Precise orbit determination for the GRACE mission using only GPS data

The GRACE (gravity recovery and climate experiment) satellites, launched in March 2002, are each equipped with a BlackJack GPS onboard receiver for precise orbit determination and gravity field recovery. Since launch, there have been significant improvements in the background force models used for satellite orbit determination, most notably the model for the geopotential. This has resulted in significant improvements to orbit accuracy for very low altitude satellites. The purpose of this paper is to investigate how well the orbits of the GRACE satellites (about 470 km in altitude) can currently be determined using only GPS data and based on the current models and methods. The orbit accuracy is assessed using a number of tests, which include analysis of orbit fits, orbit overlaps, orbit connecting points, satellite Laser ranging residuals and K-band ranging (KBR) residuals. We show that 1-cm radial orbit accuracy for the GRACE satellites has probably been achieved. These precise GRACE orbits can be used for such purposes as improving gravity recovery from the GRACE KBR data and for atmospheric profiling, and they demonstrate the quality of the background force models being used.     

Rapid orbit determination of LEO satellites using IGS clock and ephemeris products

Different types of GPS clock and orbit data provided by the International GPS Service (IGS) have been used to assess the accuracy of rapid orbit determination for satellites in low Earth orbit (LEO) using spaceborne GPS measurements. To avoid the need for reference measurements from ground-based reference receivers, the analysis is based on an undifferenced processing of GPS code and carrier-phase measurements. Special attention is therefore given to the quality of GPS clock data that directly affects the resulting orbit determination accuracy. Interpolation of clock data from the available 15 min grid points is identified as a limiting factor in the use of IGS ultra-rapid ephemerides. Despite this restriction, a 10-cm orbit determination accuracy can be obtained with these products data as demonstrated for the GRACE-B spacecraft during selected data arcs between 2002 and 2004. This performance may be compared with a 5-cm orbit determination accuracy achievable with IGS rapid and final products using 5 min clock samples. For improved accuracy, high-rate (30 s) clock solutions are recommended that are presently only available from individual IGS centers. Likewise, a reduced latency and more frequent updates of IGS ultra-rapid ephemerides are desirable to meet the requirements of upcoming satellite missions for near real-time and precise orbit determination.     

Geocoding SAR interferograms by least squares adjustment

A geocoding model for Synthetic Aperture Radar (SAR) interferometry based on a least-squares adjustment combining interferometric phase, range, Doppler centroid frequency, flight path and control point data is proposed. The complete mathematical framework for the computation of object space coordinates without approximations is presented. It provides a way to an efficient implementation of the algorithm for geocoding the pixels of an interferogram. The method is preferably applicable to spaceborne dual-pass interferometry, and independent of the orbit configuration. An accuracy analysis of object point positioning is conducted and results of geocoding an ERS tandem interferogram are shown.     

重力卫星星载GPS简化动力学精密定轨

利用GRACE和SWARM重力卫星星载GPS观测数据,基于简化动力学方法进行精密定轨,通过相位观测值残差分析、重叠轨道对比和科学轨道对比进行轨道精度检核。GRACE和SWARM卫星相位观测值残差RMS值稳定在6 mm左右,重叠轨道对比差值RMS在径向、切向和法向均优于1.24 cm;通过与GFZ和ESA提供的GRACE卫星与SWARM卫星精密轨道对比,GRACE卫星简化动力学轨道在R,T,N方向的轨道精度分别达到1.3 cm、2.1 cm和1.3 cm;SWARM卫星简化动力学轨道在径向、切向和法向的轨道精度分别达到0.8 cm、1.3 cm和1.6 cm。实验表明,基于简化动力学方法,GRACE和SWARM卫星定轨精度均到达厘米级。     

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.     

Geometry and accuracy of reflecting points in bistatic satellite altimetry

The analysis of the time and space distribution of specular (reflecting) points in bistatic altimetry between GPS and CHAMP satellites or SAC-C (taken as examples) is extended from Wagner and Klokočník (2003 J. Geod 77: 128–138). We demonstrate a significantly higher number and density of reflecting points in bistatic altimetry in comparison with traditional monostatic altimetry. After an outline of our older accuracy assessment for the vertical position of the reflecting point, we add a new independent derivation and compare both approaches. We account for orbit errors of both the transmitters (GPS) and receiver (CHAMP) satellites, and the measurement (delay) error. We found that the accuracy of the vertical position of the reflecting point decreases only slowly with increasing off-nadir angle and that the orbit errors must be accounted for if decimeter and better accuracy is required. In this paper, we do not study errors such as state of the ocean, technical parameters of the receiving system, and atmospheric corrections.     

