On the dynamical derivation of the Titius-Bode law

The Principle of Least Action Interaction, developed by the dynamical astronomer Michael W. Ovenden, is tested using a new algorithm based on the ergodic hypothesis that the time mean of the disturbing function is equal to the space mean. This algorithm is an improvement over the one that Ovenden (1972) used in testing his principle, i.e. it can be applied to systems having more than three satellites without violating the conservation law of angular momentum and these satellites may have significant inclinations. This algorithm treats the problem of finding the configuration of least action interaction as a Lagrange multiplier problem. Renormalization group techniques and existing non-gradient optimization algorithms are incorporated into this new algorithm to reduce some of the numerical complexities.This algorithm is tested on the planets and asteroids in our solar system and on the satellite systems of Jupiter, Saturn, and Uranus. In most cases the results show that the current distances of the satellites from their primary is very close to the minimum interaction-action configuration for that system. The possibility of a planet lying beyond Pluto is investigated using this algorithm.Finally, some of my results are compared with those of Ovenden (1972) for our solar system. The results indicate that the interaction-action potential is lower using this new algorithm than the potential obtained from Ovenden's. Also, greater skepticism is raised concerning the one-time existence of a planet of 90 earth masses lying between Mars and Jupiter.     

实时相关跟踪图像处理系统

文章介绍了怀柔太阳观测基地最近完成的一套实时高分辨太阳磁场观测系统。系统采用局部相关跟踪算法来提高磁场观测数据的空间分辨率，同时对相关跟踪算法的实现程序进行了优化以满足常规太阳磁场观测的要求。通过对试观测和常规观测数据的分析，我们发现：1）该系统能够大大提高单色像、磁场数据的对比度和空间分辨率；2）对相关跟踪算法的优化大大提高了系统的时间分辨率，系统可以投入常规观测使用。     

嵌入式GPS/DR车载组合导航系统EKF算法软件设计

介绍一种嵌入式GPS／DR（全球定位系统／航位推算）车载组合导航（它通过GPS与DR的优势互补,提高了车辆导航系统定位数据的可靠性）的EKF（扩展卡尔曼滤波）算法软件设计方法。采用统计学原理剔除导航数据的粗差点,用扩展卡尔曼滤波进行导航参数的实时求解,采用EKF算法的GPS／DR组合导航系统有利于导航信息的稳定性、可靠性和实时性。     

Optimal Compensation and Implementation for Adaptive Optics Systems

This paper develops a compensation algorithm based on Linear–Quadratic–Gaussian (LQG) control system design whose parameters are determined (in part) by a model of the atmosphere. The model for the atmosphere is based on the open-loop statistics of the atmosphere as observed by the wavefront sensor, and is identified from these using an auto-regressive, moving average (ARMA) model. The (LQG) control design is compared with an existing compensation algorithm for a simulation developed at ESO that represents the operation of MACAO adaptive optics system on the 8.2 m telescopes at Paranal, Chile. This revised version was published online in July 2006 with corrections to the Cover Date.     

Research and Test of Real-time Search Algorithm of Fast Radio Bursts Based on GPU Acceleration

In order to satisfy the research need of Nanshan 25 m radio telescope of Xinjiang Astronomical Observatory (XAO) and study the key technology of the planned QiTai radio Telescope (QTT), on the basis of the original CPU (Central Processing Unit)-based real-time search algorithm of FRBs (Fast Radio Bursts), we have studied the GPU (Graphics Processing Unit)-based real-time search algorithm of FRBs, and built the corresponding real-time search system of FRBs. We have made the comparison and analysis on the GPU system and CPU system, the test result shows that under a given searching accuracy, the speed of the GPU-accelerated algorithm is improved by 35–45 times compared with that of the CPU algorithm.     

