Analysis of local ionospheric time varying characteristics with singular value decomposition

In this paper, a time series from 1999 to 2007 of absolute total electron content (TEC) values has been computed and analyzed using singular value decomposition (SVD). The data set has been computed using a Kalman Filter and is based on dual frequency GPS data from three reference stations in Denmark located in the midlatitude region. The station separation between the three stations is 132–208 km (the time series of the TEC can be freely downloaded at ). For each year, a SVD has been performed on the TEC time series in order to identify the three time varying (daily, yearly, and 11 yearly) characteristics of the ionosphere. The applied SVD analysis provides a new method for separating the daily from the yearly components. The first singular value is very dominant (approximately six times larger than the second singular value), and this singular value corresponds clearly to the variation of the daily cycle over the year. The second singular value corresponds to variations of the width of the daily peak over the year, and the third singular value shows a clear yearly variation of the daily signal with peaks around the equinoxes. The singular values for each year show a very strong correlation with the sunspot number for all the singular values. The correlation coefficients for the first 5 sets of singular values are all above 0.96. Based on the SVD analysis yearly models of the TEC in the ionosphere can be recomposed and illustrate the three time varying characteristics of the ionosphere very clearly. By prediction of the yearly mean sunspot number, future yearly models can also be predicted. These can serve as a priori information for a real time space weather service providing information of the current status of the ionosphere. They will improve the Kalman filter processing making it more robust, but can also be used as starting values in the initialization phase in case of gaps in the data stream. Furthermore, the models can be used to detect variations from the normal local ionospheric activity.     

中国大陆GPS基准站的时间序列特征

利用1999年3月至2002年3月期间“中国地壳运动观测网络”25个GPS基准站与周边国家IGS站的观测资料，进行了时间序列分析研究，并对提高GPS基准站的观测精度进行了探讨。结果表明，GPS基准站的时间序列具有一定的周期性，高程分量的周期性最为明显，GPS点位高程时间序列拟舍曲线的波峰和波谷出现的时间表现为区域性的不同。     

利用GPS和GRACE研究澳大利亚地壳垂向季节性变化

为探究重力场恢复与气候实验(gravity recovery and climate experiment,GRACE)卫星与全球定位系统(global positioning system,GPS)两种独立技术获取的因陆地水储量变化引起的地壳垂向季节性位移的一致性,选取澳大利亚27个GPS站点5～10 a的高程时间序...     

Annual deformation signals from homogeneously reprocessed VLBI and GPS height time series

The first part of this paper compares homogeneously reprocessed Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS) long-term height series from 1994 to 2007. The data analysis used fully adapted state-of-the-art models (like VMF1 and a priori zenith delays from ECMWF) for the GPS and VLBI processing. The series are compared in terms of long-term non-linear behaviour, harmonic and mean annual signals (not necessarily of harmonic nature). The similarity between both techniques is very good (especially the mean annual signals), which is assumed to be due to the adapted models and consistent reprocessing of both series. As two almost independent observing techniques see the same annually recurring signals at almost all co-located sites, we expect a good geophysical interpretability as integral vertical deformation. For the second part of this paper, the height time series of 161 suitable GPS sites (of the same solution as before) are used to determine a harmonic and a mean annual signal for each of them. Comparing the annual signals for this big dataset visually to GRACE-determined load deformations described in other publications, we find good agreement. This puts emphasis to the assumption that our height data have a lot of potential to be interpreted as geophysical signals. Out of these 161, 131 are grouped to 55 clusters, if at least two nearby (some thousand kilometres) sites show similar mean annual signals, which are thus confirmed to be real regional deformation, not local or technical artefacts. These 55 signals are presented on a “world map” of regional average mean annual height signals, as easy-to-handle tool to validate geophysical models. The data of these measured regional mean annual signals can be downloaded from a web-page for numerical analysis.     

