Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS

We built a new experimental apparatus (the “Satellite/lunar laser ranging Characterization Facility”, SCF) and created a new test procedure (the SCF-Test) to characterize and model the detailed thermal behavior and the optical performance of cube corner laser retroreflectors in space for industrial and scientific applications. The primary goal of these innovative tools is to provide critical design and diagnostic capabilities for Satellites Laser Ranging (SLR) to Galileo and other GNSS (Global Navigation Satellite System) constellations. The capability will allow us to optimize the design of GNSS laser retroreflector payloads to maximize ranging efficiency, to improve signal-to-noise conditions in daylight and to provide pre-launch validation of retroreflector performance under laboratory-simulated space conditions. Implementation of new retroreflector designs being studied will help to improve GNSS orbits, which will then increase the accuracy, stability, and distribution of the International Terrestrial Reference Frame (ITRF), to provide better definition of the geocenter (origin) and the scale (length unit).     

Simulation of optical response of retroreflectors for future lunar laser ranging

We numerically examined various retroreflectors as laser ranging targets for future missions to the Moon. The geometric conditions, such as the angle of incidence and velocity aberration, with lunar targets are much more restricted than those with most of the earth-orbiting artificial satellites. The numerical optical response simulation carried out in this study indicates that a single retroreflector with a diameter of 150–250 mm performs similar to the existing Apollo retroreflector arrays. Further, no dihedral angle is required for small retroreflectors with diameters below 150 mm for uncoated ones and below 100 mm for coated and hollow ones. Retroreflectors with larger diameters require dihedral angles of 0.20, 0.25, and 0.35 arcsec for coated, uncoated and hollow types, respectively. The objective of this fundamental study is to underlie the development of future laser ranging targets that are to be placed on the Moon.     

In-orbit assessment of laser retro-reflector efficiency onboard high orbiting satellites

The navigation and geodetic satellites that orbit the Earth at altitudes of approximately 20,000 km are tracked routinely by many of the Satellite Laser Ranging (SLR) stations of the International Laser Ranging Service (ILRS). In order to meet increasing demands on SLR stations for daytime and nighttime observations, any new mission needs to ensure a strong return signal so that the target is easily acquirable. The ILRS has therefore set a minimum effective cross-section of 100 million square metres for the on-board laser retro-reflector arrays (LRAs) and further recommends the use of ‘uncoated’ cubes in the arrays. Given the large number of GNSS satellites that are currently supported by SLR, it is informative to make an assessment of the relative efficiencies of the various LRAs employed. This paper uses the laser ranging observations themselves to deduce and then compare the efficiencies of the LRAs on the COMPASS-M1 navigation satellite, two satellites from the GPS and three from the GLONASS constellations, the two GIOVE test satellites from the upcoming Galileo constellation, the two Etalon geodetic spheres and the geosynchronous communications test satellite, ETS-8. All the LRAs on this set of satellites employ back-coated retro-reflector cubes, except those on the COMPASS-M1 and ETS-8 vehicles which are uncoated. A measure of return signal strength, and thus of LRA-efficiency, is calculated using the laser-range full-rate data archive from 2007 to 2010, scaled to remove the effects of variations in satellite range, atmospheric attenuation and retro-reflector target total surface area. Observations from five SLR stations are used in this study; they are Herstmonceux (UK), Yarragadee (Australia), Monument Peak and McDonald (USA) and Wettzell (Germany). Careful consideration is given to the treatment of the observations from each station in order to take account of local working practices and system upgrades. The results show that the uncoated retro-reflector cubes offer significant improvements in efficiency.     

