Influence of higher-order ionospheric delay correction on GPS precise orbit determination and precise positioning

At present, Global Navigation Satellite Systems（GNSS） users usually eliminate the influence of ionospheric delay of the first order items by dual-frequency ionosphere-free combination. But there is still residual ionospheric delay error of higher order term. The influence of the higher-order ionospheric corrections on both GPS precision orbit determination and static Precise Point Positioning（PPP） are studied in this paper. The influence of higher-order corrections on GPS precision orbit determination, GPS observations and static PPP are analyzed by neglecting or considering the higher-order ionospheric corrections by using a globally distributed network which is composed of International GNSS Service（IGS） tracking stations. Numerical experimental results show that, the root mean square（RMS） in three dimensions of satellite orbit is 36.6 mme35.5 mm. The maximal second-order ionospheric correction is 9 cm, and the maximal third-order ionospheric correction is 1 cm. Higher-order corrections are influenced by latitude and station distribution. PPP is within 3 mm in the directions of east and up. Furthermore, the impact is mainly visible in the direction of north, showing a southward migration trend, especially at the lower latitudes where the influence value is likely to be bigger than 3 mm.

Sub-ODE's New Solutions and Their Applications to Two Nonlinear Partial Differential Equations with Higher-Order Nonlinear Terms

In the present paper, with the aid of symbolic computation, families of new nontrivial solutions of the first-order sub-ODE F12 = AF2 ＋ BF2＋p ＋ CF2＋2p （where F1= dF/dε, p 〉 0） are obtained. To our best knowledge, these nontrivial solutions have not been found in [X.Z. Li and M.L. Wang, Phys. Lett. A 361 （2007） 115] and IS. Zhang, W. Wang, and J.L. Tong, Phys. Lett. A 372 （2008） 3808] and other existent papers until now. Using these nontrivial solutions, the sub-ODE method is described to construct several kinds of exact travelling wave solutions for the generalized KdV-mKdV equation with higher-order nonlinear terms and the generalized ZK equation with higher-order nonlinear terms. By means of this method, many other physically important nonlinear partial differential equations with nonlinear terms of any order can be investigated and new nontrivial solutions can be explicitly obtained with the help of symbolic computation system Maple or Mathematics.

Application of Grey Theory to Ionospheric Short-term Forecasting

By analysis of historical data of the ionosphere, it is suggested to apply grey theory to ionospheric short-term forecasting, grey range information entropy is defined to determine the optimum grey length of the sample sequence, the prediction model based on residual error is constructed, and the observation data of multiple ionospheric observation stations in China are adopted for test. The prediction result indicates that the average grey range information entropy calculation results reflect the cyclical effects of solar rotation, precision of the forecasting method in high latitudes is higher than low latitudes, and its error is large relatively in more intense solar activity season, the effect of forecasting 1 day in advance of average relative residuals are less than 1 MHz, the average precision is more than 90%. It provides a new way of thinking for the ionospheric foF2 short-term forecast in the future.

Application of Improved Analysis of Variance to Ionospheric TEC Short-Term Forecast

An improved superposition analysis of periodical wave variance is used for short-term forecast of the ionosphere TEC in this study. Using the ionospheric TEC data provided by IGS as the real value, the forecasting precision of this me-thod at different locations in China with 40 days data is evaluated. The result shows that the improved method has a better forecasting precision which could reach 1.1 TECU. But the forecasting precision still relates to geographical position, it is proportional to longitude and inversely proportional to latitude. Compared with the current-used methods, the improved method has many advantages as higher precision, using fewer parameters and easier to calculate. So, it applied to ionosphere short-term prediction in China very well.

Hausdorff Dimension and Fractal Dimension of the Global Attractor for the Higher-Order Coupled Kirchhoff-Type Equations

This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausdorff dimension and Fractal dimension of the global attractor.

