Numerical modeling of a Global Navigation Satellite System in a general relativistic framework

In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild space–time, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are obtained analytically, describing respectively trajectories of satellites and electromagnetic signals. We implement an algorithm to calculate Schwarzschild coordinates of a GNSS user who receives proper times sent by four satellites, knowing their orbital parameters; the inverse procedure is implemented to check for consistency. The constellation of satellites therefore realizes a geocentric inertial reference system with no a priori realization of a terrestrial reference frame. We perform a simulation of position determination and show that the determination of the four coordinates with a 25–32 digit accuracy takes only around 60 ms. Effects of non-gravitational perturbations on positioning errors are assessed, and methods to reduce them are sketched. In particular, inter-links between satellites could greatly enhance stability and accuracy of the positioning system. Effects of gravitational perturbations are omitted in this paper in order to make a clearer comparison between the relativistic and non-relativistic scheme, but they will be included in subsequent work. We believe that the final algorithm will be a serious alternative to the usual post-Newtonian scheme.     

Gamma Astrometric Measurement Experiment (GAME) – Implementation and performance

The GAME mission concept is aimed at testing the General Relativity, through precise measurement of the gravitational deflection of light by the Sun, by means of an optimised telescope operating in the visible and launched in orbit on a small class satellite. We describe the proposed mission profile, the preliminary payload design and the expected performance. The targeted precision on the γ parameter of the PPN formulation of General Relativity is in the range 10⁻⁶ to 10⁻⁷. The measurement principle relies on the differential astrometric signature on the stellar positions. The instrument concept is based on a dual field, multiple aperture Fizeau interferometer, observing simultaneously two sky regions close to the solar limb. A beam combiner folds the telescope line of sight on two different directions on the sky, separated by a base angle of 4°. The diluted optics approach achieves an efficient rejection of the scattered solar radiation, while retaining an acceptable angular resolution on the science targets.     

The GFZ real-time GNSS precise positioning service system and its adaption for COMPASS

Motivated by the IGS real-time Pilot Project, GFZ has been developing its own real-time precise positioning service for various applications. An operational system at GFZ is now broadcasting real-time orbits, clocks, global ionospheric model, uncalibrated phase delays and regional atmospheric corrections for standard PPP, PPP with ambiguity fixing, single-frequency PPP and regional augmented PPP. To avoid developing various algorithms for different applications, we proposed a uniform algorithm and implemented it into our real-time software. In the new processing scheme, we employed un-differenced raw observations with atmospheric delays as parameters, which are properly constrained by real-time derived global ionospheric model or regional atmospheric corrections and by the empirical characteristics of the atmospheric delay variation in time and space. The positioning performance in terms of convergence time and ambiguity fixing depends mainly on the quality of the received atmospheric information and the spatial and temporal constraints. The un-differenced raw observation model can not only integrate PPP and NRTK into a seamless positioning service, but also syncretize these two techniques into a unique model and algorithm. Furthermore, it is suitable for both dual-frequency and sing-frequency receivers. Based on the real-time data streams from IGS, EUREF and SAPOS reference networks, we can provide services of global precise point positioning (PPP) with 5–10 cm accuracy, PPP with ambiguity-fixing of 2–5 cm accuracy, PPP using single-frequency receiver with accuracy of better than 50 cm and PPP with regional augmentation for instantaneous ambiguity resolution of 1–3 cm accuracy. We adapted the system for current COMPASS to provide PPP service. COMPASS observations from a regional network of nine stations are used for precise orbit determination and clock estimation in simulated real-time mode, the orbit and clock products are applied for real-time precise point positioning. The simulated real-time PPP service confirms that real-time positioning services of accuracy at dm-level and even cm-level is achievable with COMPASS only.     

扩频通信系统相偏纠正的一种新方案

文章提出一种新方案,利用同步扩频码不携带载波相位信息的特点来进行相偏纠正的算法避免了相位模糊,可以纠正[0,2π]内的任意相偏,不需要采用锁相环等硬件来实现。     

面向对象型有限元建模专家系统的设计与实现

介绍了运用面向对象原理与人工智能逻辑推理技术相结合的方法来构造航空结构有限元建模专家系统(OOFEMES).着重论述了系统的结构、功能设计与实现策略,包括领域知识的获取、分类、表达与组织,以及知识的推理与运算求解方式.给出了针对飞机结构不规则性(如开口、断接等情况)进行模型局部修正的任务处理流程,并通过应用实例,说明该系统应用的有效性.      

亚、超音喷管中声传播的数值模拟

采用计算气动声学方法研究了管道近音速区的声传播和声波与激波的相互作用问题。空间离散采用高阶DRP格式,时间离散采用低耗散低频散的龙格库塔方法,边界条件采用Giles的特征变量一维非定常无反射边界条件。计算结果和解析解的精确吻合表明,计算中应用的这种高阶的DRP格式有很高的分辨率和很好的稳定性,适合声传播的计算。      

高阶格式及其在内外流场计算中的应用

高阶格式这里包含两种不同的含义,一种是人们常说的高精度格式;另一种是高分辨率格式,因为它常与高精度有密切联系,但两者毕竟有严格的区别.在格式的构建上,相比之下高分辨率格式较高精度格式难得多.本文从4个方面讨论了高精度格式与高分辨率格式在相关领域中的应用并给出了大量算例,这对澄清人们对高阶格式的认识,弄清它们各自的适用范围是十分必要的.大量的数值计算与研究表明:对于复杂流场,尤其是既考虑激波与边界层相互作用,又要考虑壁面传热的流场,用低阶数值格式计算是无法得到与实验较接近的数值结果的,因此发展高阶格式对处理高温涡轮的气膜冷却问题以及高速飞行器的气动热计算是至关重要的.      

单圈分子图的第一广义Zagreb指标的极值

第一广义Zagreb指标定义为0Rα（G）=∑i∈V（G）d（i）α,其中d（i）为i顶点的度,α为除0和1之外的所有实数。单圈分子图是指最大度不超过4且边数等于顶点数的简单连通图。本文通过一个引理,给出了单圈分子图的第一广义Zagreb指标达到极值的必要条件。     

高阶精度线性耗散紧致格式的渐近稳定性

文献〔２〕提出的高阶精度线性耗散紧致格式,（ＤＣＳ）能较好地抑制高波数振荡。本文进一步研究表明：内点耗散参数α能够控制耗散紧致格式ＤＣＳ３和ＤＣＳ５的渐近稳定性,边界格式参数α１和α对以上格式的渐近稳定性的影响是次要的,并给出了 些参数的取值范围。通过平面可压缩Ｃｏｕｅｔｔｅ流的稳定性数值模拟表明,当格式ＤＣＳ５满足渐近稳定性要求且具有耗散时,计算结果与线性稳定性分析的结果十分吻合,否则,会出现较     

用BGK格式对平面可压缩自由混合剪切流动的数值模拟

本文介绍了ＢＧＫ－Ｂｏｌｔｚｍａｎｎ格式的构造与用有限体积法计算网络内宏观量的方法。文中还介绍了可压缩平面混合剪切层计算域在不同出口马赫数下的边界条件。然后将上述方法应用于四种不同情况的可压缩平面混合剪切层的数值模拟。还详细介绍了计算结果,并与其他方法所得的的结果以及实验数据进行比较。表明本文的结果较好,方法是有效的。