关于近地小行星轨道演化的初步探索

本文采用改进的显式辛算法和嵌套的PKF7（8）积分器同时对86颗已命名（或编号）的近地小行星的轨道演化进行了数值研究，在103－104年的时间尺度上，给出了这些小行星轨道演化的状况以及它们与几颗大行星靠近的最小距离，特别是与地球接近的最小距离可小于0．01天文单位，甚至可能比月球还更靠近地球．     

Detection of Coronal Mass Ejections Using Multiple Features and Space–Time Continuity

Coronal Mass Ejections (CMEs) release tremendous amounts of energy in the solar system, which has an impact on satellites, power facilities and wireless transmission. To effectively detect a CME in Large Angle Spectrometric Coronagraph (LASCO) C2 images, we propose a novel algorithm to locate the suspected CME regions, using the Extreme Learning Machine (ELM) method and taking into account the features of the grayscale and the texture. Furthermore, space–time continuity is used in the detection algorithm to exclude the false CME regions. The algorithm includes three steps: i) define the feature vector which contains textural and grayscale features of a running difference image; ii) design the detection algorithm based on the ELM method according to the feature vector; iii) improve the detection accuracy rate by using the decision rule of the space–time continuum. Experimental results show the efficiency and the superiority of the proposed algorithm in the detection of CMEs compared with other traditional methods. In addition, our algorithm is insensitive to most noise.     

On one special case of parametric resonance in problems of celestial mechanics

We consider a periodic (in time) linear Hamiltonian system that depends on a small parameter. At a zero value of this parameter, the matrix of the system is constant, has two identical pairs of purely imaginary roots, and is not reducible to diagonal form. Therefore, the unperturbed system is unstable. We propose an algorithm for determining the boundaries of the instability regions for the system at nonzero values of the small parameter. This algorithm was used to analyze the stability of triangular libration points in the elliptical restricted three-body problem and in the stability problem in one special case of stationary rotation of a satellite relative to the center of mass.     

Correction and simulation of the intensity compensation algorithm used in curvature wavefront sensing

The wavefront measuring range and recovery precision of a curvature sensor can be improved by an intensity compensation algorithm. However, in a focal system with a fast f-number, especially a telescope with a large field of view, the accuracy of this algorithm cannot meet the requirements. A theoretical analysis of the corrected intensity compensation algorithm in a focal system with a fast f-number is first introduced and afterwards the mathematical equations used in this algorithm are expressed.The corrected result is then verified through simulation. The method used by such a simulation can be described as follows. First, the curvature signal from a focal system with a fast f-number is simulated by Monte Carlo ray tracing; then the wavefront result is calculated by the inner loop of the FFT wavefront recovery algorithm and the outer loop of the intensity compensation algorithm. Upon comparing the intensity compensation algorithm of an ideal system with the corrected intensity compensation algorithm, we reveal that the recovered precision of the curvature sensor can be greatly improved by the corrected intensity compensation algorithm.     

基于GPS与三轴磁强计的联合导航算法

为了修正近地轨道(小于1000 km)地磁场模型,提高导航的精度,在地磁导航系统中引入GPS作为一个新的测量设备,提出了一种基于三轴磁强计与GPS的联合导航算法．该算法取卫星的位置和速度向量作为状态向量,建立状态方程;取卫星周围的磁场强度和GPS接收的信号作为观测量,建立观测方程;并以GPS确定的轨道状态量为标准量,去估计磁场模型参数的修正量,构成冷备冗余导航算法．仿真结果表明,提出的导航算法对轨道位置的估计误差小于50 m,速度的估计误差小于0．1 m／s,导航算法的精度和收敛性都优于使用单一地磁导航的系统．     

nmagic: a fast parallel implementation of a χ2-made-to-measure algorithm for modelling observational data

We describe a made-to-measure (M2M) algorithm for constructing N -particle models of stellar systems from observational data (χ²M2M), extending earlier ideas by Syer & Tremaine. The algorithm properly accounts for observational errors, is flexible, and can be applied to various systems and geometries. We implement this algorithm in a parallel code nmagic and carry out a sequence of tests to illustrate its power and performance. (i) We reconstruct an isotropic Hernquist model from density moments and projected kinematics and recover the correct differential energy distribution and intrinsic kinematics. (ii) We build a self-consistent oblate three-integral maximum rotator model and compare how the distribution function is recovered from integral field and slit kinematic data. (iii) We create a non-rotating and a figure rotating triaxial stellar particle model, reproduce the projected kinematics of the figure rotating system by a non-rotating system of the same intrinsic shape, and illustrate the signature of pattern rotation in this model. From these tests, we comment on the dependence of the results from χ²M2M on the initial model, the geometry, and the amount of available data.     

