Semi-dynamical Doppler satellite positioning

In semi-dynamical satellite geodesy, the satellite orbit is determined beforehand by dynamical methods, and tracking station coordinates are determined geometrically from satellite observations and the accepted satellite coordinates. This paper analyzes the use of the U.S. Navy Navigational Satellite Doppler (formerly Transit) system in the semidynamical mode, presenting some test network numberical results. Three error sources are considered: errors in the satellite coordinates, refractive errors on the Doppler observations, errors contributed by the tracking receivers. Compensatory techniques are discussed, such as relaxing the satellite orbit, ionospheric and tropospheric refraction reductions, tracking receiver time recovery, translocation.     

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.     

"嫦娥"卫星绕月飞行轨道的激光测定法

依据地月激光测距的成功实践和对卫星激光定轨的基础研究,提出了用地面对嫦娥卫星作激光测距的方法,高精度地测定嫦娥卫星绕月飞行时的实时在轨位置,论述了多站激光定轨和单站激光定轨的解算数模。     

Error model for geodetic positions derived from Doppler satellite observations

Doppler observations of Navy Navigation Satellites have been used to strengthen and extend many terrestrial geodetic networks. The main sources of errors in positions determined from these observations are random error of observations, random and systematic errors in satellite positions due to uncertainties in the gravity field, and biases in the coordinate system in which the satellite ephemeris is given. Effects of uncertainties in the gravity field on station coordinates computed with respect to a precise satellite ephemeris are reduced to about 70 cm after 20 satellite passes are observed, but systematic effects prevent assurance that additional observations will improve the accuracy further. A one part per million reduction in scale must be applied to positions computed with the ephemeris to obtain agreement with terrestrial and other precise determinations of scale. The origin of the system is coincident with the center of mass of the earth to 1 m accuracy but the polar axis may be tilted three to five meters at the earth's surface with respect to coordinate systems upon which star catalogues are based.     

EM算法在广播星历计算卫星位置中的应用

在利用广播星历计算卫星坐标时,为了提高效率,经常会采用多项式来进行拟合.由于多方面的原因,可能会导致拟合点数据的精度不够或者拟合点的个数不够,继续用此数据进行拟合则会大大降低拟合结果的精度和可靠性.文中使用EM（expectation maximization）算法添加有益于多项式拟合的“潜在数据”,即缺失数据的条件期望,有效提高缺失数据条件下卫星坐标的拟合精度和可靠性.     

Transformation between SLR/VLBI and WGS-84 reference frames

In geodetic and geophysical applications of GPS, it is important to realize the ephemerides of the GPS satellites and the coordinates of station positions in a consistent reference system. At present, more than one reference system is being used by various GPS users depending on their specific applications. The WGS-84 and various reference frames based on satellite laser ranging (SLR), very long baseline interferometry (VLBI), or a combination of SLR and VLBI are the most commonly used in high precision geophysical applications. The WGS-84 is widely used in applications which rely on the GPS broadcast ephemeris. Station coordinates estimated in one system may have to be transformed to another for further use or for evaluation/comparison purposes. This paper presents a seven-parameter transformation between the WGS-84 and SLR/VLBI reference frames. The GPS double-differenced phase measurements for two consecutive weeks from a set of five Defense Mapping Agency (DMA) sites (defined in the WGS-84 frame) and from an augmented set of fifteen CIGNET sites (defined in the SLR/VLBI frame) were processed in a least squares estimation scheme to determine station coordinates, from which the transformation parameters were determined. A scale difference of about 0.2 ppm and an orientation difference in longitude of about 31 milliarcseconds were found to be the only parameters of significance between the adopted SLR/VLBI and the WGS-84 frames. Transformation between WGS-84 and the ITRF90 is also included, in which the scale difference is the same as before but the longitude rotation is about 16 mas.     

Precise station positions from VLBI observations to satellites: a simulation study

Very long baseline interferometry (VLBI) tracking of satellites is a topic of increasing interest for the establishment of space ties. This shall strengthen the connection of the various space geodetic techniques that contribute to the International Terrestrial Reference Frame. The concept of observing near-Earth satellites demands research on possible observing strategies. In this paper, we introduce this concept and discuss its possible benefits for improving future realizations of the International Terrestrial Reference System. Using simulated observations, we develop possible observing strategies that allow the determination of radio telescope positions in the satellite system on Earth with accuracies of a few millimeters up to 1–2 cm for weekly station coordinates. This is shown for satellites with orbital heights between 2,000 and 6,000 km, observed by dense regional as well as by global VLBI-networks. The number of observations, as mainly determined by the satellite orbit and the observation interval, is identified as the most critical parameter that affects the expected accuracies. For observations of global positioning system satellites, we propose the combination with classical VLBI to radio sources or a multi-satellite strategy. Both approaches allow station position repeatabilities of a few millimeters for weekly solutions.     

