共查询到20条相似文献，搜索用时 31 毫秒
1.
Victor A. Avdyushev 《Celestial Mechanics and Dynamical Astronomy》2017,129(4):537-552
Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the method of disturbed observations, we conclude that it practically should be still entirely acceptable to adequately describe the orbital uncertainty since, from a geometrical point of view, the efficiency of the method directly depends only on the nonflatness of the estimation subspace and it gets higher as the nonflatness decreases. 相似文献
2.
V. A. Avdyushev 《Solar System Research》2009,43(6):543-551
A Monte Carlo-type method for simulating virtual values of the parameters in inverse orbital dynamics problems for highly
nonlinear cases is proposed. The method is based on imitating Fisher’s statistics employed to specify the confidence region,
and is implemented by solving repeatedly nonlinear least-squares problems with various samples of simulated observations obtainable
by suitable random variations. 相似文献
3.
Roberto Armellin Pierluigi Di Lizia Renato Zanetti 《Celestial Mechanics and Dynamical Astronomy》2016,125(4):435-450
A method to deal with uncertainties in initial orbit determination (IOD) is presented. This is based on the use of Taylor differential algebra (DA) to nonlinearly map uncertainties from the observation space to the state space. When a minimum set of observations is available, DA is used to expand the solution of the IOD problem in Taylor series with respect to measurement errors. When more observations are available, high order inversion tools are exploited to obtain full state pseudo-observations at a common epoch. The mean and covariance of these pseudo-observations are nonlinearly computed by evaluating the expectation of high order Taylor polynomials. Finally, a linear scheme is employed to update the current knowledge of the orbit. Angles-only observations are considered and simplified Keplerian dynamics adopted to ease the explanation. Three test cases of orbit determination of artificial satellites in different orbital regimes are presented to discuss the feature and performances of the proposed methodology. 相似文献
4.
Nikolay Emelyanov 《Planetary and Space Science》2010,58(3):411-420
Ephemerides of planetary satellites are needed to address many problems. These ephemerides are used for subsequent observations. A comparison of the available ephemerides with new observations allows the accuracy of the former to be assessed. However, the precision of the ephemerides must be known a priori when solving the tasks. In this paper we formulate and solve the problem of estimating the precision of the ephemerides of outer planetary satellites derived from observations when applied up to the future moments.The methods of assessing the precision of ephemerides involve producing a set of samples of the same ephemeris inferred from observations with different samples of Monte Carlo generated random errors (RO) superimposed onto it. The statistical parameters of simulated observational errors are based on the results of the reduction of real satellite observations. We compute the deviations of the samples of the ephemeris from the standard ephemeris inferred from real observations and adopt the root-mean-square deviation of the apparent coordinates as the precision of the ephemeris. We also use alternative methods: one based on the matrix of covariances of parameter errors (RP), and another one based on bootstrap samples of observations (BS).We use three methods (RO, RP, and BS) to estimate the precision of the ephemerides of all the 107 outer planetary satellites over the 2010-2020 time interval. The precision of the ephemerides of different satellites varies from 0.05 to 4.0 arcsec. For a number of satellites new observations are of vital importance for maintaining the precision of the ephemerides at a level that would allow identification of satellites during the reduction of observations. For some satellites the precision of their ephemerides is of the order of the sizes of their orbits and such satellites can be considered to have been lost. We show that the method of bootstrap samples (BS) can give doubtful results in the cases where there are few observations, which covered a time interval that is shorter than the orbital period of the satellite.Our results suggest obtaining more precise ephemeris making new observations at the times of maximum estimated errors of the ephemeris.All the inferred estimates of the precision of ephemerides are available from the MULTI-SAT ephemeris server: www.imcce.fr/sat (IMCCE), www.sai.msu.ru/neb/nss/index.htm (SAI). 相似文献
5.
提出了一种适用于天基空间目标光学观测的初始轨道确定新方法. 通过对比地基和天基观测的几何构型, 分析了利用天基光学观测数据进行初轨确定时计算收敛到观测平台自身轨道的原因. 基于轨道半通径方程和改进Gauss方程, 推导出了斜距条件方程组的解析形式, 将天基光学观测的初轨确定问题转换为求解关于观测时刻斜距变量的非线性条件方程组的问题. 利用轨道能量约束减小了解的搜索区域, 消除了方程组的奇点. 最后利用天基实测数据验证并分析了非线性条件方程组根的性质, 利用低轨光学观测平台对低、中、高轨和大椭圆轨道空间目标的仿真观测数据验证了方法的有效性. 相似文献
6.
