多星中天时角法精密测定天文方位角

在高精度天文方位角测定方法中,北极星任意时角法只适用于北半球中纬度地区,子午星对法则受限于选星配对条件.提出可适用于全球地区的多星中天时角法,观测多颗任意中天位置的南星和北星,通过线性回归模型修正测站经度误差和计时误差对方位角解算的影响.该方法只需已知测站的概略位置,对观测天体的中天位置没有限制.实测数据表明,与北极星任意时角法相比,在相同精度指标要求下,观测量可以减少一半.     

利用统计方法判断中天观测数据的参考星表

中天观测数据在建立太阳系高精度行星历表时具有重要作用.在处理由JPL(Jet Propulsion Laboratory)以及IMCCE(Institut De Mecanique Celeste Et De Calcul Des Ephemerides)提供的中天数据时发现,有若干组数据的参考星表没有被明确指出。对于这些信息不完整的数据,无从改正数据由参考星表而引起的系统差。课题研究的主要目的是利用DE421历表确定存在缺陷的这类观测数据的参考星表。通过DE421给出行星在GCRS(Geocentric Celestial Reference System)中的相应位置,并把此位置转换到参考假定的参考星表时行星的理论视位置。通过引入的两个统计量分析原始数据与理论位置的差异显著性,检验假定的数据参考星表是否恰当.结果显示,此方法能够有效区分数据的参考星表,能够确定信息不完整的数据组缺少的参考星表。最后,所有中天数据被转换到GCRS坐标系,以便在历表研制中使用。     

低纬子午环绝对测定瞬时方位差方法的改进（Ⅰ）

利用低纬子午环在卯酉圈东西两边同时观测得到的一对赤纬近似相等的恒星的天顶距，可以用来绝对确定仪器的瞬时方位差。这一方法不必对方位差的变化规律作任何假设，不需要改变现有的仪器设计方案。这将有利于改善低纬子午环的观测系统。     

一种初轨计算的稳健方法

光学测角资料的初轨计算在空间目标搜索发现中具有重要作用,当观测资料存在野值时,基于最小二乘的经典初轨计算方法不够稳健.采用最小一乘方法建立了一种初轨计算的稳健方法,方法将初轨计算问题转换为线性规划问题求解,并通过bootstrap方法给出估计精度.数值计算结果表明方法稳健有效,并具有较高的崩溃点.     

Preliminary Exploration of Orbit Determination Method by Means of Space-based Angle Measurement Data

The determination of the orbit of a target satellite by means of observed angle measurement data has a very important applicative value. In order to solve this problem, an optimization mathematic model labelled STSM is first constructed. Next is given the necessary numerical procedure of finding the initial values by polynomial fitting of the angle measurement data. Thirdly, the properties of STSM are analyzed in detail, from which the basic method for solving the optimization problem is found. Finally, the above-mentioned method is applied to a large number of simulation calculations and a preliminary analysis of the results is made. The calculated results show that for a given accuracy and density of data, it is feasible to determine the orbital elements of the target satellite by using space-based angle measurement data according to the procedure given.     

A Robust Method of Preliminary Orbit Determination

The preliminary orbit determination with optical angular measure- ments plays an important role in the survey of space objects. The classical method of orbit computation based on the least square error estimation is not robust while outliers occur in the observation. A robust method is proposed by employing the least absolute deviation estimation. The method reduces the problem of orbit determination to a linear programming problem, and gives the variance of the estimation with the bootstrap method. Numerical check shows that the method is effective and robust, and has a high breakdown point.     

疏散星团M67成员星的两点相关分析

对著名老年疏散星团M67的成员星进行了两点相关函数分析,讨论了团星的空间分布情况及质量分层现象.结果表明:M67成员星的两点相关函数能很好地用幂律形式来描述,其成员星在空间分布上具有显著的成团性和自相似性.对M67不同光度成员星两点自相关函数的分析表明,亮星相比暗星具有更强的相关强度和更大的相关指数,说明在星团内部出现了明显的空间质量分层现象,亮星比暗星具有更强的成团性和更大的中心聚度.不同光度成员星间两点交叉相关函数的分析进一步表明,不同光度成员星之间并没有表现出绝对的空间质量分层现象,亮星和暗星在空间分布上相互交织、相互渗透.     

Non-parametric star formation histories for four dwarf spheroidal galaxies of the Local Group

We use recent Hubble Space Telescope colour–magnitude diagrams of the resolved stellar populations of a sample of local dSph galaxies (Carina, Leo I, Leo II and Ursa Minor) to infer the star formation histories of these systems, SFR ( t ). Applying a new variational calculus maximum likelihood method, which includes a full Bayesian analysis and allows a non-parametric estimate of the function one is solving for, we infer the star formation histories of the systems studied. This method has the advantage of yielding an objective answer, as one need not assume a priori the form of the function one is trying to recover. The results are checked independently using Saha's W statistic. The total luminosities of the systems are used to normalize the results into physical units and derive SN type II rates. We derive the luminosity-weighted mean star formation history of this sample of galaxies.     

