Wavelet modelling in support of IRI

The slant total electron content (STEC) of the ionosphere is defined as the integral of the electron density along the ray-path of the signal between the transmitter and the receiver. So-called geometry free GPS measurements provide information on the electron density, which is basically a four-dimensional function depending on spatial position and time. Since ground-based measurements are not very sensitive to the vertical structure within the atmosphere, the ionosphere is often represented by a spherical layer, where all electrons are concentrated. Then the STEC is transformed into the vertical total electron content (VTEC), which is a three-dimensional function depending on longitude, latitude and time.In our approach, we decompose an ionospheric function, i.e. the electron density or the VTEC, into a reference part computed from a given model like the International Reference Ionosphere (IRI) and an unknown correction term expanded in a multi-dimensional series in terms of localizing base functions. The corresponding series coefficients are calculable from GPS measurements applying parameter estimation procedures. Since the GPS receivers are located rather unbalanced, finer structures are modelable just in regions with a sufficient number of observation sites. Due to the localizing feature of B-spline functions we apply a tensor product spline expansion to model the correction term regionally. Furthermore, the multi-resolution representation derived from wavelet analysis allows monitoring the ionosphere at different resolutions levels. We demonstrate the advantages of this procedure by representing a simulated VTEC data set over South America.     

Analysis of the dynamic behavior of structures using the high-rate GNSS-PPP method combined with a wavelet-neural model: Numerical simulation and experimental tests

Recently, the high rate global navigation satellite system-precise point positioning (GNSS-PPP) technique has been used to detect the dynamic behavior of structures. This study aimed to increase the accuracy of the extraction oscillation properties of structural movements based on the high-rate (10?Hz) GNSS-PPP monitoring technique. A developmental model based on the combination of wavelet package transformation (WPT) de-noising and neural network prediction (NN) was proposed to improve the dynamic behavior of structures for GNSS-PPP method. A complicated numerical simulation involving highly noisy data and 13 experimental cases with different loads were utilized to confirm the efficiency of the proposed model design and the monitoring technique in detecting the dynamic behavior of structures. The results revealed that, when combined with the proposed model, GNSS-PPP method can be used to accurately detect the dynamic behavior of engineering structures as an alternative to relative GNSS method.     

Regional 4-D modeling of the ionospheric electron density from satellite data and IRI

Accurate knowledge of the electron density is the key point in correcting ionospheric delays of electromagnetic measurements and in studying ionosphere physics. During the last decade Global Navigation Satellite Systems (GNSS) have become a promising tool for monitoring ionospheric parameters such as the total electron content (TEC). In this contribution we present a four-dimensional (4-D) model of the electron density consisting of a given reference part, i.e., the International Reference Ionosphere (IRI), and an unknown correction term expanded in terms of multi-dimensional base functions. The corresponding series coefficients are calculable from the satellite measurements by applying parameter estimation procedures. Since satellite data are usually sampled between GPS satellites and ground stations, finer structures of the electron density are modelable just in regions with a sufficient number of ground stations. The proposed method is applied to simulated geometry-free GPS phase measurements. The procedure can be used, for example, to study the equatorial anomaly.     

A comprehensive study of the 2016 Mw 6.0 Italy earthquake based on high-rate (10 Hz) GPS data