CATS: GPS coordinate time series analysis software

Over the last 10 years, several papers have established that daily estimates of GPS coordinates are temporally correlated and it is therefore incorrect to assume that the observations are independent when estimating parameters from them. A direct consequence of this assumption is the over-optimistic estimation of the parameter uncertainties. Perhaps the perceived computational burden or the lack of suitable software for time series analysis has resulted in many heuristic methods being proposed in the scientific literature for estimating these uncertainties. We present a standalone C program, CATS, developed to study and compare stochastic noise processes in continuous GPS coordinate time series and, as a consequence, assign realistic uncertainties to parameters derived from them. The name originally stood for Create and Analyze Time Series. Although the name has survived, the creation aspect of the software has, after several versions, been abandoned. The implementation of the method is briefly described to aid understanding and an example of typical input, usage, output and the available stochastic noise models are given.     

Trajectory models and reference frames for crustal motion geodesy

We sketch the evolution of station trajectory models used in crustal motion geodesy over the last several decades, and describe some recent generalizations of these models that allow geodesists and geophysicists to parameterize accelerating patterns of displacement in general, and postseismic transient deformation in particular. Modern trajectory models are composed of three sub-models that represent secular trends, annual oscillations, and instantaneous jumps in coordinate time series. Traditionally the trend model invoked constant station velocity. This can be generalized by assuming that position is a polynomial function of time. The trajectory model can also be augmented as needed, by including one or more logarithmic transients in order to account for typical multi-year patterns of postseismic transient motion. Many geodetic and geophysical research groups are using general classes of trajectory model to characterize their crustal displacement time series, but few if any of them are using these trajectory models to define and realize the terrestrial reference frames (RFs) in which their time series are expressed. We describe a global GPS reanalysis program in which we use two general classes of trajectory model, tuned on a station by station basis. We define the network trajectory model as the set of station trajectory models encompassing every station in the network. We use the network trajectory model from the each global analysis to assign prior position estimates for the next round of GPS data processing. We allow our daily orbital solutions to relax so as to maintain their consistency with the network polyhedron. After several iterations we produce GPS time series expressed in a RF similar to, but not identical with   ITRF2008. We find that each iteration produces an improvement in the daily repeatability of our global time series and in the predictive power of our trajectory models.     

Differencing Reveals Hidden Changes in Baseline Length Time-series

In order to make successful earthquake predictions, detection and monitoring of baseline changes are important for investigating their origins, including precursory crustal deformations in tectonically active areas. In this study, differencing two baselines that run approximately parallel to each other and normal to the expected crustal deformations, and that share a station is proposed for analysis. Differencing reduces common systematic baseline errors, thereby enabling detection of subtle transient systematic changes in the baseline time-series that are otherwise buried in the measurement noise. Mean shift analysis, a well-known statistical technique to determine hether the mean of a stochastic process has shifted using cumulative sum charts, can then be used to locate the change points in the time-series. The application of this method to the differences of concurrently observed very long baseline interferometry (VLBI) and global positioning system (GPS) baselines in the Japanese Keystone project, where periodic and persistent baseline changes are removed, revealed transient variations in the baseline lengths several months prior to the seismic activity in the Izu Islands that started on June 26, 2000. Reproduction of the results using GPS and VLBI, two alternative baseline measurement techniques, validated the accuracy of the proposed approach for detecting previously hidden transient changes in the baseline lengths.     

Using GPS for monitoring tall-building response to wind loading: filtering of abrupt changes and low-frequency noise,variography and spectral analysis of displacements

We compare two methods for monitoring the dynamic response of tall buildings to wind loading, using data from a 280-m-high building in Singapore. The first method is based on accelerometer measurements. The second method is based on the Global Positioning System (GPS) technology. The GPS can in principle detect absolute displacements with lower frequencies than the accelerometers, but the GPS positioning signal is usually very noisy. We propose a systematic procedure for modeling the stochastic and systematic components of the GPS displacement time series and for extracting the weak structural response from the dominant noise. The spectrum of the building response obtained from the filtered GPS data exhibits a dominant peak at 0.19 Hz. The frequency of the peak coincides with that obtained from the analysis of the accelerometer data. The proposed analysis of the GPS signal provides a method for cross-validating the GPS and accelerometer measurements, and shows that “educated” filtering of the GPS signal can reveal essential features of the building’s response to wind loading.     

