星地监测网下的北斗导航卫星轨道确定

提出层间链路的星间链路方式,即以轨道高度区分的不同类型卫星间链路,在MEO卫星上安装星载接收机即可接收GEO、IGSO卫星观测数据。根据中国卫星导航系统星座构型,从卫星跟踪时间、三维位置精度因子PDOP、定轨均方差等评价指标,分别进行地面跟踪站区域和全球非均匀分布情况下的星地链路、星地链路联合层间链路、星地链路联合星间双向测距等多种场景的定轨仿真。结果显示,基于中国区域的7个地面跟踪站1 d观测值,联合波束角为41.25°的层间星间链路,GEO、IGSO和MEO定轨均方差值由6.1 m、1.3 m和5.9 m减小到1.0 m、0.8 m和2.0 m;联合卫星波束角为45°的卫星双向测距(残余系统误差为振幅30 cm的周期项),星座整体定轨精度优于20 cm。     

HY2A卫星的GPS/DORIS/SLR数据精密定轨

采用HY2A卫星2013年2月的实测数据,研究了GPS、星载多谱勒无线电定轨定位系统(DORIS)及卫星激光测距(SLR)三种观测数据的单独和联合定轨问题。通过与法国CNES的精密轨道数据比较发现:分别采用GPS、DORIS和SLR数据进行单独定轨,GPS数据确定轨道的径向平均精度为1.3cm,三维位置约为6.2cm;DORIS定轨的径向平均精度为1.6cm,比GPS结果略差;SLR确定轨道的径向平均精度为2.3cm。用GPS、DORIS和SLR三种数据联合定轨,确定轨道的径向平均精度为1.2cm,三维位置约为6.5cm。与星载GPS定轨结果比较,三种观测数据的联合定轨在提高卫星轨道确定精度上不明显,但联合定轨有利于保持计算轨道精度相对稳定。用站星间高度角大于60°的SLR数据检验GPS/DORIS联合确定的轨道,两者在测距方向的均方差为2.5cm,可见基于HY2A的观测数据可以实现cm级的定轨需求。     

利用GOCE卫星轨道反演地球重力场模型

根据积分方程法反演地球重力场的数学模型,利用GOCE卫星2009-11-02～2010-01-02共61d的精密轨道数据反演了几组地球重力场模型。结果表明,GOCE卫星轨道能有效提取地球重力场的长波信息,弥补了GOCE卫星重力梯度带宽的限制,在106阶次的大地水准面误差为±9.6cm,该阶次精度优于EIGEN-CHAMP03S及GRACE卫星两个月轨道反演地球重力场的精度,但由于两极空白,反演的带谐位系数精度偏低。联合GOCE及GRACE卫星轨道反演的模型在106阶次的大地水准面误差为±6.9cm,弥补了GOCE卫星轨道的缺陷。     

