Proposal of application of same beam VLBI measurements in precision orbit determination of lunar orbiter and return capsule and lunar gravity field simulation in Chang’E-3 mission

High accuracy differenced phase delay can be obtained by observing multiple point frequencies of two spacecraft using the same beam Very Long Baseline Interferometry (VLBI) technology. Its contribution in lunar spacecraft precision orbit determination has been performed during the Japanese lunar exploration mission SELENE. In consideration that there will be an orbiter and a return capsule flying around the moon during the Chinese lunar exploration future mission Chang’E-3, the contributions of the same beam VLBI in spacecraft precision orbit determination and lunar gravity field solution have been investigated. Our results show that the accuracy of precision orbit determination can be improved more than one order of magnitude after including the same beam VLBI measurements. There are significant improvements in accuracy of low and medium degree coefficients of lunar gravity field model obtained from combination of two way range and Doppler and the same beam VLBI measurements than the one that only uses two way range and Doppler data, and the accuracy of precision orbit determination can reach meter level.     

连续小推力航天器自主导航及在轨参数标定

以连续小推力航天器为背景,提出了综合考虑星载加速度计和推力器在轨标定的自主导航方案。首先以精确姿态测量和引力梯度模型为标定参考信息源,建立了包含加速度计参数、推力器参数以及光压系数的完整参数测量模型;然后基于天文导航方法建立了自主导航系统状态模型和观测模型;表明各状态和参数的能观性后,采用了具备良好计算效率和鲁棒性的双重无迹卡尔曼滤波方法进行状态和参数联合估计。分析与数值仿真表明,该方法通过结合参数在轨标定直接提高了导航模型精度,在工程应用中具备可行性和有效性。     

月球轨道交会对接航天器相对状态误差分析

为分析同波束干涉测量这一高精度相对测角技术对月球交会对接两个航天器的相对位置、速度(状态)影响,文章根据协方差分析理论及各测量量的模型,推导测量量关于相对状态量的信息矩阵,建立了相对状态误差协方差模型;结合月球轨道交会对接仿真轨道,开展测量误差对两个航天器的相对状态误差影响协方差分析。结果表明,在当前测量误差条件下,相对位置、速度误差分别达到米级和厘米每秒级。在分析相对状态误差影响因子的基础上,重点对同波束干涉测量差分相时延整周模糊误差及时延率误差对相对状态影响进行了分析,结果表明整周模糊度误差对相对位置误差影响显著,时延率误差对相对速度误差影响显著。     

Lunar gravity field modeling critical analysis and challenges

This paper summarizes and provides a critical analysis of the historical developments of lunar gravitational models from the earliest use of ground based tracking systems of the Lunar Orbiter to the Lunar Prospector mission. This encompasses a comprehensive and critical analysis of the various methods used in the estimation of the gravity coefficients and the processing of large batches of diverse measurements and data types. It has been shown that weakness exists in the current models of the lunar gravity field, which is primarily due to the lack of far side lunar tracking data information, which makes the lunar potential modeling difficult but expected to be overcome as data from SELENE satellite-to-satellite tracking becomes available. Comparisons of various lunar models reveal an agreement in the low order coefficients of the spherical harmonics. However, substantial differences in the models exist in the higher-order harmonics. A numerical comparison has been presented showing the performance of all the contemporary lunar gravitational models used within the astrodynamics community and available in public domain. Improvements to the current models are part of a continuing process and the recent model improvements and future possibilities in lunar gravity modeling are discussed. A brief review of the recent missions has been presented. It is hoped that this critical review will benefit the researchers by presenting the historical as well as state of the art in this field.     

月球软着陆的高精度自主导航与控制方法研究

提出了一种月球软着陆的高精度自主导航和控制方法.根据测距波束视线相对月面的几何关系,确定本体系的月心方向,组合利用测速仪获取的本体系三维速度确定本体系相对轨道系的姿态、速度及高度,并根据确定的参数性质选取适应的制导和控制方法.算法基于直接测量数据确定和控制姿态、高度和速度,不受惯性导航误差的影响,可以有效地提高姿态、速度与高度的确定精度和控制精度.数学仿真表明了算法的有效性.     

