测定地球引力常数GM的协方差分析

编制了在ＧｉｖｅｎｓＧｅｎｔｌｅｍｅｎ正交变换算法下的多级复弧协方差分析软件．运用到引力常数ＧＭ解算的情形中,并计算了未参加估计的台站坐标的误差对产生解算结果的影响．这种影响的直接后果是降低了解算的精度．对产生解算内符精度和真实外符精度之间差别的原因进行了初步的探讨     

CAPS（Covariance Analysis Program Developed at Shanghai Observatory）的原理、结构和使用

推导了在Givens-Gentleman正交变换形式下的考察协方差分析理论,给出一些重要的统计量,如考察协方差矩阵、摄动矩阵等在此形式下的表达式。在理论分析的基础上给出编写CAPS时采用的详细流程图,并介绍在使用CAPS时应注意的一些问题。     

SLR资料解算地球自转短周期变化的协方差分析

采用统计定轨理论中的协方差分析方法讨论了卫星激光测距资料解乍地球自转的短周期变化（sub-daily）可达到的内符和外符精度,建立协方差分析的Givens-Gentlemen正交变换算法,并将精密定轨和参数解算理论中的多级复弧法推广到协方差分析中,同时考察不解算地球自转的短周期变化时,其误差对精密定轨和解算地球自转参数的影响。     

论初轨计算的最佳精度及二重解

从最优估计的角度,研究短弧测角资料初轨计算的最佳精度及准最佳精度算法．按照统计理论,对一般的参数估计问题,其估计误差的方差存在Cram’e4-Rao下界,这就是初轨理论的最佳精度;通过大量的模拟计算表明,文［1］中提出参考矢量法,其精度已充分接近C·R下界,且模拟计算轨道统计精度与观测误差成正比,可以认为是一种初轨计算的准最佳精度算法;对于小偏心率情况,发现一个重要的事实：初轨计算有二重解,更准确地说,在M0的左右两个半平面内有真假两个解,偏心率愈小,平近点角M0愈接近±π／2,给出的假解的概率愈大．针对这一情况,提出一种算法,可以给出2个解,其中必定有一个是真解,它有较高的精度.     

状态转移矩阵的差分算法及其应用

指出用数值积分方法计算状态转移矩阵在程序实现时存在的困难。根据精密定轨和参数解算的实际需要,提出用差分算法,即通过两条接近的轨道的差来计算状态转移矩阵差分算法的优点是程序具有良好的结构且编程简单,其不足之处是差分时可能损失精度。将差分算法与数值积分方法的结果进行比较,提出克服其不足处的方法。     

计算多普勒频偏的新算法

利用多普勒资料进行轨道改进,将遇到卫星信标机和测站接收机的频偏带来的系统差,如何估计各站圈的频偏,是决定定轨精度的一个关键问题．文[1]中提出的Guier导航计算频偏的方法,实践表明是行之有效的．但是,Guier导航计算较复杂,在用数值积分计算星历表的软件中,使用这一算法比较困难．提出一种基于法方程系数矩阵分块求逆的新算法,只需求6×6或7×7矩阵的逆,计算频偏十分简单．仿真表明,新算法的定轨精度近似达到C．R．下界一理论最佳精度,比Guier导航算法的精度高15％左右．     

多种资料综合处理的精度分析和相对权因子

在统计轨道理论的框架下分析多种技术资料的综合处理方法的精度．提出除了拟合剩余残差的ＲＭＳ外,皮尔逊（Ｐｅａｒｓｏｎ） χ２ 统计量和高阶矩也应作为判断解算好坏的重要指标．初步探讨了利用这些统计量评价不同技术间的相对权因子给定问题．作为对系统差来源的初步探索,利用考察协方差分析理论分析了考察参数误差对解算的影响,讨论了考察协方差与相对权因子的关系     