We evaluate the asteroid impact risk from the discovery night onwards using six-dimensional statistical orbit computation techniques to examine the a posteriori probability density of the orbital elements. Close to the discovery moment the observational data of an object are typically exiguous: the number of observations is very small and/or the covered orbital arc is very short. For such data, the covariance matrices computed in the linear approximation (e.g., with the least-squares technique) are known to fail to describe the uncertainties in the orbital parameters. The technique of statistical ranging gives us rigorous means to assess the orbital uncertainties already on the discovery night. To examine the time evolution of orbital uncertainties, we make use of a new nonlinear Monte Carlo technique of phase-space sampling using volumes of variation, which complements the ranging technique for exiguous data and the least-squares technique for extensive observational data. We apply the statistical techniques to the near-Earth Asteroid 2004 AS1, which grabbed the attention of asteroid scientists because, for one day, it posed the highest and most immediate impact risk so far recorded. We take this extreme case to illustrate the ambiguities in the impact risk assessment for short arcs. We confirm that the weighted fraction of the collision orbits at discovery was large but conclude that this was mostly due to the discordance of the discovery-night observations. This case study highlights the need to introduce a regularization in terms of an a priori probability density to secure the invariance of the probabilistic analysis especially in the nonlinear orbital inversion for short arcs. We remark that a predominant role of the a priori can give indications of the feasibility of the probabilistic interpretation, that is, how reliable the results derived from the a posteriori probability density are. Nevertheless, the strict mathematical definition of, e.g., the collision probability remains valid, and our nonlinear statistical techniques give us the means to always deduce, at the very least, order-of-magnitude-estimates for the collision probability. 相似文献
7.
We estimate the effect of trajectory measurement errors on the orbital parameters of asteroid Apophis determined from improvements. For this purpose, based on all of the optical and radar observations available to date, we have computed a nominal orbit of the asteroid. The scatter ellipsoid of the initial conditions of motion has been obtained by two methods. In the first, universally accepted method, the scatter ellipsoid is calculated by assuming a linear dependence of the errors in the parameters being determined on observational errors. In the second method, the scatter region of the orbital parameters around the nominal-orbit parameters is determined by the Monte Carlo method. We show that the region determined by the latter method at the initial epoch differs only slightly from the scatter ellipsoid for the linear approximation. We estimate the sizes of the projections of the corresponding regions onto the target plane at the time of the closest encounter of the asteroid with the Earth in 2029. The projections are approximated by ellipses. Our computations have shown that the ellipse has the following sizes: 389.6 km for the semimajor axis and 16.4 km for the semiminor axis in the linear case and 330.0 and 11.1 km, respectively, in the nonlinear case. 相似文献
8.
Xiangyuan Zeng Hexi Baoyin Junfeng Li Shengping Gong 《Celestial Mechanics and Dynamical Astronomy》2011,111(4):415-430
A new concept of three dimensional non-Keplerian trajectories with double angular momentum reversal is investigated with high
performance solar sails. The main discussion of this paper is about such 3D solar inverse orbits with inner constraints. The
problem is addressed in a time optimal control framework solved by an indirect method. Two typical solar inverse orbits have
been achieved and presented in a 3D non-dimensional dynamic model in the Heliocentric Inertial Frame. Starting from the Earth
orbit ecliptic plane, a sailcraft in the inverse orbit exhibits a butterfly shape trajectory. As such, the new orbits are
symmetrical with respect to a plane which contains the Sun-perihelion line. The relation of the sail attitude angles between
the two symmetrical parts of the orbits are used to reduce the simulation effort. The quasi-heliostationary property at its
aphelia is demonstrated with variation of the orbital radius. Evolutions of the orbital velocity and optimal sail orientations
are also outlined and discussed to benefit future design work. As is suited for space observation guaranteed by its butterfly
shape, the inverse orbits are thoroughly studied in terms of the concerned parameters. The discussion of the parametric influence
is ranked in order as perihelion distance r
E
, required maximum position z
max, perihelion position z
f
and the sail lightness number β. Suitable ranges of each parameter are adopted to illustrate the orbital variation trend. Through numerical simulations the
features of such inverse orbits are further emphasized to provide an initial reference for future researchers. 相似文献
9.
