我国进行激光测月的研究

概述了全球激光测月的现状,分析了其困难和改进方法及我国开展激光测月的意义,提出了对我国开展激光测月工作的建议。     

Length-of-day and space-geodetic determination of the Earth’s variable gravity field

The temporal variations of the Earth’s gravity field, nowadays routinely determined from satellite laser ranging (SLR) and GRACE (Gravity Recovery And Climate Experiment), are related to changes in the Earth’s rotation rate through the Earth’s inertia tensor. We study this connection from actual data by comparing the traditional length-of-day (LOD) measurements provided by the International Earth Rotation and Reference Systems Service (IERS) to the variations of the degree-2 and order-0 Stokes coefficient of the gravity field determined from fitting the orbits of the LAGEOS-1 and −2 satellites since 1985. The two series show a good correlation (0.62) and similar annual and semi-annual signals, indicating that the gravity-field-derived LOD is valuable. Our analysis also provides evidence for additional signals common to both series, especially at a period near 120 days, which could be due to hydrological effects.     

Ocean tidal parameters from starlette data

Starlette was launched in 1975 in order to study temporal variations in the Earth’s gravity field; in particular, tidal and Earth rotation effects. For the period April 1983 to April 1984 over12,700 normal points of laser ranging data to Starlette have been sub-divided into49 near consecutive 5–6 day arcs. Normal equations for each arc as obtained from a least-squares data reduction procedure, were solved for ocean tidal parameters along with other geodetic and geodynamic parameters. The tidal parameters are defined relative to Wahr’s body tides and Wahr’s nutation model and show fair agreement with other satellite derived results and those obtained from spherical harmonic decomposition of global ocean tidal models.     

Gravity-dependent signal path variation in a large VLBI telescope modelled with a combination of surveying methods

The very long baseline interferometry (VLBI) antenna in Medicina (Italy) is a 32-m AZ-EL mount that was surveyed several times, adopting an indirect method, for the purpose of estimating the eccentricity vector between the co-located VLBI and Global Positioning System instruments. In order to fulfill this task, targets were located in different parts of the telescope’s structure. Triangulation and trilateration on the targets highlight a consistent amount of deformation that biases the estimate of the instrument’s reference point up to 1 cm, depending on the targets’ locations. Therefore, whenever the estimation of accurate local ties is needed, it is critical to take into consideration the action of gravity on the structure. Furthermore, deformations induced by gravity on VLBI telescopes may modify the length of the path travelled by the incoming radio signal to a non-negligible extent. As a consequence, differently from what it is usually assumed, the relative distance of the feed horn’s phase centre with respect to the elevation axis may vary, depending on the telescope’s pointing elevation. The Medicina telescope’s signal path variation ΔL increases by a magnitude of approximately 2 cm, as the pointing elevation changes from horizon to zenith; it is described by an elevation-dependent second-order polynomial function computed as, according to Clark and Thomsen (Techical report, 100696, NASA, Greenbelt, 1988), a linear combination of three terms: receiver displacement ΔR, primary reflector’s vertex displacement ΔV and focal length variations ΔF. ΔL was investigated with a combination of terrestrial triangulation and trilateration, laser scanning and a finite element model of the antenna. The antenna gain (or auto-focus curve) ΔG is routinely determined through astronomical observations. A surprisingly accurate reproduction of ΔG can be obtained with a combination of ΔV, ΔF and ΔR.     

Solution of the geodetic boundary value problem

Summary The possibility of improving the convergence of Molodensky’s series is considered. Then new formulas are derived for the solution of the geodetic boundary value problem. One of them presents an expression for the boundary condition which involves a linear combination of Stokes’ constants and surface gravity anomalies. This differs from the usually used relation by the appearance of additional terms dependent on second order terns with respect to the elevations of the earth’s surface. The formulas are derived for Stokes’ constants and the anomalous potential in terms of surface anomalies. As compared to the Taylor’s series of Molodensky, they are presented in the form of surface harmonic series. Due regard is made to the earth’s oblateness, in addition to the terrain topography.     

