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.     

随机模型对解算西安流动SLR站坐标的影响

合理的参数估计及精度评定不仅需要可靠的函数模型,而且需要正确的随机模型。从权函数和粗差编辑两方面,研究了不同随机模型对西安流动卫星激光测距（satellite laser ranging,SLR）站坐标解算的影响,采用全球Lageos-1卫星观测数据计算了西安流动SLR站坐标。计算结果表明:①西安流动SLR站的观测精度和坐标解算精度均达到厘米级。②随机模型直接影响SLR站坐标的解算结果及可靠性;对于相同的计算弧段,抗差方差分量估计得到的站坐标精度最高、结果最稳定,残差加权均方差最小,观测资料利用率也最高;对于相同的计算方案,采用的SLR数据越多,坐标估计精度越高。     

Short note: Crustal deformation in the key stone network detected by satellite laser ranging

The paper presents the results of crustal deformation, as evidenced by changed station coordinates, in the Tokyo metropolitan area detected by the satellite laser ranging (SLR) technique. The coordinates of two Key Stone SLR stations, Tateyama and Kashima, were determined from 4 weeks of orbital arcs of the LAGEOS-1 and LAGEOS-2 satellites with respect to 16 SLR stations kept fixed in the ITRF2000 reference frame. The station coordinates were calculated using the NASA GEODYN-II orbital program. The orbital RMS-of-fit for both satellites was 16 mm. The standard deviation of the estimated positions was 3 mm. A jump of about 5 cm in the baseline length between the Kashima and Tateyama stations was detected in June–August 2000 by VLBI and GPS techniques. This work confirms this crustal deformation as determined by SLR and vice versa. Analysis of coordinates of these stations shows that this effect was caused by a 4.5-cm displacement of the Tateyama station in the north-east direction. The change in the vertical component was not significant.     

The terrestrial and lunar reference frame in lunar laser ranging

The initial value problem and the stability of solution in the determination of the coordinates of three observing stations and four retro-reflectors by lunar laser ranging are discussed. Practical iterative computations show that the station coordinates can be converged to about 1 cm, but there will be a slight discrepancy of the longitudinal components computed by various analysis centers or in different years. There are several factors, one of which is the shift of the right ascension of the Moon, caused by the orientation deviation of the adopted lunar ephemeris, which can make the longitudinal components of all observing stations rotate together along the longitudinal direction with same angle. Additionally, the frame of selenocentric coordinates is stable, but a variation or adjustment of lunar third-degree gravitational coefficients will cause a simultaneous shift along the reflectors' longitudes or rotation around the Y axis. Received: 21 August 1996 / Accepted: 17 November 1998     

Accuracy analysis for the NAD 83 geodetic reference system

The North American Datum of 1983 (NAD 83) provides horizontal coordinates for more than 250,000 geodetic stations. These coordinates were derived by a least squares adjustment of existing terrestrial and space-based geodetic data. For pairs of first order stations with interstation distances between 10km and 100km, therms discrepancy between distances derived fromNAD 83 coordinates and distances derived from independentGPS data may be suitably approximated by the empirical rulee=0.008 K^0.7 where e denotes therms discrepancy in meters and K denotes interstation distance in kilometers. For the same station pairs, therms discrepancy in azimuth may be approximated by the empirical rule e=0.020 K^0.5. Similar formulas characterize therms discrepancies for pairs involving second and third order stations. Distance and orientation accuracies, moreover, are well within adopted standards. While these expressions indicate that the magnitudes of relative positional accuracies depend on station order, absolute positional accuracies are similar in magnitude for first, second, and third order stations. Adjustment residuals reveal a few local problems with theNAD 83 coordinates and with the weights assigned to certain classes of observations.     

Simultaneous observation solutions for NASA-MOTS and SPEOPT station positions on the North American Datum

Simultaneous observations of the GEOS-I and II flashing lamps by the NASA MOTS and SPEOPT cameras on the North American Datum (NAD) have been analyzed using geometrical techniques to provide an adjustment of the station coordinates. Two separate adjustments have been obtained. An optical data—only solution has been computed in which the solution scale was provided by the Rosman-Mojave distance obtained from a dynamic station solution. In a second adjustment, scaling was provided by processing simultaneous laser ranging data from Greenbelt and Wallops Island in a combined optical-laser solution. Comparisons of these results with previous GSFC dynamical solutions indicate an rms agreement on the order of 4 meters or better in each coordinate. Comparison with a detailed gravimetric geoid of North America yields agreement of 3 meters or better for mainland U.S. stations and 7 and 3 meters, respectively, for Bermuda and Puerto Rico.     