The 2016 M_w 6.0 Italy earthquake is successfully recorded by the near-field 10?Hz GPS and 200?Hz Strong Motion (SM) stations, providing valuable data for this study. A comprehensive study of this earthquake is carried out based on GPS data, which contains coseismic deformations analysis, noise analysis, seismic wave picking, and magnitude determination. The noise of most GPS-derived displacement waveforms can be described as a combination of white noise, flicker noise, and random walk noise after the earthquake occurrence, and the spectral indices vary significantly for most stations, implying that the seismic signals have affected the noise characteristic of GPS-derived displacement waveforms. S-transform is employed to assess the GPS capability to detect the seismic arrival time. The SM station AMT and the GPS station AMAT are in good agreement in seismic wave picking, and the difference is only 1.2?s in the north component, suggesting that the outcome of seismic wave picking using GPS data is reliable. Then, a classic empirical formula is employed to determine the moment magnitude. A robust moment magnitude (Mw 5.90) can be estimated by the nine GPS stations with about 23.9?s. If four GPS stations near the epicenter is chosen to determine the magnitude, it only take 13.0?s to retrieve a reliable preliminary (Mw 5.82) magnitude, which is 5.4?s ahead of nine stations. In addition, Cross Wavelet Transform (XWT) is adopted to measuring the correlation and phase relationship between GPS and SM records. The result of XWT analysis indicates 10?Hz GPS is capable of capturing reliable and accurate coseismic dynamic deformations, as evidenced by the XWT-based semblance being close to 1 between GPS and SM records. The above results confirm the capability of 10?Hz GPS to capture coseismic dynamic deformations, detect seismic arrival time, and determine earthquake magnitude. Moreover, rapid magnitude determination based on 10?Hz GPS data can be regarded as an important supplement to Earthquake Early Warning (EEW).     

航天GPS接收机信号搜索捕获策略

航天GPS接收机的无辅助冷启动时间是一项重要指标,研究近地轨道应用的12通道C/A码导航型接收机减小冷启动时间的方法.分析GPS信号的多普勒频率和伪码相位搜索方法、捕获检测器及其参数选择、多普勒频率搜索步长和伪码搜索速率, 得到多普勒频率搜索步长为500?Hz,伪码搜索速率为475码元/s.研究轨道倾角、轨道高度、GPS天线仰角和轨道偏心率等因素对多普勒频率搜索范围的影响.阐述根据GPS卫星间夹角的统计信息选择合理的卫星分配方法.分析和仿真结果表明,根据GPS卫星间夹角的统计信息选择合理的卫星分配方法,可将冷启动时间减少25%~30%,影响多普勒频率搜索范围的因素按程度依次为:轨道倾角、轨道高度、GPS天线仰角和轨道偏心率,再考虑这些因素时可将冷启动时间减少25%~40%.     

基于小波变换和GM-ARMA的导弹备件消耗预测

针对导弹备件消耗呈现"小样本、非平稳"的特点, 为了克服传统预测方法依靠大样本数据进行建模的不足,提出了把基于小波变换和改进GM-ARMA的组合预测方法应用于导弹备件消耗预测的构想.在利用小波分解和其他模型建立组合模型的过程中,提出了先对小波基方程和分解层数2个特征进行参数化,再定量地对所有子模型的特征参数进行统一、综合的评估,以达到建立最佳组合模型的目的;然后对具有平稳特性的高频信息用阻尼最小二乘法优化的ARMA(Autoregressive and Moving Average)模型进行预测,对反映整体趋势体现非平稳的低频信息用背景值优化和数据变换技术改进的GM(1,1)模型进行预测.实例结果表明所提出的组合预测方法大大降低了预测误差,说明了该方法的有效性、可行性和实用性.     

小波分析在GPS卫星故障检测中的应用

目前基于扩展卡尔曼滤波的残差卡方检测法已在接收机自主进行GPS卫星故障检测方面得到广泛应用,但该方法存在依赖系统数学模型、检验延迟等问题。文章提出一种基于小波分析的GPS卫星故障检测法,利用小波分析在时频域表现出良好的细节处理特性,将GPS接收机的可测数据即伪距观测数据和位置定位数据作为处理对象,进行多尺度下的分析,通过识别异常点来判断故障的发生。仿真结果表明,该方法具有高效灵敏、简洁直观、易于工程实现等特性,有助于保证导航系统的可靠性和稳定性。     

Comparison of convergence time and positioning accuracy among BDS,GPS and BDS/GPS precise point positioning with ambiguity resolution