稀疏矩阵技术及其在天测与测地VLBI数据处理中的应用

介绍了稀疏矩阵的四种常见形式以及稀疏矩阵技术在天测与测地VLBI数据处理中的应用。推演了天测与测地VLBI数据综合解算中所用稀疏矩阵形式下待估参数求解和协方差矩阵估算的算法。通过对是否采用稀疏矩阵技术时方程求解 (乘法和加法 )运算对数的估算和比较 ,表明普通最小二乘方法的运算对数约为参数总数的 3次方 ,而采用稀疏矩阵技术时的运算对数近似与参数总数成线性关系 ,从而能够在现代空间对地观测技术的大样本数据处理中显著缩短计算时间。     

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     

利用非差资料的精密点定位方案解算区域GPS网

单站精密定位（Precise Point Positioning，以下简称PPP）是在同时固定GPS精密星历和卫星钟的前提下，利用载波相位和伪距资料进行单台站的精密点定位，采用该方法时不同台站之间不存在共同的待估参数，即各台站互不相关，这一特点大大降低了计算量，采用美国喷气推进实验室JPL发展的数据处理软件GIPSY处理APSG联测资料，计算表明PPP的重复率相当于目前国内普遍采用的双差解算结果，采用较好保持地面网构型的无基准算法，计算表明通过Helmert参考系转换后，PPP的解算结果与双差算法的外符精度大致相当，解算表明，采用PPP处理100个台站约需3．5小时，而处理同样的资料采用双差算法则需18－20小时，对于我国即将建成的大科学工程或地震监测的多达2000个接收机的GPS网而言，在保持精度前提下的节省计算资源和计算时间的PPP解算方案值得广泛的应用。     

The influence of the correlations between an asteroid’s orbital parameters on the estimation of the probability of planetary collision by the Monte Carlo method

The probability of an asteroid colliding with a planet can be estimated by the Monte Carlo method, in particular, through the statistical simulation of the possible initial conditions for the motion of an asteroid based on the probability density distribution set by the respective covariance matrix to be further projected with the orbital model onto the supposed time point of the collision. Hence, the collision probability is calculated as the ratio between the number of projected (virtual) asteroids striking the planet and their total number. The main problem is that different elements of the initial conditions (orbit or state vector) are correlated and, therefore, cannot be simulated independently. These correlations are reflected in the nondiagonal covariance matrix of the solution. The matrix is diagonalized by an orthogonal transformation. In the uncertainty domain constructed from the diagonal matrix elements, the initial values for each of the six orbital elements are simulated independently from the other elements, but with the accounting for their normal distribution. The program for calculating the normal distribution is based on the central limit theorem. Each sample of the initial values for the six orbital elements is transferred to the initial reference frame using an inverse transformation. Then, numerical integration is used to track the asteroid’s motion along the respective orbit to predict a possible impact event. Asteroids 99942 Apophis and 2007 WD5 are used as examples to show that disregarding the correlations when diagonalizing the covariance matrix to set the initial conditions may seriously distort the collision probability estimates. The paper gives the probabilities of the collisions of Apophis with the Earth and asteroid 2007 WD5 with Mars calculated by the author from observation sets showing nonzero collision probabilities. The author’s estimates are compared to those calculated by NASA.     

A modified χ2-test for cosmic microwave background analyses

We present a new general procedure for determining a given set of quantities. To this end, we define a certain statistic, which we call 'modified  χ²' (χ²_M)  , because of its similarity to the standard  χ²  . The terms of this  χ²_M  are made up of the fluctuations of an unbiased estimator of some statistical quantities and certain weights. Only the diagonal terms of the covariance matrix appear explicitly in our statistic, while the full covariance matrix (and not its inverse) is included implicitly in the calculation of the weights. Choosing these weights, we may obtain, through minimizing  χ²_M  , the estimator that provides the minimum rms, either for those quantities or for the parameters on which these quantities depend. In this paper, we describe our method in the context of cosmic microwave background experiments, in order to obtain either the statistical properties of the maps or the cosmological parameters. The test here is constructed out of some estimator of the two-point correlation function at different angles. For the problem of one-parameter estimation, we show that our method has the same power as the maximum-likelihood method. We have also applied this method to Monte Carlo simulations of the COBE -DMR data, as well as to the actual 4-yr data, obtaining consistent results with previous analyses. We also provide a very good analytical approximation to the distribution function of our statistic, which could also be useful in other contexts.     