GOCE卫星测量恢复地球重力场模型的理论与方法

研究了GOCE卫星测量恢复地球重力场模型的理论与方法。论文的主要工作和创新点有： (1) 建立了扰动重力梯度张量各分量没有奇异性的详细计算模型,解决了重力梯度张量Txx分量在两极地区计算的奇异性难题。 (2) 系统研究了卫星重力梯度数据向下延拓的解析法、泊松积分迭代法和卫星重力梯度数据格网化的移动平均法、反距离加权法、普通克里金法,建立了相应的数学模型,导出了相应的计算公式,并采用“直接法”和“移去-恢复法”两种方案对其向下延拓和格网化效果进行了测试。 (3) 分析了能量守恒方程中各项误差对沿轨扰动位计算结果的影响,建立了利用GOCE模拟数据确定地球重力场的最小二乘直接法、调和分析法、最小二乘配置法的实用数学模型,并做了大量的模拟计算。 (4) 建立了利用扰动引力梯度张量各单分量和组合分量确定地球重力场的最小二乘直接法去奇异性计算模型;推导了利用扰动引力梯度张量单分量和组合分量解算地球重力场的调和分析法模型;进一步推导了扰动引力梯度张量各个分量之间的自协方差和互协方差函数及其与引力位系数之间协方差函数的具体计算公式。 (5) 推导了利用不同类型重力测量数据确定地球重力场的联合平差法数学模型,介绍并分析了模型中各类数据最优定权的参数协方差法和方差分量估计法。 (6) 论述了谱组合法的基本原理,给出了多种类型重力测量数据联合处理的谱权及谱组合的通用表达式,基于调和分析方法推导了SST+SGG、SST+SGG＋Δg和SST+SGG＋Δg+N恢复地球重力场模型的谱组合公式及对应谱权的具体形式。 (7) 推导了利用迭代法联合不同类型重力测量数据反演地球重力场模型的基本原理公式,并给出了其具体实现步骤。 (8) 分析并计算了重力卫星轨道高度、卫星星间距离和卫星轨道倾角的设计指标;讨论了双星轨道长半轴的一致性要求、双星姿态俯仰角的控制要求以及双星编队保持机动的时间间隔要求。 (9) 确定了KBR系统的星间距离、星间距离变化率和星间加速度的精度指标;设计了星载GPS系统的卫星轨道位置和速度以及加速度计测量的精度指标;计算了加速度计检验质量质心到卫星质心的调整距离精度指标;分析了恒星敏感器的姿态角测量精度和稳定度;计算了参考重力场模型对于累计大地水准面精度和积分卫星轨道的影响。 (10) 研制了一套利用卫星重力测量数据反演地球重力场模型的软件平台,可对卫星重力测量数据处理及其精度评估提供一些基本方法,并为我国卫星重力测量系统的总体战技指标和主要有效载荷技术指标的量化分析、论证提供理论和技术支持,为我国未来的卫星重力测量系统提供可能的积累和参考。     

联合GRACE/GOCE重力场模型和GPS/水准数据确定我国85高程基准重力位

GRACE、GOCE卫星重力计划的实施,对确定高精度重力场模型具有重要贡献。联合GRACE、GOCE卫星数据建立的重力场模型和我国均匀分布的649个GPS/水准数据可以确定我国高程基准重力位,但我国高程基准对应的参考面为似大地水准面,是非等位面,将似大地水准面转化为大地水准面后确定的大地水准面重力位为62 636 854.395 3m~2s~(-2),为提高高阶项对确定大地水准面的贡献,利用高分辨率重力场模型EGM2008扩展GRACE/GOCE模型至2190阶,同时将重力场模型和GPS/水准数据统一到同一参考框架和潮汐系统,最后利用扩展后的模型确定的我国大地水准面重力位为62 636 852.751 8m~2s~(-2)。其中组合模型TIM_R4+EGM2008确定的我国85高程基准重力位值62 636 852.704 5m~2s~(-2)精度最高。重力场模型截断误差对确定我国大地水准面的影响约16cm,潮汐系统影响约4~6cm。     

星载BDS/GPS低轨卫星定轨精度分析

针对低轨卫星搭载BDS/GPS接收机实现定轨将成为定轨领域热点的现状,该文讨论了基于星载BDS/GPS实时定轨和精密定轨需要考虑的数学模型,阐述了实时定轨和精密定轨的模型差异。基于自主研发程序,利用高动态信号仿真器仿真的星载BDS/GPS数据研究了基于星载BDS/GPS实时定轨和精密定轨的可行性及其能达到的精度。试验结果表明,星载BDS/GPS实时定轨位置精度为1.19m,速度精度为2.35mm/s。GPS信号发生中断时即仅采用BDS观测数据进行实时定轨时,三维位置误差达到3.73m;星载BDS/GPS精密定轨位置精度为2.30cm,仅采用BDS观测数据进行精密定轨时,三维位置误差可达到8.26cm。     