Precise point positioning (PPP) usually takes about 30?min to obtain centimetre-level accuracy, which greatly limits its application. To address the drawbacks of convergence speed and positioning accuracy, we develop a PPP model with integrated GPS and BDS observations. Based on the method, stations with global coverage are selected to estimate the fractional cycle bias (FCB) of GPS and BDS. The short-term and long-term time series of wide-lane (WL) FCB, and the single day change of narrow-lane (NL) FCB are analysed. It is found that the range of GPS and BDS non-GEO (IGSO and MEO) WL FCB is stable at up to a 30-day-time frame. At times frame of up to 60?days, the stability is reduced a lot. Whether for short-term or long-term, the changes in the BDS GEO WL FCB are large. Moreover, BDS FCB sometimes undergoes a sudden jump. Besides, 17 and 10 stations were used respectively to investigate the convergence speed and positioning errors with six strategies: BDS ambiguity-float PPP (Bfloat), GPS ambiguity-float PPP (Gfloat), BDS/GPS ambiguity-float PPP (BGfloat), BDS ambiguity-fixed PPP (Bfix), GPS ambiguity-fixed (Gfix), and BDS/GPS ambiguity-fixed (BGfix). The average convergence speed of the ambiguity-fixed solution is greatly improved compared with the ambiguity-float solution. In terms of the average convergence time, the Bfloat is the longest and the BGfix is the shortest among these six strategies. Whether for ambiguity-float PPP or ambiguity-fixed PPP, the convergence reduction time in three directions for the combined system is the largest compared with the single BDS. The average RMS value of the Bfix in three directions (easting (E), northing (N), and up (U)) are 2.0?cm, 1.5?cm, and 5.9?cm respectively, while those of the Gfix are 0.8?cm, 0.5?cm, and 1.7?cm. Compared with single system, the BDS/GPS combined ambiguity-fixed system (BGfix) has the fastest convergence speed and the highest accuracy, with average RMS as 0.7?cm, 0.5?cm, and 1.9?cm for the E, N, U components, respectively.     

时钟偏差辅助的GPS完整性监测算法

对伪距残差最小二乘的接收机自主完整性监测(RAIM)算法进行了分析.在此基础上,通过对接收机时钟偏差的建模,将模型预测的时钟偏差引入伪距残差最小二乘的RAIM算法中,保证了在可见星仅为4颗的情况下,仍能利用χ2检验法对全球定位系统(GPS)进行完整性监测,从而达到提高完整性监测算法有效性的目的.计算机仿真的结果显示,这种辅助方式不仅计算简单,而且有效可行.      

GPS卫星信号模拟器中频信号处理与实现

利用数字内插、数字滤波、A/D(Analog／Digital)变换等软件无线电方法,建立GPS卫星信号模拟器中频信号处理的数学模型,提出了数字IF(Intermediate Frequency)的实现方法,且在matlab中进行了中频电路建模、优化和验证,完成了从数字基带信号处理到模拟中频信号生成.电路实现时尽量降低信号处理频率,缩小高频信号处理范围.利用verilog在ISE6.3中完成了数字中频模块的设计和仿真,对仿真输出的数字序列进行FFT(Fast Fourier Transform Algorithm)频谱分析,并在FPGA(Field Programmable Gate Arrays)中实现.      

Scaling analysis and model estimation of solar corona index

A monthly average solar green coronal index time series for the period from January 1939 to December 2008 collected from NOAA (The National Oceanic and Atmospheric Administration) has been analysed in this paper in perspective of scaling analysis and modelling. Smoothed and de-noising have been done using suitable mother wavelet as a pre-requisite. The Finite Variance Scaling Method (FVSM), Higuchi method, rescaled range (R/S) and a generalized method have been applied to calculate the scaling exponents and fractal dimensions of the time series. Autocorrelation function (ACF) is used to find autoregressive (AR) process and Partial autocorrelation function (PACF) has been used to get the order of AR model. Finally a best fit model has been proposed using Yule-Walker Method with supporting results of goodness of fit and wavelet spectrum. The results reveal an anti-persistent, Short Range Dependent (SRD), self-similar property with signatures of non-causality, non-stationarity and nonlinearity in the data series. The model shows the best fit to the data under observation.     

