Asteroid close encounters characterization using differential algebra: the case of Apophis

A method for the nonlinear propagation of uncertainties in Celestial Mechanics based on differential algebra is presented. The arbitrary order Taylor expansion of the flow of ordinary differential equations with respect to the initial condition delivered by differential algebra is exploited to implement an accurate and computationally efficient Monte Carlo algorithm, in which thousands of pointwise integrations are substituted by polynomial evaluations. The algorithm is applied to study the close encounter of asteroid Apophis with our planet in 2029. To this aim, we first compute the high order Taylor expansion of Apophis’ close encounter distance from the Earth by means of map inversion and composition; then we run the proposed Monte Carlo algorithm to perform the statistical analysis.     

High-order expansion of the solution of preliminary orbit determination problem

A method for high-order treatment of uncertainties in preliminary orbit determination is presented. The observations consist in three couples of topocentric right ascensions and declinations at three observation epochs. The goal of preliminary orbit determination is to compute a trajectory that fits with the observations in two-body dynamics. The uncertainties of the observations are usually mapped to the phase space only when additional observations are available and a least squares fitting problem is set up. A method based on Taylor differential algebra for the analytical treatment of observation uncertainties is implemented. Taylor differential algebra allows for the efficient computation of the arbitrary order Taylor expansion of a sufficiently continuous multivariate function. This enables the mapping of the uncertainties from the observation space to the phase space as high-order multivariate Taylor polynomials. These maps can then be propagated forward in time to predict the observable set at successive epochs. This method can be suitably used to recover newly discovered objects when a scarce number of measurements is available. Simulated topocentric observations of asteroids on realistic orbits are used to assess the performances of the method.     

Dealing with uncertainties in angles-only initial orbit determination

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.     

Cooperative evolutionary algorithm for space trajectory optimization

A hybrid evolutionary algorithm which synergistically exploits differential evolution, genetic algorithms and particle swarm optimization, has been developed and applied to spacecraft trajectory optimization. The cooperative procedure runs the three basic algorithms in parallel, while letting the best individuals migrate to the other populations at prescribed intervals. Rendezvous problems and round-trip Earth–Mars missions have been considered. The results show that the hybrid algorithm has better performance compared to the basic algorithms that are employed. In particular, for the rendezvous problem, a 100% efficiency can be obtained both by differential evolution and the genetic algorithm only when particular strategies and parameter settings are adopted. On the other hand, the hybrid algorithm always attains the global optimum, even though nonoptimal strategies and parameter settings are adopted. Also the number of function evaluations, which must be performed to attain the optimum, is reduced when the hybrid algorithm is used. In the case of Earth–Mars missions, the hybrid algorithm is successfully employed to determine mission opportunities in a large search space.     

Space Event and Outlier Detection Based on Expectation Maximization Algorithm

The United States provide Element Sets (ELSET) database in Two-Line Element (TLE) format for public use, which plays an important role in the inversion of atmospheric density in the thermosphere, ballistic coefficient estimation, early-warning and so on. Due to large uncertainties existing in the TLE generation process, space environment changes, and space events, ELSET database contains a large number of abnormal TLE data to be filtered, such as corrected TLE, orbital element outlier, and Bstar outlier. The existing methods to filter out the outliers lack general applicability and are very complicated, which are only applicable to a few space targets in certain orbit regions. To overcome the shortcomings of the existing methods, a filtering method is proposed based on Expectation Maximization (EM) algorithm employing a sliding window and polynomial fitting method, which can detect outliers for different orbital elements and space events. The research shows that the algorithm can effectively single out the outliers in TLE sequences and is suitable for all orbital debris.     

Application of high order expansions of two-point boundary value problems to astrodynamics

Two-point boundary value problems appear frequently in space trajectory design. A remarkable example is represented by the Lambert’s problem, where the conic arc linking two fixed positions in space in a given time is to be characterized in the frame of the two-body problem. Classical methods to numerically solve these problems rely on iterative procedures, which turn out to be computationally intensive in case of lack of good first guesses for the solution. An algorithm to obtain the high order expansion of the solution of a two-point boundary value problem is presented in this paper. The classical iterative procedures are applied to identify a reference solution. Then, differential algebra is used to expand the solution of the problem around the achieved one. Consequently, the computation of new solutions in a relatively large neighborhood of the reference one is reduced to the simple evaluation of polynomials. The performances of the method are assessed by addressing typical applications in the field of spacecraft dynamics, such as the identification of halo orbits and the design of aerocapture maneuvers.     