The LAGEOS satellites orbit and Yukawa-like interactions

LAGEOS II general relativity pericenter precession has been analysed in terms of the errors produced by the mismodelling of both the gravitational and non-gravitational perturbations acting on the satellite orbit. The accuracy in the pericenter determination may be considered as an upper-bound value for the estimate of the strength α of a possible new-long-range-interaction described by a Yukawa-like potential. In the present work we have focused on the constraints in α that can be obtained with the current best multi-satellites gravity field model EGM96 (α < 2.6 × 10⁻¹⁰) and also with the first promising models from the CHAMP (α < 1.8 × 10⁻¹⁰) and GRACE (α < 1.2 × 10⁻¹⁰) gravimetric missions. These results represent, potentially, an improvement of two or three orders-of-magnitude with respect to the best constraints obtained in the past with Earth–LAGEOS and Lunar–LAGEOS data (|α| < 10⁻⁵–10⁻⁸). The impact of the non-gravitational perturbations mismodelling in the final error budget has been determined together with the improvements obtainable in the constraint of the strength α with the proposed LARES satellite.     

Spin axis orientation of Ajisai determined from Graz 2 kHz SLR data

The Graz 2 kHz Satellite Laser Ranging (SLR) measurements allow determination of the spin axis orientation of the geodetic satellite Ajisai. The high repetition rate of the laser makes it possible to determine the epoch time when the laser is pointing directly between two corner cube reflector (CCR) rings of the satellite. Identification of many such events during a few (up to 3) consecutive passes allows to state the satellite orientation in the celestial coordinate system. Six years of 2 kHz SLR data (October 2003–October 2009) delivered 331 orientation values which clearly show precession of the axis along a cone centered at 14^h56^m2.8^s in right ascension and 88.512° in declination (J2000.0 celestial reference frame) and with an half-aperture angle θ of 1.405°. The spin axis precesses with a period of 117 days, which is equal to the period of the right ascension of the ascending node of Ajisai’s orbit. We present a model of the axis precession which allows prediction of the satellite orientation – necessary for the envisaged laser time transfer via Ajisai mirrors.     

Spectral response of Experimental Geodetic Satellite determined from high repetition rate SLR data

The design of the retroreflector array (RRA) of the fast spinning Experimental Geodetic Satellite (Ajisai) allows to determine orientation of its spin axis by means of frequency analysis. Moving spectral analysis (MSA) of the simulated Satellite Laser Ranging (SLR) data gives information about frequencies which can be obtained for the whole range of the incident angle between the laser beam vector and the spin axis of the spacecraft. This frequency signal changes as the incident laser beam crosses consecutive rings of the RRA.     

Spin parameters of nanosatellite BLITS determined from Graz 2 kHz SLR data

The nanosatellite BLITS (Ball Lens In The Space) is the first object designed as a passive, spherical retroreflector of the Luneburg type, dedicated for Satellite Laser Ranging (SLR). The 2 kHz SLR station Graz measures spin parameters of this satellite, providing information about the rotational dynamics of the body. The measurements obtained during the period from September 26, 2009 to November 24, 2010 show a significant change of the spin configuration. The spin axis was dynamically precessing since the launch and currently is sinus-like behaving between coordinates RA 120°…150°, Dec 30°…60° (J2000 inertial reference frame). The angle between the symmetry axis and the spin axis of BLITS is not constant, but is decreasing since the launch, while its spin period is rather stable with a mean value of 5.613 s (clockwise rotation). The satellite was dynamically changing its attitude during the first three months after deployment; after this time the spin parameters are relatively stable.     

两种J_2摄动模型下卫星编队相对位置误差分析

为了研究一个轨道周期内卫星和卫星编队的运动规律,在J2摄动理论基础之上,采用摄动加速度分析方法,给出了J2瞬时摄动模型。以近地太阳同步轨道卫星和双星编队为例,与只考虑J2一阶长期项的平均摄动模型比较,仿真分析结果表明,对卫星而言,一个轨道周期内,卫星半长轴相对平均半长轴漂移达到18km,偏心率相对平均偏心率漂移达到10-3量级,轨道倾角相对平均轨道倾角漂移达到0.01°,即由于J2瞬时摄动的影响,卫星运动发生了摄动;对双星编队而言,一个轨道周期内,两星相对位置的径向误差达到5km,沿迹向误差达到19km,法向误差相对较小,在10-2量级上,相对距离的误差达到了19km,随着时间的推移,误差会越来越大。     