Preliminary Exploration of Orbit Determination Method by Means of Space-based Angle Measurement Data
Wu-sheng Chen Qing-bo Gan Jing Zhang Ben-kui Lu Jing-yuan Ma 《Chinese Astronomy and Astrophysics》2008,32(2):197-208
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. 相似文献
10.
A new calibration model for pointing a radio telescope that considers nonlinear errors in the azimuth axis 总被引：1，自引：0，他引：1
A new calibration model of a radio telescope that includes pointing error is presented, which considers nonlinear errors in the azimuth axis. For a large radio telescope, in particular for a telescope with a turntable, it is difficult to correct pointing errors using a traditional linear calibration model, because errors produced by the wheel-on-rail or center bearing structures are generally nonlinear. Fourier expansion is made for the oblique error and parameters describing the inclination direction along the azimuth axis based on the linear calibration model, and a new calibration model for pointing is derived. The new pointing model is applied to the 40 m radio telescope administered by Yunnan Observatories, which is a telescope that uses a turntable. The results show that this model can significantly reduce the residual systematic errors due to nonlinearity in the azimuth axis compared with the linear model. 相似文献
11.
12.
We present comparison results of our Independent Latitude (IL) catalogue of μδ determinations for 1120 bright stars with the Hipparcos, new Hipparcos and Earth Orientation Catalogue (EOC‐2) values. Also, we took into consideration the EOC3 and EOC4 (recent versions of EOC catalogues). Our μδ values are based on zenith telescope observations from seven Independent Latitude (IL) observatories. The IL measures are spanning a time baseline of up to 90 years which is the key advantage to the accurate determination of μδ. The short interval of the Hipparcos satellite observations is a disadvantage for a good accuracy of stellar proper motion, especially in the case of double and multiple stars. For this reason many astrometric catalogues have appeared after the publication of the Hipparcos including our IL catalogue. These catalogues are an appropriate combination of the Hipparcos satellite and ground‐based data which yields more accurate stellar coordinates and/or their proper motions. Among various types of ground‐based observations the latitude and universal time variations obtained from several million observations of stars reduced to the Hipparcos reference system were used for this purpose. These observations were obtained during almost the entire last century and were originally used to determine the Earth Orientation Parameters. It is also possible to use these data in the inverse task of checking the accuracy of stellar coordinates and/or their proper motions listed in the Hipparcos Catalogue. Such latitude and universal time variations data are the basis of the EOC and IL catalogues. In this paper, we computed the differences in μδ values between pairs of catalogues and analyzed the results to characterize the μδ errors for the four catalogues with a special focus on our IL catalogue. The standard errors of μδ for IL stars observed over more than 20 years are mostly smaller than or equal to the Hipparcos errors, and close to the accuracy level of the EOC‐2 (EOC‐3, EOC‐4) and the new Hipparcos. The resulting investigations of errors of differences of μδ, show that all four catalogues have relatively small random and systematic errors which are close to each other meaning that the corresponding μδ values have a high accuracy. Our sample also contains detected double and multiple stars for which the effects of the orbital and proper motions are difficult to separate. The differences of μδ values for these stars generally exceed those obtained for single stars. Also, these discrepancies could be attributed to effect of possible, still unrecognized, astrometric binaries. These investigations about the proper motions and double stars are in line with the activity of the IAU Working Group on Astrometry by Small Ground‐Based Telescopes. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
14.
A novel scheme of plasma simulation particularly suited for computing the one-dimensional nonlinear evolution of parallel propagating solar wind Alfvén waves is presented. The scheme is based on the Vlasov and the MHD models, for solving the longitudinal and the transverse components, respectively. As long as the nonlinearity is not very large (so that the longitudinal and transverse components are well separated), our Vlasov-MHD model can correctly describe evolution of finite amplitude parallel Alfvén waves, which are typical in the solar wind, both in the linear and nonlinear stages. The present model can be applied to discussions of phenomena where the parallel Alfvén waves play major roles, for example, the solar coronal heating and solar wind acceleration by the Alfvén waves propagating from the photosphere. 相似文献
15.
选取前文中所列出的29个累积光谱型为F型的球状星团中的3个作为样本，深入研究了初始观测资料的不确定性和选用不同的银河系引力势模型，对样本星团轨道参数的影响。首先采用Monte Carlo方法产生3个样本球状星团的模拟初始观测数据，而后，以这些模拟数据为初始条件，在3种不同的银河系引力势模型下进行轨道计算，得到此3个样本的模拟轨道参数。模拟计算的结果表明：根据模拟初始数据生成的样本轨道参数分布形态大致可分为高斯分布、准高斯分布和非高斯分布等3类；初始观测数据的不确定性对样本轨道参数分布的影响，与样本星团的选择和轨道参数的类型有关；选用不同的银河系引力势模型，对3个样本星团的各个轨道参数的分布和形态结构也会产生不同程度的影响。该工作的结果，可供深入研究球状星团的整体运动和动力学性质等问题参考。 相似文献
16.