车载3D激光扫描系统集成技术

移动激光扫描技术是从上世纪90年代初逐步发展起来的一门测绘技术,也是当今测绘界最为前沿的技术之一,可用于工程测量和制图等诸多领域。地面3D激光扫描仪具有测量速度快,精度高等优点。本文以奥地利RIEGL公司的地面三维激光扫描仪VZ400为例,研究将其作为移动测量系统的主要传感器所涉及的关键技术,包括联机控制、时间基准统一和空间基准统一三个方面:解析了激光扫描仪的接口定义,并结合联机控制的开发库——RiVLIB实现的仪器的联机控与数据通信;给出了基于GPS秒脉冲信号的时间同步原理,实现了系统时间基准的传递与统一;分析了移动测量系统中的坐标系,并根据地面三维激光扫描仪的实际情况,构建了单站的参数标定模型。通过本文的研究与实验,使测量系统实现常见移动测量的二维帧扫描模式以及针对重点区域的三维全景扫描模式,同时,当它闲置时还可将激光扫描仪拆卸进行静态的扫描,丰富了系统的测量方式,提高了系统的适应性与使用效率。     

Web-based resources on software GPS receivers

This column provides the Web-based GPS resources and their technical background information. Its purpose is to inform the reader about the data, software, electronic documents that are available online. This column is coordinated by Dr. Jinling Wang, The University of New South Wales, Sydney. Comments and suggestions are appreciated (jinling.wang@unsw.edu.au). In this issue’s column, Mr. Ravindra Babu introduces the online resources on software GPS receivers.     

Performance analysis of the spaceborne laser ranging system

The Spaceborne Laser Ranging System is a proposed short pulse laser on board an orbiting spacecraft.^1,2,3,4 It measures the distance between the spacecraft and many laser retroreflectors (targets) deployed on the Earth’s surface. The precision of these range measurements is assumed to be about ±2 cm (M. W. Fitzmaurice, private communication). These measurements are then used together with the orbital dynamics of the spacecraft, to derive the relative position of the laser ground targets. Assuming a six day observing period with 50% cloud cover, uncertainties in the baseline for target separations of 50 km to 1200 km were estimated to be on the order of 1 to 3 cm and the corresponding values in the vertical direction, ranged from 1 cm to 12 cm. By redetermining the measurements of the relative target positions, the estimated precision in the baseline for a target separation of 50 km is less than 0.3 cm and for a separation of 1200 km is less than 1 cm. In the vertical direction, the estimated precision ranged from 0.4 cm to 4.0 cm respectively. As a result of the repeated estimation of the relative laser target positions, most of the non-temporal effects of error sources as exemplified by the errors in geopotential are reduced. The Spaceborne Laser Ranging System’s capability of determining baselines to a high degree of precision provides a measure of strain and strain rate as shown byCohen, 1979. These quantities are essential for crustal dynamic studies which include determination and monitoring of strain near seismic zones, land subsidence, and edifice building preceding volcanic eruptions. It is evident that such a system can also be used for geodetic surveys where such precisions are more than adquate.     

THE THEORY AND APPLICATION OF THE STRUCTURE LIGHT ENGINEERING SURVEYING BASED ON A LASER THEODOLITE WITH THREE FREEDOMS OF ROTATION

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Modeling of earth’s gravity fields visualization based on Quad Tree

The problems of the earth’s gravity fields’ visualization are both focus and puzzle currently. Aiming at multiresolution rendering, modeling of the Earth’s gravity fields’ data is discussed in the paper by using LOD algorithm based on Quad Tree. First, this paper employed the method of LOD based on Quad Tree to divide up the regional gravity anomaly data, introduced the combined node evaluation system that was composed of viewpoint related and roughness related systems, and then eliminated the T-cracks that appeared among the gravity anomaly data grids with different resolutions. The test results demonstrated that the gravity anomaly data grids’ rendering effects were living, and the computational power was low. Therefore, the proposed algorithm was a suitable method for modeling the gravity anomaly data and has potential applications in visualization of the earth’s gravity fields.     

Contribution au probleme de la compensation des reseaux de triangulation

Résumé Dans cette étude on expose une adaptation de la méthode des directions —pour la compensation d’un réseau de triangulation—aux possibilités de l’ordinateur électronique. On présente les formules par lesquelles on calcule les coefficients des inconnues dans les équations de condition (équations aux angles et équations aux c?tés) et on dresse leur matrice. Ensuite on traite de la formation de la matrice des coefficients des équations normales et son inversion, qui fournit les quantités corrélatives de Lagrange. Enfin, après avoir déterminé les corrections à apporter aux directions observées, on calcule l’erreur moyenne quadratique d’une observation isolée et l’erreur moyenne de chacune des directions compensées.

