预报模型及建模序列长度对钟差短期预报精度影响研究

针对全球定位系统(Global Positioning System, GPS)星载原子钟在钟差预报时与不同模型的适应度不同的问题,采用二次多项式(Quadratic Polynomial, QP)模型、灰色(Grey Model, GM(1,1)模型和灰色+自回归(GM(1,1)+Autoregressive, GM(1,1)+AR)模型对不同类型原子钟的钟差进行预报,着重分析不同类型原子钟的预报精度、不同长度钟差序列建模预报效果以及钟差序列波动对预报结果的影响。实验结果表明:(1)钟差预报精度与建模序列长度有一定关系,二次多项式模型受影响最大,灰色+自回归模型受影响最小;(2)不同卫星原子钟在不同预报模型下最佳建模序列长度不同,铷钟受建模序列长度的影响小于铯钟;(3)二次多项式模型对铯钟预报效果较差,对铷钟预报效果可与灰色模型和灰色+自回归模型相当;(4)钟差序列波动时,建模预报精度降低,不同模型的预报结果受钟差波动幅度大小的影响不同。     

灰色模型修正及其在实时GPS卫星钟差预报中的应用研究

在GPS实时精密单点定位中,卫星钟差的实时可靠预报是实现GPS实时高精度单点定位的关键之一.星载GPS原子钟频率高,非常敏感,极易受到外界及其本身因素的影响,从而很难掌握其复杂细致的变化规律,这些属性符合灰色系统理论的特点.因此,考虑将钟差的变化过程看作一个灰色系统.在探讨二次多项式和灰色模型卫星钟差预报局限性基础上,提出了利用改进的灰色模型实时预报GPS卫星钟差的研究,最后利用3个不同时段的GPS卫星钟差资料进行不同采样间隔钟差预报精度分析、灰色模型指数系数与预报精度的关系、与二次多项式预报精度比较分析,总结不同卫星钟差类型与模型指数系数的一般关系,并与IGS最终钟差星历产品比较,验证本文提出的改进预报模型的可行性和有效性.为实时GPS动态精密单点定位提供较高精度的卫星钟差产品.     

附有周期项的预报模型及其在GPS卫星钟差预报中的应用研究

为了有效进行GPS卫星钟差预报和更好地反映卫星钟差特性,除了考虑卫星原子钟频移、频漂和频漂率等物理性质外,还应考虑到卫星钟差的周期性变化特点.在二次多项式模型基础上,增加了周期项因素,构造了新的预报模型.选取部分GPS卫星铯钟(Cs.clock)和铷钟(Rb.clock)钟差资料,根据钟差变化趋势分3种情况,按不同时间长度进行钟差预报分析,并与二次多项式模型的预报结果比较分析,大量数据分析表明:附有周期项的二次多项式模型预报精度优于二次多项式模型,铷钟预报精度略优于铯钟.     

一种改进钟差二次多项式模型的导航卫星钟差预报方法

为了更好地反映钟差特性并提高其预报精度,建立一种能够同时考虑星载原子钟物理特性、钟差周期性变化与随机性变化特点的钟差预报模型.首先采用附有周期项的二次多项式模型进行拟合提取卫星钟差(Satellite Clock Bias,SCB)的趋势项与周期项,然后根据拟合残差的特点采用时间序列ARIMA(Auto-Regressive Integrated Moving Average)模型对残差进行建模;最后将两种模型的预报结果结合得到最终钟差预报值.使用IGS(International GNSS Service)精密钟差数据进行预报试验,将新方法与二次多项式模型、灰色模型及ARIMA模型进行对比,证明了新方法能够更高精度地预报卫星钟差,且可以一定程度上改善ARIMA存在模型识别与定阶不准的不足.     