基于注意力机制LSTM的电离层TEC预测

电离层总电子含量(Total Electron Content,TEC)的监测与预报是空间环境研究的重要内容,对卫星通讯和导航定位等有重要意义.TEC值影响因素较多,很难确定精确物理模型来对其进行预测.本文设计了基于注意力机制的LSTM模型(Att-LSTM),采用过去24小时TEC观测数据对未来TEC进行预测.选择北半球东经100°上,每2.5°纬度选择一个位置,共计36个位置来验证本文提出模型的性能,并与主流的深度学习模型如DNN、RNN、LSTM进行对比实验.取得了如下成果:(1)在选定的36个地区未来2小时单点预测上,基于本文的Att-LSTM模型的TEC预测性能明显优于其他对比模型;(2)讨论了纬度对Att-LSTM预测未来2小时TEC值时性能的影响,发现在北纬0°到60°之间,Att-LSTM预测性能随着纬度的升高而略有降低,在北纬62.5°~87.5°之间,模型预测性能出现扰动,预测效果略差;(3)讨论了磁暴期和磁静期模型的预测性能,发现无论是磁暴期还是磁静期,本文模型预测性能均较好;(4)还讨论了对未来多时点预测效果,实验结果表明,本文所提出的模型对未来2、4个小时的预测拟合度R-Square均超过0.95,预测结果比较可靠,对未来6、8、10个小时预测拟合度最高为0.7934,预测拟合度R-Square下降迅速,预测结果不可靠.

利用VMD-SSA-LSTM的电离层总电子含量预报研究

针对太阳活动影响下机器学习模型对电离层总电子含量(TEC)短期预报精度不高的问题,本文提出了一种基于变分模态分解(VMD)、麻雀搜索算法(SSA)、长短期记忆神经网络(LSTM)的组合模型(VMD-SSA-LSTM),以期提高TEC短期预报精度。利用VMD算法对不同时期太阳活动程度影响下的东、西半球TEC格网点数据分解,利用SSA优化LSTM模型,将分解的TEC样本分量及模型最优初始权值和阈值输入到LSTM模型中,将分量预测序列合并重构,得到电离层TEC预测值。实验表明:VMD-SSA-LSTM组合模型在东、西半球太阳活动强烈、适中、较弱时期的均方根误差分别为0.77、0.56、0.69;0.92、0.76、0.73个TECu,平均绝对误差平均值分别为0.69、0.47、0.56;0.79、0.65、0.58个TECu,平均相对精度分别达到94%、94%、93%;93%、91%、91%以上,残差绝对值分布在0~1个TECu的比例均值分别为75.56%、96.11%、85%;74.44%、80.55%、78.33%,较VMD-LSTM、LSTM两种模型预报精度有显著提升。

2015年3月特大磁暴期间中国区域电离层TEC NeuralProphet预报模型研究

延迟是全球卫星导航定位中重要的误差源之一,提高电离层TEC建模和预报精度对改善卫星导航定位精度至关重要.本文构建了以太阳辐射通量指数F_(10.7)、地磁活动指数Dst、地理坐标和中国科学院(Chinese Academy of Sciences,CAS)GIM数据为输入参数的NeuralProphet神经网络模型(NP模型),实现在2015年3月特大磁暴期中国区域电离层TEC短期预报.为验证NP模型的预报精度,本文同时构建了长短期记忆神经网络(Long Short-term Memory Neural Network,LSTM)模型进行对比分析.结果统计分析表明,NP模型在磁暴期(2015年DOY076-078)TEC预报值RMSE和RD分别为0.83 TECU和3.13%,绝对和相对精度较LSTM模型分别提高1.49 TECU和10.25%;且NP模型RMSE优于1.5 TECU的比例达97.24%,远高于LSTM模型.NP模型预报值与CAS具有较好一致性和无偏性,偏差均值仅为-0.01 TECU,而LSTM模型预报值的均值偏大,偏差均值为1.49 TECU.从低纬到中纬度的三个纬度带内,NP模型RMSE分别为1.12、0.83和0.44 TECU,精度比LSTM模型提高1.94、1.56和1.23 TECU.整体上,在磁暴期NP模型预报性能明显优于LSTM模型,能够精细描述中国区域电离层TEC时空变化.

