Numerical orbit integration based on Lie series with use of parallel computing techniques

This article outlines necessary steps to perform numerical orbit integrations based on a Lie series approach. Its implementation requires an efficient evaluation of resulting series coefficients. As an example we treat the classical main problem in satellite orbit calculation (_J2$J_2$ only) and the case of a 4×4$4\times 4$-gravity field. All calculations were performed in very high precision with up to 100 significant digits. In comparison to independent third party computations this approach led to superior results referring to the verifiable constancy of various integrals of motion. To achieve a performance similar to classical numerical integrations in terms of acceptable computing time, at least for non-Keplerian motion problems, we exploited parallel computing capabilities. For our examples, run times were improved by several orders of magnitude, depending on the actual chosen precision level (up to a factor of 50,000 in case of double precision). Here we present the mathematical framework of the proposed orbital integration scheme as well as the work flow for its application in a multi-core, parallel computing environment.     

Severe disruption of the cytoskeleton and immunologically relevant surface molecules in a human macrophageal cell line in microgravity—Results of an in vitro experiment on board of the Shenzhou-8 space mission

During spaceflight the immune system is one of the most affected systems of the human body. During the SIMBOX (Science in Microgravity Box) mission on Shenzhou-8, we investigated microgravity-associated long-term alterations in macrophageal cells, the most important effector cells of the immune system. We analyzed the effect of long-term microgravity on the cytoskeleton and immunologically relevant surface molecules. Human U937 cells were differentiated into a macrophageal phenotype and exposed to microgravity or 1g on a reference centrifuge on-orbit for 5 days. After on-orbit fixation, the samples were analyzed with immunocytochemical staining and confocal microscopy after landing. The unmanned Shenzhou-8 spacecraft was launched on board a Long March 2F (CZ-2F) rocket from the Jiuquan Satellite Launch Center (JSLC) and landed after a 17-day-mission. We found a severely disturbed actin cytoskeleton, disorganized tubulin and distinctly reduced expression of CD18, CD36 and MHC-II after the 5 days in microgravity. The disturbed cytoskeleton, the loss of surface receptors for bacteria recognition, the activation of T lymphocytes, the loss of an important scavenger receptor and of antigen-presenting molecules could represent a dysfunctional macrophage phenotype. This phenotype in microgravity would be not capable of migrating or recognizing and attacking pathogens, and it would no longer activate the specific immune system, which could be investigated in functional assays. Obviously, the results have to be interpreted with caution as the model system has some limitations and due to numerous technical and biological restrictions (e.g. 23 °C and no CO₂ supply during in-flight incubation). All parameter were carefully pre-tested on ground. Therefore, the experiment could be adapted to the experimental conditions available on Shenzhou-8.     

Optimal H∞ robust output feedback control for satellite formation in arbitrary elliptical reference orbits

A two degree-of-freedom signal-based optimal H_∞ robust output feedback controller is designed for satellite formation in an arbitrary elliptical reference orbit. Based on high-fidelity linearized dynamics of relative motion, uncertainties introduced by non-zero eccentricity and gravitational J2 perturbation are separated to construct a robust control model. Furthermore, a distributed robust control model is derived by modifying the perturbed robust control model of each satellite with the eigenvalues of the Laplacian matrix of the communication graph, which represent uncertainty in the communication topology. A signal-based optimal H_∞ robust controller is then designed primarily. Considering that the uncertainties involved in the distributed robust control model have a completely diagonal structure, the corresponding analyses are made through structured singular value theory to reduce the conservativeness. Based on simulation results, further designs including increasing the degrees of freedom of the controller, modifying the performance and control weighted functions, adding a post high-pass filter according to the dynamic characteristics, and reducing the control model are made to improve the control performance. Nonlinear simulations demonstrate that the resultant optimal H_∞ robust output feedback controller satisfies the robust performance requirements under uncertainties caused by non-zero eccentricity, J2 perturbation, and varying communication topology, and that 5 m accuracy in terms of stable desired formation configuration can be achieved by the presented optimal H_∞ robust controller. In addition to considering the widely discussed uncertainties caused by the orbit of each satellite in a formation, the optimal H_∞ robust output feedback control model presented in the current work considers the uncertainties caused by varying communication topology in the satellite formation that works in a cooperative way. Other new improvements include adopting a new method to more accurately describe and analyze the effects of the higher-order J2 perturbation, combining all the uncertainties into a diagonal structure, and utilizing a structured singular value to synthesize and analyze the controller.     

Generation of satellite tracking profile: Problems and validation algorithms

Recently, as a satellite mission becomes complicated, it has been required to generate the schedule of satellite antenna movements automatically without relying upon operator’s ad hoc knowledge. To generate the satellite antenna schedule autonomously, this paper first addresses geometrical problems associated with the antenna scheduling and mission planning problems that can be formulated from satellite navigation and antenna orientation information. Then, based on the solutions of the geometrical problems, a set of antenna azimuth and elevation angles that enables the antenna to point towards the desired ground station is obtained systematically. Using the computed azimuth and elevation angles, the satellite tracking profile (TP) is generated, and to validate it, TP validation algorithms are developed.     