22 Years of AJISAI spin period determination from standard SLR and kHz SLR data

Satellite Laser Ranging (SLR) is a powerful and efficient technique to measure spin parameters of satellites equipped with corner cube reflectors. We obtained spin period determination of the satellite AJISAI from SLR data only: 17246 pass-by-pass estimates from standard 1–15 Hz SLR data (14/Aug/1986–30/Dec/2008) and 1444 pass-by-pass estimates (9/Oct/2003–30/Dec/2008) from data of the first 2 kHz SLR system from Graz, Austria. A continuous history of the slowing down of AJISAI spin is derived from frequency analysis, and corrected for the apparent effects. The apparent corrections, elaborated here, allowed very accurate determination of AJISAI initial spin period: 1.4855 ± 0.0007 [s]. The paper identifies also non-gravitational effects as a source of the periodical changes in the rate of slowing down of the satellite.     

Optical response of nanosatellite BLITS measured by the Graz 2 kHz SLR system

The nanosatellite BLITS (Ball Lens In The Space) is the first object designed as a passive, spherical retroreflector of the Luneburg type, dedicated for Satellite Laser Ranging (SLR). The optical response of BLITS has been measured by the Graz 2 kHz SLR station and compared with the response of the classical retroreflector arrays (RRA) of the Low Earth Orbiting satellites such as ERS-2 and Stella. This work demonstrates that the optical response of BLITS is flat and featureless, comparable with the signature of a point-source or a flat target, and suggests that this innovative design will deliver a higher normal point (NP) accuracy (2.55 mm) than any other SLR target currently in orbit. The high reflectivity of the glassy BLITS (about 60% of the return rate from the multi-reflector Stella) is found to be decreasing by about 30% per year, probably due to the solar irradiation. Detailed analysis of the reflective half-shell demonstrates that a high return rate of SLR measurements can be achieved regardless of the incident angle of the laser beam, thus making the spherical lens a perfect successor of the classical RRA panels mounted on active satellites such as CHAMP, GOCE and GRACE.     

Some comparisons of orbit determination and parameter estimation based on LAGEOS 1 and LAGEOS 2 data

The modelling accuracy of the LAGEOS 1 orbit was continously improved since its launch in 1976. In spite of these experiences the modelling accuracy of LAGEOS 2 is still about 20 per cent worse. Considering e. g. only the influence of different gravity field models it has been shown that the orbital fits for arc lengths of one month is generally about 25 mm for LAGEOS 1 and more than 30 mm for LAGEOS 2. This is mainly due to the fact that LAGEOS 2 has not yet been used for the determination of most gravity field models. The influences of different model parameters on the estimation of station coordinates, Earth rotation parameters, the geogravitational coefficient, the radiation pressure coefficient, and the empirical acceleration has been studied. The differences and peculiarities of both satellites are discussed. Although the analysis of LAGEOS 2 data still does not reach the high level of LAGEOS 1 combination solutions using both satellites allow new insights, higher accuracies, and a higher time resolution for the parameters and phenomena investigated.     

Determination of station positions and velocities from laser ranging observations to Ajisai,Starlette and Stella satellites

