用神经网络方法转换GPS高程

本文提出用神经网络方法转换ＧＰＳ高程为正高或正常高,给出一种改进了的ＢＰ神经网络拓扑结构和算法,并用ＧＰＳ的实际定位资料构成４３个样本集作了在计算分析,估算的精度达到厘米级、最后用网络方法与二次多项式曲面拟合大地水准面转换ＧＰＳ高程的方法作了比较,神经网络方法的精度优于二次多项式曲面拟合法,而且精度比较稳定,对已知样本点的数量要求较少。     

A new technique to determine geoid and orthometric heights from satellite positioning and geopotential numbers

This paper takes advantage of space-technique-derived positions on the Earth’s surface and the known normal gravity field to determine the height anomaly from geopotential numbers. A new method is also presented to downward-continue the height anomaly to the geoid height. The orthometric height is determined as the difference between the geodetic (ellipsoidal) height derived by space-geodetic techniques and the geoid height. It is shown that, due to the very high correlation between the geodetic height and the computed geoid height, the error of the orthometric height determined by this method is usually much smaller than that provided by standard GPS/levelling. Also included is a practical formula to correct the Helmert orthometric height by adding two correction terms: a topographic roughness term and a correction term for lateral topographic mass–density variations.     

局部无缝垂直参考基准面的建立方法研究

为在局域建立一个无缝垂直参考基准面，提出了两步转换的思想和方法，即从大地高到正高然后到海图高。利用该方法。构造了Saint John河高程转换模型，并在该河段建立了无缝垂直参考基准面，且得到了实际验证。     

Calibration of geoid error models via a combined adjustment of ellipsoidal, orthometric and gravimetric geoid height data

The well-known statistical tool of variance component estimation (VCE) is implemented in the combined least-squares (LS) adjustment of heterogeneous height data (ellipsoidal, orthometric and geoid), for the purpose of calibrating geoid error models. This general treatment of the stochastic model offers the flexibility of estimating more than one variance and/or covariance component to improve the covariance information. Specifically, the iterative minimum norm quadratic unbiased estimation (I-MINQUE) and the iterative almost unbiased estimation (I-AUE) schemes are implemented in case studies with observed height data from Switzerland and parts of Canada. The effect of correlation among measurements of the same height type and the role of the systematic effects and datum inconsistencies in the combined adjustment of ellipsoidal, geoid and orthometric heights on the estimated variance components are investigated in detail. Results give valuable insight into the usefulness of the VCE approach for calibrating geoid error models and the challenges encountered when implementing such a scheme in practice. In all cases, the estimated variance component corresponding to the geoid height data was less than or equal to 1, indicating an overall downscaling of the initial covariance (CV) matrix was necessary. It was also shown that overly optimistic CV matrices are obtained when diagonal-only cofactor matrices are implemented in the stochastic model for the observations. Finally, the divergence of the VCE solution and/or the computation of negative variance components provide insight into the selected parametric model effectiveness.     

利用车载动态PPP技术检核SRTM、ASTER GDEM和AW3D模型的高程精度

SRTM、ASTER GDEM和AW3D是比较有代表性的全球数字高程模型。本文探讨了采用车载动态PPP技术对上述3类模型的区域高程精度进行检核,首先沿广州至肇庆公路进行连续数据采集,采用动态精密单点定位（PPP）技术解算动态点的WGS-84坐标;然后利用EGM2008重力场模型和仪器高获得动态点的正常高;最后采用4种不同的插值方法对SRTM、ASTER GDEM和AW3D模型进行高程检验。检核结果显示：不同的插值方法具有较好的一致性,SRTM3 V4.1、ASTER GDEM V2、AW3D30的高程标准差分别优于3.4 m、4.1 m和3.3 m,均优于其全球标称高程精度;本文检核方法快速高效,有较好的适用性。     

The orthometric height and the holonomity problem

When height networks are being adjusted, many geodesists advocate the approach where the adjustment should be done by using geopotential numbers rather than the orthometric or normal heights used in practice. This is based on a conviction that neither orthometric nor normal heights can be used for the adjustment because these height systems are not holonomic, meaning–among other things–that height increments (orthometric or normal) when summed around a closed loop do not sum up to zero. If this was the case, then the two height systems could not be used in the adjustment; the non-zero loop closure would violate the basic, usually unspoken, assumption behind the adjustment, namely that the model claiming that height differences are observable is correct. In this paper, we prove in several different ways that orthometric and normal heights are theoretically just as holonomic as the geopotential numbers are, when they are obtained from levelled height differences using actual gravity values. This disposes of the argument that geopotential numbers should be used in the adjustment. Both orthometric and normal heights are equally qualified to be used in the adjustment directly.     