Error study for the determination of the center of mass of the earth from Pageos observations

The least squares adjustment for the station coordinates of the worldwide satellite triangulation net gives, in addition to the station positions, the positions of the satellites observed in a simultaneous event from two or more stations. Through successive events short arcs can be fitted and the coordinates of the center of mass of the earth can be determined. It is shown that the center of mass will be obtained with an accuracy consistent with the accuracy of the station positions, if well distributed Pageos arcs of about one quarter of a revolution are taken and if three events per arc are given.     

Apropos laser tracking to GPS satellites

. Laser tracking to GPS satellites (PRN5 and 6) provides an opportunity to compare GPS and laser systems directly and to combine data of both in a single solution. A few examples of this are given in this study. The most important results of the analysis are that (1) daily SLR station coordinate solutions could be generated with a few cm accuracy; (2) coordinates of nine stations were determined in a 2.3-year-long arc solution; (3) the contribution of laser data on the `SLR-GPS' combined orbit, resulting from the simultaneous processing of SLR and GPS data, is significant and (4) laser-only orbits have an accuracy of 10–20 cm, 1-day predictions of SLR orbits differ from IGS orbits by about 20–40 cm, 2-day predictions by 50–60 cm. Received: 1 October 1996 / Accepted: 14 February 1997     

Baseline estimation with semidynamic and geometric satellite methods

Accurate relative positioning via dynamic satellite methods is a complicated process. In an attempt to simplify this process a semidynamic method has been investigated in a real data environment. In this method quasi-simultaneous observations from pairs of stations are transformed to Simultaneous Range Differences(SRD's). With this transformation it is anticipated to reduce the effects of orbital and observational residual biases and, therefore, to obtain baselines the accuracy of which is less sensitive to the overall orbital accuracy and yet compatible to that of the observations. Using laser range observations to Lageos collected during theMERIT Main Campaign, baselines have been estimated via both theSRD and the geometric methods. Baselines estimated via the geometric method are independent of orbital errors and any inconsistencies affecting the implementation of the Terrestrial Reference Frame, and therefore they have been used in the present study as standards of comparison. From this comparison it was concluded that for baselines of regional extent, theSRD method is very efficient and at least as accurate as the more complex dynamic methods.     

Precision orbit computations for Starlette

The Starlette satellite, launched in February 1975 by the French Centre National d'Etudes Spatiales, was designed to minimize the effects of non-gravitational forces and to obtain the highest possible accuracy for laser range measurements. Analyses of the first four months of laser tracking data from nine stations. have confirmed the stability of the orbit and the precision to which the satellite's position can be established. Initial orbit computations using the GSFC GEM-7 gravity model produced rms fits of about 8 to 10 meters for arc lengths of 5 days. After tailoring a gravity model specifically to Starlette, the rms fits for the 5 day arcs were reduced significantly to the 1 to 2 meter level. An rms fit of 4.3 meters was obtained for a 90 day arc. Five day arcs overlapped by 2.5 days showed rms satellite position differences generally less than 2 meters. Prediction errors at the end of two months were less than 30 milliseconds.     

云南及周边地区GNSS数据处理方法优化

采用麻省理工学院开发的GAMIT／GLOBK软件,将2015年-2016年全球347个IGS站观测数据分七个子网解算,得到一个固定的参考框架来解算云南及周边地区的35个全球卫星导航系统（GNSS）基准站的坐标,测站坐标均方根误差水平方向在0.7 mm以内,垂直方向在0.3 mm以内,水平方向的坐标重复性精度在5 mm以内,垂向坐标的重复性精度大多数在2.5 cm以内;与在ITRF2014下解算的测站坐标、基线长度、水平速度场结果对比表明:测站坐标存在系统误差,水平方向上的差异在8.5 mm以内,垂直方向上在3 cm以内;基线长度差异在2 mm以内,水平速度场在数值上存在毫米级的差异,方向上基本一致．      

Contribution of Starlette,Stella, and AJISAI to the SLR-derived global reference frame