Automatic Solar Filament Detection Using Image Processing Techniques

We present an automatic solar filament detection algorithm based on image enhancement, segmentation, pattern recognition, and mathematical morphology methods. This algorithm cannot only detect filaments, but can also identify spines, footpoints, and filament disappearances. It consists of five steps: (1) The stabilized inverse diffusion equation (SIDE) is used to enhance and sharpen filament contours. (2) A new method for automatic threshold selection is proposed to extract filaments from local background. (3) The support vector machine (SVM) is used to differentiate between sunspots and filaments. (4) Once a filament is identified, morphological thinning, pruning, and adaptive edge linking methods are used to determine the filament properties. (5) Finally, we propose a filament matching method to detect filament disappearances. We have successfully applied the algorithm to Hα full-disk images obtained at Big Bear Solar Observatory (BBSO). It has the potential to become the foundation of an automatic solar filament detection system, which will enhance our capabilities of forecasting and predicting geo-effective events and space weather.     

Particle swarm optimization based space debris surveillance network scheduling

The increasing number of space debris has created an orbital debris environment that poses increasing impact risks to existing space systems and human space flights. For the safety of in-orbit spacecrafts, we should optimally schedule surveillance tasks for the existing facilities to allocate resources in a manner that most significantly improves the ability to predict and detect events involving affected spacecrafts. This paper analyzes two criteria that mainly affect the performance of a scheduling scheme and introduces an artificial intelligence algorithm into the scheduling of tasks of the space debris surveillance network. A new scheduling algorithm based on the particle swarm optimization algorithm is proposed, which can be implemented in two different ways: individual optimization and joint optimization. Numerical experiments with multiple facilities and objects are conducted based on the proposed algorithm, and simulation results have demonstrated the effectiveness of the proposed algorithm.     

On the numerical transformation of variables in perturbation theory

Once the generating function of a Lie-type transformation is known, canonical variables can be transformed numerically by application of a Runge-Kutta type integration method or any other appropriate numerical integration algorithm. The proposed approach avails itself of the fact, that the transformation is defined by a system of differential equations with a small parameter as the independent variable. The integration of such systems arising in the perturbation theories of Hori and Deprit is discussed. The method allows to compute numerical values of periodic perturbations without deriving explicitly the perturbation series. This saving of an algebraic work is achieved at the expense of multiple evaluations of the generator's derivatives.     

大面积硅微条探测器在轨数据压缩算法的设计与实现

硅微条探测器具有位置分辨高、响应快、低噪声、低功耗等优点,广泛应用在各大加速器试验中,测量粒子径迹.新世纪以来,逐渐应用于空间探测领域.计划中的"悟空"2号暗物质粒子探测卫星的硅微条探测器将至数十万计,将产生海量的原始数据.如何实现探测器快速实时的数据压缩,是其需要解决的一大难题.立足于面向空间应用的硅微条探测器在轨实时压缩算法,算法采用FPGA (Field-programmable Gate Array)搭建流水线结构的方式实现,在提高系统集成度、节省逻辑资源的同时,批量数据处理时最高可将数据压缩率提升至38.4 M通道/s.算法结构具有通用性,设计思想和方案将为"悟空"2号的径迹探测器的研制提供参考.     

The Taylor series method for the problem of the rotational motion of a rigid satellite

This paper presents the Taylor series method for integration of differential equations describing the rotational motion of a rigid satellite. We compared the presented algorithm with other methods, and we show that it gives the most accurate results with reasonable efficiency.     

On the Sun's differential rotation and pole-equator temperature difference

The Sun's differential rotation can be understood in terms of a preferential stabilization of convection (by rotation) in the polar regions of the lower part of the convection zone (where the Taylor number is large). A significant pole-equator difference in flux () can develop deep inside the convection zone which would be unobservable at the surface, because can be very efficiently reduced by large scale meridional motions rising at the poles and sinking at the equator. This is the sense of circulation needed to produce the observed equatorial acceleration of the Sun. Differential rotation is generated, therefore, in the upper part of the convection zone (where the interaction of rotation with convection is small) and results as the convection zone adjusts to a state of negligible Taylor number.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Notes on Hori Method for Non-Canonical Systems

In this paper the new approach for the integration theory of the canonical version of Hori method recently proposed is extended to the non-canonical one. It will be shown that the non-homogeneous ordinary differential equation with an auxiliary parameter t* associated with the mth order equation of the algorithm can also be replaced by a non-homogeneous partial differential equation in the time t. Using a generalized canonical approach, the general algorithm proposed by Sessin is then revised; as well as the Lagrange variational equations for the non-canonical version of Hori method. A simplified algorithm derived from Sessin's algorithm is presented for non-linear oscillations problem.     

