基于经验模式分解和最小二乘支持向量机的卫星钟差预报

针对卫星钟差(satellite clock bias,SCB)呈现非线性、非平稳变化的特性,提出结合经验模式分解(empirical mode decomposition,EMD)和最小二乘支持向量机(least squares support vector machines,LSSVM)的钟差预报方法.首先对钟差相邻历元间作一次差,并利用经验模式分解将差分序列分解成若干不同频率的平稳分量,分解后的分量突出了差分序列不同的局部特征;然后根据各个分量的变化规律,选择合适的核函数和相关参数构造不同的最小二乘支持向量机模型分别预报;最后将各分量预报值叠加得到一次差预报值,再将其还原得到钟差预报值.实验结果表明,所提方法与常用的二次多项式(quadratic polynomial,QP)模型、灰色系统(grey model,GM)模型和单一的最小二乘支持向量机模型相比,具有较高的预报精度和较强的泛化能力.     

基于灰色模型和最小二乘支持向量机的卫星钟差预报

提出一种联合灰色模型（Grey Model,GM）和最小二乘支持机（Least-Squares Support Vector Machines,LS-SVM）回归算法的卫星钟差智能组合预报方法。首先根据历史钟差数据建立不同的GM（1,1）灰色模型,然后利用这些模型进行钟差预报,最后采用最小二乘支持向量机回归算法对不同GM（1,1）模型的预报结果进行非线性组合,以获得最终预报值。该方法在充分利用灰色模型所需原始数据少、建模简单等优点的基础上,结合最小二乘支持向量机所具有的小样本、非线性、泛化能力强等特性,提高了预报可靠性和精度。实例验证了该组合方法的可行性、有效性和实用性。     

附有高程约束的卫星导航系统精度因子分析方法

高程约束定位方法是一种可以改善定位精度的方法,相对于最小二乘定位方法引入了地球椭圆约束方程。约束方程的引入改变了定位解算过程,使得来源于最小二乘定位方法的精度因子计算公式不再适用于新的方法。针对这一问题,从精度因子定义出发,结合高程约束定位方法原理,提出一种新的计算高程约束定位精度因子的方法。利用某一监测站的地球同步轨道卫星和倾斜地球同步轨道卫星数据,进行了两组精度因子值分析试验和一组定位试验,试验结果表明提出的高程约束定位方法精度因子的计算方法是正确的,高程约束定位方法的定位精度也远高于最小二乘方法。     

利用端点延拓提高LS + NN模型的UT1-UTC预报精度

现有UT1-UTC预报模式在进行周期项与残差项拟合分离时,通常没有考虑最小二乘拟合序列的端部效应,预报精度难以取得较大提高。针对最小二乘拟合存在的端部效应,首先采用灰色模型在UT1-UTC序列的两端进行数据延拓,形成一个新序列,然后对新序列进行最小二乘拟合,最后再联合最小二乘和神经网络(LS+NN)模型对UT1-UTC原始序列进行外推。结果表明,对UT1-UTC序列进行端点数据延拓再进行最小二乘拟合,能够有效地改善最小二乘拟合序列的端部效应;相对于常规LS+NN模型,端部效应改善的LS+NN模型的UT1-UTC预报精度有一定提高,尤其对中长期预报精度提高更为明显。     

伪距测量中的时标偏差影响分析

伪距是卫星导航系统的基本观测量,是实现导航定位、精密定轨和精确授时的基础。基于伪距、钟差和时标偏差的概念与定义,讨论了时标偏差对卫星伪距测量的影响特性;在此基础上,给出了利用伪距O-C(观测值与计算值之差)进行时标偏差解算的计算模型;理论分析表明:时标偏差影响主要体现在伪距变率项;对于MEO卫星,时标偏差影响不仅会使真实的O-C曲线斜率变大、曲线变长,而且会使多个弧段O-C曲线呈现锯齿状,表现为每个弧段解算的参数不能用于跨弧段预报。最后,利用北斗试验系统MEO卫星实测数据进行了验证分析,试验结果表明:采用实测数据计算的时标偏差精度约在0.02s左右,不同弧段解算结果比较稳定,并且扣除时标偏差后的O-C计算结果也与理论结果具有较好的一致性,从而验证了本文时标偏差理论分析和计算模型的正确性。     