Comparative analysis of different environmental loading methods and their impacts on the GPS height time series

Three different environmental loading methods are used to estimate surface displacements and correct non-linear variations in a set of GPS weekly height time series. Loading data are provided by (1) Global Geophysical Fluid Center (GGFC), (2) Loading Model of Quasi-Observation Combination Analysis software (QLM) and (3) our own daily loading time series (we call it OMD for optimum model data). We find that OMD has the smallest scatter in height across the selected 233 globally distributed GPS reference stations, GGFC has the next smallest variability, and QLM has the largest scatter. By removing the load-induced height changes from the GPS height time series, we are able to reduce the scatter on 74, 64 and 41 % of the stations using the OMD models, the GGFC model and QLM model respectively. We demonstrate that the discrepancy between the center of earth (CE) and the center of figure (CF) reference frames can be ignored. The most important differences between the predicted models are caused by (1) differences in the hydrology data from the National Center for Atmospheric Research (NCEP) vs. those from the Global Land Data Assimilation System (GLDAS), (2) grid interpolation, and (3) whether the topographic effect is removed or not. Both QLM and GGFC are extremely convenient tools for non-specialists to use to calculate loading effects. Due to the limitation of NCEP reanalysis hydrology data compared with the GLDAS model, the GGFC dataset is much more suitable than QLM for applying environmental loading corrections to GPS height time series. However, loading results for Greenland from GGFC should be discarded since hydrology data from GLDAS in this region are not accurate. The QLM model is equivalent to OMD in Greenland and, hence, could be used as a complement to the GGFC product to model the load in this region. We find that the predicted loading from all three models cannot reduce the scatter of the height coordinate for some stations in Europe.     

Stochastic assessment of GPS carrier phase measurements for precise static relative positioning

 Global positioning system (GPS) carrier phase measurements are used in all precise static relative positioning applications. The GPS carrier phase measurements are generally processed using the least-squares method, for which both functional and stochastic models need to be carefully defined. Whilst the functional model for precise GPS positioning is well documented in the literature, realistic stochastic modelling for the GPS carrier phase measurements is still both a controversial topic and a difficult task to accomplish in practice. The common practice of assuming that the raw GPS measurements are statistically independent in space and time, and have the same accuracy, is certainly not realistic. Any mis-specification in the stochastic model will inevitably lead to unreliable positioning results. A stochastic assessment procedure has been developed to take into account the heteroscedastic, space- and time-correlated error structure of the GPS measurements. Test results indicate that the reliability of the estimated positioning results is improved by applying the developed stochastic assessment procedure. In addition, the quality of ambiguity resolution can be more realistically evaluated. Received: 13 February 2001 / Accepted: 3 September 2001     

Performance analysis of integrated GPS/GLONASS carrier phase-based positioning

Due to the different signal frequencies for the GLONASS satellites, the commonly-used double-differencing procedure for carrier phase data processing can not be implemented in its straightforward form, as in the case of GPS. In this paper a novel data processing strategy, involving a three-step procedure, for integrated GPS/GLONASS positioning is proposed. The first is pseudo-range-based positioning, that uses double-differenced (DD) GPS pseudo-range and single-differenced (SD) GLONASS pseudo-range measurements to derive the initial position and receiver clock bias. The second is forming DD measurements (expressed in cycles) in order to estimate the ambiguities, by using the receiver clock bias estimated in the above step. The third is to form DD measurements (expressed in metric units) with the unknown SD integer ambiguity for the GLONASS reference satellite as the only parameter (which is constant before a cycle slip occurs for this satellite). A real-time stochastic model estimated by residual series over previous epochs is proposed for integrated GPS/GLONASS carrier phase and pseudo-range data processing. Other associated issues, such as cycle slip detection, validation criteria and adaptive procedure(s) for ambiguity resolution, is also discussed. The performance of this data processing strategy will be demonstrated through case study examples of rapid static positioning and kinematic positioning. From four experiments carried out to date, the results indicate that rapid static positioning requires 1 minute of single frequency GPS/GLONASS data for 100% positioning success rate. The single epoch positioning solution for kinematic positioning can achieve 94.6% success rate over short baselines (<6 km).     