Quality assessment of FORMOSAT-3/COSMIC and GRACE GPS observables: analysis of multipath, ionospheric delay and phase residual in orbit determination

The precise orbit determination antennas of F3/C and GRACE-A satellites are from the same manufacturer, but are installed in different configurations. The current orbit accuracy of F3/C is 3 cm at arcs with good GPS data, compared to 1 cm of GRACE, which has a larger ratio of usable GPS data. This paper compares the qualities of GPS observables from F3/C and GRACE. Using selected satellites and time spans, the following average values for the satellite F3/C and satellite A of GRACE are obtained: multipath effect on the pseudorange P1, 0.78 and 0.38 m; multipath effect on the pseudorange P2, 1.03 and 0.69 m; occurrence frequency of cycle slip, 1/29 and 1/84; standard error of unit weight, 4 and 1 cm; dynamic–kinematic orbit difference, 10 and 2 cm. For gravity determination using F3/C GPS data, a careful selection of GPS data is critical. With six satellites in orbit, F3/C’s large amount of GPS data will make up the deficiency in data quality.     

相对轨道根数的重轨InSAR卫星基线分析与控制

星载重轨干涉SAR卫星在高程测绘和形变测量中有着全天时全天候和大范围的优势,其中干涉基线是决定干涉性能的重要指标,而卫星重访轨道对干涉基线起着决定性的作用。通过对现有高分三号干涉数据轨道参数的分析,发现干涉基线相比国外先进卫星过长且稳定性有待提高。本文通过对相对轨道根数和机动控制的分析,得到满足重轨干涉SAR系统要求的稳定基线。以第一次观测的轨道为参考轨道,基于在摄动情况下重复观测轨道与参考轨道的相对轨道根数,计算得到重轨干涉基线的变化规律,并对不同纬度的观测目标进行了样例分析。在基线变化规律的基础上,利用机动速度和相对轨道根数的关系,进一步计算得到满足基线状态需求的机动控制方法。通过实际数据分析,给出了相对轨道根数变化对初始理想构型的影响,验证了重轨干涉基线变化规律符合本文的分析,并利用仿真样例给出了使得重轨干涉基线达到预期要求的机动控制方案。实际数据和仿真实验表明该模型能够通过可长时间观测并准确获得的轨道根数直接计算基线状态,并能从干涉基线需求出发,快速准确的得出对卫星的控制策略。     

The celestial mechanics approach: application to data of the GRACE mission

The celestial mechanics approach (CMA) has its roots in the Bernese GPS software and was extensively used for determining the orbits of high-orbiting satellites. The CMA was extended to determine the orbits of Low Earth Orbiting satellites (LEOs) equipped with GPS receivers and of constellations of LEOs equipped in addition with inter-satellite links. In recent years the CMA was further developed and used for gravity field determination. The CMA was developed by the Astronomical Institute of the University of Bern (AIUB). The CMA is presented from the theoretical perspective in (Beutler et al. 2010). The key elements of the CMA are illustrated here using data from 50 days of GPS, K-Band, and accelerometer observations gathered by the Gravity Recovery And Climate Experiment (GRACE) mission in 2007. We study in particular the impact of (1) analyzing different observables [Global Positioning System (GPS) observations only, inter-satellite measurements only], (2) analyzing a combination of observations of different types on the level of the normal equation systems (NEQs), (3) using accelerometer data, (4) different orbit parametrizations (short-arc, reduced-dynamic) by imposing different constraints on the stochastic orbit parameters, and (5) using either the inter-satellite ranges or their time derivatives. The so-called GRACE baseline, i.e., the achievable accuracy of the GRACE gravity field for a particular solution strategy, is established for the CMA.     

基于Kalman滤波的InSAR基线估计方法

针对目前SAR干涉测量中基线估计现存的问题,提出了利用Kalman滤波和配准参数进行基线估计的方法.所提出的方法具有不需地面控制点、不受地形限制和不依赖于轨道参数等优点,并可以估计时变的基线参数.利用南京地区的ERS-1/2 tandem数据进行了试验研究,并对提出的方法进行了验证.结果表明,在精确的卫星轨道数据和地面控制点不能获取时,所提出的方法仍能有效地估计InSAR基线.这在一定程度上补偿了轨道偏移带来的误差,为获取高精度的DEM奠定了基础.     