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Summary In this study, an adaptation to the computers’ possibilities, regarding the method of directions, is disclosed in order to realise the adjustment of triangulation nets. The computing formulae of the coefficients of the unknown quantities in the condition equations and the creation of their matrix are given herebelow. The treatment leading towards the construction of the matrix of normal equations and its inversion, that furnishes Lagrange’s quantities, follows. After the computation of the corrections applied on the observed directions, the mean error of a single observation and the mean error of every adjusted direction are determined. The study is executed in such a way that it can be included in only one programme for automatic computation.

     

Assessing consistency of Chang’E-1 and SELENE reference frames using nearly-colocated laser altimetry footprint positions

The consistency of the Chang’E-1 and SELENE reference frames as realized by the footprint positions of laser altimetry measurements of the lunar surface during both missions was analyzed using a global 12-parameter model for small (with respect to unity) deformations and rigid body motions. The rigid body motion and deformation parameters between the two reference frames estimated from nearly-colocated without tie measurements are found to be consistent, i.e., nearly zero for the estimates of the translations, rotations and shear parameters. However, the estimated three strain parameters, which are similar in magnitude and sign, reveal a prominent scale difference, between the Chang’E-1 and SELENE reference frames, of about 0.9 × 10⁻⁵. The scale difference can be attributed to calibration of the data sets using the known coordinates of the lunar laser ranging stations all located on the near side of the Moon.     

Triangulated spherical splines for geopotential reconstruction

We present an alternate mathematical technique than contemporary spherical harmonics to approximate the geopotential based on triangulated spherical spline functions, which are smooth piecewise spherical harmonic polynomials over spherical triangulations. The new method is capable of multi-spatial resolution modeling and could thus enhance spatial resolutions for regional gravity field inversion using data from space gravimetry missions such as CHAMP, GRACE or GOCE. First, we propose to use the minimal energy spherical spline interpolation to find a good approximation of the geopotential at the orbital altitude of the satellite. Then we explain how to solve Laplace’s equation on the Earth’s exterior to compute a spherical spline to approximate the geopotential at the Earth’s surface. We propose a domain decomposition technique, which can compute an approximation of the minimal energy spherical spline interpolation on the orbital altitude and a multiple star technique to compute the spherical spline approximation by the collocation method. We prove that the spherical spline constructed by means of the domain decomposition technique converges to the minimal energy spline interpolation. We also prove that the modeled spline geopotential is continuous from the satellite altitude down to the Earth’s surface. We have implemented the two computational algorithms and applied them in a numerical experiment using simulated CHAMP geopotential observations computed at satellite altitude (450 km) assuming EGM96 (n _max = 90) is the truth model. We then validate our approach by comparing the computed geopotential values using the resulting spherical spline model down to the Earth’s surface, with the truth EGM96 values over several study regions. Our numerical evidence demonstrates that the algorithms produce a viable alternative of regional gravity field solution potentially exploiting the full accuracy of data from space gravimetry missions. The major advantage of our method is that it allows us to compute the geopotential over the regions of interest as well as enhancing the spatial resolution commensurable with the characteristics of satellite coverage, which could not be done using a global spherical harmonic representation. The results in this paper are based on the research supported by the National Science Foundation under the grant no. 0327577.     

Upward and downward continuations in the geopotential determination

Summary The geopotential on and outside the earth is represented as a series in surface harmonics. The principal terms in it correspond to the solid harmonics of the external potential expansion with the coefficients being Stokes’ constantsC _nm andS _nm . The additional terms which occur near the earth’s surface due to its non-sphericity and topography are expressed in terms of Stokes’ constants too. This allows performing downward continuation of the potential derived from satellite observations. In the boundary condition which correlates Stokes’ constants and the surface gravity anomalies there occur additional terms due to the earth’s non-sphericity and topography. They are expressed in terms of Stokes’ constants as well. This improved boundary condition can be used for upward and downward continuations of the gravity field. Simple expressions are found representingC _nm andS _nm as explicit functions of the surface anomalies and its derivatives. The formula for the disturbing potential on the surface is derived in terms of the surface anomalies. All the formulas do not involve the earth’s surface in clinations.     