PERFORMANCE ANALYSIS OF INTEGRATED GPS/GLONASS CARRIER PHASE-BASED POSITIONING

1　ＩｎｔｒｏｄｕｃｔｉｏｎＲｅａｌ＿ｔｉｍｅｋｉｎｅｍａｔｉｃＧＰＳｐｒｅｃｉｓｅｐｏｓｉｔｉｏｎｉｎｇｈａｓｂｅｅｎｐｌａｙｉｎｇａｎｉｎｃｒｅａｓｉｎｇｒｏｌｅｉｎｂｏｔｈｓｕｒｖｅｙｉｎｇａｎｄｎａｖｉｇａｔｉｏｎ ,ａｎｄｈａｓｂｅｃｏｍｅａｎｅｓｓｅｎｔｉａｌｔｏｏｌｆｏｒｐｒｅｃｉｓｅｒｅｌａｔｉｖｅｐｏｓｉｔｉｏｎｉｎｇ .Ｈｏｗｅｖｅｒ,ｒｅｌｉａｂｌｅａｎｄｃｏｒｒｅｃｔａｍｂｉｇｕｉｔｙｒｅｓｏｌｕｔｉｏｎｄｅｐｅｎｄｓｏｎｏｂｓｅｒｖａ ｔｉｏｎｓｕｐｏｎａｌａｒｇｅｎｕｍｂｅ…     

On the significance of periodic signals in noise analysis of GPS station coordinates time series

Each of the GPS-derived time series consists of the deterministic (functional) and stochastic part. We propose that the deterministic part includes all periodicities from 1st to 9th harmonics of residual Chandler, tropical and draconitic periods and compare it with commonly used calculations of the annual and semi-annual tropical curve. Then, we address the issues of whether all residual periodicities, as proposed here, need to be taken into consideration when performing noise analysis. We use the position time series from 180 International GNSS Service stations obtained at the Jet Propulsion Laboratory using the GIPSY-OASIS software in a Precise Point Positioning mode. The longest series has 22.1 years of GPS daily solutions. The spectral indices range from –0.12 to –0.92, while the median values of “global” spectral indices are equal to: –0.41 ± 0.15, –0.38 ± 0.12 and –0.33 ± 0.18 for North, East and Up components, respectively. All non-modelled geophysical processes or non-included artificial effects in time series lead to an underestimation of errors of velocities, but also to changes in the velocity values themselves. The proposed assumption of seasonals subtraction caused the Akaike information criterion values to show a decrease in the median value of 30 %, which in fact means that all the seasonals mentioned here must be taken into account when analyzing noises. Finally, we noticed that there are some of the GPS stations that improved their velocity uncertainty even of 56 %.     

GPS民用信号的改进与发展

随着科学技术的发展,GPS被越来越广泛地应用到社会生活多个领域。为了能够为用户提供更好的服务,GPS从投入使用以来就在不断地改进和完善。我们系统地阐述了GPS民用信号的发展历程和发展趋势,分析了各阶段民用信号的信号结构和技术改进措施,并对各种关键技术进行了阐释。     

顾及轨道误差BDS/GPS实时钟差融合估计的观测权函数设计

实时钟差产品是高精度广域差分位置服务(亚米级、分米级、厘米级)的基础产品,本文针对BDS/GPS轨道精度差异,设计了一种顾及轨道精度差异观测权函数,优化了实时钟差估计的随机模型,在此基础上基于非差法实现了BDS/GPS联合的实时钟差估计。采用MGEX和iGMAS跟踪站的实时观测数据进行实时钟差解算,并与iGMAS产品综合中心提供的事后精密钟差产品进行了比较分析。结果表明:基于该方法估计的钟差精度对单GPS、单BDS和BDS/GPS融合都有提高,其中BDS钟差精度整体较GPS更为显著,提高幅度约12.8%,其中IGSO/MEO更为突出,提高幅度约20%,验证了方法的有效性。     