The contribution of Starlette, Stella, and AJISAI is currently neglected when defining the International Terrestrial Reference Frame, despite a long time series of precise SLR observations and a huge amount of available data. The inferior accuracy of the orbits of low orbiting geodetic satellites is the main reason for this neglect. The Analysis Centers of the International Laser Ranging Service (ILRS ACs) do, however, consider including low orbiting geodetic satellites for deriving the standard ILRS products based on LAGEOS and Etalon satellites, instead of the sparsely observed, and thus, virtually negligible Etalons. We process ten years of SLR observations to Starlette, Stella, AJISAI, and LAGEOS and we assess the impact of these Low Earth Orbiting (LEO) SLR satellites on the SLR-derived parameters. We study different orbit parameterizations, in particular different arc lengths and the impact of pseudo-stochastic pulses and dynamical orbit parameters on the quality of the solutions. We found that the repeatability of the East and North components of station coordinates, the quality of polar coordinates, and the scale estimates of the reference are improved when combining LAGEOS with low orbiting SLR satellites. In the multi-SLR solutions, the scale and the \(Z\) component of geocenter coordinates are less affected by deficiencies in solar radiation pressure modeling than in the LAGEOS-1/2 solutions, due to substantially reduced correlations between the \(Z\) geocenter coordinate and empirical orbit parameters. Eventually, we found that the standard values of Center-of-mass corrections (CoM) for geodetic LEO satellites are not valid for the currently operating SLR systems. The variations of station-dependent differential range biases reach 52 and 25 mm for AJISAI and Starlette/Stella, respectively, which is why estimating station-dependent range biases or using station-dependent CoM, instead of one value for all SLR stations, is strongly recommended. This clearly indicates that the ILRS effort to produce CoM corrections for each satellite, which are site-specific and depend on the system characteristics at the time of tracking, is very important and needs to be implemented in the SLR data analysis.     

The effect of earth orientation errors in baseline determination

The determination of baseline lengths from certain space techniques is based on the derived coordinates of the terminal stations. As such, the estimated baselines are susceptible to systematic errors that affect the relative coordinates. One source of error is in the set of parameters which describes the continuously changing relative orientation of the Conventional Terrestrial (CTS) and Inertial (CIS) Reference frames. Due to these errors, the coordinates of each terminal station may in fact refer to a slightly different coordinate svstem, and, therefore, when used for computing the length between the stations, errors will result. The expected magnitudes of such errors and their possible presence in current solutions are investigated. In conclusion, we find that the present level of accuracy and stability of the available parameters connecting the CTS and CIS (e.g., the ERP series) is unsatisfactory for centimeter level baseline length determinations. The available options are either the use of strictly simultaneous SLR data sets (similar to the VLBI data sets) or the improvement of the parameters connecting the CTS and the CIS. The first long-range step in the latter direction is the support of the IAG/IAU Joint Working Group COTES proposal [CSTG Bulletin, 1982], endorsed by both the IAG and IAU in various resolutions [IAU, 1983; IAG, 1982]. Presented at the Annual Fall Meeting of the American Geophysical Union, San Francisco, December 7–15, 1982, and at the Fifth Annual NASA Geodynamics Program Conference and Crustal Dynamics Project Review, Washington, D.C., January 24–28, 1983.     

Demonstration of sub-meter GPS orbit determination and 1.5 parts in 108 three-dimensional baseline accuracy

Differential tracking of theGPS satellites in high-earth orbit provides a powerful relative positioning capability, even when a relatively small continental U.S. fiducial tracking network is used with less than one-third of the fullGPS constellation. To demonstrate this capability, we have determined baselines of up to2000 km in North America by estimating high-accuracyGPS orbits and ground receiver positions simultaneously. The2000 km baselines agree with very long baseline interferometry(VLBI) solutions at the level of1.5 parts in10 ⁸ and showrms daily repeatability of0.3–2 parts in10 ⁸. The orbits determined for the most thoroughly trackedGPS satellites are accurate to better than1 m. GPS orbit accuracy was assessed from orbit predictions, comparisons with independent data sets, and the accuracy of the continental baselines determined along with the orbits. The bestGPS orbit strategies included data arcs of at least one week, process noise models for tropospheric fluctuations, estimation ofGPS solar pressure coefficients, and combined processing ofGPS carrier phase and pseudorange data. For data arcs of two weeks, constrained process noise models forGPS dynamic parameters significantly improved the solutions.     

