度。针对这一问题,本文提出了基于拟合点独立解算的GPS水准拟合方法,并结合实测数据对该方法进行了测试,结果证明该拟合方案相对于传统模型在精度上有成倍的提高。     

Local geoid determination combining gravity disturbances and GPS/levelling: a case study in the Lake Nasser area, Aswan, Egypt

 The use of GPS for height control in an area with existing levelling data requires the determination of a local geoid and the bias between the local levelling datum and the one implicitly defined when computing the local geoid. If only scarse gravity data are available, the heights of new data may be collected rapidly by determining the ellipsoidal height by GPS and not using orthometric heights. Hence the geoid determination has to be based on gravity disturbances contingently combined with gravity anomalies. Furthermore, existing GPS/levelling data may also be used in the geoid determination if a suitable general gravity field modelling method (such as least-squares collocation, LSC) is applied. A comparison has been made in the Aswan Dam area between geoids determined using fast Fourier transform (FFT) with gravity disturbances exclusively and LSC using only the gravity disturbances and the disturbances combined with GPS/levelling data. The EGM96 spherical harmonic model was in all cases used in a remove–restore mode. A total of 198 gravity disturbances spaced approximately 3 km apart were used, as well as 35 GPS/levelling points in the vicinity and on the Aswan Dam. No data on the Nasser Lake were available. This gave difficulties when using FFT, which requires the use of gridded data. When using exclusively the gravity disturbances, the agreement between the GPS/levelling data were 0.71 ± 0.17 m for FFT and 0.63 ± 0.15 for LSC. When combining gravity disturbances and GPS/levelling, the LSC error estimate was ±0.10 m. In the latter case two bias parameters had to be introduced to account for a possible levelling datum difference between the levelling on the dam and that on the adjacent roads. Received: 14 August 2000 / Accepted: 28 February 2001     

利用重力场模型和局部重力资料计算GPS水准高的精度探讨

利用大地水准面高，结合GPS测量的高程信息,直接计算GPS水准高，是一种全新诱人的解决方案。本文就这种方案，根据其核心技术－大地水面高的性质：长波长－全球重力场；中波长－局部重力资料，短波长－数据地形，对它的具体实现，适用范围以及精度分析作了详尽的探讨，在此基础上，提出一些GPS水准应用规范和要求，并利用实验数据对其进行验证。     

基于不同基准面的水位控制测量高程之比较分析

探讨了在水位控制测量时,因各种测量方法依据的基准面的不同而引起的所测高程之间的差异,着重对全站仪三角高程、GPS高程与水准高程三者之间的差异进行了理论分析和实测数据比对,给出了几种高程之间相互转换的方法。     

GPS水准

本文根据国内外GPS水准研究的文献资料,结合作者的研究心得,分析、探讨了各种GPS水准的理论与方法。比较其特点和应用条件及有待深入研究的课题。本文共分三部分;第一部分先说明GPS水准概念,然后探讨了GPS大地高(差)的精度及GPS水准——几何法求定大地水准面的各种算法;第二部分讨论了如何应用重力资料精化大地水准面的几何解;第三部分介绍了国内外一些重要的试验结果,以使读者有一明确的数字概念。     

Models for Fitting Gravimetric Geoids and GPS Results

The aim of this investigation is to study how to use a gravimetric(quasi) geoid for levelling by GPS data in an optimal way.The advent of precise geodetic GPS has made the use of a technique possible,which might be called GPS- gravimetric geoid determination.In this approach,GPS heights above the reference ellipsoid are determined for points whose levelled (orthometric) height H is above sea level people have already surveyed;for these points,we thus have the values of the geoid undulation N.These values are then used to constrain the geoid undulations N‘ obtained from the gravimetric solution.     

Robust estimation and optimal selection of polynomial parameters for the interpolation of GPS geoid heights

The polynomial interpolation of least squares and interpolation moving least squares based on control stations with known GPS (global positioning system) ellipsoidal heights and levelling orthometric heights are the most often used methods for the interpolation of the geoid heights. But in their applications there occur two problems: one lies in selecting the suitable polynomial parameters; the other in reducing the influences of some possibly abnormal data points. To solve both of the problems, without emphasizing a sound theoretical basis, a heuristic solution with the help of robust estimation technique and optimization criteria for the regression equation is presented. Through two actual numerical examples it is shown that the new solution concept is efficient and can be realized easily on computers. Received: 23 May 1996 / Accepted: 27 March 1997     