利用经验模态分解提高极移预报精度（英文）

经验模态分解(Empirical Mode Decomposition,EMD)是一种数据驱动的自适应非线性、非平稳信号分解方法。为提高极移预报精度,将经验模态分解应用于极移预报中。首先利用经验模态分解方法对极移序列进行分解,获得极移的高频分量和低频分量;然后采用最小二乘(Least Squares,LS)外推模型对极移低频分量进行拟合,获得最小二乘拟合残差;其次采用自回归(Autoregressive,AR)模型对极移高频分量和最小二乘拟合残差之和进行建模预报;最后将最小二乘模型和自回归模型外推值相加获得极移预报值。将经验模态分解和LS+AR组合模型预报结果与LS+AR模型预报以及地球定向参数预报比较竞赛(Earth Orientation Parameters Prediction Comparison Campaign,EOP PCC)的预报结果进行比较,结果表明,将经验模态分解应用于极移预报中,可以明显改善极移预报精度。     

利用端部效应改善的最小二乘外推模型进行UT1-UTC预报

现有的UT1-UTC预报模式在进行周期项与残差项拟合分离时,通常没有考虑最小二乘拟合序列的端部畸变现象(数据处理中称为端部效应),预报精度难以取得较大改善。针对最小二乘拟合存在的端部畸变现象,首先采用时序分析方法在UT1-UTC序列两端进行数据延拓,形成一个新序列,然后用新序列求解最小二乘外推模型系数,最后再联合最小二乘外推模型及神经网络对UT1-UTC序列进行预测。结果表明,在UT1-UTC序列端部增加延拓数据,可以有效地抑制最小二乘拟合序列的端部畸变,相对于常规的最小二乘外推模型,基于端部效应改善的最小二乘(Edge-effect Corrected Least Squares,ECLS)外推模型的UT1-UTC中长期预报精度改善明显。     

离轴大口径全反射式平行光管装调技术研究

随着空间光学系统的发展,光学检测设备的精度要求也更高.介绍了一套口径525 mm、大视场离轴平行光管光学系统的高精度计算机辅助装调方法.该大型平行光管要求全视场波像差优于1/20波长,给装调策略带来了挑战.该方法基于多视场点灵敏度矩阵模型,利用5个不同视场点干涉测得的像差数据,采用阻尼最小二乘法求解系统失调量.通过多次迭代装调,快速成功完成装调,在波长λ=632.8 nm时,该平行光管系统取得了中心视场点波像差均方根粗糙度(rms)值0.036λ、全像面波像差rms平均值0.045λ的装调精度.     

用重复重力测量测定垂线偏差时变的精度

列举两种垂线偏差时变测定的微分公式,从理论上对用重复重力测量的方法测定垂线偏差时变的精度进行了探讨．在目前情况下,垂线偏差时变测定精度可以达到0．005＂．远区域的点对它的影响可以忽略不计,通过对重力网的模拟计算,进一步得到验证．探讨了有效积分半径对垂线偏差时变测量精度的影响,并在此基础上讨论了重力网优化的问题．     

基于混沌时间序列的Volterra自适应滤波极移预报方法

针对极移复杂的时变特性, 根据混沌相空间坐标延迟重构理论, 提出一种基于Volterra自适应滤波的极移预报方法. 首先, 利用最小二乘拟合算法分离极移序列中的线性趋势项、钱德勒项和周年项, 获得线性极移、钱德勒极移和周年极移的外推值; 其次, 通过C-C关联积分法对最小二乘拟合残差序列进行相空间重构, 并利用小数据量法计算残差序列的最大Lyapunov指数验证其混沌特性, 在此基础上, 构建Volterra自适应滤波器对残差序列进行预测; 最后, 将线性极移、钱德勒极移和周年极移的外推值以及最小二乘拟合残差的预测值相加获得极移最终预报值. 利用国际地球自转服务局(International Earth Rotation and Reference Systems Service, IERS)提供的极移数据进行1--60d跨度预报, 并将预报结果分别与国际地球定向参数预报比较竞赛(Earth Orientation Parameters Prediction Comparison Campaign, EOP PCC)结果和IERS A公报发布的极移预报产品进行对比, 结果表明: 对于1--30d的短期预报, 该方法的预报精度与EOP PCC最优预报方法相当, 当预报跨度超过30d时, 该方法的预报精度低于EOP PCC最优预报方法, 优于参与EOP PCC的其他方法; 与IERS A公报相比, 该方法的短期预报效果较好, 当预报跨度增加时预报精度低于IERS A公报. 预报结果表明该方法更适合于极移短期预报.     

