A kinematic statistical method is proposed to determine the position for Chang'E-3(CE-3) lunar lander.This method uses both ranging and VLBI measurements to the lander for a continuous arc,combing with precise knowledge about the motion of the moon as provided by planetary ephemeris,to estimate the lander's position on the lunar surface with high accuracy.Accuracy analyses are carried out with simulation data using the software developed at Shanghai Astronomical Observatory in this study to show that measurement errors will dominate the position accuracy.Application of lunar digital elevation model(DEM) as constraints in the lander positioning is also analyzed.Simulations show that combing range/doppler and VLBI data,single epoch positioning accuracy is at several hundred meters level,but with ten minutes data accumulation positioning accuracy is able to be achieved with several meters.Analysis also shows that the information given by DEM can provide constraints in positioning,when DEM data reduce a 3-dimensional positioning problem to 2-dimensional.Considering the Sinus Iridum,CE-3 lander's planned landing area,has been observed with dedicated details during the CE-1 and CE-2 missions,and its regional DEM model accuracy may be higher than global models,which will certainly support CE-3's lander positioning.
HUANG YongHU XiaoGongLI PeiJiaCAO JianFengJIANG DongRongZHENG WeiMinFAN Min
When only data transmission signals with a bandwidth of 1 MHz exist in the rover, the position can be obtained using the differential group delay data of the same-beam very long baseline interferometry (VLBI). The relative position between a lunar rover and a lander can be determined with an error of several hundreds of meters. When the guidance information of the rover is used to determine relative position, the rover's wheel skid behavior and integral movement may influence the accuracy of the determined position. This paper proposes a new method for accurately determining relative position. The differential group delay and biased differential phase delay are obtained from the same-beam VLBI observation, while the modified biased differential phase delay is obtained using the statistic mean value of the differential group delay and the biased phase delay as basis. The small bias in the modified biased phase delay is estimated together with other parameters when the relative position of the rover is calculated. The effectiveness of the proposed method is confirmed using the same-beam VLBI observation data of SELENE. The radio sources onboard the rover and the lander are designed for same-beam VLBI observations. The results of the simulations of the differential delay of the same-beam VLBI observation between the rover and the lander show that the differential delay is sensitive to relative position. An approach to solving the relative position and a strategy for tracking are also introduced. When the lunar topography data near the rover are used and the observations are scheduled properly, the determined relative position of the rover may be nearly as accurate as that solved using differential phase delay data.
We analyze the post-fit residuals of one-way Doppler tracking data from the Mars Express(MEX) spacecraft to test possible violations of local Lorentz invariance(LLI) and local position invariance(LPI).These one-way Doppler observations were carried out on 2011 August 7 for about 20 minutes at Sheshan Station of Shanghai Astronomical Observatory in China.These downlink signals were sent by MEX for telemetry at X-band.Because we are not able to decode the data in the form of telemetry and separate them from the carrier frequency,this makes the post-fit residuals of the Doppler data degrade to the level of 0.1 m s^(-1).Even so,the residuals can still impose upper bounds on LLI and LPI at 10^(-1),which is consistent with the prediction based on our analysis of the detectability.Although the upper bounds given by three-way Doppler tracking of MEX are better than those obtained in the present work,one-way Doppler measurements still provide a unique chance to test possible violations of LLI and LPI far from the ground stations.
Chang’E-3 landed on the east of Sinus Iridum area on December 14,2013,performing China’s first successful soft landing on the lunar surface.We present the results on precision orbit determination and positioning of the lander and the rover.We describe the data,modeling,and methods used to achieve position knowledge over the period December 2–21,2014.In addition to the radiometric X-band range and Doppler tracking data,delta differential one-way ranging data are also used in the calculation,which show that they strongly improve the accuracy of the orbit reconstruction.Total position overlap differences are about 20 and 30 m for the 100 km 9 100 km and100 km9 15 km lunar orbit,respectively,increased by*50%with respect to CE-2 and at the same level as other lunar spacecrafts of recent era such as SELENE and lunar reconnaissance orbiter(LRO).The position error of the soft landing trajectory is less than 100 m.A kinematic statistical method is applied to determine the position of the lander and relative position of the rover with respect to the lander.The position difference of the lander is better than50 m compared to LRO photograph result.Compared with the delta very long baseline interferometry(VLBI)group delay between the lander and the rover,the delta VLBI phase delay can improve the relative position of the rover from*1,000 to*1 m.