Geocenter variations derived from GPS tracking of the GRACE satellites

Two 4.5-year sets of daily geocenter variations have been derived from GPS-LEO (Low-Earth Orbiter) tracking of the GRACE (Gravity Recovery And Climate Experiment) satellites. The twin GRACE satellites, launched in March 2002, are each equipped with a BlackJack global positioning system (GPS) receiver for precise orbit determination and gravity recovery. Since launch, there have been significant improvements in the background force models used for satellite orbit determination, most notably the model for the geopotential, which has resulted in significant improvements to the orbit determination accuracy. The purpose of this paper is to investigate the potential for determining seasonal (annual and semiannual) geocenter variations using GPS-LEO tracking data from the GRACE twin satellites. Internal comparison between the GRACE-A and GRACE-B derived geocenter variations shows good agreement. In addition, the annual and semiannual variations of geocenter motions determined from this study have been compared with other space geodetic solutions and predictions from geophysical models. The comparisons show good agreement except for the phase of the z-translation component.     

基于几何配准的多模式SAR影像配准及其误差分析

星载合成孔径雷达影像干涉处理时所需方位向配准精度因成像模式的差异而有所不同,目前在精密轨道条件下以几何配准为基础辅以影像信息的配准方案因其严格的理论模型和较高的精度成为干涉处理的首选。本文以TerraSAR-X影像为例,论证了不同成像模式影像所需的配准精度和卫星轨道精度,并通过理论分析和试验证明了精密轨道条件下,利用几何配准即可满足TerraSAR-X等卫星的条带模式影像干涉处理的需要;聚束模式影像需要在几何配准的基础上利用影像相干性或谱分集进一步优化配准结果。鉴于增强谱分集偏移量估计精度最高,本文进一步利用增强谱分集对比分析了不同轨道不同DEM条件下的几何配准误差。研究结果表明:卫星轨道切向误差是几何配准的主要误差源,目前常用3种DEM几何配准差异远小于0.001个像素,均可满足Sentinel-1影像干涉配准的需要。     

多源星载SAR地形干涉测量精度分析

星载InSAR技术具有高效率、高精度获取全球DEM数据及其他增值产品的优势，是地形测绘领域的研究热点。本文综合利用国内外多源星载SAR影像数据，开展地形干涉测量试验及精度对比分析，旨在为全球测绘提供技术参考。现有的X/C/L波段卫星SAR系统，如COSMO-SkyMed、GF-3、ALOS-2获取的干涉数据集，在青海典型复杂地形实验区均成功获取了DEM数据产品。分析结果表明，在3种典型数据源中，基于COSMO-SkyMed干涉测量DEM的精度与细节质量相对较高，GF-3干涉结果次之，ALOS-2数据也实现了较好的地形测图精度。相关结果从侧面论证了国产GF-3数据具备在空间基线合适的条件下获得高精度DEM数据产品的潜力。     

粗／精轨道数据对卫星InSAR DEM精度影响的对比分析

本文在介绍InSAR系统中卫星轨道状态矢量内插方法的基础上，从理论和实际两方面分析了轨道数据误差对参考椭球面相位、地形干涉相位和数字高程模型（DEM）精度的影响。以上海局部地区作为实验场，采用ERS-1／2卫星SAR影像数据，分别使用欧洲空间局粗略轨道数据和荷兰Delft大学空间研究中心精密轨道数据进行了干涉处理，生成了两种情况下的DEM，并对相关精度进行了对比与分析。研究结果表明，使用精轨数据建立的DEM的精度明显高于基于粗轨数据建立的DEM的精度。     

Precise orbit determination for the FORMOSAT-3/COSMIC satellite mission using GPS

The joint Taiwan–US mission FORMOSAT-3/ COSMIC (COSMIC) was launched on April 17, 2006. Each of the six satellites is equipped with two POD antennas. The orbits of the six satellites are determined from GPS data using zero-difference carrier-phase measurements by the reduced dynamic and kinematic methods. The effects of satellite center of mass (COM) variation, satellite attitude, GPS antenna phase center variation (PCV), and cable delay difference on the COSMIC orbit determination are studied. Nominal attitudes estimated from satellite state vectors deliver a better orbit accuracy when compared to observed attitude. Numerical tests show that the COSMIC COM must be precisely calibrated in order not to corrupt orbit determination. Based on the analyses of the 5 and 6-h orbit overlaps of two 30-h arcs, orbit accuracies from the reduced dynamic and kinematic solutions are nearly identical and are at the 2–3 cm level. The mean RMS difference between the orbits from this paper and those from UCAR (near real-time) and WHU (post-processed) is about 10 cm, which is largely due to different uses of GPS ephemerides, high-rate GPS clocks and force models. The kinematic orbits of COSMIC are expected to be used for recovery of temporal variations in the gravity field.     