基于GM(1,1)和MECM组合模型的GPS卫星钟差中短期预报

针对卫星钟差呈现趋势项和随机项变化的特点,提出了基于GM(1,1)(灰色预报模型)和修正指数曲线法(Modified Exponential Curve Method,MECM)的组合预报模型.该模型首先采用GM(1,1)预报钟差的趋势项,然后利用MECM模型对GM(1,1)残差序列进行建模和预报,最后将GM(1,1)和MECM模型的预报结果相加得到钟差的最终预报值.此外,采用IGS(International Global Navigation Satellite System Service)公布的精密卫星钟差进行预报试验,通过与卫星钟差预报中常用的二次多项式和MECM模型预报结果的对比分析,结果表明:该方法可以对GPS卫星钟差进行高精度的中短期预报.使用12 h钟差建模时,预报6 h、12 h、18 h和24 h的平均预报精度分别为0.43 ns、0.63 ns、0.74 ns和0.79 ns,相比于二次多项式的平均预报精度分别提高了57.43%、69.71%、80.47%和86.74%,相比于MECM模型的平均预报精度分别提高了50.57%、64.41%、76.80%和84.20%;使用24 h钟差建模时,预报6 h、12 h、18h和24 h的平均预报精度分别为0.57 ns、0.61 ns、1.02 ns和1.48 ns,相比于二次多项式的平均预报精度分别提高了32.94%、55.47%、55.07%和53.16%,相比于MECM模型的平均预报精度分别提高了92.98%、66.30%、65.42%和63.99%.     

基于Vondrák滤波1阶差分灰色模型的卫星钟差预报方法

为了提高卫星钟差预报的精度,提出基于Vondrák滤波1阶差分的灰色模型算法.首先,对原始钟差数据序列采用Vondrák滤波处理后,得到1组新的钟差数据序列.然后,对相邻历元的钟差数据序列作1阶差分处理.最后,基于Vondrák滤波后的1阶差分的钟差差值数据序列,建立了GPS钟差预报的灰色模型.此外,采用了IGS(International Global Navigation Satellite System Service)公布的精密卫星钟差数据进行了预报试验,通过与卫星钟差预报中常用的2次多项式模型和直接采用原始钟差数据建立灰色预报模型预报结果的对比分析,结果表明:该方法可以对GPS卫星钟差进行高精度的中短期预报.在12 h、16 h、20 h和24 h的平均预报精度分别为0.50 ns、0.85 ns、1.08 ns和1.27 ns,相比于2次多项式模型的平均预报精度分别提高了24.24%、15.84%、12.90%和11.81%;相比于直接采用原始钟差数据建立灰色预报模型的平均预报精度分别提高了56.14%、49.40%、48.82%和47.80%.     

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.     

基于一次差的灰色模型在卫星钟差预报中的应用

根据星载原子钟钟差的特点,提出一种基于一次差的灰色GM(1,1)钟差预报方法.该方法首先对相邻历元的钟差作一次差,然后以一次差后的值建立灰色模型预报一次差的值,最后将预报的一次差还原即得到钟差预报值.以IGS(International GNSS Service)提供的采样率为5 min的精密钟差为实验数据,通过对不同长度的建模数据和不同预报步长进行对比分析.结果表明:该方法的预报精度较传统的灰色模型有了较大提高,特别是对于PRN01原子钟,其预报效果最好;采用一次差原理可有效改善和提高模型预报的精度和稳定性,应用于钟差较长时间预报是可行的,可靠性较强.     

泛函网络在导航卫星钟差中长期预报中的应用

为了更好地反映导航卫星钟差特性以及提高导航卫星钟差中长期预报精度,在对卫星原子钟差预报建模时,除考虑卫星原子钟频移、频漂和频漂率等物理性质外,还考虑了卫星钟差的周期性变化和随机性等特点.在传统多项式预报模型基础上,采用泛函网络对卫星钟差的周期项和随机项部分进行建模,利用GPS导航卫星钟差数据进行预报实验,并与传统的多项式模型、灰色系统模型、差分自回归滑动平均(ARIMA)模型以及Kalman滤波方法的预报结果进行比对,结果表明,基于泛函网络建立的混合预报模型能有效减小导航卫星钟差的中长期预报误差.     

基于ARMA模型的导航卫星钟差长期预报

卫星钟差长期可靠预报是实现卫星自主导航定轨所要解决的重要前提之一.针对多项式模型(PM)、灰色模型(GM)等常用的钟差预报方法存在的预报误差较大的情况,为了有效地进行卫星钟差预报和更好地反映卫星钟差变化特性,将ARMA(Auto-Regressive Moving Average)模型引入到卫星钟差预报中,利用IGS(International GNSS Service)提供的卫星钟差观测数据进行90 d的长期预报,根据各个卫星钟差的变化特性,对其进行模式识别、建模和预报,并与其它3种模型进行了较为细致的比较.计算结果表明,采用ARMA模型可以有效地提高卫星钟差的长期预报精度.     