Yong HuangShengqi ChangPeijia LiXiaogong HuGuangli WangQinghui LiuWeimin ZhengMin Fan
The Unified S-Band(USB) ranging/Doppler system and the Very Long Baseline Interferometry(VLBI) system as the ground tracking system jointly supported the lunar orbit capture of both Chang'E-2(CE-2) and Chang'E-1(CE-1) missions.The tracking system is also responsible for providing precise orbits for scientific data processing.New VLBI equipment and data processing strategies have been proposed based on CE-1 experiences and implemented for CE-2.In this work the role VLBI tracking data played was reassessed through precision orbit determination(POD) experiments for CE-2.Significant improvement in terms of both VLBI delay and delay rate data accuracy was achieved with the noise level of X-band band-width synthesis delay data reaching 0.2-0.3 ns.Short-arc orbit determination experiments showed that the combination of only 15 min's range and VLBI data was able to improve the accuracy of 3 h's orbit using range data only by a 1-1.5 order of magnitude,confirming a similar conclusion for CE-1.Moreover,because of the accuracy improvement,VLBI data was able to contribute to CE-2's long-arc POD especially in the along-track and orbital normal directions.Orbital accuracy was assessed through the orbital overlapping analysis(2 h arc overlapping for 18 h POD arc).Compared with about 100 m position error of CE-1's 200 km 200 km lunar orbit,for CE-2's 100 km 100 km lunar orbit,the position errors were better than 31 and 6 m in the radial direction,and for CE-2's 15 km 100 km orbit,the position errors were better than 45 and 12 m in the radial direction.In addition,in trying to analyze the Delta Differential One-Way Ranging(DOR) experiments data we concluded that the accuracy of DOR delay was dramatically improved with the noise level better than 0.1 ns and systematic errors better calibrated,and the Short-arc POD tests with DOR data showed excellent results.Although unable to support the development of an independent lunar gravity model,the tracking data of CE-2 provided evaluations of different lunar gravity models through POD.I
Li PeiJiaHu XiaoGongHuang YongWang GuangLiJiang DongRongZhang XiuZhongCao JianFengXin Nan
针对CE-3(嫦娥三号)月球探测器动力下降弧段,特别是悬停避障段频繁机动的特点,提出了采用B样条函数逼近方法进行落月轨迹确定。仿真分析表明:在动力下降运动较平滑弧段,B样条逼近法计算结果略优于多项式拟合法;而在频繁机动弧段,B样条逼近法有明显优势。计算结果表明,加入VLBI(Very Long Baseline Interferometry,甚长基线干涉测量)数据后能有效提高落月轨迹确定精度,在没有系统误差的情况下联合定位后位置精度优于50m。此外,还分析了三向测量系统差对定位的影响,可对CE-3任务提供参考。最后对CE-3实测数据进行处理,动力落月段末点位置和着陆器定位计算值相差不到200m。
Constellations of regional satellite navigation systems are usually constituted of geostationary satellites (GEO) and inclined geostationary satellites (IGSO) for better service availability. Analysis of real data shows that the pseudorange measurements of these two types of satellites contain significant multipath errors and code noise, and the multipath for GEO is extremely serious, which is harmful to system services. In contrast, multipath error of carrier phase measurements is less than 3 cm, which is smaller than the multipath of pseudorange measurements by two orders of magnitude. Using a particular combination of pseudorange and dual-frequency carrier phase measurements, the pseudorange multipath errors are detected, and their time varying features are analyzed. A real-time multipath correction algorithm is proposed in this paper, which is called CNMC (Code Noise and Multipath Correction). The algorithm decreases the influence of the multipath error and therefore ensures the performance of the system. Data processing experiments show that the multipath error level may be reduced from 0.5 m to 0.15 m by using this algorithm, and 60% of GEO multipath errors and 42% of IGSO multipath errors are successfully corrected with CNMC. Positioning experiments are performed with a constellation of 3 GEO plus 3 IGSO satellites. For dual-frequency users the East-West position accuracy is improved from 1.31 m to 0.94 m by using the CNMC algorithm, the South-North position accuracy is improved from 2.62 m to 2.29 m, and the vertical position accuracy is improved from 4.25 m to 3.05 m. After correcting multipath errors, the three-dimensional position accuracy is improved from 5.16 m to 3.94 m.