The relation between rigorous and Helmert’s definitions of orthometric heights

Following our earlier definition of the rigorous orthometric height [J Geod 79(1-3):82–92 (2005)] we present the derivation and calculation of the differences between this and the Helmert orthometric height, which is embedded in the vertical datums used in numerous countries. By way of comparison, we also consider Mader and Niethammer’s refinements to the Helmert orthometric height. For a profile across the Canadian Rocky Mountains (maximum height of ~2,800 m), the rigorous correction to Helmert’s height reaches ~13 cm, whereas the Mader and Niethammer corrections only reach ~3 cm. The discrepancy is due mostly to the rigorous correction’s consideration of the geoid-generated gravity disturbance. We also point out that several of the terms derived here are the same as those used in regional gravimetric geoid models, thus simplifying their implementation. This will enable those who currently use Helmert orthometric heights to upgrade them to a more rigorous height system based on the Earth’s gravity field and one that is more compatible with a regional geoid model.     

不同高程系统的比较

Geopotential, dynamic, orthometric and normal height systems and the corrections related to these systems are evaluated in this paper. Along two different routes, with a length of about 5 kilometers, precise leveling and gravity measurements are done. One of the routes is in an even field while the other is in a rough field. The magnitudes of orthometric, normal and dynamic corrections are calculated for each route. Orthometric, dynamic, and normal height differences are acquired by adding the corrections to the height differences obtained from geometric leveling. The magnitudes of the corrections between the two routes are compared. In addition, by subtracting orthometric, dynamic, and normal heights from geometric leveling, deviations of these heights from geometric leveling are counted.     

An evaluation of orthometric height accuracy using bore hole gravimetry

Errors are introduced in orthometric height computations by the use of standard formulas to estimate mean gravity along the plumb line. Direct measurements of gravity between the Earth’s surface and sea level from bore hole gravimetry were used to determine the magnitude of these errors. For the seven cases studied, errors in orthometric height, due to the use of the Helmert method for computing mean gravity along the plumb line, were generally small (<2 cm). However, in one instance the error was substantial, being9.6 cm. The results verified the general validity of the Poincaré-Prey approach to estimation of gravity along the plumb line and demonstrated that the suggestion byVanicek (1980) that the air gradient is more appropriate is incorrect. With sufficient topographic information to compute terrain corrections, and density estimates from surface gravity, errors in mean gravity along the plumb line should contribute no more than 3cm to orthometric height computation.     

Data transformation for super-totalstation positioning system integrated by GPS and totalstation

This paper focuses on the integration and data transformation between GPS and totalstation.It emphasizes on the way to transfer the WGS84 Cartesian coordinates to the local two-dimensional plane coordinates and the orthometric height GPS receiver,totalstation,radio,notebook computer and the corresponding solftware work,together to form a new surveying system(SPS) and a new surveying model for terrestrial surveying.With the help of this system,the positions of detail points can be measured.     

Absolute Calibration of an Ashtech Z12-T GPS Receiver

Dual-frequency carrier phase and code measurements from geodetic type receivers are a promising tool for frequency and time transfer. In order to use them for clock comparisons, all instrumental delays should be calibrated. We have carried out the calibration of one such receiver, an Ashtech Z12-T type, by two different methods: first, by absolute calibration using a GPS simulator; second, by differential calibration with respect to a time transfer receiver that had previously been calibrated. We present the experimental set-ups and the results of the two experiments and estimate the uncertainty budget. An ultimate uncertainty of order 1 ns in the absolute calibration seems to be attainable. ? 2001 John Wiley & Sons, Inc.     

The effect of EGM2008-based normal, normal-orthometric and Helmert orthometric height systems on the Australian levelling network

This paper investigates the normal-orthometric correction used in the definition of the Australian Height Datum, and also computes and evaluates normal and Helmert orthometric corrections for the Australian National Levelling Network (ANLN). Testing these corrections in Australia is important to establish which height system is most appropriate for any new Australian vertical datum. An approximate approach to assigning gravity values to ANLN benchmarks (BMs) is used, where the EGM2008-modelled gravity field is used to ‘re-construct’ observed gravity at the BMs. Network loop closures (for first- and second-order levelling) indicate reduced misclosures for all height corrections considered, particularly in the mountainous regions of south eastern Australia. Differences between Helmert orthometric and normal-orthometric heights reach 44 cm in the Australian Alps, and differences between Helmert orthometric and normal heights are about 26 cm in the same region. Normal-orthometric heights differ from normal heights by up to 18 cm in mountainous regions >2,000 m. This indicates that the quasigeoid is not compatible with normal-orthometric heights in Australia.     