利用卷积长短期记忆网络预测全球电离层Ne

由于电离层电子密度随时间变化,且空间分布不均匀,对不同频段的无线电波产生延缓和折射,因此电离层电子密度变化是影响短波通信、卫星通信、全球导航卫星系统和其他空间通信质量的一个主要因素,本文对全球电离层电子密度(Number of electron,Ne)的预测工作对短波通信设备三维射线实时追踪定位提供必要条件。本文采用国际电离层参考模型提供的2016年电离层Ne数据,根据数据的三维空间时间序列特征,搭建了自编码器和卷积长短期记忆(Convolutional Long Short-Term Memory Network,Conv LSTM)网络组成的网络结构,在不引入地球自转周期之外任何先验知识的条件下,对Ne数据进行深度学习并实现预测,首先通过实验对比了SGD、Adagrad、Adadelta、Adam、Adamax和Nadam六种优化算法的性能,又对比了三种预测策略的均方根误差(Root Mean Square Error, RMSE),1h-to-1h预测策略的全球平均RMSE为1.0 NEU(最大值的0.4%),1h-to-24h和24h-to-24h预测策略的全球平均RMSE为6.3 NEU(2.6%)。由实验结果得出以下结论,一是Nadam优化算法更适合电离层Ne的深度学习,二是1h预测策略的性能与之前类似的电离层TEC预测工作(RMSE高于1.5 TECU,最大值的1%)相比有竞争力,但预测时间太短且对数据的实时性要求较高,三是两种24h预测策略虽能实现长期预测但性能不理想,要实现三维空间时间序列的长期高精度预测需要进一步改善神经网络、模型结构和预测策略。

融合电离层参数相似特征的f_(0)F_(2)参数深度学习预测方法

电离层临界频率f_(0)F_(2)参数是重要的电离层参数之一,开展f_(0)F_(2)参数预测具有重要的研究意义和应用价值.提出了一种融合f_(0)F_(2)参数变化特性的深度学习预测方法,采用双向长短时记忆神经网络(BiLSTM)和电离层参数相似特征相结合的模型实现电离层临界频率f_(0)F_(2)参数提前24 h预测.结果表明,BiLSTM结合电离层参数相似特征模型预测f_(0)F_(2)参数的平均相对误差在8%~10%.对不同纬度的探测站的f_(0)F_(2)参数预测结果表明,随着纬度降低,预测难度和误差都会增大,预测精度降低.对地磁暴期间的f_(0)F_(2)参数预测结果分析发现,地磁暴期间的预测效果会受到一定程度的干扰,预测误差增大.在地磁暴期间,相比长短时记忆神经网络(LSTM)模型和BiL-STM模型,BiLSTM结合电离层参数相似特征模型对于f_(0)F_(2)参数的预测效果更优.

预测全球电离层的多通道ConvLSTM模型

为了进一步提升导航高精度实时定位的精度,提出一种预测全球电离层的多通道ConvLSTM模型:根据全球电离层地图(GIM)时空变化非线性的特征以及电离层总电子含量(TEC)与太阳活动和地磁活动的相关性,提出以行星际三小时磁情指数(Kp)、太阳黑子数(SSN)以及TEC作为多通道输入的基于编码器-解码器的卷积-长短期记忆神经网络(ConvLSTM)模型;然后将2018-2020年的电离层TEC及相关数据作为数据集,提前1 d预测GIM。结果表明,基于多通道输入的模型在预测任务上具有显著优势,且不同输入的ConvLSTM模型皆优于欧洲定轨中心1 d预报GIM(C1PG)模型;在地磁平静期和磁暴期,多通道输入的模型表现良好。

基于OARO-GRU网络的高频地波雷达电离层杂波短期预测

电离层杂波的精确预测对提升高频地波雷达的目标探测性能具有重要推动作用。为此,提出了一种基于改进人工兔子算法优化门控循环单元(Opposite Artificial Rabbits Optimization optimized Gated Recurrent Unit,OARO-GRU)网络的电离层杂波短期预测模型。首先,依据高频地波雷达接收到的电离层杂波具有混沌特性这一先验知识,通过相空间重构技术构造GRU网络的输入和输出样本集;然后,融入反向学习和柯西变异两种改进策略用于改善标准ARO的寻优能力,并将其用于执行GRU网络的包含隐层节点个数、初始学习速率和最大迭代次数在内的三个超参数值的优选;最后,重新训练优化后的GRU网络,输入测试样本集进行测试,并依据给定的评价指标评估模型。实测结果表明:相较于其他7种对照模型,所提出的OARO-GRU网络预测模型在预测精度和可靠性上均具有明显的优越性,为有效改善高频地波雷达的目标探测性能提供了一种新的思路与方法。