Precise topography- and aperture-dependent motion compensation for airborne SAR

Efficient synthetic aperture radar (SAR) processing algorithms are unable to exactly implement the aperture- and topography-dependent motion compensation due to the superposition of the synthetic apertures of several targets having different motion errors and potentially different topographic heights. Thus, during motion compensation, a reference level is assumed, resulting in residual phase errors that impact the focusing, geometric fidelity, and phase accuracy of the processed SAR images. This letter proposes a new short fast Fourier transform-based postprocessing methodology capable of efficient and precise compensation of these topography- and aperture-dependent residual phase errors. In addition to wide beamwidth (very high resolution) SAR systems, airborne repeat-pass interferometry especially benefits from this approach, as motion compensation can be significantly improved, especially in areas with high topographic changes. Repeat-pass interferometric data of the E-SAR system of the German Aerospace Center (DLR) are used to demonstrate the performance of the proposed approach.     

Orbit and clock analysis of Compass GEO and IGSO satellites

China is currently focussing on the establishment of its own global navigation satellite system called Compass or BeiDou. At present, the Compass constellation provides four usable satellites in geostationary Earth orbit (GEO) and five satellites in inclined geosynchronous orbit (IGSO). Based on a network of six Compass-capable receivers, orbit and clock parameters of these satellites were determined. The orbit consistency is on the 1–2 dm level for the IGSO satellites and on the several decimeter level for the GEO satellites. These values could be confirmed by an independent validation with satellite laser ranging. All Compass clocks show a similar performance but have a slightly lower stability compared to Galileo and the latest generation of GPS satellites. A Compass-only precise point positioning based on the products derived from the six-receiver network provides an accuracy of several centimeters compared to the GPS-only results.     

Generation and validation of DEM using SAR interferometry and differential GPS supported by multispectral optical data

Digital elevation model (DEM) and the derived terrain parameters e.g. contour, slope, aspect, drainage pattern, etc are required for natural resources management, infrastructure planning and disaster management. The present paper aims at generating DEM from ERS tandem pair using interferometric technique supported by differential GPS measurements (DGPS) and multispectral optical data. Validation of DEM has been carried out by DGPS measurements. Ground Control Points (GCP) established by DGPS measurements have been used to georeference the IRS-1D optical data that has finally been co-registered with SAR amplitude image. Optical data, co-registered with ERS - I SAR data has helped in locating the GCP’s and check points, precisely, for refinement of DEM and its validation.     

Detection of Slope Instability in Hong Kong Based on Multi-baseline Differential SAR Interferometry Using ALOS PALSAR Data

The monitoring of slope instability requires detailed observations of mass movements, which generally cannot be obtained by geodetic methods or global positioning systems (GPS). Differential synthetic aperture radar (SAR) interferometry has proven to be an effective way of measuring land deformation with millimeter accuracy over wide areas. Using data from the newly launched L-band ALOS PALSAR interferometer and the multi-baseline differential SAR interferometry technique, slope instability in Hong Kong was analyzed by means of measured surface displacement along look vectors. Owing to its enhanced vegetation penetration, less temporal decorrelation enabled the L-band data to improve spaceborne radar sensor land-surface deformation measurements. The results were validated by ENVISAT ASAR-derived outcomes and other ground survey data.     

Precision real-time navigation of LEO satellites using global positioning system measurements

Continued advancements in remote sensing technology along with a trend towards highly autonomous spacecraft provide a strong motivation for accurate real-time navigation of satellites in low Earth orbit (LEO). Global Navigation Satellite System (GNSS) sensors nowadays enable a continuous tracking and provide low-noise radiometric measurements onboard a user spacecraft. Following the deactivation of Selective Availability a representative real-time positioning accuracy of 10 m is presently achieved by spaceborne global positioning system (GPS) receivers on LEO satellites. This accuracy can notably be improved by use of dynamic orbit determination techniques. Besides a filtering of measurement noise and other short-term errors, these techniques enable the processing of ambiguous measurements such as carrier phase or code-carrier combinations. In this paper a reference algorithm for real-time onboard orbit determination is described and tested with GPS measurements from various ongoing space missions covering an altitude range of 400–800 km. A trade-off between modeling effort and achievable accuracy is performed, which takes into account the limitations of available onboard processors and the restricted upload capabilities. Furthermore, the benefits of different measurements types and the available real-time ephemeris products are assessed. Using GPS broadcast ephemerides a real-time position accuracy of about 0.5 m (3D rms) is feasible with dual-frequency carrier phase measurements. Slightly inferior results (0.6–1 m) are achieved with single-frequency code-carrier combinations or dual-frequency code. For further performance improvements the use of more accurate real-time GPS ephemeris products is mandatory. By way of example, it is shown that the TDRSS Augmentation Service for Satellites (TASS) offers the potential for 0.1–0.2 m real-time navigation accuracies onboard LEO satellites.