Geoid undulation computations at laser tracking stations

This paper studies the use of two new methods for gravimetric geoid undulation computations: The Molodenskii's and Sjöberg's methods that both modify the original Stokes'function so that certainrms errors are minimized. These new methods were checked against the traditional methods of Stokes' and Meissl's modification with the criterion of the globalrms undulation error that each method implies. Sjöberg's method gave consistently the smallest globalrms undulation error of all the other methods for capsizes 0° to 10°. However with the exception of Stokes' method, for capsizes between 0° to 5°, all the methods gave approximately (within±5cm) the same globalrms undulation error. Actual gravity data within a cap of 2° and potential coefficient information were then combined to compute the undulation of 39 laser stations distributed around the world. Therms discrepancy between the gravimetric undulations using all the four methods and the undulations computed as the ellipsoidal minus the orthometric height of 28 at the above stations was±1.70,±1.65,±1.66,±1.65m for the Stokes', Meissl's, Molodenskii's and Sjöberg's method respectively. For five oceanic laser stations where no terrestrial gravity data was available, theGEOS-3/SEASAT altimeter sea surface heights were used to compute the undulations of these stations in a collocation method. Therms discrepancy between the altimeter derived undulation and the ellipsoidal mirus orthometric value of the undulation was ±1.30m for the above five laser stations.     

Evaluation of EGM 2008 with EGM96 and its Utilization in Topographical Mapping Projects

Precise terrain elevation information is required in various remote sensing and Engineering projects. There are many technologies to derive the terrain elevation information like GPS, ground surveys, LiDAR, Photogrammetry. GPS is the most widely used technology to obtain information due to its ease of operation. However the usage of ellipsoidal heights, i.e. with respect to WGS84 has limited usage in hydrological applications. GPS heights must be converted into orthometric heights for use in hydrological applications, and this requires geoid undulation information. These geoid undulations can be deduced from earth gravity models. There are various earth gravity models available for ready usage like EGM96, EGM2008, GFZ96 in the public domain. This paper discusses the improvements observed in deriving orthometric heights using EGM2008 over its predecessor model EGM96. The utilization of the new model in topographical mapping projects are also presented.     

The rigorous determination of orthometric heights

The main problem of the rigorous definition of the orthometric height is the evaluation of the mean value of the Earth’s gravity acceleration along the plumbline within the topography. To find the exact relation between rigorous orthometric and Molodensky’s normal heights, the mean gravity is decomposed into: the mean normal gravity, the mean values of gravity generated by topographical and atmospheric masses, and the mean gravity disturbance generated by the masses contained within geoid. The mean normal gravity is evaluated according to Somigliana–Pizzetti’s theory of the normal gravity field generated by the ellipsoid of revolution. Using the Bruns formula, the mean values of gravity along the plumbline generated by topographical and atmospheric masses can be computed as the integral mean between the Earth’s surface and geoid. Since the disturbing gravity potential generated by masses inside the geoid is harmonic above the geoid, the mean value of the gravity disturbance generated by the geoid is defined by applying the Poisson integral equation to the integral mean. Numerical results for a test area in the Canadian Rocky Mountains show that the difference between the rigorously defined orthometric height and the Molodensky normal height reaches ∼0.5 m.     

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     

Time Transfer for TAI Using a Geodetic Receiver: An Example with the Ashtech ZXII-T

The International Atomic Time scale (TAI) is computed by the Bureau International des Poids et Mesures (BIPM) from a set of atomic clocks distributed in about 40 time laboratories around the world. The time transfer between these remote clocks is mostly performed by the so-called GPS common view method: The clocks are connected to a GPS time receiver whose internal software computes the offsets between the remote clocks and GPS time. These data are collected in a standard formal called CCTF. In the present study we develop both the procedure and the software tool that allows us to generate the CCTF files needed for time transfer to TAI, using RINEX files produced by geodetic receivers driven by an external frequency. The CCTF files are then generated from the RINEX observation files. The software is freely available at ftp://omaftp.oma.be/dist/astro/time/RINEX_CCTF. Applied to IGS (International GPS Service) receivers, this procedure will provide a direct link between TAI and the IGS clock combination. We demonstrate here the procedure using the RINEX files from the Ashtech Metronome (ZXII-T) GPS receiver, to which we apply the conventional analysis to compute the CCTF data. We compared these results with the CCTF files produced by a time receiver R100-30T from 3S-Navigation. We also used this comparison with the results of a calibrated time receiver to determine the hardware delay of the geodetic receiver. ? 2001 John Wiley & Sons, Inc.     

2005珠峰高程测定

2005年我国对珠穆朗玛峰高程进行了新的测定,为此在珠峰及其邻近地区开展了大规模的大地测量数据获取和数据处理工作。相对于1975年珠峰测高,2005年在珠峰以北地区的地面控制和珠峰高程测定中采用了GPS技术,采用了雷达探测技术测定珠峰峰顶冰雪覆盖层的深度,利用地球重力场模型、重力和数字地形数据、以及GPS水准等资料,精化珠峰地区的大地水准面,提高了测量珠峰高程和探测峰顶冰雪覆盖层深度的精度和可靠性。由此测得珠峰峰顶雪面正常高为8 846.67 M,珠峰峰顶雪面正高(海拔高)为8 847.93 M,珠峰峰顶岩面正高为8 844.43 M,珠峰峰顶相应点的冰雪层厚度为3.50 M。     

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