组合式深度学习的电离层TEC短期预报模型

针对磁暴期间电离层总电子含量TEC异常扰动导致预报精度大幅降低的问题,提出基于强化学习的Q学习算法,对遗传算法优化BP神经网络模型和长短时记忆网络模型进行优化组合,进而建立了一种组合式深度学习的电离层TEC预报模型。分别利用组合模型、两个单一模型对CODE提供的中国地区TEC数据进行3 d预报。结果表明,在不同磁暴等级(强、中、弱、无)下,组合模型预报的平均相对精度分别为95.9%、95.7%、92.6%和95.3%,较两个单一模型平均提高了约6%;其中预报残差小于1 TECu的占比分别达到60%、59%、76%和98%,相比两个单一模型平均提升了约27%。

基于SSA-PSO-LSTM模型的电离层TEC预报

受多种因素影响,电离层电子总含量(TEC)时间序列具有非线性、非平稳性特征,为提升长短期记忆(LSTM)神经网络模型在电离层TEC预报中的精度,本文在该神经网络模型的基础上,引入奇异谱分析(SSA)与粒子群优化(PSO)算法,构建了新的SSA-PSO-LSTM模型。一方面,利用了SSA对TEC时间序列进行数据预处理;另一方面,利用粒子群优化算法改进LSTM神经网络模型参数。选用欧洲地球参考框架(EUREF)提供的格网点电离层TEC时间序列数据进行实验,实验结果表明,在磁平静期与磁暴期,该组合模型的TEC预报结果均方根误差分别为0.28个总电子含量单位(TECu)、0.83个TECu,平均相对精度分别为96.35%、91.33%,均优于对比模型,验证了本文提出的组合预报模型的有效性与优越性。平均相对精度分别为96.35%、91.33%,均优于对比模型,验证了本文提出的组合预报模型的有效性与优越性。

Solitons and Other Solutions for the Generalized KdV-mKdV Equation with Higher-order Nonlinear Terms

The generalized sub-ODE method, the rational （G＇/G）-expansion method, the exp-function method and the sine-cosine method are applied for constructing many traveling wave solutions of nonlinear partial differential equations （PDEs）. Some illustrative equations are investigated by these methods and many hyperbolic, trigonometric and rational function solutions are found. We apply these methods to obtain the exact solutions for the generalized KdV-mKdV （GKdV-mKdV） equation with higherorder nonlinear terms. The obtained results confirm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear partial differential equations in mathematical physics. We compare between the results yielding from these methods. Also, a comparison between our new results in this paper and the well-known results are given.

A Software Package Generating Long Term and Near Real Time Predictions of the Critical Frequencies of the F2 Layer over Europe and Its Applications

Long term prediction and near real time (nowcasting) maps of the critical frequency of the F2 layer (foF2), over the geographic area extending in latitude from 34°N to 60°N and in longitude from -5°W to 40°E, have been provided since 2006 by the DIAS (European Digital Upper Atmosphere Server) system. This work describes the software package PRODUCTION_DATABASE_foF2 & Extract_Real_Time_Grid_foF2 constituted by two original software packages called PRODUCTION_ DATABASE_foF2 and Extract_Real_Time_Grid_foF2 which have been developed in the framework of the ESA SSA Programme P2-SWE-1, in order to provide numerical grids of foF2 prediction on a mapping area more extended than that offered by the DIAS both in latitude (from 34°N to 80°N) and in longitude (from -10°W to 40°E). PRODUCTION_DATABASE_foF2, by means of the CCIR and SIRM models, provides a database of long term predictions of foF2 for all the months and the solar activities characterized by the 12-month smoothed mean value of the monthly sunspots number (R12) ranged between -50 and 150 with step = 1. On the basis of two effective sunspots numbers, R12eff_Northern and R12eff_Southern, which are calculated each hour using the foF2 autoscaled values provided by some reference stations, Extract_Real_Time_Grid_foF2 extracts from the database of long term predictions of foF2 the numerical grids representing the near real time ionospheric conditions for the hour and month under consideration. Some applications of PRODUCTION_DATABASE_foF2 and Extract_Real_Time_Grid_foF2 in terms of long term forecast and nowcasting maps of foF2 are shown and their usefulness is discussed.