An alternative computation of a gravity field model from GOCE

GOCE is the first satellite with a gravitational gradiometer (SGG). This allows to determine a gravity field model with high spatial resolution and high accuracy. Four of the six independent components of the gravitational gradient tensors (GGT) are measured with high accuracy in the so-called measurement band (MB) from 5 to 100 mHz by the GOCE gradiometer. Based on more than 1 year of GOCE measurements, two gravity field models have been derived. Here, we introduce a strategy for spherical harmonic analysis (SHA) from GOCE measurements, with a bandpass filter applied to the SGG data, combined with orbit analysis based on the integral equation approach, and additional constraints (or stabilization) in the polar areas where no observation is available due to the orbit geometry. In addition, we combined the GOCE SGG part with a set of GRACE normal equations. This improves the accuracy of the gravity field in the long-wavelength parts, due to the complementarity of GOCE and GRACE. Comparison with other models and with external data shows that our results are rather close to the GPS-levelling data in well-selected test regions, with an uncertainty of 4–7 cm, for truncation at degree 200.     

Long-wavelength lunar gravity field recovery from simulated orbit and inter-satellite tracking data

As has been demonstrated recently, inter-satellite Ka-band tracking data collected by the GRAIL (Gravity Recovery And Interior Laboratory) spacecraft have the potential to improve the resolution and accuracy of the lunar gravity field by several orders of magnitude compared to previous models. By means of a series of simulation studies, here we investigate the contribution of inter-satellite ranging for the recovery of the Moon’s gravitational features; the evaluation of results is made against findings from ground-based Doppler tracking. For this purpose we make use of classical dynamic orbit determination, supported by the analysis of satellite-to-satellite tracking observations. This study sheds particularly light on the influence of the angular distance between the two satellites, solar radiation modeling and the co-estimation of the lunar Love number k₂. The quality of the obtained results is assessed by gravity field power spectra, gravity anomalies and precision orbit determination. We expect our simulation results to be supportive for the processing of real GRAIL data.     

基于X射线脉冲星的深空探测器自主导航方案

X射线脉冲星自主导航系统可以为深空探测器提供位置、速度、时间和姿态等丰富且自主的导航信息,以X射线脉冲星测得的信息作为量测量,结合轨道动力学方程,对航天器的轨道进行自主估计确定。论文阐述了该方案的导航原理,在借鉴现有航天器导航系统的基础上,提出了基于X射线脉冲星导航的方案,介绍了方案的硬件组成、系统结构,并针对方案中导航敏感器多冗余的特征,给出了基于多传感器组合导航技术的结构,最后用仿真资料对方案做了性能概算和精度估计。     

Instrument study of the Lunar Dust eXplorer (LDX) for a lunar lander mission

One of the highest-priority issues for a future human or robotic lunar exploration is the lunar dust. This problem should be studied in depth in order to develop an environment model for a future lunar exploration. A future ESA lunar lander mission requires the measurement of dust transport phenomena above the lunar surface. Here, we describe an instrument design concept to measure slow and fast moving charged lunar dust which is based on the principle of charge induction. LDX has a low mass and measures the speed and trajectory of individual dust particles with sizes below one micrometer. Furthermore, LDX has an impact ionization target to monitor the interplanetary dust background. The sensor consists of three planes of segmented grid electrodes and each electrode is connected to an individual charge sensitive amplifier. Numerical signals were computed using the Coulomb software package. The LDX sensitive area is approximately 400 cm². Our simulations reveal trajectory uncertainties of better than 2° with an absolute position accuracy of better than 2 mm.     