天体轨道长期数值积分的误差估计方法

数值积分方法是进行天体力学研究的重要工具, 尤其对于行星历表的研究工作而言. 由于在使用数值方法计算天体轨道时, 最终误差通常是难以预知的, 所以在面对精度要求较高或者积分时间较长的工作时具体积分方案的设计---尤其是当使用定步长方法时的步长选择---需要十分谨慎, 因为这将意味着是否能在时间成本可以被接受的范围内使解的精度达到要求. 因此, 在使用数值方法解决实际问题时如何快速寻找效率与精度之间的最佳平衡点是每一个数值积分方法的设计者与使用者都会面临的难题. 为解决这一问题, 在定步长条件下对数值积分方法的舍入误差概率分布函数以及截断误差积累量对步长的依赖关系和随时间的增长关系进行了深入研究. 基于所得结论, 提出了一种仅需较少的数值实验资料即可对选择任意时间步长积分至任意积分时刻时的舍入误差概率分布函数与截断误差积累量进行准确估计的方法, 并使用Adams-Cowell方法对该误差估计方法在圆周期轨道条件下进行了验证. 该误差估计方法在未来有望用于不同数值算法的性能对比研究, 同时也可以对数值积分方法求解实际轨道问题时的决策工作带来重要帮助.     

Multiple methods for estimating the bispectrum of the cosmic microwave background with application to the MAXIMA data

We describe different methods for estimating the bispectrum of cosmic microwave background data. In particular, we construct a minimum-variance estimator for the flat-sky limit and compare results with previously studied frequentist methods. Application to the MAXIMA data set shows consistency with primordial Gaussianity. Weak quadratic non-Gaussianity is characterized by a tunable parameter   f _NL  , corresponding to non-Gaussianity at a level of  ∼10⁻⁵ f _NL  (the ratio of non-Gaussian to Gaussian terms), and we find limits of   f _NL= 1500 ± 950  for the minimum-variance estimator and   f _NL= 2700 ± 1650  for the usual frequentist estimator. These are the tightest limits on primordial non-Gaussianity, which include the full effects of the radiation transfer function.     

Consistency Analysis of the Data of GRBs Observed by Different Satellites

The BATSE (Compton Gamma-ray Observatory/Bursts and Transient Source Experiment), Swift (Swift Gamma-ray Burst Explorer) and Fermi (Fermi Gamma-ray Space Telescope) satellites have provided us with a large amount of GRB sample. After a systematical study and comparison of the properties of the GRBs detected by these 3 kinds of instruments, it is found that although significant differences exist in the number of red-shifted bursts, the proportion of long bursts in total bursts and the photon flux distribution (lgN − lg P), but no significant difference exists in the duration time, the total flux of Gamma-ray radiation and the spectral hardness ratio. Considering that the observational energy bands of the Swift- and Fermi-detected bursts are different, after making corrections the difference in the lgN − lg P distribution can be basically eliminated. The differences in the number of red-shifted bursts and the proportion of long bursts in total bursts are caused by the different sensitivities of instruments. Namely, various instruments give different observed characteristics of GRBs, but they are consistent in nature.     

Calculating Method and Characteristics of the Distribution of Neutron Exposures in the Radiative S-process Nucleosynthesis Model for AGB Stars

A study on the distribution of neutron exposures in a low-mass asymptotic giant branch (AGB) star is presented, according to the s-process nucleosynthesis model with the ¹²C(α, n)¹⁶O reaction occurred under radiative conditions in the interpulse phases. The model parameters, such as the over- lap factor r of two successive convective thermal pulses, the mass ratio q of the ¹³C shell with respect to the He intershell, and the effective mass of ¹³C in the ¹³C shell, vary with the pulse number. Considering these factors, a calculating method for the distribution of neutron exposures in the He intershell has been presented. This method has the features of simplicity and universality. Using this method, the exposure distribution for the stellar model of a star with the mass of 3 M_? and the solar metallicity has been calculated. The results suggest that under the reasonable assumption that the number density of neutrons is uniform in the ¹³C shell, the ?nal exposure distribution approaches to an exponential distribution. For a stellar model with the de?nite initial mass and metallicity, there is a de?nite relation between the mean neutron exposure τ₀ and the neutron exposure Δτ of each pulse, namely τ₀ = 0.434λ(q1, q2, …, qm_max +1, …, r₁, r₂, …, rm_max +1)Δτ, where m_max is the total number of thermal pulses with the third dredge-up episode, and the proportional coeffcient λ(q₁, q₂, …, qm_max +1, …, r₁, r₂, …, rm_max +1) can be determined by an exponential curve ?tting to the ?nal exposure distribution. This new formula quantitatively uni?es the classical model with the s-process nu- cleosynthesis model by means of neutron exposure distribution, and makes the classical model continue to offer guidance and constraints to the s-process nu- merical calculations of stellar models.     