基于长短期记忆网络的扩展F事件短临预测

考虑到我国区域电离层扩展F发生的物理机制和相关因素以及观测数据的可获取性,利用适宜于时间序列预测的长短期记忆网络建立了我国不同区域电离层扩展F事件的预测模型,对未来3 h是否会发生扩展F事件进行预测.以处于我国典型纬度地区的满洲里、北京、海口站为例,利用2015和2016年测试数据集对模型预测精度进行了检验,满洲里、北京、海口站平均准确率分别为92.4%、95.3%、96.0%,平均精确率分别为75.0%、61.2%、62.6%,平均召回率分别为73.0%、50.6%、31.5%.由此可见:在某些情况下,比如在低纬度地区的海口站,模型的召回率较低;除此之外,所建立的扩展F模型在多数情况下具有较高的预测能力.

Long-Term Changes in Night Time Airglow Emission at 557.7 nm over Mid Latitude Japanese Station i.e., Kiso (35.79oN, 137.63oE)

The present study describes the long-term changes in Pre-midnight and Midnight airglow intensities of 557.7 nm during the period 1979-1994 over mid latitude Japanese station i.e., Kiso, Tokyo Astronomical Observatory, University of Tokyo (35.79oN, 137.63oE;1130 m), Japan. It has observed that there is a positive increasing decadal change in Midnight and Pre-midnight mesospheric airglow intensity of the range 25 - 88 R. This range is the order of 10 to 30% of the observed MARV and average night airglow intensity of 250 R. Besides this long-term trend, inter-annual monthly variation is also seen from fluctuation of yearly variation of deviation values from MARV to particular average monthly values. The present observations about the positive decadal change in night time mesospheric airglow intensity has been further linked to the reduction of mesospheric electron densities and temperature or shrinking and cooling of the lower ionosphere as established from the long-term behavior of mesospheric parameters such as a negative decadal change in thermal structure, electron density, neutral density parameters as per studies reported by other researchers.

一种组合模型的电离层总电子含量预报方法

针对电离层总电子含量(TEC)的非线性、非平稳等多种因素影响会导致全球导航定位服务数据的高噪声问题,提出一种小波分解、长短期记忆(LSTM)网络模型、埃尔曼(Elman)神经网络模型组合的方法:采用国际全球卫星导航系统服务组织(IGS)中心提供的不同纬度、不同时间段的TEC格网点数据,利用db4小波分解对前20 d的TEC样本序列进行分解得到高频信息与低频信息;再分别利用LSTM模型和Elman模型对高频信息和低频信息进行预报;然后将2种模型的预报值进行重构;最后利用滑动窗口预测连续多个2 d数据进行分析研究。实验结果表明,组合模型在春、夏、秋、冬不同季节的电离层预报的均方根误差分别为0.85、0.68、0.84和0.84个总电子含量单位(TECu),平均绝对值残差分别为0.66、0.55、0.60和0.69个TECu,平均相对精度分别为97.1%、97.1%、96.7%、95.9%,与2种单一模型相比可有大幅度提升。

一种改进的单站TEC快速估计与短期预报方法

为解决电离层产品大多基于格网形式及传统预报模型精度较低等问题,采用加权函数方法计算单站TEC,并提出一种基于滑动窗口改进的MEA-BP(MW-MEA-BP)预报模型。选取不同纬度的IGS测站,分别对太阳活动低年和太阳活动高年的观测数据进行分析验证。结果表明,本文单站TEC估计方法快速可靠,在短期预报方面,MEA-BP模型较BP模型有明显改进。当TEC变化剧烈时,本文MW-MEA-BP模型的预报精度较BP模型提高71.8%~90.6%,较MEA-BP模型提高13.9%~54.4%。本文研究结果可为定位用户提供先验准确的电离层信息。