Alignment of geodetic and satellite coordinate systems to the average terrestrial system

The parallelism of geodetic and satellite systems to the average terrestrial system is examined, under the assumption that a geodetic system is a fixed framework invariant with respect to geodetic network adjustment. In this case a geodetic system is rotated with respect to the average terrestrial system only about the ellipsoid normal of the initial point. The method is demonstrated using coordinates and covariance matrices for BC-4 and SECOR satellite tracking stations computed by Mueller and his co-workers. It is shown that the NAD geodetic system is scaled significantly larger than the satellite systems; the SECOR satellite systems have significant Z-rotations with respect to the average terrestrial system; and the ETH geodetic system may have a significant rotation with respect to the average terrestrial system.     

Improved GRACE kinematic orbit determination using GPS receiver clock modeling

Kinematic positions of Low Earth Orbiters based on GPS tracking are frequently used as pseudo-observations for single satellite gravity field determination. Unfortunately, the accuracy of the satellite trajectory is partly limited because the receiver synchronization error has to be estimated along with the kinematic coordinates at every observation epoch. We review the requirements for GPS receiver clock modeling in Precise Point Positioning (PPP) and analyze its impact on kinematic orbit determination for the two satellites of the Gravity Recovery and Climate Experiment (GRACE) mission using both simulated and real data. We demonstrate that a piecewise linear parameterization can be used to model the ultra-stable oscillators that drive the GPS receivers on board of the GRACE satellites. Using such a continuous clock model allows position estimation even if the number of usable GPS satellites drops to three and improves the robustness of the solution with respect to outliers. Furthermore, simulations indicate a potential accuracy improvement of the satellite trajectory of at least 40 % in the radial direction and up to 7 % in the along-track and cross-track directions when a 60-s piecewise linear clock model is estimated instead of epoch-wise independent receiver clock offsets. For PPP with real GRACE data, the accuracy evaluation is hampered by the lack of a reference orbit of significantly higher accuracy. However, comparisons with a smooth reduced-dynamic orbit indicate a significant reduction of the high-frequency noise in the radial component of the kinematic orbit.     

基于BDS广播星历的卫星坐标拟合精度分析

针对利用广播星历计算卫星位置时,需反复计算、效率较低的问题。提出利用切比雪夫多项式对广播星历进行卫星轨道拟合,即先计算部分固定时间间隔的卫星坐标作为已知节点,利用不同的拟合阶数,将拟合点与直接法求出的对应点求差,分析其拟合精度。实例表明,只要采取合适的拟合时间间隔和拟合阶数,广播星历拟合精度就可以满足要求。      

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.     

基于SDP4模型的导航卫星仰角及方位角预报

地面站可控天线可以不借助接收机而直接监测导航卫星的信号质量,地面天线伺服系统根据卫星的实时位置计算出仰角及方位角来确定天线的指向。广播星历及历书等常用的计算卫星位置的方法虽误差较小,但其误差随时间迅速扩大,基于该问题,论文论述了双行星历（TLE）结合SDP4模型进行卫星轨道预报方法,利用SDP4模型计算GPS导航卫星的实时位置并预报卫星的仰角及方位角,采用IGS 事后精密星历对其角度预报误差进行了评估,同时,还将该方法的预报误差与广播星历、历书、STK高精度轨道预报等方法的预报误差进行了对比。实验结果表明：采用SDP4模型对导航卫星进行位置预报可满足误差要求,且时间有效性长、通用性好,具备实际应用价值。     

Lasers and satellites: A geodetic application

Experiments photographing satellite reflected laser pulses have been made to demonstrate the feasibility of using an earth-based light source to illuminate satellites. The reflection was also recorded photoelectrically for range information. The reflections are photographed against stellar backgrounds from which the angular positions of the satellites relative to the laser site can be determined. With the angular information and the range data from the laser-illuminator, the position of the satellite in space is uniquely determined. When other widely separated laser-camera sites make simultaneous observations, the location of these sites relative to the “control” site can be found.     