Total Least Squares: An Ideal Mathematical Tool for Galactic Kinematics

Problems of Galactic kinematics have usually been solved by the method of least squares. As has been known for over forty years, this may lead to biased results because least squares assume that error resides only in the observations, not in the equations of condition. The latter, however, generally incorporate error, at least in some of the columns of the data matrix. Total least squares represents the ideal mathematical tool for just this sort of problem. In this paper the method, or better stated a mixed total-ordinary least squares method, is applied to 3100 stars taken from the Bright star Catalog to calculate eight parameters of Galactic kinematics: two corrections to the precessional constants, the Oort A and B parameters, the components of solar motion, and the K term. Total least squares calculates a reasonable solution, whereas ordinary least squares fails completely.     

The distance to the Galactic center determined by OB stars

The OB stars are concentrated near the Galactic plane and should permit a determination of the distance to the Galactic center. van Leeuwen’s new reduction of the Hipparcos catalog provides, after 824 Gould belt stars have been excluded, 6288 OB stars out to 1 kpc and Westin’s compilation an additional 112 stars between 1 kpc and 3 kpc. The reduction model involves 14 unknowns: the Oort A and B constants, the distance to the Galactic center R ₀, 2 second-order partial derivatives, the 3 components of solar motion, a K term, a first order partial derivative for motion perpendicular to the Galactic plane, a second-order partial for acceleration perpendicular to the plane, two terms for a possible expansion of the OB stars, and a C constant. The model is nonlinear, and the unknowns are calculated by use the simplex algorithm for nonlinear adjustment applied to 14313 equations of condition, 12694 in proper motion and 1619 in radial velocity. Various solutions were tried: an L₁ solution, a least squares solution with modest (2.7 %) trim of the data, and two robust least squares solutions (biweight and Welsch weighting) with more extreme trimming. The Welsch solution seems to give the best results and calculates a distance to the Galactic center 6.72±0.39 kpc. Statistical tests show that the data are homogeneous, that the reduction model seems adequate and conforms with the assumptions used in its derivation, and that the post-fit residuals are random. Inclusion of more terms, such as streaming motion induced by Galactic density waves, degrades the solution.     

The simplex method for nonlinear mass determinations

The Gauss-Newton method, and calculating a mass that minimizes the variation of residuals are standard techniques for determining planetary masses, but both may fail under certain circums tances. The Gauss-Newton method, in particular, may diverge, and when it converges may converge to a local, rather than global, minimum of the nonlinear regression problem. The simplex method of nonlinear optimization needs no initial estimate for the solution and can be made to converge to a global minimum. It may also be used with non-least squares criteria, such as the L₁ criterion, for greater robustness. But the simplex method achieves these advantages at a high computational price. To test the method as a tool for dynamical astronomy, over 12,000 observations of Neptune were used to calculate Pluto's mass. From an initial estimate of 1/1, 812,000 the Gauss-Newton method diverged. The simplex method converged to a more satisfactory 1/22,000,000 with a range of 1/47,000,000 to 1/14,000,000 as indicated by the mean error. Because the simplex method is considerably slower than competing methods, it should be reserved for refractory problems that do not yield facil solutions when tackled by other methods.     

Error estimates with L1 solutions

A method is given, based on the pseudoinverse of the equations of condition, to obtain error estimates for the solution in the normL ₁ of an over-determined linear system. The computational labor to obtain the errors, while not trivial, is less than that for various competing methods, particularly if there are many more equations of condition than unknowns. The error estimates for anL ₁ solution are substantially larger than those for a least squares solution of the some data. It is suggested that a complete discussion of a linear system include at least bothL ₁ and least squares solutions with their respective errors and the condition number of the linear system.     

Laplacian Orbit Determination and Differential Corrections

Laplace’s method is a standard for the calculation of a preliminary orbit. Certain modifications, briefly summarized, enhance its efficacy. At least one differential correction is recommended, and sometimes becomes essential, to increase the accuracy of the computed orbital elements. Difficult problems, lack of convergence of the differential corrections, for example, can be handled by total least squares or ridge regression. The differential corrections represent more than just getting better agreement with the observations, but a means by which a satisfactory orbit can be calculated. The method is applied to three examples of differing difficulty: to calculate a preliminary orbit of Comet 122/P de Vico from 59 observations made during five days in 1995; a more difficult calculation of a possible new object with a poor distribution of observations; Herget’s method fails for this example; and finally a really difficult object, the Amor type minor planet 1982 DV (3288 Seleucus). For this last object use of L₁ regression becomes essential to calculate a preliminary orbit. For this orbit Laplace’s method compares favorably with Gauss’s.     