Theoretical model of flares and prominences

A theoretical model of flare which explains observed quantities in H, EUV, soft X-ray and flare-associated solar wind is presented. It is assumed that large mass observed in the soft X-ray flare and the solar wind comes from the chromosphere by the process like evaporation while flare is in progress. From mass and pressure balance in the chromosphere and the corona, the high temperature in the soft X-ray flare is shown to be attained by the larger mass loss to the solar wind compared with the mass remained in the corona, in accord with observations. The total energy of 10³² erg, the electron density of 10^13.5 cm^–3 in H flare, the temperature of the X-ray flare of 10^7.3K and the time to attain maximum H brightness (600 s) are derived consistent with observations. It is shown that the top height of the H flare is located about 1000 km lower than that of the active chromosphere because of evaporation. So-called limb flares are assigned to either post-flare loops, surges or rising prominences.The observed small thickness of the H flare is interpreted by free streaming and/or heat conduction. Applications are suggested to explain the maximum temperature of a coronal condensation and the formation of quiescent prominences.     

A model and map of Amalthea

A topographic model of Amalthea (JV) was derived from the shapes of limbs and terminators in Voyager images, modified locally to accommodate large craters and ridges. The model is presented in tabular and graphic form, including the first detailed shaded relief maps of the satellite. The shape is very irregular, with radii varying between about 53 and 151 ± 5 km. The minimum value occurs in a deep crater at the south pole. The volume is estimated to be 2.5 ± 0.5 × 10⁶km³. A prominent groove or valley extends some 150 km across the trailing side. High albedo, spectrally distinct markings are mapped and found to have a less obvious relationship with relief than previously suggested.     

Flare model chromospheres and photospheres

Homogeneous plane-parallel model atmospheres for solar flares have been constructed to approximately simulate observations of flares. The wings of the Ca II lines have been used to derive flare upper photosphere models, which indicate temperature increases of ～100 K over the temperature distribution in the pre-existing facula at a height of 300 km above τ₅₀₀₀ = 1. In the case of flares covering sunspots the temperature rise seems to occur much higher in the atmosphere. We solve the transfer and statistical equilibrium equations for a three-level hydrogen atom and a five-level calcium atom in order to obtain the chromospheric flare models. The general properties of flares, including n _e, N ₂, linear thickness, and Lyman continuum intensity are approximately reproduced. We find that with increasing flare importance the height of the upper chromosphere and transition region occur lower in the solar atmosphere, accounting for the factor of 60–600 increase in pressure in these regions relative to the quiet Sun. The Ca II line profiles agree with observations only by assuming a macro-velocity distribution that increases with height. Also the chromospheric parts of flares appear to be highly inhomogeneous. We show that shock and particle heated flare models do not agree with the observations and propose a thermal response model for flares. In particular, it appears that heating in the photosphere is an essential aspect of flares.     

A model of solar flares and faculae

Theories of solar flares based on the storage of energy (usually as magnetic energy) in the solar atmosphere are shown to be incompatible with observational data.The sunspot energy deficit and the photospheric faculae both involve energy fluxes comparable with the flare requirement ( 3 × 10²⁹ erg s^–1). Both also require a subsurface system of waves or oscillations, perhaps those discussed by Danielson and Savage and by Wilson. The flare model proposed is based on a temporary diversion of this energy carried by Alfvén waves through spots and magnetic elements or micro-pores; the calculated plasma perturbation velocity in the umbra is about 6 km s^–1 for a major flare.In the atmosphere the wave energy divides into two parts to produce the cool, stationary optical flare and the particle flare. The first part is dissipated around flux tubes which are mainly horizontal in the chromosphere and which tend to concentrate along the magnetic neutral line (B = 0). Each tube vibrates individually as a taut wire in a viscous fluid, to excite the fluid just outside the tube. The second part of the energy emerges along tubes mainly vertical in the chromosphere and is converted to shock waves in the corona and then to particle energy for the radio and X-ray flare and the blast wave.The model includes white-light faculae, quasi-permanent X-ray and fast-particle emissions, sympathetic flares and surges. An unambiguous test would be provided by observations of plasma motions of a few kilometres per second in spots and micro-pores.     

Non-radial oscillations and stability of Prendergast's model

The frequencies of the linear and adiabatic oscillations of Prendergast's model are determined with the aid of a perturbation method. The influence of the magnetic field on the frequencies of the different types of spheroidal oscillation modes is discussed.     