星载GPS接收机定位误差对卫星轨道根数的影响分析

在低轨卫星上安装星载GPS接收机、为卫星提供位置速度与轨道参数的应用已越来越广泛。星载接收机实时定位的位置误差和速度误差会对计算出的卫星轨道根数产生影响。本文用模拟数据分析了定位误差对卫星轨道根数的影响。结果表明:速度误差对轨道根数的影响远大于位置误差对轨道根数的影响。     

北斗高精度长弧历书模型设计

历书参数可同时用于辅助常规导航和自主导航的信号捕获。延长历书参数的有效期不但可以使地面接收机启动时充分利用历书数据,对于基于星间链路观测的自主导航,历书参数的有效期还决定了地面注入历书的频度和占用的星上存储资源。通过对北斗3类导航卫星主要摄动力及其对轨道根数的长期项和长周期项的影响分析,设计了以6个轨道根数和5个摄动参数为播发参数的历书拟合模型。以一个自主运行周期90 d为时间尺度,对北斗在轨卫星进行了长弧段历书拟合试验,并同时分析了卫星位置和速度的拟合精度。结果表明新的历书拟合模型提高了历书拟合的精度,尤其对于地球静止轨道和倾斜地球同步轨道卫星,拟合精度提高显著。对于GEO和IGSO卫星,位置拟合误差大约从200 km降低至十几千米甚至几千米,速度拟合误差大约从15 m/s降低至0.6 m/s,新方法拟合精度提高了约20~30倍;对于中圆地球轨道卫星,无论采用哪种历书模型,位置拟合误差都在5 km左右,速度拟合误差都在0.6 m/s左右,新方法拟合精度提高约15%。针对星间链路卫星10 km位置误差上限的使用需求,对比了新老历书模型的拟合弧长,常规模型最大拟合弧长约为14 d,而新历书模型的最大拟合弧长可延长至45 d,新历书模型延长了历书使用期限,优化了北斗历书模型设计。     

利用谱分析法估计GRACE Follow-On地球重力场的空间分辨率

利用轨道扰动引力谱和大地水准面累计误差谱分析的方法估计未来GRACE(gravity recovery and climateexperiment)Follow-On卫星反演地球重力场的空间分辨率。基于GRACE Follow-On卫星的轨道特性,计算其在高空所受到的径向扰动引力,并根据谱特性及星载加速度计的测量噪声水平分析该卫星能反演重力场的阶数。利用EGM96重力场模型分别计算200 km和250 km轨道高度处的扰动引力谱。分析其特性表明:在两个轨道高度处分别能反演281阶和242阶的地球重力场模型。给出大地水准面累计误差谱模型,并计算200 km和250 km轨道高度处大地水准面累计误差谱。分析其谱特性表明:在两个轨道高度处分别能反演至286阶和228阶的地球重力场模型。     

渤海湾航空重力及其在海域大地水准面精化中的应用

近海航空重力数据在陆海大地水准面统一中起着重要作用。近3年来,利用我国首套航空重力测量系统(CHAGS)完成了渤海湾地区近20万平方千米的5′×5′格网平均重力异常数据的获取。本文首先介绍了渤海湾地区航空重力测量的概况,给出航空重力测量数据的处理要点;然后,详细讨论了航空重力测量的精度评估方法,其中针对该区域的测线布设特点,提出了"重叠格网比较法"以评估格网平均重力异常的内符合精度。结果表明,对于5′的波长分辨率,交叉点重力异常不符值在抗差后的中误差约为1.5 mGal,重叠格网法获得的5′×5′格网平均重力异常的中误差约为1.6 mGal;5′×5′格网重力异常与卫星测高和船测重力的比较精度优于3.0mGal;由航空重力测量获得的1°×1°格网平均重力异常与GOCE卫星重力位模型的计算值相比较,其系统性差异小于0.5 mGal、中误差约为2.7 mGal。利用航空重力数据后,渤海湾区域大地水准面与16个GPS水准点的比较精度由EGM2008模型的约23 cm提高到约12 cm。     