A motion planning algorithm for the feed support system of FAST

The paper relates to a motion planning algorithm for the feed support system of the Five-hundred-meter Aperture Spherical radio Telescope(FAST).To enhance the stability of the feed support system,the start/termination planning segments are adopted with an acceleration and deceleration section.The source switching planning adopts a combination of a line segment and focal segment to realize stable control of the feed support system.Besides,during the observation trajectory,a transition segment which is not used for observation data is planned with a required time.Through an example simulation,a smooth change is realized via the motion planning algorithm and presented in this paper.     

A novel algorithm for generating libration point orbits about the collinear points

This paper presents a numerical algorithm that can generate long-term libration points orbits (LPOs) and the transfer orbits from the parking orbits to the LPOs in the circular-restricted three-body problem (CR3BP) and the full solar system model without initial guesses. The families of the quasi-periodic LPOs in the CR3BP can also be constructed with this algorithm. By using the dynamical behavior of LPO, the transfer orbit from the parking orbit to the LPO is generated using a bisection method. At the same time, a short segment of the target LPO connected with the transfer orbit is obtained, then the short segment of LPO is extended by correcting the state towards its adjacent point on the stable manifold of the target LPO with differential evolution algorithm. By implementing the correction strategy repeatedly, the LPOs can be extended to any length as needed. Moreover, combining with the continuation procedure, this algorithm can be used to generate the families of the quasi-periodic LPOs in the CR3BP.     

An analysis of close binaries (CB) based on photometric measurements

The subject of the paper is the problem of stellar differntial rotation in close binaries (CB) ofRS CV n type. The differential-rotation parameters we find on the basis of the migration of the depression in the light curves caused by the spot effect over the orbital phase. For that purpose, a simple model (Bussoet al., 1985) and inverse-problem procedure, based on the Marquardt (1963) algorithm, are used. To verify the obtained solutions, the SIMPLEX algorithm (Torczon, 1991) is applied, suitable for the nonlinear parameter optimisation. This algorithm enables a correct solution of the nonlinear equation system describing the differential rotation. The procedure is applied in the determination of the parameters of differential rotation forCV Cam, VV Mon andSS Boo binaries.     

A multiple shooting approach for the numerical treatment of stellar structure and evolution

We present a new numerical method for solving the system of partial differential equations describing the structure and evolution of a spherically symmetric star. As usual, we employ the transversal method of lines in order to split the equations into a coupled spatial and temporal part. The novel features of the algorithm are the following: (a) Instead of using the Lagrangian picture we formulate the system of partial differential equations in the Eulerian picture. (b) We reformulate the equations of stellar structure as a multipoint boundary-value problem. By means of this reformulation the rather clumsy iterative matching procedure of stellar atmosphere and interior is avoided. (c) The multipoint boundary-value problem is solved by the multiple shooting method. This approach not only ensures a high accuracy of the stellar models calculated at each time step but also allows the free boundaries inside the star due to different energy transport mechanisms to be located exactly. (d) The time derivatives involved in the stellar-structure equations are discretized implicitly to second order accuracy. Moreover, at each time step, the chemical abundances are determined by using a sophisticated update procedure. In this way, a high accuracy is achieved with respect to the integration in time. The algorithm has turned out to be exceedingly reliable and numerically accurate. This is shown by the evolution of a 1 M_⊙ star up to the hydrogen-shell burning phase. In this example, the virial theorem, the law of mass conservation, and the law of energy conservation is fulfilled to a hitherto unattainable degree of accuracy. Since the multiple shooting method, which is at the heart of our approach, is a perfect example of a parallel algorithm, the computational speed of the algorithm might be substantially improved provided easy-to-program, high-performance parallel computers with sufficiently many processors become available in the near future.     