Multivariate orthogonal regression in astronomy

Total least squares considers the problem of data reduction when error resides in both the data itself and also in the equations of condition. Error may be found in all of the columns of the matrix of the equations of condition, or merely in some; the latter situation is referred to as a mixed total least squares problem. A covariance matrix may be derived for total least squares. Both memory and operation count requirements are more severe than for ordinaty least squares: about four times more memory and, if the problem involves n unknowns, 15n + 4 more arithmetic operations. The method, applicable in any situation where ordinary least squares is relevant, including the estimation of scaled variables, is applied to three examples, one artificial and two taken from astronomy: the estimation of various parameters of Galactic kinematics, and the differential correction of a planetary orbit. In these two examples the results from total least squares are superior to those from ordinary least squares.     

Light‐curve inversions with truncated least‐squares principal components: Tests and application to HD 291095 = V1355 Orionis

We present a new inversion code that reconstructs the stellar surface spot configuration from the light curve of a rotating star. Our code employs a method that uses the truncated least‐squares estimation of the inverse problem's objects principal components. We use spot filling factors as the unknown objects. Various test cases that represent a rapidly‐rotating K subgiant are used for the forward problem. Tests are then performed to recover the artificial input map and include data errors and input‐parameter errors. We demonstrate the robustness of the solution to false input parameters like photospheric temperature, spot temperature, gravity, inclination, unspotted brightness and different spot distributions and we also demonstrate the insensitivity of the solution to spot latitude. Tests with spots peppered over the entire stellar surface or with phase gaps do not produce fake active longitudes. The code is then applied to ten years of V and I ‐band light curve data of the spotted sub‐giant HD291095. A total of 22 light curves is presented. We find that for most of the time its spots were grouped around two active longitudes separated on average by 180°. Switches of the dominant active region between these two longitudes likely occurred about every 3.15±0.23 years while the amplitude modulation of the brightness occurred with a possible period of 3.0±0.15 years. For the first time, we found evidence that the times of the activity flips coincide with times of minimum light as well as minimum photometric amplitude, i.e. maximum spottedness. From a comparison with simultaneous Doppler images we conclude that the activity flips likely take place near the rotational pole of the star. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Active Optics in LAMOST

Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) is one of the major national projects under construction in China. Active optics is one of the most important technologies for new large telescopes. It is used for correcting telescope errors generated by gravitational and thermal changes. Here, however, we use this technology to realize the configuration of LAMOST, -a task that cannot be done in the traditional way. A comprehensive and intensive research on the active optics used in LAMOST is also reported, including an open-loop control method and an auxiliary closed-loop control method. Another important development is in our pre-calibration method of open-loop control, which is with some new features: simultaneous calculation of the forces and displacements of force actuators and displacement actuators; the profile of mirror can be arbitrary; the mirror surface shape is not expressed by a fitting polynomial, but is derived from the mirror surface shape formula which is highly accurat     

Astronomical data reduction with total least squares

Although astronomers have been involved with the development and use of least squares, and alternatives, they have made insufficient use of total least squares: least squares that allow for error in the equations of condition as well as the observations. There exist, however, problems of astronomical data reduction for which total least squares represents the ideal mathematical tool. Among these problems are the differential correction of an orbit and the determination of parameters of Galactic kinematics. Total least squares, although more computationally demanding than ordinary least squares, can be used in any situation where the latter is applicable. However, care must be paid to the proper scaling of the data matrix. The method merits greater attention by the astronomical community.     

Probability distribution functions for the Sun's magnetic field

Magnetoconvection structures the Sun's magnetic field cover a vast range of scales, down to the magnetic diffusion scale that is orders of magnitude smaller than the resolution of current telescopes. The statistical properties of this structuring are governed by probability density functions (PDFs) for the flux densities and by the angular distribution functions for the orientations of the field vectors. The magnetic structuring on sub‐pixel scales greatly affects the field properties averaged over the resolution element due to the non‐linear relation between polarization and magnetic field. Here we use a Hinode SOT/SP data set for the quiet Sun disk center to explore the complex behavior of the 6301–6302 Å Stokes line profile system and identify the observables that allow us to determine the distribution functions in the most robust and least model dependent way. The angular distribution is found to be strongly peaked around the vertical direction for large flux densities but widens with decreasing flux density to become isotropic in the limit of zero flux density. The noise‐corrected PDFs for the vertical, horizontal, and total flux densities all have a narrowly peaked maximum at zero flux density that can be fitted with a stretched exponential, while the extended wings decline quadratically (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)