Åland GPS levelling campaign in 1987

In October 1987 a four day satellite GPS campaign was performed over the Åland archipelago to test the possibility of connecting the Swedish and Finnish national height systems. This paper summarizes the gained experiences using 5 WM 101 GPS receivers and the PoPS software.The computing results for the connection between the two height systems are considerably dependent on the choice of geoidal undulation model and systematic error parameter model. Using the NKG Scandinavian geoid 1989, which is probably the most accurate geoid available for the region, and a bias and tilt parameter model the difference between the Swedish RH70 system and the Finnish N60 system is estimated to 11.4 ± 4.0 cm. An independent check is provided by two connecting border bench marks in northern Scandinavia yielding the difference 19.2 ± 4.2 cm. In view of that merely single frequency GPS receivers were used together with the PoPS software, we consider this result most satisfactory.     

Baltic Sea Level project with GPS

In order to study the Baltic Sea Level change and to unify national height systems a two week GPS campaign was performed in the region in Autumn 1990. Parties from Denmark, Finland, Germany, Poland and Sweden carried out GPS measurements at 26 tide gauges along the Baltic sea and 8 VLBI and SLR fiducial stations with baseline lengths ranging from 230 km to 1600 km. The observations were processed in the network mode with the Bernese version 3.3 software using orbit improvement techniques. To get rid of the scale error introduced by the ionospheric refraction from single-frequency data, the local models of the ionosphere were estimated using L4 observations. The tropospheric zenith corrections were also considered. The preliminary results show average root mean square (RMS) errors of about ±3 cm in the horizontal position and ±7 cm in the vertical position relative to the Potsdam SLR station in ITRF89 system. After transformation of the GPS results to geoid heights using the levelled heights, an absolute comparison with gravimetric geoid heights using the least squares modification of Stokes' formula (LSMS), the modified Molodensky and the NKG Scandinavian geoid 1989 (NGK-89) models gives a standard deviation of the difference of ±7cm to ±9cm for the NKG-89 model and of ±9cm to ±30cm for the LSMS and the modified Molodensky model. The Swedish height system is found to be about 8-37cm higher than those of the other Baltic countries for NKG-89 model.     

联合GOCE卫星数据和GRACE法方程确定SWJTU-GOGR01S全球重力场模型

联合地球重力场和海洋环流探测器（Gravity Field and Steady-State Ocean Circulation Explorer,GOCE）和重力恢复与气候实验（Gravity Recovery and Climate Experiment,GRACE）卫星观测数据确定全球静态重力场模型是当前大地测量学的研究热点之一。联合近3 a的GOCE卫星梯度数据和7 a左右的GRACE星间距离变率数据计算的ITG-GRACE2010S模型的法方程恢复了210阶次的重力场模型SWJTU-GOGR01S。采用带通数字滤波方法处理GOCE卫星的4个高精度梯度观测分量,利用梯度数据恢复重力场模型的观测方程直接建立在梯度仪坐标系中,可以避免坐标转换过程中高精度的梯度观测分量受低精度分量的影响;联合法方程解的最优权采用方差分量估计迭代计算,GOCE数据的两极空白引起的病态问题采用Kaula正则化方法进行约束。基于EIGEN-6C2模型和北美地区的GPS水准网观测数据,对SWJTU-GOGR01S模型进行内外符合精度分析,结果表明,SWJTU-GOGR01S模型在210阶次的大地水准面误差和累计误差分别为1.3 cm和5.7 cm,精度与欧洲空间局公布的第四代时域法模型相当,略优于GOCO02S和GOCO03S模型的精度。     

GALILEO系统仿真与分析

本文着重阐述了GALILEO仿真系统星座和误差模型的构建过程,利用该系统进行DOP值分析并通过定位解算验证了GALILEO系统的性能指标。通过与GPS系统性能指标进行比较,得出GALILEO系统的星座设计具有较好的DOP值分布特性,定位精度优于GPS定位精度。在进行差分定位时,其误差贡献比较大的是接收机噪声和卫星钟差,因此提高差分定位的关键是降低接收机的噪声水平和提高卫星钟差预报精度。     