A model of thermospheric temperature and composition

An empirical model of thermospheric temperature (T_∞T₁₂₀, and s) and composition (H, He, N, O, N₂, O₂, and Ar) was derived from measurements of 8 satellites (AE-C, AE-E, AEROS-A, AEROS-B, ARIEL-3, ESRO-4, OGO-6, and SAN MARCO-3) and 4 incoherent scatter stations (Arecibo, Jicamarca, Millstone Hill, and St Santin). The altitude covered extends from 120 km up to about 600 km over the time period 1967 to 1976. The analytical framework used in the model resembles closely the MSIS setup: time independent terms, solar flux terms, geomagnetic activity (K_p) effect, annual (semiannual) and diurnal (semidiurnal, terdiurnal) variations, longitudinal terms, the U.T. effect, and corrections compensating for deviations from diffusive equilibrium at altitudes below 200 km. The model describes quiet to medium disturbed geomagnetic conditions (K_p ? 4) at solar fluxes (10.7cm) ranging from 60 to 180 × 10^?22 Wm^?2Hz^?1. To get an impression of the accuracy presently obtained, the model is compared with MSIS, Jacchia (1977), and the models of Thuillier (T_∞ and Engebretson (N). The best agreement is found for the temperature and the constituents He, O, and N₂ with increasing deviations in the order of H, N, Ar, and O₂.     

A photochemical model of Titan's atmosphere and ionosphere

A global-mean model of coupled neutral and ion chemistry on Titan has been developed. Unlike the previous coupled models, the model involves ambipolar diffusion and escape of ions, hydrodynamic escape of light species, and calculates the H₂ and CO densities near the surface that were assigned in some previous models. We tried to reduce the numbers of species and reactions in the model and remove all species and reactions that weakly affect the observed species. Hydrocarbon chemistry is extended to C₁₂H₁₀ for neutrals and C₁₀H⁺₁₁ for ions but does not include PAHs. The model involves 415 reactions of 83 neutrals and 33 ions, effects of magnetospheric electrons, protons, and cosmic rays. UV absorption by Titan's haze was calculated using the Huygens observations and a code for the aggregate particles. Hydrocarbon, nitrile, and ion chemistries are strongly coupled on Titan, and attempt to calculate them separately (e.g., in models of ionospheric composition) may result in significant error. The model densities of various species are typically in good agreement with the observations except vertical profiles in the stratosphere that are steeper than the CIRS limb data. (A model with eddy diffusion that facilitates fitting to the CIRS limb data is considered as well.) The CO densities are supported by the O⁺ flux from Saturn's magnetosphere. The ionosphere includes a peak at 80 km formed by the cosmic rays, steplike layers at 500-700 and 700-900 km and a peak at 1060 km (SZA = 60°). Nighttime densities of major ions agree with the INMS data. Ion chemistry dominates in the production of bicyclic aromatic hydrocarbons above 600 km. The model estimates of heavy positive and negative ions are in reasonable agreement with the Cassini results. The major haze production is in the reactions C₆H + C₄H₂, C₃N + C₄H₂, and condensation of hydrocarbons below 100 km. Overall, precipitation rate of the photochemical products is equal to 4-7 kg cm⁻² Byr⁻¹ (50-90 m Byr⁻¹ while the global-mean depth of the organic sediments is ∼3 m). Escape rates of methane and hydrogen are 2.9 and 1.4 kg cm⁻² Byr⁻¹, respectively. The model does not support the low C/N ratio observed by the Huygens ACP in Titan's haze.     

Mathematical model of orbital and ground-based cross-dispersion spectrographs

We present the technique and algorithm of numerical modeling of high-resolution spectroscopic equipment. The software is implemented in C++ using nVidia CUDA technology. We report the results of currently developedmodeling of new-generation echelle spectrographs. To validate the algorithms used to construct the mathematical model, we present the results of modeling of NES spectrograph of the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. A comparison of simulated and real images of the spectra acquired with NES spectrograph demonstrates good agreement between the model constructed and experimental data.     

Oscillating peak model of basin and crater formation

A model of crater and basin formation is presented in which the interior morphology is most strongly influenced by the amount of central rebound occurring rapidly after the initial crater excavation. In large craters the rebound is so great that it has started to collapse again under its own weight, and in small basins this collapse is so rapid that a second interior depression is formed. In large basins such as Orientale, the central region is considered to have undergone a more extensive damped vertical oscillation.Field evidence, particularly stratigraphical relations in Orientale and the morphometry of central peaks and basin inner rings, strongly support this theory.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.