一种适用于大偏心率轨道密集星历精密计算的快速处理方法

空间目标探测和编目是航天器安全的重要课题, 空间目标数量巨大, 造成轨道计算的工作量十分繁重. 分析方法虽然计算速度快, 却不能适应高精度观测资料的处理工作, 因而数值方法将成为目标轨道计算的重要方法. 空间目标编目工作普遍涉及密集星历的产生和计算问题, 针对这一问题的大偏心率轨道数值计算目前尚未形成兼具计算精度和计算效率的有效技术手段, 难以满足编目工作的处理要求. 在此背景下, 提出一种适用于大偏心率轨道密集星历精密计算的快速处理方法, 并通过数值实验对模型参数进行优选, 最后通过计算实例证实了该计算方案的优越性.     

面向单脉冲信号分类的集成特征选择与评价

受大量射频干扰信号影响,快速从海量观测数据中准确识别出单脉冲信号已成为天文数据处理的一项重要任务,而设计和提取有效数据特征,是利用机器学习进行单脉冲信号高效识别的决定因素.针对如何选择最优特征,进而提升单脉冲信号的分类精度这一关键问题,设计了面向单脉冲信号分类的集成特征选择方法.方法首先混合单脉冲信号的参数特征、统计特征和抽象特征,然后分别利用5种单一特征选择方法选出各自的最优特征集,最后利用贪心策略对5种单一方法获取的最优特征集进行集成筛选,获取最优集成特征集.实验表明,最优特征集合既包含统计特征也包含抽象特征.在相同特征数量下,利用集成特征选择比单一特征选择能获得更高的模型精度,可使F1值最高提升1.8%.在海量数据背景下,集成特征选择对减少特征数量、提升分类性能和加快数据处理速度具有重要作用.     

Adams—Cowell方法与KSG积分器的比较

在人造地球卫星精密定轨中,有摄星历等量的计算常采用Adams-Cowell方法,美国Texas大学空间研究中心(CSR)的定轨软件中则采用了一种有别于Adams-Cowell方法的KSG积分器。本文对这两种线性多步法作了全面比较,并用典型算例作了数值验证,列出了两种方法中卫星轨道沿迹误差的状况,以此表明为什么人们常采用Adams-Cowell方法。     

光压摄动计算中地影间断的处理

人卫精密定轨中受摄星历（或称精密星历,即状态转移）,可由分析解或数值解提供,相应的定轨方法亦有分析法定轨与数值法定轨之称。对于后者,在一般情况下,现有的常微分方程数值解法（或称积分器）已能满足精度要求,除长弧定轨外,有一定问题是值得注意的,即地影“间断”问题的处理,这关系到如何在保证星历精度的前提下提高计算效率的问题。本文针对这一问题,给出了相应的改进算法,并通过数值验证表明算法的有效性。     

Numerical integration methods for orbital motion

The present report compares Runge-Kutta, multistep and extrapolation methods for the numerical integration of ordinary differential equations and assesses their usefulness for orbit computations of solar system bodies or artificial satellites. The scope of earlier studies is extended by including various methods that have been developed only recently. Several performance tests reveal that modern single- and multistep methods can be similarly efficient over a wide range of eccentricities. Multistep methods are still preferable, however, for ephemeris predictions with a large number of dense output points.     

A numerical comparison with the Ceplecha analytical meteoroid orbit determination method

Abstract– Analytic methods by Ceplecha have long been used for the determination of meteoroid heliocentric orbits. These methods include both the derivation of an initial atmospheric contact position and velocity state, and the calculation of an orbit at infinity based on zenithal attraction assumptions. Herein, we describe a numerical integration‐based verification for a portion of the Ceplecha methods, a verification driven by the need for an accurate meteoroid ephemeris in the hours before atmospheric contact. We show a close correspondence in analytic and numerical results, with a previously undocumented minor correction to a meteoroid’s longitude of the ascending node.     

建立同步卫星精密星历表的最佳数值方法

简要介绍当前天体力学中常用的各种数值计算方法,结合同步卫星运动方程的特点和轨道解的性质,分析各种数值计算方法在同步卫星情况下使用的优劣,确定一次和分形式的Cowell方法是建立同步卫星精密星历表的最佳方法,最后通过有效的数值实验,给出不同精度要求下Cowell方法的最佳阶和相应的最大步长.     

两行根数辅助的SLR单站定轨

单站测距资料定轨的困难限制了漫反射SLR(Satellite Laser Ranging)测距资料的应用.为此,提出利用两行根数模拟多站SLR测距资料作为辅助,实现单站SLR测距资料定轨的方法.该方法对卫星Ajisai单站SLR测距资料定轨并生成5 d预报轨道,误差小于40 m,实现利用单站测距资料的轨道改进,验证了方法的可行性.     

