综合评价线性多步积分公式轨道积分性能的两项新指标

概述了制约线性多步积分公式轨道积分状态的多种因素 ;提出了综合评价线性多步积分公式积分性能的两项新指标。建议在对数值计算有较高精度要求的科研项目中 ,应将构造并选择适合研究项目的线性多步积分公式以及高效的积分方式列为课题前期工作的重要部分     

Orbitally stable multistep methods

Lambert and Watson (1976) examine the family of symmetric linear multistep methods for the special second-order initial value problem, and connect the property of symmetry with a property of periodicity. The problems of celestial mechanics may be formulated as second-order initial value problems, but these frequently incorporate the first derivative explicity. It is common for such equations to be reduced to a system of first-order equations. Thus motivated, we utilize ideas from the aforementioned paper to determine the family of linear multistep methods for first-order initial value problems that possess an analogous property of periodicity. This family of orbitally stable methods is illustrated by examining the regularized equations of motion of an artificial earth satellite in an oblate atmosphere.     

Symplectic methods and their application to the motion of small bodies in the Solar System

Symplectic methods have been widely used in Solar System dynamics. This paper discusses both single step and multistep symplectic methods. For single step methods we point out that the modified algorithm (Wisdom et al., 1991, Kinoshita et. al., 1991) can be executed in the mass center coordinate system and in the Jacobian coordinate system. For multistep methods we describe the connections between symmetric and symplectic methods.     

Symplectic methods and their application to the motion of small bodies in the Solar System

Symplectic methods have been widely used in Solar System dynamics. This paper discusses both single step and multistep symplectic methods. For single step methods we point out that the modified algorithm (Wisdom et al., 1991, Kinoshita et. al., 1991) can be executed in the mass center coordinate system and in the Jacobian coordinate system. For multistep methods we describe the connections between symmetric and symplectic methods.     

A new family of multistep numerical integration methods based on Hermite interpolation

In this paper, a new family of explicit and implicit multistep methods is presented both for the error-controlled and uncontrolled modes. The main concept is to replace the Newton interpolation with the Hermite interpolation, where the Hermite polynomial is fitted to the function values and its derivatives. This idea is very useful in the numerical solution of problems (e.g., orbit propagation problem) where higher-order derivatives can easily be computed. In addition to the theoretical concept, the stability regions of the proposed methods are determined. The new methods are more stable than the well-known multistep numerical integrators (i.e., Adams–Bashforth and Adams–Bashforth–Moulton) in the explicit, implicit, and predictor–corrector forms. Using the second-order derivatives gives smaller error constants in the proposed method. The new integrators are numerically tested for a few examples, and the solutions are compared with those of the well-known multistep methods. Moreover, the CPU time and absolute integration error are compared in the satellite orbit propagation problem using various integration methods. The CHAMP mission, i.e., a German small-satellite mission for geoscientific and atmospheric research and applications, is considered as a case study for comparing the achievable accuracy of the proposed method with the existing method for solving the two-body problem.     

适用于人造卫星轨道数值积分的线性多步法的研究

总结了多年来构造适合卫星轨道计算的线性多步积分方法的研究进展;介绍了在构造积分公式的过程中选取伪根的三条原则。结合具体算例,对推荐的适用于不同类型卫星轨道的五线性多积分公式的性能与对称文坛及科威尔方法作了详细地比对和评述。     

Two multiderivate multistep (MDMS) integrators

A preliminary survey of multiderivative multistep integrators is carried out. It is found that all of them are much more accurate than the classical linear multistep methods, but most of them have poor stability. After parameter adjustment, two of them (called MDMS I and MDMS II by us) are competitive with or superior to the classical methods in some aspects, such as accuracy and stability. MDMS I behaves especially well in all the cases which have been studied.     

Maximum Entropy Regularization Method of Ionospheric Occultation

With the increasing of applications of Global Positioning System (GPS), the research on the factors affecting the radio signals is becoming more and more important. One of the most significant effects on ionosphere monitoring is the ionospheric radio occultation (IRO), and the IRO data is now serving as one of the most important monitoring sources for the ionospheric measurements. Meanwhile the inversion of the occultation data is a popular topic. The traditional Abel inversion process through compensated total electron content (TEC) is a linear inversion method, thus it would transfer the measurement errors directly to the inversion results. In order to improve the occultation results, we introduce in this paper two nonlinear methods, namely the regularization method and the maximum entropy regularization method. Through designed simulative experiments, we verify and compare these three methods, and conclude that the maximum entropy regularization method can reduce significantly the influence of measurement errors.     

Round-off error in long-term orbital integrations using multistep methods

Techniques for reducing roundoff error are compared by testing them on high-order Störmer and summetric multistep methods. The best technique for most applications is to write the equation in summed, function-evaluation form and to store the coefficients as rational numbers. A larger error reduction can be achieved by writing the equation in backward-difference form and performing some of the additions in extended precision, but this entails a larger cpu cost.     

可用于带耗散力卫星轨道长间隔积分的数值积分方法

本文分析了对称方法不适合带耗散力的卫星轨道长间隔积分的缺陷和本质原因,并针对这个问题,采用文所介绍的方法,构造并推荐了一组积分公式。     

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。     

Exploring three faint source detections methods for aperture synthesis radio images

Wide-field radio interferometric images often contain a large population of faint compact sources. Due to their low intensity/noise ratio, these objects can be easily missed by automated detection methods, which have been classically based on thresholding techniques after local noise estimation. The aim of this paper is to present and analyse the performance of several alternative or complementary techniques to thresholding. We compare three different algorithms to increase the detection rate of faint objects. The first technique consists of combining wavelet decomposition with local thresholding. The second technique is based on the structural behaviour of the neighbourhood of each pixel. Finally, the third algorithm uses local features extracted from a bank of filters and a boosting classifier to perform the detections. The methods’ performances are evaluated using simulations and radio mosaics from the Giant Metrewave Radio Telescope and the Australia Telescope Compact Array. We show that the new methods perform better than well-known state of the art methods such as SExtractor, SAD and DUCHAMP at detecting faint sources of radio interferometric images.     