The Bootstrap Estimation of the Accuracy of Preliminary Orbit Determination

From the point of view of the non-parametric statistics, a general estimation method of the accuracy and con?dence interval of preliminary orbit determination is proposed for the occasion without any other information but observational data. Based on the bootstrap method, the estimation relies only on the observational data and does not require the precise orbit determination as a reference, or the assumption of normal distribution of observational errors. Numerical experiments show that this method is very simple in implementa- tion, and may serve as an easy accuracy evaluation for the preliminary orbit determination and for the follow-up employments.     

Research on the Method of Orbit Determination Based on the Self-adaptive Stable Least p-norm Estimate

The traditional least square estimation (LSE) method for orbit determination will not be optimal if the error of observational data does not obey the Gaussian distribution. In order to solve this problem, the least p-norm (Lp) estimation method is presented in this paper to deal with the non-Gaussian distribution cases. We show that a suitable selection of parameter p may guarantee a reasonable orbit determination result. The character of Lp estimation is analyzed. It is shown that the traditional Lp estimation method is not a robust method. And a stable Lp estimating based on data depth weighting is put forward to deal with the model error and outlier. In the orbit determination process, the outlier of observational data and coarse model error can be quantitatively described by their weights. The farther is the data from the data center, the smaller is the value of data depth and the smaller is the weighted value accordingly. The result of the new Lp method is stabler than that of the traditional Lp estimation and the breakdown point could be up to 1/2. In addition, the orbit parameter is adaptively estimated by residual analysis and matrix estimation method, and the estimation efficiency is enhanced. Finally, by taking the Space-based Space Surveillance System as an example and performing simulation experiments, we show that if there are system error or abnormal value in the observational data or system error in satellite dynamical model and space-based observation platform, LSE will not be optimal even though the observational data obeys the Gaussian distribution, and the orbit determination precision by the self-adaptive robust Lp estimation method is much better than that by the traditional LSE method.     

A robust statistical estimation of the basic parameters of single stellar populations – I. Method

The colour–magnitude diagrams of resolved single stellar populations, such as open and globular clusters, have provided the best natural laboratories to test stellar evolution theory. Whilst a variety of techniques have been used to infer the basic properties of these simple populations, systematic uncertainties arise from the purely geometrical degeneracy produced by the similar shape of isochrones of different ages and metallicities. Here we present an objective and robust statistical technique which lifts this degeneracy to a great extent through the use of a key observable: the number of stars along the isochrone. Through extensive Monte Carlo simulations we show that, for instance, we can infer the four main parameters (age, metallicity, distance and reddening) in an objective way, along with robust confidence intervals and their full covariance matrix. We show that systematic uncertainties due to field contamination, unresolved binaries, initial or present-day stellar mass function are either negligible or well under control. This technique provides, for the first time, a proper way to infer with unprecedented accuracy the fundamental properties of simple stellar populations, in an easy-to-implement algorithm.     

A Study on Orbit Determination by Using the Data of Crossovers from Satellite-borne Altimeter

Starting with the status of the developments of oceanic altimetry satellites, the significance of orbit determination by using altimeter data is introduced. Then the error correction model of the altimeter data and the calculational method of the data of crossovers are analyzed. The modification quantities of the errors and the adopted model concerned in the files of the altimeter data from the aircraft JASON-1 are also introduced in detail. Finally, through the calculations of the simulated data and the data of actual measurements, the highest accuracies of the orbit determination reached by solely using the altimeter data and the data of crossovers are analyzed, respectively. And this work provides a valuable reference to the practical applications in future.     

A Model of Relation between Fluctuation of Double Differential Total Ionospheric Electron Content and Angular Distance of the Two Satellites Observed by Same-beam VLBI

Time delay and phase fluctuation are produced when the signals of a spacecraft are transmitted through the ionosphere of the earth, which give rise to a great influence on the measurement precision of VLBI (Very Long Baseline Interferometry). Using the 1-year same-beam VLBI data of 2 satellites (Rstar and Vstar) in the Japanese lunar exploration project SELENE, we obtained a model of the relation between the fluctuation of double differential total electron content in the ionosphere and the angular distance of the two satellites. For the 6 baselines, the root mean square r of fluctuation (in units of TECU) and the angular distance of the two satellites θ (in units of ^°) has a relation of r = 0.773θ + 0.562, and for the 4 VLBI stations, the relation is r = 0.554θ + 0.399 from the baselines inversion. The results can serve as a reference for the derivation of differential phase delay and for the occultation observation and study of planetary ionospheres.     

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.     

考虑地球扁率摄动影响的初轨计算方法

在二体问题意义下的短弧定轨,Laplace型方法是最主要最典型的一种初轨计算方法。若测角资料达到10^-4-10^-5精度(相当于2″—20″之间),那么要使定轨精度达到与其相应的程度,地球非球形引力位中的扁率项摄动应该考虑,在此前提下,同样可以采用相应的Laplace型定轨方法。即给出这种严格包含扁率摄动的初轨计算方法的原理和具体计算过程以及计算实例,除采用多资料定轨方法外,这种方法也是提高初轨计算精度的一种途径,它同样可用于多资料的情况,这种方法对于大扁率主天体(即中心天体)的卫星定轨将更有实用价值。