轨道改进中计算状态转移矩阵的分析方法

对当今人卫轨道改进问题,由于力学模型的复杂,精密星历和状态转移矩阵的计算均采用数值方法,这就需要积分两组常微分方程．本文针对状态转移矩阵在定轨中的作用,对定轨弧段不太长的情况,给出了状态转移矩阵的一种分析算法,从而避免数值求解两组常微分方程的问题,并以实际算例证实了这种算法的有效性     

GPS数据处理策略对成果精度的影响及可靠性分析

高精度全球定位系统(Global Positioning System,GPS)数据处理的成果精度往往受海潮模型、卫星轨道约束模式、星历产品等数据类型及处理策略的制约。在考虑上述影响因素的前提下进行相关实验,并基于误差理论提出一种增加基线解算次数组合平差的方法,以提高基线解算精度。实验结果表明,数据处理中置入海潮模型较未采用前精度更高,FES2004模型的内外符合精度整体最优,近海区NAO99b外符合精度占优,其它海潮模型基本相当;松弛轨道模式内符合精度较固定轨道模式内符合精度高,但外符合精度较轨道固定模式稍差。不同的精密轨道产品对最终解算结果影响较小,增加基线解算次数组合平差的方法对数据处理成果精度的提高具有明显效果,且在几种精密星历下均表现出良好的收敛性。     

Ephemeris of a highly eccentric orbit: Explorer 28

An ephemeris has been obtained for Explorer 28 (IMP 3) which agrees well with 2 years of radio observations and with SAO observations a year later. This ephemeris is generated over the 3 year lifetime by a numerical integration method utilizing a set of initial conditions, at launch and without requiring further differential correction. Because highly eccentric orbits are difficult to compute with acceptable accuracy and because a long continuous arc has been obtained which compares with actual data to a known precision, this ephemeris may be used as a standard for computing highly eccentric orbits in the Earth-Moon system.Orbit improvement was used to obtain the initial conditions which generated the ephemeris. This improvement was based on correcting the energy by adjusting the semimajor axis to match computed times of perigee passage with the observed. This procedure may generate errors in semimajor axis to compensate for model errors in the energy; however this compensation error is also implicit in orbit determination itself.     

A Research on the Orbit Determination Method by Means of Sparse Data of Electronic Fences

Based on the Lambert equation and knowledge of space geometry a method of orbit determination is given using the sparse observational data provided by the space monitoring electronic fence device. Our simulated experiment of a large number of targets shows that the initial orbit determined by this method can be improved and can converge to a final accuracy better than 100 m, so proving that the method can be applied to the orbit determination of an overwhelming majority of space targets with the observed data of the electronic fence. Finally, the effect of the latitude of the observing station on the application of the method is discussed.     

A fast,accurate, and smooth planetary ephemeris retrieval system

Precise trajectory simulations typically require an ephemeris retrieval system, i.e. some mechanism to identify planetary body states and orientations at given times. However, the ephemeris systems most commonly used throughout industry and academia are, by design, general in their capabilities and application. Here, we introduce a new system called FIRE (Fast Interpolated Runtime Ephemeris) that is designed for custom trajectory applications that favor speed and smooth derivatives. The new system minimizes the overhead associated with ephemeris calls through the use of archived splines, a runtime ephemeris (stored in random access memory of the computer), and batch processing routines. Further, our approach naturally provides first and second time derivatives for a small additional computational cost. The derivative capability is particularly attractive for optimization and targeting where smooth and accurate derivatives are important. Relative performance comparisons with the Jet Propulsion Laboratory’s Spacecraft Planet Instrument C-matrix Events ephemeris system show typical speed improvements of approximately two orders of magnitude (250 times) for various state and orientation calls. Performance comparisons for high fidelity trajectory propagations are also considered and a factor of 70 in performance increase is achieved for typical cases. The new tool has potential value to any high precision application or software requiring fast, accurate, and smooth ephemeris data.     

Methode rapide de calcul d'une trajectoire de petite planete par l'approximation de tchebycheff,et son ajustement aux observations

It is shown that the application of the Chebyshev theory of approximation to the calculation of the orbit of a minor planet allows the production of a compact ephemeris, based on data gathered over only a short time, which is both accurate, and simple and rapid to produce. Adjustment of numerical data to fit observational results is readily performed. Using Clenshaw's algorithm, an ephemeris may even be worked out on a pocket calculator. Further applications of Chebyshev polynomials to the calculation of parameters usually obtainable only by interpolation of classical ephemerides, and to the calculation of minor planetary orbits from observations of short duration by an orbiting telescope are discussed.