Effect of heteroscedasticity and heterogeneousness on outlier detection for geodetic networks

The robustness of an outlier detection method strongly depends on the weights of observations, i.e., the type of the stochastic model applied (homoscedasticity, heteroscedasticity and heterogeneousness). In this paper, we have investigated how the reliability of the robust methods and tests for outliers changes depending on the weights of the observations in geodetic networks. Furthermore, the contribution of the directions and distances to horizontal control network with regard to reliability are investigated separately. The concept of a breakdown point is used as a global measure of robustness against outliers. The mean success rate (MSR) is found to be a practical tool for confirming the breakdown point. Many different “good” data samples are generated for each network and then deliberately contaminated using a Monte-Carlo simulation. Six robust methods and Baarda’s test are applied to the corrupted samples and the degree of corruption is varied. The performance of each method is measured using both local and global MSRs. Our research shows: (1) The MSRs of Baarda’s test change depending on the strength of the heteroscedasticity, but do not change for trilateration and leveling networks, (2) the global MSRs of robust methods do not differ considerably from the local ones     

Small-world characteristics on transportation networks: a perspective from network autocorrelation

Studies on small-world networks have received intensive interdisciplinary attention during the past several years. It is well-known among researchers that a small-world network is often characterized by high connectivity and clustering, but so far there exist few effective approaches to evaluate small-world properties, especially for spatial networks. This paper proposes a method to examine the small-world properties of spatial networks from the perspective of network autocorrelation. Two network autocorrelation statistics, Moran’s I and Getis–Ord’s G, are used to monitor the structural properties of networks in a process of “rewiring” networks from a regular to a random network. We discovered that Moran’s I and Getis–Ord’s G tend to converge and have relatively low values when properties of small-world networks emerge. Three transportation networks at the national, metropolitan, and intra-city levels are analyzed using this approach. It is found that spatial networks at these three scales possess small-world properties when the correlation lag distances reach certain thresholds, implying that the manifestation of small-world phenomena result from the interplay between the network structure and the dynamics taking place on the network.      

A simulation study of multi-beam altimetry for lunar reconnaissance orbiter and other planetary missions

The combined use of altimetry, Earth-based Doppler and Earth-based range measurements in the lunar reconnaissance orbiter (LRO) mission (Chin et al. in Space Sci Rev 129:391–419, 2007) has been examined in a simulation study. It is found that in the initial phases of the mission orbit and altimeter geolocation accuracies should be better than 10 m in the radial component and 60 m overall. It is demonstrated that LRO’s precise 1-way laser range measurement from Earth-based stations (Smith et al. in Proceedings of the 15th International Laser Ranging Workshop, Canberra, Australia, October 15–20, 2006) will be useful for gravity recovery. The advantages of multiple laser beams are demonstrated for altimeter calibration, orbit determination and gravity recovery in general planetary settings as well as for LRO.     

Methods for the computation of geoid undulations from potential coefficients

The undulations of the geoid may be computed from spherical harmonic potential coefficients of the earth’s gravitational field. This paper examines three procedures that reflect various points of view on how this computation should be carried out. One method requires only the flattening of a reference ellipsoid to be defined while the other two methods require a complete definition of the parameters of the ellipsoid. It was found that the various methods give essentially the same undulations provided that correct parameters are chosen for the reference ellipsoid. A discussion is given on how these parameters are chosen and numerical results are reported using recent potential coefficient determinations.     

Far-zone effects for different topographic-compensation models based on a spherical harmonic expansion of the topography

The determination of the gravimetric geoid is based on the magnitude of gravity observed at the surface of the Earth or at airborne altitude. To apply the Stokes’s or Hotine’s formulae at the geoid, the potential outside the geoid must be harmonic and the observed gravity must be reduced to the geoid. For this reason, the topographic (and atmospheric) masses outside the geoid must be “condensed” or “shifted” inside the geoid so that the disturbing gravity potential T fulfills Laplace’s equation everywhere outside the geoid. The gravitational effects of the topographic-compensation masses can also be used to subtract these high-frequent gravity signals from the airborne observations and to simplify the downward continuation procedures. The effects of the topographic-compensation masses can be calculated by numerical integration based on a digital terrain model or by representing the topographic masses by a spherical harmonic expansion. To reduce the computation time in the former case, the integration over the Earth can be divided into two parts: a spherical cap around the computation point, called the near zone, and the rest of the world, called the far zone. The latter one can be also represented by a global spherical harmonic expansion. This can be performed by a Molodenskii-type spectral approach. This article extends the original approach derived in Novák et al. (J Geod 75(9–10):491–504, 2001), which is restricted to determine the far-zone effects for Helmert’s second method of condensation for ground gravimetry. Here formulae for the far-zone effects of the global topography on gravity and geoidal heights for Helmert’s first method of condensation as well as for the Airy-Heiskanen model are presented and some improvements given. Furthermore, this approach is generalized for determining the far-zone effects at aeroplane altitudes. Numerical results for a part of the Canadian Rocky Mountains are presented to illustrate the size and distributions of these effects.