基于 IGS 参考站的 CGCS2000坐标系控制测量探讨

为了使新疆某铜矿1980西安坐标系转换到2000国家大地坐标系（CGCS2000）,利用IGS站数据进行GPS联测,通过GAMIT/GLOBK等专业软件进行基线和坐标解算,实现1980西安坐标系向WGS-84坐标系再到CGCS2000坐标系的转换。     

激光跟踪仪坐标测量精度分析

激光跟踪仪是目前精度最高的移动式坐标测量系统,其实际测量精度是否符合标称精度,直接决定了测量精度能否满足需求精度,因此对仪器坐标测量精度的分析显得十分重要。坐标转换模型是反应多站测量坐标精度的理论基础,不同模型在反应仪器精度的准确性、精确性、稳定性和计算速度等方面有较大差别。本文对常用的坐标转换模型进行了对比分析,得出结论是四元数模型具有算法严谨、抗奇异性、表达简洁、运算快速和易于实现等优点,适用于计算坐标转换精度。本文以Leica AT901_b激光跟踪仪为例,进行坐标测量精度分析。多次设站获取同一组目标点数据,每测站与目标点保持良好网形结构,数据处理时首先排除粗差并检验可靠性,然后采用四元数模型计算坐标转换参数,并通过最小二乘平差算法解算参数精度及坐标测量精度。另外,为了反应激光跟踪仪的坐标测量精度与目标点距离的关系,本文以Leica AT901_b为例进行实验,在测程内由远及近多次设站获取数据,计算坐标测量内符合精度并给出了目标点距离与坐标精度的关系曲线。     

A demonstration of 1–2 parts in 107 accuracy using GPS

By interferometric analysis ofGPS phase observations made at Owens Valley, Mojave, and Mammoth Lakes, California, we determined the coordinate components of the71–245–313 km triangle of baselines connecting these sites. A separate determination was made on each of four days, April 1–4, 1985. The satellite ephemerides used in these determinations had been derived from observations on other baselines. Therms scatters of the four daily determinations of baseline vector components about their respective means ranged from a minimum of6 mm for the north component of the71-km baseline to a maximum of34 mm for the vertical component of the245-km baseline. To test accuracy, we compared the mean of ourGPS determinations of the245-km baseline between Owens Valley and Mojave with independent determinations by others using very-long-baseline interferometry(VLBI) and satellite laser ranging(SLR). TheGPS-VLBI difference was within 2 parts in10 ⁷ for every vector component. TheGPS-SLR difference was within6 parts in10 ⁸ in the horizontal coordinates, but83 mm in height.     

Study of a wide-angle laser ranging system for relative positioning of ground-based benchmarks with millimeter accuracy

A wide-angle airborne laser ranging system (WA-ALRS) is developed at the Institut Géographique National (IGN), France, with the aim of providing a new geodesy technique devoted to large (100 km²) networks with a high density (1 km⁻²) of benchmarks. The main objective is to achieve a 1-mm accuracy in relative vertical coordinates from aircraft measurements lasting a few hours. This paper reviews the methodology and analyzes the first experimental data achieved from a specific ground-based experiment. The accuracy in relative coordinate estimates is studied with the help of numerical simulations. It is shown that strong accuracy limitations arise with a small laser beam divergence combined with short range measurements when relatively few simultaneous range data are produced. The accuracy is of a few cm in transverse coordinates and a few mm in radial coordinates. The results from ground-based experimental data are fairly compatible with these predictions. The use of a model for systematic errors in the vehicle trajectory is shown to be necessary to achieve such a high accuracy. This work yields the first complete validation of modelization and methodology of this technique. An accuracy better than 1 mm and a few mm in vertical and horizontal coordinates, respectively, is predicted for aircraft experiments. Received: 19 June 1997 / Accepted: 17 February 1998     

Least squares collocation and statistical testing

The authors address the issue of statistical testing in least squares collocation (LSC) in two stages. The first stage concerns the extension and focusing of theLSC equations to the task of statistical testing. The second stage deals with statistical testing titself and is introduced in the second portion of the paper. The paper commences with an overview of the development ofLSC and its relationship to least squares adjustment (LSA). Expressions for the various random variables and their corresponding covariance matrices are derived and in some instances are gleaned from the literature for the following quantities: (i) corrections to the unknown parameters with a priori covariance information; (ii) estimated signal at both the observation and computation points; and (iii) the noise at the observation points. Some of the needed covariance matrices are either obscurely hidden in the literature or not available at all, but, nevertheless are given in the paper. Also given are expressions for the estimated variance factor which forms the basis of various statistical tests. The paper closes with an overview and enumeration of possible statistical tests for detection of outliers in the observations.     

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.