Satellite Doppler solutions in terms of a single parameter

By an appropriate combination of the integrated doppler counts for a motionless ground station over two consecutive arcs, of a satellite path, it is possible to obtain a linear mathematical model relating the coordinates of the ground station to the observations. In this mathematical model, the involvement of the fourth unknown of the problem—the frequency off-set parameter, is, however, not linear. By application of the least squares technique, the solutions for the coordinates are obtained as analytical functions of the frequency off-set, parameter only. These, in turn, reduce the basic formula for the doppler count to be an implicit function of the same single variable. The value of the variable which provides the best fit of this function with the observed doppler counts, minimizing the sum of squares of the deviations for all involved pairs of satellite positions is the best value for the unknown frequency off-set parameter and an iterative technique is devised to compute this value. The desired values for the coordinates of the ground station can then be obtained by substitution of the best value of the frequency off-set parameter into the corresponding formula, and correcting for reducing the effects of the random noise in the observed dopple data.     

Laser station coordinates and baselines from long-ARC and short-ARC analyses of starlette

Laser ranging to Starlette from April 1983 to April 1984 has been used to determine a coordinate set, UASC.ST1, of laser reference points for 18 tracking stations. The coordinates were derived by application of the least-squares data reduction procedure in a simultaneous solution along with geodynamic parameters for 49 near consecutive 5–6 day arcs. Comparisons with the University of Texas station coordinates,LSC 8112 andLSC 8402, and theRGO, Herstmonceux, coordinates,RGOSC.LG2, reveal consistency to near 30 cm in each coordinate. Furthermore, the translation vectors of the comparisons are not significantly different from zero indicating consistency in the implied origins of the systems. The period of analysis included seven occasions in which STARLETTE was tracked near simultaneously by three or four laser stations in North America. Using the short arcs as reference frameworks, station coordinates were determined by application of two contrasting methods, namely, a multi-arc simultaneous analysis and a weighted mean of the individual pass solutions. The former compared more favourably with baselines from the long-arc solution with anRMS error of near 16 cm. Comparison against theLSC 8402 coordinates confirmed that baselines accurate to within 15 cm can be achieved by satellite laser ranging to Starlette.     

GPS卫星坐标的计算

GPS卫星的坐标计算是利用GPS进行定位的关键环节，在利用GPS进行导航和测量时，需要多次计算卫星的坐标，因此快速准确地计算出卫星任意时刻的坐标，对于提高GPS定位精度和速度具有重要的意义。通过实例分析了利用广播星历的轨道参数、拉格朗日多项式插值和切比雪夫多项式拟合这三种方法计算卫星任意时刻的坐标，并进行了精度比较。     

广播星历与精密星历切比雪夫插值的比较

在GPS数据处理后,用户需根据广播星历或者精密星历选择合理的插值方法解算任意观测时刻的卫星位置,从而得到目标物的空间位置。文中介绍拉格朗日和切比雪夫插值的基本原理,对精密星历进行切比雪夫多项式插值,并与同时段广播星历的拉格朗日插值进行比较分析,并得出一系列有益的结论。     

GPS卫星定轨研究及STK仿真分析

首先对GPS卫星的轨道定轨的原理进行了简单描述,以卫星的广播星历数据为基础,计算出卫星的16个轨道参数,进而得到该卫星任一时刻的瞬时坐标。以2017年4月7日的GPS07号卫星的广播星历数据为例,计算该GPS卫星当天的轨道坐标,并将结果与当天IGS提供的精密星历所提供的卫星轨道坐标进行比较,计算结果显示广播星历误差可达5 m。最后使用STK软件调用MATLAB软件读取数据进行仿真分析,模拟出卫星的轨道,并计算出卫星的坐标,数值结果可为轨道设计提供技术参考。     

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。     

Measuring rapid variations in Earth orientation,geocenter and crust with satellite laser ranging

This analysis was performed with the GEOSAT software developed at NDRE for high-precision analysis of satellite tracking and VLBI data for geodetic and geodynamic applications. To determine the amplitudes of the tidally coherent daily and sub-daily variations in the Earth's orientation, geocenter, and crust, we have analyzed twelve months of SLR tracking data from the LAGEOS I & II and ETALON I & II satellites, obtained between October 1992 and September 1993. Station coordinates and mean geocenter are determined with an accuracy of 1 to 2 cm. Amplitudes of diurnal and semidiurnal variations in UT1, polar motion, and geocenter are determined with a precision of ~2µts, ~20µas, and 1–3 mm in each component. It is demonstrated that it is possible to determine a one-year continuous high-precision series in UT1 using multi-satellite laser ranging.