Precise orbit determination using the batch filter based on particle filtering with genetic resampling approach

In this study, genetic resampling (GRS) approach is utilized for precise orbit determination (POD) using the batch filter based on particle filtering (PF). Two genetic operations, which are arithmetic crossover and residual mutation, are used for GRS of the batch filter based on PF (PF batch filter). For POD, Laser-ranging Precise Orbit Determination System (LPODS) and satellite laser ranging (SLR) observations of the CHAMP satellite are used. Monte Carlo trials for POD are performed by one hundred times. The characteristics of the POD results by PF batch filter with GRS are compared with those of a PF batch filter with minimum residual resampling (MRRS). The post-fit residual, 3D error by external orbit comparison, and POD repeatability are analyzed for orbit quality assessments. The POD results are externally checked by NASA JPL’s orbits using totally different software, measurements, and techniques. For post-fit residuals and 3D errors, both MRRS and GRS give accurate estimation results whose mean root mean square (RMS) values are at a level of 5 cm and 10–13 cm, respectively. The mean radial orbit errors of both methods are at a level of 5 cm. For POD repeatability represented as the standard deviations of post-fit residuals and 3D errors by repetitive PODs, however, GRS yields 25% and 13% more robust estimation results than MRRS for post-fit residual and 3D error, respectively. This study shows that PF batch filter with GRS approach using genetic operations is superior to PF batch filter with MRRS in terms of robustness in POD with SLR observations.     

On the effects of each term of the geopotential perturbation along the time I: Quasi-circular orbits

This paper provides a useful new method to determine minimum and maximum range of values for the degree and order of the geopotential coefficients required for simulations of orbits of satellites around the Earth. The method consists in a time integration of the perturbing acceleration coming from each harmonic of the geopotential during a time interval T. More precisely, this integral represents the total velocity contribution of a specific harmonic during the period T  . Therefore, for a pre-fixed minimum contribution, for instance 1×10^-8$1\times {10}^{-8}$ m/s during the period of time T, any harmonic whose contribution is below this value can, safely, be neglected. This fact includes some constraints in the degree and order of the terms which are present in the geopotential formula, saving computational efforts compared to the integration of the full model. The advantage of this method is the consideration of other perturbations in the dynamics (we consider the perturbations of the Sun, the Moon, and the direct solar radiation pressure with eclipses), since these forces affect the value of the perturbation of the geopotential, because these perturbations depend on the trajectory of the spacecraft, that is dependent on the dynamical model used. In this paper, we work with quasi-circular orbits and we present several simulations showing the bounds for the maximum degree and order (M) that should be used in the geopotential for different situations, e. g., for a satellite near 500 km of altitude (like the GRACE satellites at the beginning of their mission) we found 35?M?198$35?M?198$ for T=1$T=1$ day. We analyzed the individual contribution of the second order harmonic (_J2$J_2$) and we use its behavior as a parameter to determine the lower limit of the number of terms of the geopotential model. In order to test the accuracy of our truncated model, we calculate the mean squared error between this truncated model and the “full” model, using the CBERS (China-Brazil Earth Resources Satellite) satellite in this test.     

空间目标距离像畸变分析及运动参数估计

针对卫星目标的宽带雷达回波信号,从理论上详细分析了目标运动产生的多项式相位模型,指出三次以上的相位对一维距离像的畸变可以忽略。以频谱主瓣的展宽程度为判据,推导了二次相位需补偿时的目标速度边界条件。结果表明,在典型参数条件下卫星目标的径向速度远大于该临界速度（约560m/s）,需在成像前予以补偿。最后,结合雷达目标散射中心的稀疏分布特性,提出了基于L1范数的空间目标运动参数估计算法。结果表明,该算法对速度的估计误差接近克拉美-罗下界,且远小于临界速度,可用于卫星目标成像。     

A new approach to the telescope operation method for satellite tracking using a time synchronization technique

For the development of a telescope that is capable of precisely tracking satellites and high-speed operation such as satellite laser ranging, a special method of telescope operation is required. This study aims to propose a new telescope operation method and system configuration for the independent development of a mount and an operation system which includes the host computer. Considering that the tracking of a satellite is performed in real time, communication and synchronization between the two independent subsystems are important. Therefore, this study applied the concept of time synchronization, which is used in various fields of industry, to the communication between the command computer and the mount. In this case, communication delays do not need to be considered in general, and it is possible to cope with data loss. Above all, when the mount is replaced in the future, only the general communication interface needs to be modified, and thus, it is not limited by replacement in terms of the overall system management. The performance of the telescope operation method developed in this study was verified by applying the method to the first mobile SLR system in Korea. This study is significant in that it proposed a new operation method and system configuration, to which the concept of time synchronization was applied, for the observation system that requires an optical telescope.     

A comparison of radiation shielding effectiveness of materials for highly elliptical orbits

The Canadian Space Agency (CSA) has proposed a Polar Communications and Weather (PCW) satellite mission, in conjunction with other partners. The PCW will provide essential communications and meteorological services to the Canadian Arctic, as well as space weather observations of in situ ionizing radiation along the orbit. The CSA has identified three potential Highly Elliptical Orbits (HEOs) for a PCW satellite constellation, Molniya, Modified Tundra and Triple Apogee (TAP), each having specific merits, which would directly benefit the performance/longevity of a PCW spacecraft. Radiation shielding effectiveness of various materials was studied for the three PCW orbit options to determine the feasibility of employing materials other than conventional aluminium to achieve a specified spacecraft shielding level with weight savings over aluminium. It was found that, depending on the orbit-specific radiation environment characteristics, the benefits of using polyethylene based materials is significant enough (e.g., 22% in Molniya for PE at 50 krad TID) to merit further investigation.     

皮卫星星箭分离机构运动系统设计

为实现“皮星一号A”卫星无干涉分离,达到分离初始姿态要求,对皮卫星星箭分离机构运动系统进行了分析设计。首先,根据皮卫星与凸轮限位机构间的受力情况和能量守恒定理确定了凸轮轮廓尺寸和分离弹簧结构参数,在此基础上建立了星箭分离过程动力学模型,通过对动力学模型的数值计算确定满足无干涉分离条件的舱门扭簧弹性系数。星箭分离过程的仿真计算和试验校验了“皮星一号A”星箭分离机构可实现无干涉分离,皮卫星初始速度、角速率均满足所提出的各项初始分离姿态要求。