The positions and velocities of the four Satellite Laser Ranging (SLR) stations: Yarragadee (7090), Greenbelt (7105), Graz (7839) and Herstmonceux (7840) from 5-year (2001–2005) SLR data of low orbiting satellites (LEO): Ajisai, Starlette and Stella were determined. The orbits of these satellites were computed from the data provided by 20 SLR stations. All orbital computations were performed by means of NASA Goddard’s GEODYN-II program. The geocentric coordinates were transformed to the topocentric North–South, East–West and Vertical components in reference to ITRF2005. The influence of the number of normal points per orbital arc and the empirical acceleration coefficients on the quality of station coordinates was studied. To get standard deviation of the coordinates determination lower than 1 cm, the number of the normal points per site had to be greater than 50. The computed positions and velocities were compared to those derived from LAGEOS-1/LAGEOS-2 data. Three parameters were used for this comparison: station coordinates stability, differences from ITRF2005 positions and velocities. The stability of coordinates of LEO satellites is significantly worse (17.8 mm) than those of LAGEOS (7.6 mm), the better results are for Ajisai (15.4 mm) than for Starlette/Stella (20.4 mm). The difference in positions between the computed values and ITRF2005 were little bit worse for Starlette/Stella (6.6 mm) than for LAGEOS (4.6 mm), the results for Ajisai were five times worse (29.7 mm) probably due to center of mass correction of this satellite. The station velocities with some exceptions were on the same level (≈1 mm/year) for all satellites. The results presented in this work show that results from Starlette/Stella are better than those from Ajisai for station coordinates determination. We can applied the data from LEO satellites, especially Starlette and Stella for determination of the SLR station coordinates but with two times lower accuracy than when using LAGEOS data.     

Non-conservative forces on LAGEOS I and II

The behavior of the empirically determined along-track accelerations from the LAGEOS satellites has been attributed to a variety of physical phenomena. Of these, the models for Yarkovsky thermal drag, anisotropic reflectivity and Yarkovsky-Schach drag are dependent on the spin axis orientation of the satellite. This investigation explores the utilization of these models in an attempt to recover the spin axis orientation history, particularly for the LAGEOS I satellite.     

Spin rate and spin axis orientation of LARES spectrally determined from Satellite Laser Ranging data

Satellite Laser Ranging (SLR) is a powerful technique able to measure spin rate and spin axis orientation of the fully passive, geodetic satellites. This work presents results of the spin determination of LARES – a new satellite for testing General Relativity. 529 SLR passes measured between February 17 and June 9, 2012, were spectrally analyzed. Our results indicate that the initial spin frequency of LARES is f₀ = 86.906 mHz (RMS = 0.539 mHz). A new method for spin axis determination, developed for this analysis, gives orientation of the axis at RA = 12^h22^m48^s (RMS = 49^m), Dec = −70.4° (RMS = 5.2°) (J2000.0 celestial reference frame), and the clockwise (CW) spin direction. The half-life period of the satellite’s spin is 214.924 days and indicates fast slowing down of the spacecraft.     

立方体实体化的遗传算法设计与实现

多维立方体由基本立方体和基本立方体的聚集产生的立方体组成.为了实时响应查询,查询优化非常重要.多维立方体实体化是一种很好的解决方案.在整个立方体集中实体化一个适当的子集,满足较好的空间和时间的平衡,并且满足对视图查询频率不同的要求.为了实体化一个合适的立方体子集,通过介绍启发策略,提出了立方体实体化的启发式遗传算法.该算法可以在用户要求的限定的存储空间约束条件下,较快的求出全局最优解.经实验测试,该算法具有良好的性能和快速的求解能力.      

差分技术在双星快速定位通信系统中的应用

卫星定位通信系统是具有10米以内高精度的第二代卫星导航定位系统。达到高精度的关键是应用了伪随机码扩谱及差分定位技术。诸如星历误差、电离层时延变化和地球模型不准等误差,通过应用差分技术可以大部分消除。本文阐述了差分技术的应用和系统精度分析。     

Precision orbit determination for TOPEX/Poseidon using TDRSS doppler tracking data

