GPS interactive time series analysis software

Time series analysis is an important part of geodetic and geodynamic studies, especially when continuous GPS observations are used to explore areas with a low rate of deformation. In this domain, having precise and robust tools for processing and analyzing position time series is a prerequisite. To meet this requirement, a new software package called GPS Interactive Time Series Analysis was developed using the MATLAB language. Along with calculating basic statistics and quality parameters such as mean and variance, the software is capable of importing and visualizing different time series formats, determining and removing jumps and outliers, interpolating data, and producing numerical and publication quality graphical outputs. Furthermore, bivariate statistical analysis (such as correlation coefficients, curvilinear and nonlinear regression), residual analysis, and spectral analysis (such as auto-spectrum, Lomb–Scargle spectrum, evolutionary power spectrum, and wavelet power spectrum) form the main analysis features of the software.     

Theory of second order stationary random processes applied to GPS coordinate time-series

The analysis of Global Positioning System (GPS) coordinates time series is a valuable tool in quantifying crustal deformations. The longer continuous GPS time series allow estimation of nonlinear signatures. As a matter of fact, besides the linear and periodic behaviors, other relevant signals are present in such time series as the so-called transient deformations. They can be related to, e.g., slow slip events, which play a crucial role in studying fault mechanisms. To give reliable estimates of these signals, an appropriate and rigorous approach for defining the deterministic and the stochastic models of the data is needed. We prove that the theory of the second order stationary random process (SOSRP) can be used to describe the stochastic behavior of the daily GPS time series. In particular, the second order stationarity condition has to be verified for the daily GPS coordinate time series to be described as a SOSRP. This method has been already used for modeling the gravity field of the earth and in predicting/filtering problems, and this work shows that it can also be useful for characterizing the colored noise in the GPS time series.     

Nontectonic signals in reprocessed continuous GPS position time series of CMONOC

The nearly nine-year continuous GPS data collected since 1 March 1999 from the Crustal Motion Observation Network of China (CMONOC) were consistently analyzed. Most of the nonlinear movements in the cumulative position time series produced by CMONOC data center disappeared; and more accurate vertical terms and tectonic signals were extracted. Displacements caused by atmospheric pressure loading, nontidal ocean loading, soil moisture mass loading, and snow cover mass loading using the National Centers for Environmental Prediction (NCEP) Reanalysis I/II models and Estimation of the Circulation and Climate of the Ocean (ECCO) data can explain most of the vertical annual terms at many stations, while only parts can be explained at Lhasa and southern coastal sites, indicating that there are some deformation mechanisms that are still unknown or not modeled accurately. The remarkable differences in vertical position time series for short-baseline sites reveal that GPS stations can be greatly affected by local factors; and attention should be paid when explaining observed GPS velocity vectors.     

Nontectonic signals in reprocessed continuous GPS position time series of CMONOC

The nearly nine-year continuous GPS data collected since 1 March 1999 from the Crustal Motion Observation Network of China(CMONOC) were consistently analyzed.Most of the nonlinear movements in the cumulative position time series pro-duced by CMONOC data center disappeared;and more accurate vertical terms and tectonic signals were extracted.Displacements caused by atmospheric pressure loading,nontidal ocean loading,soil moisture mass loading,and snow cover mass loading using the National Centers for Environmental Prediction(NCEP) Reanalysis I/II models and Estimation of the Circulation and Climate of the Ocean(ECCO) data can explain most of the vertical annual terms at many stations,while only parts can be explained at Lhasa and southern coastal sites,indicating that there are some deformation mechanisms that are still unknown or not modeled accurately.The remarkable differences in vertical position time series for short-baseline sites reveal that GPS stations can be greatly affected by lo-cal factors;and attention should be paid when explaining observed GPS velocity vectors.     