Orbit injection error analysis for the Lageos III mission

An analysis is presented of the orbital injection errors for the Lageos III satellite mission. Several methods are introduced for the solution of the Inverse Problem in the Theory of Errors. The novelty of the present approach consists in the use of the full geopotential covariance matrix in the error propagation equations. The GEM-T1 covariance matrix is used. It is found that by properly accounting for the correlation among the even zonal harmonic coefficients the acceptable error bounds increase by an order of magnitude with respect to the case when only the variances are used. The most stringent constraint, even when using the full covariance, is on inclination, whose nominal value must be realized within approximately 0.1° for the recovery of the Lense-Thirring precession to be successful at the 3% level (accounting only for injection errors). The associated tolerance in the semimajor axis is about 30 km while that in eccentricity is approximately 0.2. However, if the errors in semimajor axis and eccentricity can be kept to the routinely achievable levels respectively of 10 km and 0.004, then the tolerance in inclination can be relaxed to 0.2°.     

星载GPS自主定轨的长期稳定性

通过模拟长达100天的星载GPS伪距观测资料,进行卡尔曼滤波定轨仿真计算．重点研究：1)采用简化的动力学模型与简化状态转移矩阵,是否保证滤波的长期稳定性；2)模型误差矩阵Q的选取对滤波定轨精度的影响；3)与事后最小二乘批处理相比较,在简化模型下自主定轨的精度．同时给出了相应的结论．     

Topographic comparisons of uplift features on Venus and Earth: Implications for Venus tectonics

Venus and Earth display different hypsography. We use topographic profiles to search for well-understood terrestrial analogs to venusian features. Specifically, by using cross-correlation, we correlate average profiles for terrestrial rifts (slow and fast, “ultra-slow,” incipient and inactive) and also hotspots (oceanic and continental) with those for venusian chasmata and regiones, to draw inferences as to the processes responsible for shaping Venus’ surface. Correlations tend to improve with faster spreading rates; Venus’ correlations rank considerably lower than terrestrial ones, suggesting that if chasmata are analogous to terrestrial spreading centers, then spreading on Venus barely attains ultra-slow rates. Individual features’ normalized average profiles are correlated with profiles of other such features to establish the degree of similarity, which in turn allows for the construction of a covariance matrix. Principal component analysis of this covariance matrix shows that Yellowstone more strongly resembles Atla, Beta and W. Eistla regiones than it does the terrestrial oceanic hotspots, and that venusian chasmata, especially Ganis, most closely resemble the ultra-slow spreading Arctic ridge.     

Madam– a map-making method for CMB experiments

We present a new map-making method for cosmic microwave background (CMB) measurements. The method is based on the destriping technique, but it also utilizes information about the noise spectrum. The low-frequency component of the instrument noise stream is modelled as a superposition of a set of simple base functions, whose amplitudes are determined by means of maximum-likelihood analysis, involving the covariance matrix of the amplitudes. We present simulation results with  1/ f   noise and show a reduction in the residual noise with respect to ordinary destriping. This study is related to Planck Low Frequency Instrument (LFI) activities.     

Optimal solutions of unobservable orbit determination problems

The method of data augmentation, in the form ofa priori covariance information on the reference solution, as a means to overcome the effects of ill-conditioning in orbit determination problems has been investigated. Specifically, for the case when ill-conditioning results from parameter non-observability and an appropriatea priori covariance is unknown, methods by which thea priori covariance is optimally chosen are presented. In problems where an inaccuratea priori covariance is provided, the optimal weighting of this data set is obtained. The feasibility of these ridge-type solution methods is demonstrated by their application to a non-observable gravity field recovery simulation. In the simulation, both ridge-type and conventional solutions are compared. Substantial improvement in the accuracy of the conventional solution is realized by the use of these ridge-type solution methods. The solution techniques presented in this study are applicable to observable, but ill-conditioned problems as well as the unobservable problems directly addressed. For the case of observable problems, the ridge-type solutions provide an improvement in the accuracy of the ordinary least squares solutions.