基于小波降噪和神经网络的GPS高程时序预测模型

全球定位系统（GPS）时序数据预测的工作中发现,通常时序数据中含有的噪声会干扰数据预测的结果.为了降低时序数据中噪声对预测结果的负面影响,将提升小波阈值降噪技术和长短期记忆（LSTM）神经网络相结合,实现一种GPS时序数据降噪预测模型.该模型在预测之前首先利用提升小波与平滑阈值函数对GPS时序数据中的噪声进行剥离,然后构建多层LSTM神经网络对时序数据进行单步预测.通过实验与多种时间序列预测模型进行对比,结果表明所提出的LSTM预测模型对GPS时间序列的预测具有较强的适用性和较高的准确性.      

一种改进的GPS区域叠加滤波算法

GPS时间序列的空间滤波可以提高观测数据的信噪比,有利于获取更高精度的地壳形变信息。区域叠加滤波算法的空间滤波结果随着测站数和空间尺度不同而不同,不利于研究GPS时间序列中的形变信息。为了削弱区域叠加滤波受空间尺度的影响,提出一种不以空间尺度作为约束条件,同时引入相关系数和距离因子的区域叠加滤波算法。采用2010—2017年中国区域260个GPS连续观测站的时间序列展开空间滤波方法的研究,计算结果表明,对比相关性区域叠加滤波算法,考虑GPS时间序列之间的相关系数和距离因子更有利于提取GPS时间序列中的共模误差,且受空间尺度的影响较小。对比3种不同距离因子的区域叠加滤波算法,可知引入距离反比的空间滤波算法可实现更优的空间滤波。采用该方法空间滤波后可使GPS时间序列残差降低30%~40%,GPS速度场精度提高30%~40%。此算法实现了更优的GPS形变场估计,为研究中国区域的地壳运动和其动力学机制提供了可靠的数据基础。     

Precision, Cross Correlation, and Time Correlation of GPS Phase and Code Observations

In high-precision Global Positioning System (GPS) relative positioning applications, the stochastic properties of the GPS observables play a crucial role. The misspecification of the a priori covariance matrix can lead ton non-optimal results and false decisions. In this article, the noise characteristics of seven commonly used GPS receivers are examined. The main areas of our study are the precision of the observations, the time correlation of the observations, and the correlation between the different observation types. In order to examine these characteristics, an experiment was carried out, which will be briefly discussed. As results, the autocorrelation functions, standard deviation, and correlation numbers will be given for the undifferenced observations of the seven receivers. The standard deviation of the phase observation is usually at the submillimeter level, and that of the code observations is some centimeters to decimeters. It will be also shown that none of the receivers are free from correlation between observation types and time correlation, especially the code observations, which suffer from time correlation. The results presented can help to refine stochastic models currently in use. ? 2000 John Wiley & Sons, Inc.     

北斗二代导航卫星系统地壳运动监测能力

为了评估北斗卫星导航系统（BeiDou navigation satellite system, BDS）监测中国大陆地区地壳变形的技术能力,利用GAMIT/GLOBK软件处理了2017—2019年中国大陆构造环境监测网络23个基准站的全球定位系统（global positioning system, GPS）与BDS-2双模观测数据。结果显示,北斗二代的水平和垂向单日测站定位精度分别约为5~7 mm和13 mm,基线相对定位精度水平分量达到3~4 mm+（1~2）×10-8,水平位移速度测定精度约为0.6 mm/a。北斗二代的精密定位水平大致与20世纪90年代初GPS相当,可用于测定大尺度的板块运动及板内变形,但受卫星星座和定轨精度限制,不能准确反映季节性变动状态。作为对现有GPS监测的补充,可将基准站3年尺度的地壳运动监测精度最多提高20%。