LEO navigation augmentation constellation design with the multi-objective optimization approaches

Low Earth Orbit (LEO) satellite for navigation augmentation applications can significantly reduce the precise positioning convergence time and attract increasing attention recently. A few LEO Navigation Augmentation (LEO-NA) constellations have been proposed, while corresponding constellation design methodologies have not been systematically studied. The LEO-NA constellation generally consists of a huge number of LEO satellites and it strives for multiple optimization purposes. It is essentially different from the communication constellation or earth observing constellation design problem. In this study, we modeled the LEO-NA constellation design problem as a multi-objective optimization problem and solve this problem with the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm. Three objectives are used to strive for the best tradeoff between the augmentation performance and deployment efficiency, namely the Position Dilution of Precision (PDOP), visible LEO satellites and the orbit altitude. A fuzzy set approach is used to select the final constellation from a set of Pareto optimal solutions given by the MOPSO algorithm. To evaluate the performance of the optimized constellation, we tested two constellations with 144 and 288 satellites and each constellation has three optimization schemes: the polar constellation, the single-layer constellation and the two-layer constellation. The results indicate that the optimized two-layer constellation achieves the best global coverage and is followed by the single-layer constellation. The MOPSO algorithm can help to improve the constellation design and is suitable for solving the LEO-NA constellation design problem.     

Geostationary Satellite Navigation Systems

The concept of position determination using geostationary satellites as an alternative to the global positioning system (GPS) is studied. The advantage of a geostationary system is that only three, or at most four, satellites are required to cover the continental United States. A total of twelve satellites are sufficient for global coverage (excluding polar regions), or eight if only longitude and latitude, but not altitude, are measured. The system involves the determination of the range to either four geostationary satellites or, if the altitude is not measured, three geostationary satellites. The accuracy of the proposed systems are evaluated to obtain the rms error associated with position determination, and the concept for the implementation of measurements required by the systems is presented. The accuracy of the systems are adequate for civilian use in the continental United States; however, there is a degradation in accuracy as the location of the user approaches the equator.     

Geostationary tether satellite system and its application tocommunication systems

The geostationary tether satellite system expands the geostationary orbit resource from a one-dimensional arc into a two-dimensional disk. The tethered satellites, each several thousand kilometers apart and aligned along the local vertical, are stabilized at the altitude of the geosynchronous orbital speed. When this system is applied to communications systems, it is estimated that the number of satellites can be increased as much as thirteenfold and the communication capacity can be increased more than seventeenfold, compared with a conventional geostationary satellite orbit system     

Design of Satellite Constellations for Optimal Continuous Coverage

A satellite-borne sensor can view a region at or above the Earth's surface. The size of this region depends on the satellite's altitude, the maximum range and scan angle of the sensor, the minimum above-the-horizon viewing angle required, the extent in altitude of the region to be viewed, and the maximum altitude of sensor obscuration by the atmosphere. Except for geosynchronous satellites this region moves relative to the Earth, so that constellations of satellites are generally necessary for continuous coverage. Satellite constellations which minimize the number of satellites required for continuous coverage are derived as a function of the angle subtended at the Earth's center by the coverage of a single satellite. This is done for single and triple continuous coverage of the entire Earth and of the polar regions extending to arbitrary latitude. Simple, cogent approximations for the configurations and numbers of satellites are found. Expressions which relate sensor capabilities and surveillance requirements to are presented. Examples are given to illustrate the use and accuracy of the results.     

HOI延迟对LEO卫星简化动力学POD的影响

通常使用无电离层(IF)线性组合(LC)消除低地球轨道(LEO)卫星简化动力学精密定轨(POD)一阶电离层延迟误差,忽略了高阶电离层(HOI)延迟误差。随着LEO卫星POD技术的发展,计算不同轨道高度的HOI延迟并探索其变化已成为进一步提高POD精度的重要手段。首先,使用国际参考电离层-2016(IRI-2016)和国际地磁参考场第13代(IGRF-13)模型,计算电离层穿刺点(IPP)位置和地磁场强度。其次,使用平滑星载GNSS数据计算电离层斜路径总电子含量(STEC)。然后,分别计算GOCE、GRACE-A和SWARM-A/B卫星的二阶和三阶电离层延迟。最后,评估了HOI延迟对LEO卫星重叠轨道分析、卫星激光测距(SLR)检核和精密科学轨道(PSO)比较结果的影响。实验结果表明：HOI延迟对LEO卫星简化动力学POD的影响大约在毫米至厘米的数量级上;HOI延迟对LEO卫星简化动力学POD外符合精度的影响分别达到0.92,0.22,0.21和0.18 mm;随着LEO卫星轨道高度的增加,HOI延迟对LEO卫星简化动力学POD的影响减小。     