航天器自主交会对接的视觉相对导航方法

针对航天器自主交会对接在最终逼近阶段的相对导航问题,研究了基于特征光标的航天器视觉相对导航方法。首先建立了小角度假设条件下的相对导航模型。给出了航天器相对位置和采用欧拉角描述的相对姿态的近似解析算法。其次利用相对姿态的解析解作为观测信息,采用降阶的无迹卡尔曼滤波方法对目标航天器的姿态角和惯性角速度进行了估计,间接得到了相对姿态和相对姿态角速度的估计值。数值仿真表明提出的解析算法能够有效获得相对位置和相对姿态测量信息,通过降阶滤波可明显提高相对姿态确定精度。     

VLBI for better gravimetry in SELENE

The Japanese lunar explorer SELENE (SElenological and Engineering Explorer), to be launched in 2007, will for the first time utilize VLBI observations in lunar gravimetry investigations. This will particularly improve the accuracy to which the low degree gravitational harmonics and the gravity field near the limb can be measured, and when combined with Doppler measurements will enable three-dimensional information to be extracted. Differential VLBI Radio sources called VRAD experiment involves two on-board sub-satellites, Rstar and Vstar. These will be observed using differential VLBI to measure the trajectories of the satellites with the Japanese network named VERA (VLBI Exploration of Radio Astrometry) and an international VLBI network.     

Testing Modified Newtonian Dynamics with LISA Pathfinder

We suggest that LISA Pathfinder, a technology demonstrator for the future gravitational wave observatory LISA, could be used to carry out a direct experimental test of Modified Newtonian Dynamics (MOND). The LISA Pathfinder spacecraft is currently being built and the launch date is just a few years away. No modifications of the spacecraft are required, nor any interference with its nominal mission. The basic concept is to fly LISA Pathfinder through the region around the Sun-Earth saddle point, in an extended mission phase, once the original mission goals are achieved. We examine various strategies to reach the saddle point, and find that the preferred strategy, yielding relatively short transfer times of just over 1 year, probably involves a lunar fly-by. LISA Pathfinder will be able to probe the intermediate MOND regime, i.e. the transition between deep MOND and Newtonian gravity. We present robust estimates of the anomalous gravity gradients that LISA Pathfinder should be exposed to, based on MONDian effects as derived from the Tensor-Vector-Scalar (TeVeS) theory. The spacecraft speed and spatial scale of the MOND signal combine in a way that the spectral signature of the signal falls precisely into LISA Pathfinder’s measurement bandwidth. We find that if the gravity gradiometer on-board the spacecraft achieves its currently predicted sensitivity, these anomalous gradients could not just be detected, but measured in some detail.     

Simulation study for the determination of the lunar gravity field from PRARE-L tracking onboard the German LEO mission

A simulation study has been performed at GFZ Potsdam, which shows the anticipated improvement of the lunar gravity field model with respect to current (LP150Q model) or near-future (SELENE) knowledge in the framework of the planned German Lunar Explorations Orbiter (LEO) mission, based on PRARE-L (Precise Range And Range-rate Equipment – Lunar version) Satellite-to-Satellite (SST) and Satellite-Earth-Satellite (SEST) tracking observations. It is shown that the global mean error of the lunar gravity field can be reduced to less than 0.1 mGal at a spatial resolution of 50 km. In the spectral domain, this means a factor of 10 (long wavelengths) and some 100 (mid to short wavelengths) improvement as compared to predictions for SELENE or a factor of 1000 with respect to LP150Q. Furthermore, a higher spatial resolution of up to 28 km seems feasible and would correspond to a factor of 2–3 improvement of SELENE results. Moreover, PRARE-L is expected to derive the low-degree coefficients of the lunar gravity field with unprecedented accuracy. Considering long mission duration (at least 1 year is planned) this would allow for the first time a precise direct determination of the low-degree tidal Love numbers of the Moon and, in combination with high precision SEST, would provide an experimental basis to study relativistic effects such as the periselenium advance in the Earth–Moon system.     

The present status of the Japanese Penetrator Mission: LUNAR-A

The scientific objective of the LUNAR-A Japanese Penetrator Mission is to explore the lunar interior by seismic and heat-flow experiments. Two penetrators containing two-component seismometer and heat-flow probes will be deployed from a spacecraft onto the lunar surface, one on the nearside and the other on the farside of the moon. The data obtained by the penetrators will be transmitted to the ground station by way of the LUNAR-A mother spacecraft orbiting at an altitude of about 200 km. The seismic observations are expected to provide key data on the size of the lunar core, as well as data on the deep mantle structure. The heat-flow measurements at two different sites will also provide important data on the thermal structure and bulk concentrations of heat-generating elements in the Moon. These data will provide much stronger geophysical constraints on the origin and evolution of the Moon than has ever been obtained. The LUNAR-A mission was supposed to be launched in 2004. However, a malfunction of spacecraft subsystem and technical issues for penetrator system occurred during the course of the qualification level test. Therefore, further improvements and some modifications were considered to be required for reliability and robustness. The development of the mother spacecraft was temporarily suspended, while we have put a three-year program into effect to solve the penetrator technology issues.     