Hamilton系统数值计算的新方法

系统地介绍了近年来对Ｈａｍｉｌｔｏｎ系统数值计算新建立的辛算法和线性对称多步法，并对它们在动力天文中的应用作了一简要回顾。     

用周期图谱分析方法计算Blazar天体的光变周期

对适用于等间隔时间序列的周期图谱分析方法进行了研究,用模拟信号进行了检验,证实了它适用于有噪声的时间序列.并把这种方法应用到类星体3C 279、3C 345,BL Lac天体OJ 287、ON 231的光变周期分析中,得到它们的光变周期分别为7.14年、10.00年、11.76年、6.80年.结果表明用周期图谱分析方法得到的结论和其他文献用Jurkevich方法得到的结论一致.获得的周期对进一步研究Blazar天体的物理机制很有帮助.还分析了窗函数的影响,指出它们的优缺点,便于在实际工作中做出正确选择.     

Multistep methods of numerical integration using back-corrections

A new class of linear multistep methods is proposed for the solution of the equations of motion of certain dynamical systems encountered in celestial mechanics and astrodynamics. These methods are distinguished from the classical predictor-corrector methods in that they permit back-corrections of the solution to be made. As the integration advances in time, the numerical solution is corrected or improved at certain points in the past. The enhanced numerical stability of these methods allows the meaningful application of high-order algorithms. Consequently, stepsizes larger than those attainable with the classical methods may be adopted and thus greater over-all efficiency may be realized. The application of these methods to the problem of determining the orbit of an artificial satellite is accomplished and the results are compared with those obtained using classical methods.     

On the reduction and presentation of data in astronomical two-channel photopolarimetry

Many different methods exist for reducing data obtained when an astronomical source is studied with a two-channel polarimeter, such as a Wollaston prism system. This paper presents a rigorous method of reducing the data from raw aperture photometry, and evaluates errors both by a statistical treatment, and by propagating the measured sky noise from each frame. The reduction process performs a hypothesis test for the presence of linear polarization. The probability of there being a non-zero polarization is obtained, and the best method of obtaining the normalized Stokes Parameters is discussed. Point and interval estimates are obtained for the degree of linear polarization, which is subject to positive bias; and the polarization axis is found.     

Orbit Determination Using Satellite—to—Satellite Tracking Data

1 INTRODUCTIONThe tracking arc-length should be increased in order to approve the accuracy in orbitdetermination of LEO (Low Earth Orbit) satellites. The local ground-based tracking networkdoes not provide sufficient orbit coverage for the user satellites. The most promising methodis to use high orbiting satellites, such as GPS and TDRS, as trackers to observe the usersatellites. For examPle, tWO geosynclironous satellites could cover more than 85% of the orbitof any given user sate…     

Dynamics and gravitational waveforms in spinning compact eccentric binaries

The effects of eccentricity on the Hamiltonian dynamics of post-Newtonian spinning compact binaries and gravitational radiation from eccentric orbits are discussed. The simulation results of scans for chaos show that the eccentricity has a great effect on the dynamics without considering dissipation due to gravitational radiation. Moreover, both the dynamics behavior and the orbital eccentricity jointly modulate the gravitational waveforms, and the spin–spin coupling effect play an important role during the gravitational radiation of inspiral and coalescence. Moreover, the imprint of characteristic of the original system can be deduced from the time-domain and frequency-domain waveforms.     

Bayesian foreground analysis with CMB data

The quality of CMB observations has improved dramatically in the last few years, and will continue to do so in the coming decade. Over a wide range of angular scales, the uncertainty due to instrumental noise is now small compared to the cosmic variance. One may claim with some justification that we have entered the era of precision CMB cosmology. However, some caution is still warranted: The errors due to residual foreground contamination in the CMB power spectrum and cosmological parameters remain largely unquantified, and the effect of these errors on important cosmological parameters such as the optical depth τ and spectral index n_s is not obvious. A major goal for current CMB analysis efforts must therefore be to develop methods that allow us to propagate such uncertainties from the raw data through to the final products. Here we review a recently proposed method that may be a first step towards that goal.     

基于小波模极大值相关信息的脉冲星标准脉冲轮廓累积方法

讨论了产生脉冲星标准脉冲轮廓的重要性.在分析经典脉冲轮廓生成方法的基础上,提出了基于小波模极大值相关处理的脉冲轮廓累加方法.首先将观测数据按周期分组,分别进行小波分解,生成粗尺度上以脉峰为特征点的小波系数;然后,选择某组高信噪比信号的系数为参考数据,分别与其它各组变换系数进行相关,确定脉峰的相对时延.最后,对分组的原始观测数据按此相对时延量进行累加,生成脉冲轮廓.观测信号可先通过背景噪声估计和平滑处理而得到信噪比较高的归一化标准轮廓.实例分析以及与模板相关法的比较结果表明:该方法简单而有效,不需要设计近似模板,且对噪声类型不敏感,具有较高的工程应用价值.