Overview of multiple satellite communication networks

Recently interest in packet communications has stimulated an interest in constellations of low altitude satellites. Such a configuration would have less propagation delay and be cheaper to launch than satellites at higher or geosynchronous altitude. However, many more satellites are necessary at low altitude to achieve reasonable coverage of the earth and insure availability of the resource. Further, the geometry of such a constellation would be dynamic with communication links of short duration as the satellites speed past each other or a ground site. The most difficult design issue in these systems is a stable method of routing messages that will sustain a reasonable level of traffic. This paper explores the problems of routing and switching messages through a constellation of low altitude satellites and examines some of the related demands on technology. The dynamic nature of crosslinks, uplinks, and downlinks requires a very agile antenna system, and the volume of information for routing of traffic is overwhelming. Use of some type of facetted phased array antenna is advocated to solve the former problem, but the latter problem is more subtle. Since the volume of ephemeris and constellation data as well as the rate of update is unmanageable, schemes relying on some form of broadcast or random access may be considered. It is concluded that none of the known or examined approaches to routing and switching is completely satisfactory     

Large angle pitch attitude maneuver of a satellite using solarradiation pressure

The force exerted by the solar radiation, though very small in magnitude, produces significant effects, especially in the case of high altitude satellites. The solar radiation pressure represents one freely available environmental force that may be put to use for various purposes. This may lead to enhancement of the life of the satellite since it consumes a very nominal amount of on-board energy. The advantages offered by the solar radiation pressure have drawn the attention of several researchers. Various controllers were proposed for many space missions, particularly for attitude control and stabilization of satellites. A controller for achieving large angle pitch attitude maneuver is described. The proposed control law is very simple in its form and requires a minimum number of on-board computations. Varieties of cases are tried and the effect of various parameters is studied     

Global communication using a constellation of low Earth meridianorbits

The concept of meridian orbits is briefly reviewed. It is shown that, if a satellite in the meridian orbit makes an odd number (>1) of revolutions per day, then the satellite passes over the same set of meridians twice a day. Satellites in such orbits pass over the same portion of the sky twice a day and every day. This enables a user to adopt a programmed mode of tracking, thereby avoiding a computational facility for orbit prediction, look angle generation, and auto tracking. A constellation of 38 or more satellites placed in a 1200-km altitude circular orbit is favorable for global communications due to various factors. It is shown that appropriate phasing in right ascension of the ascending node and mean anomaly results in a constellation wherein each satellite appears over the user's horizon one satellite after another. Visibility and coverage plots are provided to verify the continuous coverage     

Rosette Constellations of Earth Satellites

Satellite constellations having rosette (flowerlike) orbital patterns are described which exhibit better worldwide coverage properties than constellations previously reported in U.S. literature. The best rosettes with 5-15 satellites are identified and evaluated relative to prior results. In most cases, the best results are obtained by placing one satellite in each of N separate planes and by using inclined rather than polar orbits. Coverage properties of these constellations are analyzed in terms of the largest possible great circle range between an observer anywhere on the Earth's surface and the nearest subsatellite point. When evaluated in this manner, coverage properties are invariant with deployment altitude. As deployment altitude is reduced, however, higher order constellations must be used to maintain a fixed minimum viewing angle. Coverage properties are also invariant with deployment orientation relative to Earth coordinates, although specific orientations can cause the satellite patterns to appear quasi-stationary. Thus these constellations offer a promising alternative to the use of geostationary satellites. Rosette constellations can also be used to guarantee multiple satellite visibility on a continuous worldwide basis. It is shown that 5, 7, 9, and 11 satellites are the minimum numbers required for single, double, triple, and quadruple visibility, respectively. Examples of rosette constellations which achieve these bounds are given.     

MEO/LEO双层卫星网络中层间链路的连接度分析

作为未来卫星移动通信系统的一个重要的研究方向,提出了一种由MEO卫星和LEO卫星共同组成的双层卫星网络(Double-Layer Satellite Network,DLSN),以更好为用户提供多媒体服务.作为多层卫星网络的一个重要的研究内容,连接不同高度上卫星的层间链路(Inter-Orbit-Links,IOLs)的特性对于整个DLSN网络的性能会有很大的影响.根据所设计的多层卫星网络的星座参数,通过对层间链路几何特性的研究,分析了多层卫星网络中MEO卫星与LEO卫星的连接度性能.采用计算机仿真的方法,给出了层间链路连接度的特性.结果表明,为了提高网络性能,在多层卫星网络中应按照一定参数有选择的建立层间链路,而不是简单的采用视距可见原则建立层间链路.     