利用GPS技术实时监测上海区域电离层变化

基于GPS技术实时监测电离层变化原理, 利用载波平滑伪距观测值建立区域电离层模型的方法, 计算了电离层延迟量和硬件延迟, 根据硬件延迟值相对稳定的特点, 采取一定时段求解出硬件延迟量, 对实时硬件延迟量进行预报, 进而实时分离GPS信号传播路径上的垂直总电子含量VTEC. 利用上海区域内的GPS网的观测数据, 建立实时上海区域电离层延迟模型, 监测上海区域的电离层变化. 数据分析结果表明, 这种方法的内符合精度优于3 TECU.      

Variations of mid-term periodicities in solar activity physical phenomena

In this work we make an analysis of significant periodicities shown by phenomena linked to solar activity such as coronal hole area, radio emission in the 10.7 cm band and sunspots. We use the wavelet method that gives information in the frequency and time domains. Of particular interest are the mid-term periodicities (1–2 yrs). Over the whole period, coronal holes and radio variations show an important annual variation and a quasi-biannual periodicity. The increase in these variations is most important around the years of maximum solar activity. When the time series are separated in low and high frequencies, the latter are modulated by the general solar cycle. Although somewhat shifted in frequency, these periodicities might well correspond with those found in cosmic ray intensity, solar magnetic flux and other terrestrial and interplanetary phenomena as a wavelet coherence analysis of these series with the solar magnetic flux reveals.     

Noise analysis of continuous GPS coordinate time series for CMONOC

The Crustal Movement Observation Network of China (CMONOC) is one of the major scientific infrastructures, mainly using Global Positioning System (GPS) measurements, to monitor crustal deformation in the Chinese mainland. In this paper, decade-long coordinate time series of 26 continuous GPS sites of CMONOC are analyzed for their noise content using maximum likelihood estimation (MLE). We study the noise properties of continuous GPS time series of CMONOC for the unfiltered, filtered solutions and also the common mode signals in terms of power law plus white noise model. In the spatial filtering, we remove for every time series a common mode error that was estimated from a modified stacking of position residuals from other sites within ∼1000 km of the selected site. We find that the common mode signal in our network has a combination of spatially correlated flicker noise and a common white noise with large spatial extent. We demonstrate that for the unfiltered solutions of CMONOC continuous GPS sites the main colored noise is a flicker process, with a mean spectral index of ∼1. For the filtered solutions, the main colored noise is a general power law process, indicating that a major number of the filtered regional solutions have a combination of noise sources or local effects. The velocity uncertainties from CMONOC continuous GPS coordinate time series may be underestimated by factors of 8–16 if a pure white noise model is assumed. In addition, using a white plus flicker noise model, the median values of velocity errors for the unfiltered solutions are 0.16 (north), 0.17 (east) and 0.58 (vertical) mm/yr, and the median values for the filtered solutions are 0.09 (north), 0.10 (east) and 0.40 (vertical) mm/yr.     

十二通道GPS信号发生器方案研制

为了测试GPS(全球定位系统)接收机的性能,需要应用GPS信号模拟器来模拟各种条件下真实的GPS信号.分析了单通道与多通道GPS信号的时域及频域特性,建立了十二通道GPS信号模拟器的数学模型.该模型应用了软件无线电的设计思想和内插理论,可以直接产生35.42MHz的中频信号,以降低硬件设计的复杂度.文中用SystemView软件的仿真结果验证了系统设计的可行性,并提出了该系统的硬件实现.      

Study of seasonal and long-term vertical deformation in Nepal based on GPS and GRACE observations