A novel hybrid algorithm for lucky imaging

Lucky imaging is a high-resolution astronomical image recovery technique with two classic implementation algorithms, i.e. image selecting, shifting and adding in image space, and data selecting and image synthesizing in Fourier space. This paper proposes a novel lucky imaging algorithm where with space-domain and frequency-domain selection rates as a link, the two classic algorithms are combined successfully, making each algorithm a proper subset of the novel hybrid algorithm. Experimental results show that with the same experiment dataset and platform, the high-resolution image obtained by the proposed algorithm is superior to that obtained by the two classic algorithms. This paper also proposes a new lucky image selection and storage scheme, which can greatly save computer memory and enable lucky imaging algorithm to be implemented in a common desktop or laptop with small memory and to process astronomical images with more frames and larger size. In addition, through simulation analysis,this paper discusses the binary star detection limits of the novel lucky imaging algorithm and traditional ones under different atmospheric conditions.     

Neural network prediction of solar cycle 24

The ability to predict the future behavior of solar activity has become extremely import due to its effect on the environment near the Earth.Predictions of both the amplitude and timing of the next solar cycle will assist in estimating the various consequences of space weather.The level of solar activity is usually expressed by international sunspot number (Rz).Several prediction techniques have been applied and have achieved varying degrees of success in the domain of solar activity prediction.We predict a...     

使用SOFM方法进行恒星光谱自动分类

ＳＯＦＭ是人工神经网络的非监督学习算法,可以将数据组织到一个特征图上,而保存 大多数原始数据空间的拓扑特征．使用这种方法进行恒星光谱自动分类,分类结果与哈佛 序列十分相似．ＳＯＦＭ方法应该是进行大数量恒星光谱样本在线分类的有用方法,它能 够自动执行,因此可用于处理大数量天体光谱．     

Analytical solutions for the equations of motion of a space vehicle during the atmospheric re-entry phase on a 2-D trajectory

A practical and important problem encountered during the atmospheric re-entry phase is to determine analytical solutions for the space vehicle dynamical equations of motion. The author proposes new solutions for the equations of trajectory and flight-path angle of the space vehicle during the re-entry phase in Earth’s atmosphere. Explicit analytical solutions for the aerodynamic equations of motion can be effectively applied to investigate and control the rocket flight characteristics. Setting the initial conditions for the speed, re-entering flight-path angle, altitude, atmosphere density, lift and drag coefficients, the nonlinear differential equations of motion are linearized by a proper choice of the re-entry range angles. After integration, the solutions are expressed with the Exponential Integral, and Generalized Exponential Integral functions. Theoretical frameworks for proposed solutions as well as, several numerical examples, are presented.     

Spatio-temporal variations of density of the particles generating the optical emission of meteor plasma

The data of absolute spectrophotometry of meteors permit to determine number densities of particles of different elements.It is possible to solve mathematically the problem on space-time structure of the meteor with the model of a spherically symmetrical flare.The space distribution of radiating matter can be estimated by the integral equation of Abel type.Variation of density of particles in time can be found from the differential equations of kinetics.     

Quantized Redshifts of Galaxies: Stimulated Raman Scattering in Cold Intergalactic Rydberg Matter

That the redshifts for galaxies in the local supercluster are quantizedwas recently confirmedby Guthrie and Napier(A&Amp;Amp;A310 (1996) 353). These redshifts are here proposed to be due to stimulatedStokes Raman processes in intergalactic matter in the form of Rydberg Matter (RM). Rydberg Matteris an electronically excited material, as demonstrated by its use as laser medium in a thermally excitedultra-broadband tunable IR laser (Chem. Phys. Lett. 376 (2003) 812). Its existence in interstellar andintergalactic space is demonstrated by several observational results, notably the unidentified IR bands,that agree well with the emission from Rydberg Matter. A stimulated Raman process will allow theH I 21 cm radiation to proceed without deflection, in agreement with observation. Such redshiftswill be additive during the passage through space. The process in Rydberg Matter here proposed togive rise to the Stokes Raman process is excitation of electronic translational modes in the planarclusters forming the matter. The specific cluster sizes found in laboratory experiments give rise toa few differently sized redshift quanta, which is in good agreement with the observed quanta. Anexcitation level (principal quantum number) of Rydberg Matter in intergalactic space between 175and 200 gives the correct size of the redshift quanta.     

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.