Selenodetic experiments of SELENE: Relay subsatellite,differential VLBI,and laser altimeter

Since 1960s, the gravitational potential of the Moon has been extensively studied from Doppler tracking data between a ground station and spacecraft orbiting in front of the Moon (e. g., Lorell and Sjogren, 1968; Bills and Ferrari, 1980; Konopliv et al., 1993; Lemoine et al., 1997). Because direct radio communication is interrupted while spacecraft is orbiting behind the Moon, however, the coverage of tracking data has been limited mostly to the nearside of the Moon so far. In order to compensate for such lack of tracking data, we propose satellite-to-satellite Doppler measurement by using a relay subsatellite in Japanese mission to the Moon in 2003. A complete coverage of Doppler tracking from an orbiter at sufficiently low altitude will significantly improve lunar gravity model and will contribute for future geophysical study of interior and tectonics on the Moon. Further, we propose differential VLBI experiment between the subsatellite and a propulsion module landed on the surface of the Moon. The differential VLBI is about 10 times more accurate than conventional Doppler measurement for long-wavelength gravity field. Besides, differential VLBI is sensitive to the displacement perpendicular to the line of sight. Thus the VLBI experiment provides precise estimates of the lunar gravity potential at low degree. The last proposal for selenodetic experiments is a laser altimeter. Global topography model has been already developed from the analysis of Clementine LIDAR data (Zuber et al., 1994), but it is suggested that the model includes appreciable anisotropy between NS and E-W directions due to highly eccentric orbit of Clementine spacecraft (Bills and Lemoine, 1995). The laser altimeter experiment from an orbiter in nearly circular orbit will provide a new reference for the isotropic lunar topography model.     

Comparison analyses on the 150 × 150 lunar gravity field models by gravity/topography admittance,correlation and precision orbit determination

We analyzed the 150 × 150 lunar gravity field models, LP150Q, GLGM-3 and SGM150, using the power spectrum on the lunar nearside and farside, the lunar global and localized gravity/topography admittance and correlation, and Chang’E-2 precision orbit determination to investigate which model is a more effective tool to estimate geophysical parameters and determine the lunar satellite precision orbit. Results indicate that all gravity field models can be used to estimate the lunar geophysical parameters of the nearside of the Moon. However, SGM150 is better in such computation of the farside. Additionally, SGM150 is shown to be the most useful model for determining the lunar satellite orbit.     

基于引力场不对称性的三体系统轨道自主导航

以月球背面的中继通信为背景,提出了基于三体系统引力场不对称特性的星–星测距自主定轨方案。该方案以环月极轨卫星和地–月L2点Halo轨道卫星组成中继通信网,以实现对月球两极和背面的覆盖。通过采集极轨卫星与Halo轨道卫星的测距信息,结合卡尔曼滤波在日–地–月动力学模型下获得两颗卫星的绝对轨道。数值仿真结果表明:本文方法能将导航的位置精度和速度精度分别提高到百米和厘米/秒量级。该自主导航方法还可以扩展到不规则引力场小天体附近星群运动的自主导航。     

"嫦娥一号"卫星轨控标定方法研究与实现

在航天测控任务中,对轨控效果进行标定并合理利用可以实现更为精准的轨道控制.提出了一种综合利用控前控后精密轨道、轨控过程遥测姿态数据、遥测加速度计测量数据对沉底发动机、轨控发动机、加速度计刻度系数进行标定的方法;介绍了该方法在中国首次月球探测任务中的应用情况;最后分析了标定结果对定轨及定姿精度的敏感程度,从而在理论上进一步说明在后续深空探测中利用精密轨道进行轨控标定的可行性和重要性.