Lithospheric deformation signal can be detected by combining data from continuous global positioning system (CGPS) and satellite observations from the Gravity Recovery and Climate Experiment (GRACE). In this paper, we use 2.5- to 19-year-long time series from 35 CGPS stations to estimate vertical deformation rates in Nepal, which is located in the southern side of the Himalaya. GPS results were compared with GRACE observations. Principal component analysis was conducted to decompose the time series into three-dimensional principal components (PCs) and spatial eigenvectors. The top three high-order PCs were calculated to correct common mode errors. Both GPS and GRACE observations showed significant seasonal variations. The observed seasonal GPS vertical variations are in good agreement with those from the GRACE-derived results, particularly for changes in surface pressure, non-tidal oceanic mass loading, and hydrologic loading. The GPS-observed rates of vertical deformation obtained for the region suggest both tectonic impact and mass decrease. The rates of vertical crustal deformation were estimated by removing the GRACE-derived hydrological vertical rates from the GPS measurements. Most of the sites located in the southern part of the Main Himalayan Thrust subsided, whereas the northern part mostly showed an uplift. These results may contribute to the understanding of secular vertical crustal deformation in Nepal.     

航空发动机性能参数预测方法

航空发动机性能参数预测对于发动机的视情维修具有重要的意义.为了提高预测精度,在分析发动机性能参数数据特点的基础上,提出了一种新的应用于此领域的组合预测模型.首先利用小波变换将原始数据分解为不同尺度上的几组子序列,根据各子序列的特点分别选用自回归滑动平均(ARMA,Autoregressive Moving Average)模型或求和自回归滑动平均(ARIMA,Autoregressive Integrated Moving Average)模型进行预测,然后将所有预测结果合成,得到最终预测结果.通过仿真实验,验证了该组合模型提高短期和中长期预测精度的有效性,并分析了小波分解层数对于预测精度的影响.      

应用空间技术 GPS 监测地震

空间定位技术GPS 可以达到很高的相对定位精度(10~(-6)～10~(-8)),是监测地壳运动、进行地震预报的一种新手段。中国华北是一个地震活跃地区。应用GPS 技术在华北布设了一个地震监测网,经过精心观测、优化设计和严密平差,获得了高精度的第一期成果。华北GPS 网的建立将为大震预测和地球科学各领域的研究提供重要的科学依据。     

时间序列法在临近空间大气风场预报中的应用

受多种因素影响，临近空间大气环境要素复杂多变，预报难度很大.本文采用时间序列法中的自回归滑动平均（ARMA）模型对临近空间大气风场开展统计预报方法研究，基于廊坊（39.4°N，116.7°W）中频雷达在88km高度的大气纬向风数据开展预报试验.本次预报试验的样本数据为2015年9月24日至10月24日风场数据，利用过去7天数据对未来第8天风场数据进行预报.试验结果显示，ARMA模型对临近空间大气风场预报有一定的适用性.当风场变化规律性较强，即样本数据风场呈现出比较显著的24h周期性变化时，ARMA模型预报效果较好；当风场发生突变时，预报效果变差.与实测数据的对比结果表明，ARMA模型预报结果的误差在9~27m·s-1，预报效果优于同阶自回归（AR）模型，略优于高阶AR模型.      

Analysis of the turbulence observed in the outer cusp turbulent boundary layer

One of the prominent features of the cusp Turbulent Boundary Layer (TBL) is a persistent low frequency electromagnetic turbulence that extends from <1Hz up to the electron cyclotron frequency, accompanied by what appears to be purely electrostatic noise above this frequency range. The Plasma Wave Instrument onboard Polar obtained plasma wave measurements in the cusp TBL in the form of waveform captures simultaneously from 6 different sensors (3 each orthogonal electric and magnetic) in the frequency range 1 Hz up to 25 kHz. This allowed us to directly calculate the phase velocity from the measured ratio of |dE| to |dB| and compare it to theoretical values for various modes. Using this technique, we have gained some insight into the mode of the electromagnetic turbulence that extends in frequency from 1 Hz up to the electron cyclotron frequency (several hundred Hz to a few kHz) in the TBL. The whistler and kinetic Alfvén wave modes are discussed as the possible modes of this turbulence. By analyzing the high time resolution waveforms, we isolate and identify some of these modes. The electrostatic turbulence above the electron cyclotron frequency is associated with pulses and quasi-sinusoidal waveforms observed in the measured time series. These do not fit any known mode, although work is continuing in this area to show that some of them may be associated with electron holes or with downshifted Langmuir waves produced through a two-stream instability.