Precision orbit determination on the TOPEX/Poseidon (T/P) altimeter satellite is now being routinely achieved with sub-5cm radial and sub-15 cm total positioning accuracy using state-of-the-art modeling with precision tracking provided by a combination of: (a) global Satellite Laser Ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), or (b) the Global Positioning System (GPS) Constellation which provides pseudo-range and carrier phase observations. The geostationary Tracking and Data Relay Satellite System (TDRSS) satellites are providing the operational tracking and communication support for this mission. The TDRSS Doppler data are of high precision (0.3 mm/s nominal noise levels). Unlike other satellite missions supported operationally by TDRSS, T/P has high quality independent tracking which enables absolute orbit accuracy assessments. In addition, the T/P satellite provides extensive geometry for positioning a satellite at geostationary altitude, and thus the TDRSS-T/P data provides an excellent means for determining the TDRS orbits. Arc lengths of 7 and 10 days with varying degrees of T/P spacecraft attitude complexity are studied. Sub-meter T/P total positioning error is achieved when using the TDRSS range-rate data, with radial orbit errors of 10.6 cm and 15.5 cm RMS for the two arcs studied. Current limitations in the TDRSS precision orbit determination capability include mismodeling of numerous TDRSS satellite-specific dynamic and electronic effects, and in the inadequate treatment of the propagation delay and bending arising from the wet troposphere and ionosphere.     

风云三号星载天线的准光学分析与设计

利用准光学原理分析了风云三号卫星湿度仪天馈系统. 利用等效面磁流和等效面电流法分析得到栅网在高斯波束入射时交叉极化小于-42 dB. 应用高斯模耦合法代替传统的ABCD矩阵分析偏馈反射面, 在大焦径比情况下, 推导出较为简单的高斯模耦合矩阵解析式. 系统实测方向图与仿真结果对比显示, 准光学分析能够快速处理偏馈反射面天线系统, 得到较高精度的结果.      

板式空心角锥棱镜的研制

在远距离测量、特别是距离达到一公里左右时,角锥棱镜几乎是唯一可行的反射器件。远距离测量的需求是增大角锥棱镜的通光口径,以便于捕捉目标,并增大反射光的能量。常用的整体式角锥棱镜,以及国外的柱式空心角锥棱镜,随着通光口径的增大,都会显著增加棱镜的体积与重量,造成使用不便与工艺困难。解决办法是采用板式结构,经试验,通光口径为80mm的板式空心角锥棱镜,工作距离可达一公里以上,出射光对入射光的平行度达角秒级,体积与重量在可以接受的范围内,而且可以降低工艺难度。     

Time synchronization of new-generation BDS satellites using inter-satellite link measurements

Autonomous satellite navigation is based on the ability of a Global Navigation Satellite System (GNSS), such as Beidou, to estimate orbits and clock parameters onboard satellites using Inter-Satellite Link (ISL) measurements instead of tracking data from a ground monitoring network. This paper focuses on the time synchronization of new-generation Beidou Navigation Satellite System (BDS) satellites equipped with an ISL payload. Two modes of Ka-band ISL measurements, Time Division Multiple Access (TDMA) mode and the continuous link mode, were used onboard these BDS satellites. Using a mathematical formulation for each measurement mode along with a derivation of the satellite clock offsets, geometric ranges from the dual one-way measurements were introduced. Then, pseudoranges and clock offsets were evaluated for the new-generation BDS satellites. The evaluation shows that the ranging accuracies of TDMA ISL and the continuous link are approximately 4?cm and 1?cm (root mean square, RMS), respectively. Both lead to ISL clock offset residuals of less than 0.3?ns (RMS). For further validation, time synchronization between these satellites to a ground control station keeping the systematic time in BDT was conducted using L-band Two-way Satellite Time Frequency Transfer (TWSTFT). System errors in the ISL measurements were calibrated by comparing the derived clock offsets with the TWSTFT. The standard deviations of the estimated ISL system errors are less than 0.3?ns, and the calibrated ISL clock parameters are consistent with that of the L-band TWSTFT. For the regional BDS network, the addition of ISL measurements for medium orbit (MEO) BDS satellites increased the clock tracking coverage by more than 40% for each orbital revolution. As a result, the clock predicting error for the satellite M1S was improved from 3.59 to 0.86?ns (RMS), and the predicting error of the satellite M2S was improved from 1.94 to 0.57?ns (RMS), which is a significant improvement by a factor of 3–4.