多状态空间信息网络拓扑生成优化算法

依据空间信息网络（SIN）高动态性的特点，并考虑卫星工作的多状态特性，兼顾星间通信时延和拓扑抗毁性的要求，研究了多状态下空间信息网络拓扑生成及动态优化的问题。根据卫星星座的周期性，建立了一种卫星网络的拓扑周期表。综合卫星的可视性和连接度等约束条件，以网络平均和最大时延作为通信性能的优化目标，建立拓扑的多目标优化模型。提出一种改进的多目标模拟退火（IMOSA）算法，求解全局时延最优的卫星拓扑，并在考虑多状态情况下对链路进行优化，以满足网络高动态性。最后基于具有66颗低轨（LEO）的铱星星座进行仿真，研究表明：针对多状态条件下的铱星星座，该算法最大化减小了通信时延，得到抗毁性良好的拓扑结构，通信性能较之原有静态拓扑明显得到改善。     

Lunar Magnetic Field Observation and Initial Global Mapping of Lunar Magnetic Anomalies by MAP-LMAG Onboard SELENE (Kaguya)

The magnetic field around the Moon has been successfully observed at a nominal altitude of ～100 km by the lunar magnetometer (LMAG) on the SELENE (Kaguya) spacecraft in a polar orbit since October 29, 2007. The LMAG mission has three main objectives: (1) mapping the magnetic anomaly of the Moon, (2) measuring the electromagnetic and plasma environment around the Moon and (3) estimating the electrical conductivity structure of the Moon. Here we review the instrumentation and calibration of LMAG and report the initial global mapping of the lunar magnetic anomaly at the nominal altitude. We have applied a new de-trending technique of the Bayesian procedure to multiple-orbit datasets observed in the tail lobe and in the lunar wake. Based on the nominal observation of 14 months, global maps of lunar magnetic anomalies are obtained with 95% coverage of the lunar surface. After altitude normalization and interpolation of the magnetic anomaly field by an inverse boundary value problem, we obtained full-coverage maps of the vector magnetic field at 100 km altitude and the radial component distribution on the surface. Relatively strong anomalies are identified in several basin-antipode regions and several near-basin and near-crater regions, while the youngest basin on the Moon, the Orientale basin, has no magnetic anomaly. These features well agree with characteristics of previous maps based on the Lunar Prospector observation. Relatively weak anomalies are distributed over most of the lunar surface. The surface radial-component distribution estimated from the inverse boundary value problem in the present study shows a good correlation with the radial component distribution at 30 km altitude by Lunar Prospector. Thus these weak anomalies over the lunar surface are not artifacts but likely to be originated from the lunar crustal magnetism, suggesting possible existence of an ancient global magnetic field such as a dynamo field of the early Moon. The possibility of the early lunar dynamo and the mechanism of magnetization acquisition will be investigated by a further study using the low-altitude data of the magnetic field by Kaguya.     

21世纪AMSS／GNSS空间段发展方向兼论卫星资源国际共享问题

航空移动卫星系统（ＡＭＳＳ）空间段采用单一的ＧＥＯ轨道卫星，未来将有ＭＥＯ和ＬＥＯ轨道卫星加入运行，仍然不排斥ＧＥＯ轨道卫星的使用。全球导航卫星系统（ＧＮＳＳ）空间段采用ＭＥＯ轨道卫星，未来将仍然以ＭＥＯ为主，可能有ＨＥＯ轨道卫星加入运行。２１世纪的空间段将为不同轨道卫星的多星座组合，采用一星多用、星座共用，形成多功能卫星和多功能星座。和平时期卫星资源的国际民间共建共营共享将更为普遍，要有全球观点，国内各行各业要有全局观点，对监测和增强系统统一筹建共用系统，防止分散投资、重复建设     

Basic performance of BeiDou-2 navigation satellite system used in LEO satellites precise orbit determination

The visibility for low earth orbit（LEO） satellites provided by the BeiDou-2 system is analyzed and compared with the global positioning system（GPS）. In addition, the spaceborne receivers＇ observations are simulated by the BeiDou satellites broadcast ephemeris and LEO satellites orbits. The precise orbit determination（POD） results show that the along-track component accuracy is much better over the service area than the non-service area, while the accuracy of the other two directions keeps at the same level over different areas. However, the 3-dimensional（3D） accuracy over the two areas shows almost no difference. Only taking into consideration the observation noise and navigation satellite ephemeris errors, the 3D accuracy of the POD is about30 cm. As for the precise relative orbit determination（PROD）, the 3D accuracy is much better over the eastern hemisphere than that of the western hemisphere. The baseline length accuracy is 3.4 mm over the service area, and it is still better than 1 cm over the non-service area. This paper demonstrates that the BeiDou regional constellation could provide global service to LEO satellites for the POD and the PROD. Finally, the benefit of geostationary earth orbit（GEO） satellites is illustrated for POD.     