Modelling local GPS/levelling geoid undulations using artificial neural networks

The use of GPS for establishing height control in an area where levelling data are available can involve the so-called GPS/levelling technique. Modelling of the GPS/levelling geoid undulations has usually been carried out using polynomial surface fitting, least-squares collocation (LSC) and finite-element methods. Artificial neural networks (ANNs) have recently been used for many investigations, and proven to be effective in solving complex problems represented by noisy and missing data. In this study, a feed-forward ANN structure, learning the characteristics of the training data through the back-propagation algorithm, is employed to model the local GPS/levelling geoid surface. The GPS/levelling geoid undulations for Istanbul, Turkey, were estimated from GPS and precise levelling measurements obtained during a field study in the period 1998–99. The results are compared to those produced by two well-known conventional methods, namely polynomial fitting and LSC, in terms of root mean square error (RMSE) that ranged from 3.97 to 5.73 cm. The results show that ANNs can produce results that are comparable to polynomial fitting and LSC. The main advantage of the ANN-based surfaces seems to be the low deviations from the GPS/levelling data surface, which is particularly important for distorted levelling networks.     

On the combined adjustment of a gravimetrically determined geoid and GPS levelling stations

Summary A new basic geodetic network using the GPS technique is now being set up in France. There will be altogether 1000 benchmarks connected to the French levelling network. Obviously, the GPS levelling points are not dense enough to produce a national levelling reference surface. A gravimetrically determined geoid has therefore been proposed to be used for the interpolation between the GPS levelling points. However, because of long-wavelength errors, we consider that a gravimetric geoid does not have sufficient accuracy. A regression by fitting the gravimetrically determined geoid to the GPS levelling points is generally proposed. Unfortunately, this country-wide geoid fitting work cannot eliminate local deformations in the geoid, which happen in areas where there are errors or shortages of gravity or DTM data. This paper proposes and discusses a combined adjustment method. The principle is to divide up the geoid into small pieces and then to adjust them to the GPS levelling points locally with constraint conditions for the common points of the adjacent pieces. In order to benefit from the advantages of the high resolution and high relative accuracy of the gravimetric geoid, as well as the high absolute accuracy of the GPS levelling points, we establish respectively a relative observation equation for the difference of the gravimetric geoid undulation and an absolute observation equation for the GPS levelling points. Finally, we adjust the observation equations as a whole. Several global and local systematic errors are also taken into account and some special cases, such as adjustment in groups and blunder detection, are also discussed.     

Geoid models around Sognefjord using depth data

Bathymetry data from Sognefjord, Norway, have been included in a terrain model, and their influence on the geoid has been calculated. The test area, located in the western part of Norway, was chosen due to its deep fjords and high mountains. Inclusion of bathymetry data in the terrain model altered the computed gravimetric geoid by as much as a few decimeters. The effect was detectable to a distance of more than 100 km. All calculated geoids, both with and without bathymetry data in the terrain model, fit the geoidal heights determined by available Global Positioning System (GPS) and levelling heights at the sub-decimetre level. Contrary to expectations, the accuracy in geoid prediction was reduced when using bathymetric data. The geoid changes were largest over the fjord where no GPS points were located. Different methods on the same area [isostatic and Residual Terrain Model (RTM)-terrain reductions] showed differences of approximately 1 m. Rigorous distinction between quasigeoid and geoid was found to be essential in this kind of area. Received: 12 May 1997 / Accepted 7 May 1998     

Geoid undulation modelling and interpretation at Ladak, NW Himalaya using GPS and levelling data

Fast and accurate relative positioning for baselines less than 20 km in length is possible using dual-frequency Global Positioning System (GPS) receivers. By measuring orthometric heights of a few GPS stations by differential levelling techniques, the geoid undulation can be modelled, which enables GPS to be used for orthometric height determination in a much faster and more economical way than terrestrial methods. The geoid undulation anomaly can be very useful for studying tectonic structure. GPS, levelling and gravity measurements were carried out along a 200-km-long highly undulating profile, at an average elevation of 4000 m, in the Ladak region of NW Himalaya, India. The geoid undulation and gravity anomaly were measured at 28 common GPS-levelling and 67 GPS-gravity stations. A regional geoid low of nearly −4 m coincident with a steep negative gravity gradient is compatible with very recent findings from other geophysical studies of a low-velocity layer 20–30 km thick to the north of the India–Tibet plate boundary, within the Tibetan plate. Topographic, gravity and geoid data possibly indicate that the actual plate boundary is situated further north of what is geologically known as the Indus Tsangpo Suture Zone, the traditionally supposed location of the plate boundary. Comparison of the measured geoid with that computed from OSU91 and EGM96 gravity models indicates that GPS alone can be used for orthometric height determination over the Higher Himalaya with 1–2 m accuracy. Received: 10 April 1997 / Accepted: 9 October 1998