Ashraf Owis Francesco Topputo Franco Bernelli-Zazzera 《Celestial Mechanics and Dynamical Astronomy》2009,103(1):1-16
The solution of a feedback optimal control problem arising in orbital mechanics is addressed in this paper. The dynamics is
that of a massless body moving in a central gravitational force field subject also to a drag and a radial modulated force.
The drag is linearly proportional to the velocity and inversely proportional to the square of the distance from the center
of attraction. The problem is tackled by exploiting the properties of a suitably devised linearizing map that transforms the
nonlinear dynamics into an inhomogeneous linear system of differential equations supplemented by a quadratic objective function.
The generating function method is then applied to this new system, and the solution is back transformed in the old variables.
The proposed technique, in contrast to the classical optimal control problem, allows us to derive analytic closed-loop solutions
without solving any two-point boundary value problem. Applications are discussed. 相似文献
17.
Mikael Granvik Jenni Virtanen Dagmara Oszkiewicz Karri Muinonen 《Meteoritics & planetary science》2009,44(12):1853-1861
Abstract— We are making an open‐source asteroid orbit computation software package called OpenOrb publicly available. OpenOrb is built on a well‐established Bayesian inversion theory, which means that it is to a large part complementary to orbit‐computation packages currently available. In particular, OpenOrb is the first package that contains tools for rigorously estimating the uncertainties resulting from the inverse problem of computing orbital elements using scarce astrometry. In addition to the well‐known least‐squares method, OpenOrb also contains both Monte‐Carlo (MC) and Markov‐Chain MC (MCMC; Oszkiewicz et al. [2009]) versions of the statistical ranging method. Ranging allows the user to obtain sampled, non‐Gaussian orbital‐element probability‐density functions and is therefore optimized for cases where the amount of astrometry is scarce or spans a relatively short time interval. Ranging‐based methods have successfully been applied to a variety of different problems such as rigorous ephemeris prediction, orbital element distribution studies for transneptunian objects, the computation of invariant collision probabilities between near‐Earth objects and the Earth, detection of linkages between astrometric asteroid observations within an apparition as well as between apparitions, and in the rigorous analysis of the impact of orbital arc length and/or astrometric uncertainty on the uncertainty of the resulting orbits. Tools for making ephemeris predictions and for classifying objects based on their orbits are also available in OpenOrb. As an example, we use OpenOrb in the search for candidate retrograde and/or high‐inclination objects similar to 2008 KV42 in the known population of transneptunian objects that have an observational time span shorter than 30 days. 相似文献
18.
N. B. Zheleznov 《Solar System Research》2010,44(2):136-143
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. 相似文献
19.
Gojko Djurašević 《Astrophysics and Space Science》1993,206(1):119-127
The paper is devoted to the actual problematics in the determination of orbital and physical parameters of active CB on the basis of the interpretation of photometric observations. One solves the problem in two stages: by obtaining a synthetic light curve in the case when the parameters of the corresponding CB model are given a priori (direct problem) and by determining the parameters of the given model for which the best fit between the synthetic light curve and the observations is achieved (inverse problem). In this paper, the above procedure is applied to a particular case of CB AG Vir. 相似文献
20.
H. G. Abdelwahed 《Astrophysics and Space Science》2012,341(2):491-500
Using the Viking Satellite observations data in the dayside auroral zone, a theoretical investigation is carried out for contribution of the higher-order nonlinearity to nonlinear obliquely electron-acoustic solitary waves (EASWs) in a magnetized collisionless plasma consisting of a cold electron fluid and non-thermal hot electrons obeying a non-thermal distribution, and stationary ions. A Zakharov–Kuznetsov (ZK) equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (ZK-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution for equations resulting from higher-order perturbation theory has been found using the renormalization method. The effects of the external magnetic field and the obliqueness are found to significantly change the higher-order properties (viz. the amplitude, width, electric field and energy) of the EASWs. The effect of higher-order nonlinearity on the amplitude and width of the soliton are also discussed. A comparison with the Viking Satellite observations in the dayside auroral zone are taken into account. 相似文献