Existence and uniqueness of GPS solutions

The existence and uniqueness of positions computed from global positioning system (GPS) pseudorange measurements is studied. Contrary to the claims of S. Bancroft (1985) and L.O. Krause (1987), in the case of n=4 satellites a fix may not exist, and, if a fix exists, it is not guaranteed to be unique. In the case of n>or=5 satellites, a unique fix is assured, except in certain degenerate cases such as coplanar satellites. An alternate formulation of the direct n=4 pseudorange to three-space position solutions of Bancroft and Krause is presented, and simple tests for existence and uniqueness are derived.<>     

Integrating BDS and GPS for precise relative orbit determination of LEO formation flying

Low-Earth-Orbit(LEO) formation-flying satellites have been widely applied in many kinds of space geodesy. Precise Relative Orbit Determination(PROD) is an essential prerequisite for the LEO formation-flying satellites to complete their mission in space. The contribution of the BeiDou Navigation Satellite System(BDS) to the accuracy and reliability of PROD of LEO formation-flying satellites based on a Global Positioning System(GPS) is studied using a simulation method. Firstly, when BDS is added to GPS, the mean number of visible satellites increases from9.71 to 21.58. Secondly, the results show that the 3-Dimensional(3 D) accuracy of PROD, based on BDS-only, GPS-only and BDS + GPS, is 0.74 mm, 0.66 mm and 0.52 mm, respectively. When BDS co-works with GPS, the accuracy increases by 29.73%. Geostationary-Earth-Orbit(GEO) satellites and Inclined Geosynchronous-Orbit(IGSO) satellites are only distributed over the Asia-Pacific region; however, they could provide a global improvement to PROD. The difference in PROD results between the Asia-Pacific region and the non-Asia-Pacific region is not apparent. Furthermore, the value of the Ambiguity Dilution Of Precision(ADOP), based on BDS + GPS, decreases by 7.50% and 8.26%, respectively, compared with BDS-only and GPS-only. Finally, if the relative position between satellites is only a few kilometres, the effect of ephemeris errors on PROD could be ignored. However, for a several-hundred-kilometre separation of the LEO satellites, the SingleDifference(SD) ephemeris errors of GEO satellites would be on the order of centimetres. The experimental results show that when IGSO satellites and Medium-Earth-Orbit(MEO) satellites co-work with GEO satellites, the accuracy decreases by 17.02%.     

Geomagnetic Observations for Main Field Studies: From Ground to Space

Direct measurements of the geomagnetic field have been made for more than 400 years, beginning with individual determinations of the angle between geographic and magnetic North. This was followed by the start of continuous time series of full vector measurements at geomagnetic observatories and the beginning of geomagnetic repeat stations surveys in the 19th century. In the second half of the 20th century, true global coverage with geomagnetic field measurements was accomplished by magnetometer payloads on low-Earth-orbiting satellites. This article describes the procedures and instruments for magnetic field measurements on ground and in space and covers geomagnetic observatories, repeat stations, automatic observatories, satellites and historic observations. Special emphasis is laid on the global network of geomagnetic observatories.     

The radiant angle of GPS satellite antenna affecting the appliedaltitude of GPS in a space vehicle

In this paper, the advantages and development of GPS applied in a space vehicle are introduced first. Then, the software employed to calculate the applied altitude of GPS in a space vehicle is explained. The detailed software flowchart is also given, and the process of choosing used GPS satellites is described in detail. In order to study the receiving condition in a space vehicle, we also make a simulating calculation with our software. The results of receiving GPS satellites over a certain place are given. The paper has not only the value for using GPS in a space vehicle, but also the significance for an aircraft whose navigation system is GPS     

Inter-satellite link augmented BeiDou-3 orbit determination for precise point positioning

Precise Point Positioning(PPP) requires precise products, including high-accuracy satellite orbit and clock parameters. It is impossible to obtain an orbit solution that is sufficiently accurate for PPP services with a regional tracking network; therefore, satellite orbits are usually estimated by a global tracking network with a large number of ground stations. However, it is expensive to build globally distributed stations. Fortunately, BeiDou-3 satellites carry an InterSatellite Link(ISL) pay...     

Sensitivity analysis of dual-satellite geolocation

An analytic solution is presented for the linearized estimation problem arising from the dual-satellite geolocation of the source of a narrowband signal using time- and frequency-difference-of-arrival (TDOA and FDOA, respectively) observations and an altitude constraint. This solution is used to analyze the covariance matrix of the resultant source location estimate, along with the sensitivity of its mean to errors in the presumed source altitude and velocity, and the measured or predicted positions and velocities of the satellites. Following the practice of differential Global Positioning System, the technique of differential calibration is used to reduce or eliminate various sources of solution bias which would otherwise require tight, and consequently expensive, individual calibration