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.     

Second kind Chebyshev operational matrix algorithm for solving differential equations of Lane–Emden type

In this paper, we present a new second kind Chebyshev (S2KC) operational matrix of derivatives. With the aid of S2KC, an algorithm is described to obtain numerical solutions of a class of linear and nonlinear Lane–Emden type singular initial value problems (IVPs). The idea of obtaining such solutions is essentially based on reducing the differential equation with its initial conditions to a system of algebraic equations. Two illustrative examples concern relevant physical problems (the Lane–Emden equations of the first and second kind) are discussed to demonstrate the validity and applicability of the suggested algorithm. Numerical results obtained are comparing favorably with the analytical known solutions.     

An Event-Based Verification Scheme for the Real-Time Flare Detection System at Kanzelhöhe Observatory

In the framework of the Space Situational Awareness program of the European Space Agency (ESA/SSA), an automatic flare detection system was developed at Kanzelhöhe Observatory (KSO). The system has been in operation since mid-2013. The event detection algorithm was upgraded in September 2017. All data back to 2014 was reprocessed using the new algorithm. In order to evaluate both algorithms, we apply verification measures that are commonly used for forecast validation. In order to overcome the problem of rare events, which biases the verification measures, we introduce a new event-based method. We divide the timeline of the H\(\upalpha\) observations into positive events (flaring period) and negative events (quiet period), independent of the length of each event. In total, 329 positive and negative events were detected between 2014 and 2016. The hit rate for the new algorithm reached 96% (just five events were missed) and a false-alarm ratio of 17%. This is a significant improvement of the algorithm, as the original system had a hit rate of 85% and a false-alarm ratio of 33%. The true skill score and the Heidke skill score both reach values of 0.8 for the new algorithm; originally, they were at 0.5. The mean flare positions are accurate within \({\pm}\,1\) heliographic degree for both algorithms, and the peak times improve from a mean difference of \(1.7\pm 2.9~\mbox{minutes}\) to \(1.3\pm 2.3~\mbox{minutes}\). The flare start times that had been systematically late by about 3 minutes as determined by the original algorithm, now match the visual inspection within \(-0.47\pm 4.10~\mbox{minutes}\).     

Interval Algorithm for the Planetary Problem

To calculate the dynamics of celestial bodies, we suggest the nonclassic interval algorithm based on taking into account explicitly the limitations of the resolving capacity of instrumental observation facilities. This algorithm is consistent with the correspondence principle (has a classic limit) and is a system of integer mappings of a recurrent type which is free of the effect of the round-off error accumulation. Another feature is its relative simplicity, which allowed us to make the calculations less time-consuming as compared to the classic approach. This algorithm was used to calculate the evolution of the Solar System's planetary orbits over times of about 500 million years. The calculations support the results obtained earlier by classic methods and make it possible to conclude that the suggested interval approach can be adequately applied to the planetary problem under consideration.     

A Research on the Algorithm of Local Atomic Time

The goal of all time laboratories’ pursue is to produce and keep a stable, precise and reliable time scale. The long-term stability of the time scale is mainly taken into account in the traditional ALGOS algorithm, while the local atomic time scale should give consideration to both the long-term and shortterm stabilities. From the analysis and research on the atomic clock noise model and under the condition that the long-term stability of the local atomic time scale does not drop, a complete algorithm is proposed which is suitable for the calculation of the local time scale TA (NTSC) carried out at the time laboratory with the time-keeping clocks of a unitary type and being close in performance at the National Time Service Center, called the NTSC for short, of Chinese Academy of Sciences. The data of all the clocks in the NTSC which participated in the calculation of the International Atomic Time (TAI) all the year round in 2008 are applied to the test and verification of the new algorithm, with the result showing that both the short- and long-term stability indexes of the obtained TA (NTSC) are improved. The research result is suitable for the calculation of the atomic time scale of the time laboratory whose time keeping system is similar to that of the NTSC.