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Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.     

The Effect of GPS Ephemeris on the Accuracy of Precise Orbit Determination of LEO Satellite-borne GPS

The satellite-borne GPS receivers dedicated to precise orbit determination are now being carried by more and more low earth orbit (LEO) satellites and the satellite-borne GPS has become one of the main means for the precise orbit determination of low earth orbit satellites. The accuracy of satellite-borne GPS precise orbit determination depends on the accuracies of the GPS ephemeris and the clock error. Based on the orbit determination function of SHORDEIII zero-difference dynamics and using the observational data obtained by the GRACE satellites for the week from 2005 August 1 to 7 as an example, three versions of GPS ephemerides (igs, igr and igu) are used to carry out orbit determination under the same conditions and to estimate the effect of the GPS ephemeris accuracy on the accuracy of orbit determination of low earth orbit satellites. Our calculated results show that the two ephemerides, igs and igr, are equivalent to each other in orbit determination accuracy (about 9.5 cm), while igu is slightly less accurate, at about 10.5 cm. The effect produced by the data of the high frequency GPS satellite clock error on the accuracy of orbit determination is 1–6 cm.     

利用IGS星历预报GPS卫星轨道

在动力学轨道拟合以及轨道积分的基础上,提出了基于IGS精密星历的GPS卫星轨道预报方法。该方法首先利用已知的IGS精密星历作为虚拟观测值,采用动力学方法拟合出GPS卫星的初始轨道和动力学参数,然后再通过积分来预报GPS卫星的轨道。主要讨论了基于不同弧段的IGS星历时,该方法对GPS卫星轨道的拟合和预报情况。研究结果显示:对于6 d弧段以内的IGS精密星历,其拟合轨道与IGS精密星历差值的三维RMS值均优于4 cm,随着拟合弧段的增加,拟合残差变大;当利用2～6 d弧段的IGS星历来预报GPS轨道时,大部分卫星第1天、第7天和第30天的三维预报精度可优于0.1 m、3 m和100 m。其中,2d弧段的IGS星历对GPS卫星第1天和第7天的预报结果最好,5 d弧段的IGS星历对GPS卫星第30天的预报结果最好。     

On the Laplacian orbit determination of asteroids

A modified Laplacian technique is described for initial orbit determination of asteroids from CCD observations and its applications for orbit determination of the main belt asteroids and near Earth asteroids. The proposed modification is based on a simultaneous improvement of both the orbital elements and the derivatives of spherical coordinates in frames of Laplace's method. It provides an orbit which represents the used observations with the residuals comparable with errors of these observations. The improved values of the derivatives might be used as ephemeris parameters for identification of newly discovered objects.     

Multiple Poincaré sections method for finding the quasiperiodic orbits of the restricted three body problem

A new fully numerical method is presented which employs multiple Poincaré sections to find quasiperiodic orbits of the Restricted Three-Body Problem (RTBP). The main advantages of this method are the small overhead cost of programming and very fast execution times, robust behavior near chaotic regions that leads to full convergence for given family of quasiperiodic orbits and the minimal memory required to store these orbits. This method reduces the calculations required for searching two-dimensional invariant tori to a search for closed orbits, which are the intersection of the invariant tori with the Poincaré sections. Truncated Fourier series are employed to represent these closed orbits. The flow of the differential equation on the invariant tori is reduced to maps between the consecutive Poincaré maps. A Newton iteration scheme utilizes the invariance of the circles of the maps on these Poincaré sections in order to find the Fourier coefficients that define the circles to any given accuracy. A continuation procedure that uses the incremental behavior of the Fourier coefficients between close quasiperiodic orbits is utilized to extend the results from a single orbit to a family of orbits. Quasi-halo and Lissajous families of the Sun–Earth RTBP around the L2 libration point are obtained via this method. Results are compared with the existing literature. A numerical method to transform these orbits from the RTBP model to the real ephemeris model of the Solar System is introduced and applied.     

SLR新星历及其在卫星预报中的应用

目前卫星激光测距(SLR)中所采用的IRV星历已经使用了近20年,近几年来随着对高轨卫星的测距和卫星白天测距的开展以及考虑到今后激光测距技术的发展,需要对SLR所采用的星历进行改进,以适应SLR发展的需求。从2006年8月起国际激光测距网(ILRS)将使用一种新的可用于多种目标测距的星历——CPF星历,该星历不仅可用于人造卫星的激光测距,而且还可用于月球及其转发器等目标的激光测距。该文介绍了这种SLR新星历和应用它进行卫星位置台站预报的情况,分析了其预报精度。