Precise geoid determination over Sweden using the Stokes–Helmert method and improved topographic corrections

 Four different implementations of Stokes' formula are employed for the estimation of geoid heights over Sweden: the Vincent and Marsh (1974) model with the high-degree reference gravity field but no kernel modifications; modified Wong and Gore (1969) and Molodenskii et al. (1962) models, which use a high-degree reference gravity field and modification of Stokes' kernel; and a least-squares (LS) spectral weighting proposed by Sj?berg (1991). Classical topographic correction formulae are improved to consider long-wavelength contributions. The effect of a Bouguer shell is also included in the formulae, which is neglected in classical formulae due to planar approximation. The gravimetric geoid is compared with global positioning system (GPS)-levelling-derived geoid heights at 23 Swedish Permanent GPS Network SWEPOS stations distributed over Sweden. The LS method is in best agreement, with a 10.1-cm mean and ±5.5-cm standard deviation in the differences between gravimetric and GPS geoid heights. The gravimetric geoid was also fitted to the GPS-levelling-derived geoid using a four-parameter transformation model. The results after fitting also show the best consistency for the LS method, with the standard deviation of differences reduced to ±1.1 cm. For comparison, the NKG96 geoid yields a 17-cm mean and ±8-cm standard deviation of agreement with the same SWEPOS stations. After four-parameter fitting to the GPS stations, the standard deviation reduces to ±6.1 cm for the NKG96 geoid. It is concluded that the new corrections in this study improve the accuracy of the geoid. The final geoid heights range from 17.22 to 43.62 m with a mean value of 29.01 m. The standard errors of the computed geoid heights, through a simple error propagation of standard errors of mean anomalies, are also computed. They range from ±7.02 to ±13.05 cm. The global root-mean-square error of the LS model is the other estimation of the accuracy of the final geoid, and is computed to be ±28.6 cm. Received: 15 September 1999 / Accepted: 6 November 2000     

利用GOCE模拟观测反演重力场的Torus法

在介绍Torus方法反演地球重力场模型的基本原理和方法的基础上,基于圆环面上均匀分布的卫星引力梯度模拟观测值解算了200阶次的地球重力场模型,在无误差情况下,Torus方法解算模型的阶误差RMS小于10-16,验证了该方法的严密性。利用61dGOCE卫星轨道上无误差的模拟引力梯度观测值解算了200阶次的地球重力场模型,分析了格网化误差、极空白对解算精度的影响,迭代3次后,在不考虑低次系数情况下,模型的大地水准面阶误差和累积误差均较小,最大值仅为0.022mm和0.099mm。在沿轨卫星引力梯度模拟数据中加入5mE/Hz1/2的白噪声,基于Torus方法和空域最小二乘法解算了200阶次的地球重力场模型,Torus方法的精度略低于空域最小二乘法的精度,在不考虑低次项的情况下,两种方法解算模型的大地水准面阶误差最大值分别为1.58cm和1.45cm,累积误差最大值分别为6.37cm和5.55cm。但由于采用了二维快速傅里叶技术和块对角最小二乘法,极大地提高了计算效率。本文数值结果说明Torus方法是一种独立有效的方法,可用于GOCE任务海量卫星引力梯度观测值反演重力场的快速解算。     

The height datum problem and the role of satellite gravity models

Regional height systems do not refer to a common equipotential surface, such as the geoid. They are usually referred to the mean sea level at a reference tide gauge. As mean sea level varies (by ±1 to 2 m) from place to place and from continent to continent each tide gauge has an unknown bias with respect to a common reference surface, whose determination is what the height datum problem is concerned with. This paper deals with this problem, in connection to the availability of satellite gravity missions data. Since biased heights enter into the computation of terrestrial gravity anomalies, which in turn are used for geoid determination, the biases enter as secondary or indirect effect also in such a geoid model. In contrast to terrestrial gravity anomalies, gravity and geoid models derived from satellite gravity missions, and in particular GRACE and GOCE, do not suffer from those inconsistencies. Those models can be regarded as unbiased. After a review of the mathematical formulation of the problem, the paper examines two alternative approaches to its solution. The first one compares the gravity potential coefficients in the range of degrees from 100 to 200 of an unbiased gravity field from GOCE with those of the combined model EGM2008, that in this range is affected by the height biases. This first proposal yields a solution too inaccurate to be useful. The second approach compares height anomalies derived from GNSS ellipsoidal heights and biased normal heights, with anomalies derived from an anomalous potential which combines a satellite-only model up to degree 200 and a high-resolution global model above 200. The point is to show that in this last combination the indirect effects of the height biases are negligible. To this aim, an error budget analysis is performed. The biases of the high frequency part are proved to be irrelevant, so that an accuracy of 5 cm per individual GNSS station is found. This seems to be a promising practical method to solve the problem.     

空域最小二乘法用于重力卫星误差分析

重力测量卫星性能不仅与轨道参数、载荷误差、数据分辨率等因素密切相关,也与反演算法有关。传统的分析方法如动力学法、短弧法等用于误差分析,不可避免将算法误差引入分析结果,使得分析结论确定性不足。为解决这一问题,提出了空域最小二乘分析法,用空域格网重力扰动数据替代重力卫星载荷数据反演地球重力场,有效避免了算法误差对于分析结果的影响。分析结果表明,重力卫星在500 km轨道高度、一次数据覆盖条件下,测量重力场最高阶数约为240阶,载荷误差为1×10-10 m·s-2·Hz-1/2水平时,测量重力场最高阶数为136阶,其累积重力异常误差为2.7 mGal,累积大地水准面误差为14 cm。要达到最优测量能力,轨道倾角通常不小于89°。为减小地球引力高频信号对于地球重力场低阶位系数估计值的影响,估计位系数最高阶数需大于240阶。     

Precise orbit determination of the Fengyun-3C satellite using onboard GPS and BDS observations

The GNSS Occultation Sounder instrument onboard the Chinese meteorological satellite Fengyun-3C (FY-3C) tracks both GPS and BDS signals for orbit determination. One month’s worth of the onboard dual-frequency GPS and BDS data during March 2015 from the FY-3C satellite is analyzed in this study. The onboard BDS and GPS measurement quality is evaluated in terms of data quantity as well as code multipath error. Severe multipath errors for BDS code ranges are observed especially for high elevations for BDS medium earth orbit satellites (MEOs). The code multipath errors are estimated as piecewise linear model in \(2{^{\circ }}\times 2{^{\circ }}\) grid and applied in precise orbit determination (POD) calculations. POD of FY-3C is firstly performed with GPS data, which shows orbit consistency of approximate 2.7 cm in 3D RMS (root mean square) by overlap comparisons; the estimated orbits are then used as reference orbits for evaluating the orbit precision of GPS and BDS combined POD as well as BDS-based POD. It is indicated that inclusion of BDS geosynchronous orbit satellites (GEOs) could degrade POD precision seriously. The precisions of orbit estimates by combined POD and BDS-based POD are 3.4 and 30.1 cm in 3D RMS when GEOs are involved, respectively. However, if BDS GEOs are excluded, the combined POD can reach similar precision with respect to GPS POD, showing orbit differences about 0.8 cm, while the orbit precision of BDS-based POD can be improved to 8.4 cm. These results indicate that the POD performance with onboard BDS data alone can reach precision better than 10 cm with only five BDS inclined geosynchronous satellite orbit satellites and three MEOs. As the GNOS receiver can only track six BDS satellites for orbit positioning at its maximum channel, it can be expected that the performance of POD with onboard BDS data can be further improved if more observations are generated without such restrictions.