PCA空间滤波在高频GPS定位中的应用研究

利用主成分分析法(PCA)对高频GPS时间序列进行空间滤波,并结合Karhunen-Loeve展开法(KLE)对其结果进行判定,可有效地提取共模误差,提高单历元定位精度。通过对四川GPS连续观测网的计算分析表明,PCA方法可较好地减弱区域共模误差,并能准确地反映共模误差的空间分布,且精度优于传统的堆栈法,这对高频GPS技术的应用和发展具有重要意义。     

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。     

A MATLAB-based Kriged Kalman Filter software for interpolating missing data in GNSS coordinate time series

GNSS coordinate time series data for permanent reference stations often suffer from random, or even continuous, missing data. Missing data interpolation is necessary due to the fact that some data processing methods require evenly spaced data. Traditional missing data interpolation methods usually use single point time series, without considering spatial correlations between points. We present a MATLAB software for dynamic spatiotemporal interpolation of GNSS missing data based on the Kriged Kalman Filter model. With the graphical user interface, users can load source GNSS data, set parameters, view the interpolated series and save the final results. The SCIGN GPS data indicate that the software is an effective tool for GNSS coordinate time series missing data interpolation.     

Estimates of ocean tide loading displacements and its impact on position time series in Hong Kong using a dense continuous GPS network

Three-dimensional ocean tide loading (OTL) displacements of eight diurnal and semidiurnal constituents at 12 sites in Hong Kong were estimated using 3–7 years of continuous global positioning system (GPS) observations. OTL displacements were estimated using the precise point positioning (PPP) technique on a daily basis and then combined. The OTL displacements obtained by GPS were compared with predictions using seven recent global ocean tide models. The effect of OTL displacements on GPS position time series was also investigated. The study shows that the GPS-derived OTL displacements (excluding K1 and K2 constituents) agree best with those predicted by the GOT4.7 and NAO99b models. The GPS/model agreement is generally at the sub-millimeter level, except for S2, K1, and K2 constituents with relatively large errors. After systematic biases between the GPS and model values are removed, the misfits of all sites for M2, S2, N2, O1, P1, and Q1 are less than 0.5 and 1.0 mm in the horizontal and vertical components, respectively, while larger misfits (within 2.5 mm) are observed for K1 and K2. Integer ambiguity fixing slightly improves the east component of OTL displacement estimates. The study also finds that GPS-derived OTL corrections, instead of model predicts, can be used in daily data processing with the exception of K1 and K2. Including K2 corrections, a secular vertical rate of up to 1 mm/year in position time series can be induced, which needs to be confirmed by further studies.     

GPS坐标时间序列中的异常高频周期性噪声

本文分析了中国地壳运动观测网络GPS基准站及中国周边IGS连续站坐标中的周期性噪声,在北、东和垂向分量坐标时间序列中均发现了周期约351/n(n=1,…,6)天的正弦项,而地表质量负荷造成的位移序列中并没有对应的成分,不能解释异常周期项的来源。在估计台站的运动速率时,如考虑此类"异常"周期项,速率误差略微减小,而周年项振幅的估计误差显著增大,且残差离散度未见明显改善。因此,不推荐在GPS速率矢量反演中加入异常周期项参数。     

我国GPS跟踪站在汶川地震前后的运动特征分析

利用国家测绘局及其它部委布设的GPS跟踪站连续10年的观测数据,通过数据处理和分析得到了汶川地震前这些站的运动速度场和震后位移量,同时获得了各站近10年的坐标时间序列,在此基础上初步分析了地震前、后各站时间序列表现出的站点的运动特征信息。为我国地心坐标框架的进一步更新和维护提供了重要数据,也为地球动力学研究提供了重要的基础信息。     

震后GPS坐标时序中对数弛豫时间的估计

全球定位系统（global positioning system, GPS）坐标时序去除同震形变和震前稳态速度场后,采用加权非线性最小二乘估计震后对数弛豫时间,可更准确地提取震后对数弛豫项,从而可以分析震后弛豫项对测站位移的独立物理贡献,并为震后余滑和黏滞性松弛效应等现象的分析提供参考。以日本2009—2019年GPS坐标时序为例,估计2011年Mw 9.0地震震后对数弛豫时间,发现不同站点的对数弛豫时间与其震中距关系显著,且服从高斯分布。据此,构建高斯函数加常数模型,可由震中距概略估计震后对数弛豫时间。高斯分布曲线的峰值、峰值位置、半宽度信息、最低位置分别为3.5 a、0 km、262 km、0.5 a,由此得出震后对数弛豫项影响时间大于0.5 a的站点主要集中在震中距约524 km范围内。震后弛豫效应区域分布的差异性显著,对数弛豫时间越长的区域,弛豫项水平位移表征越大,其中存在两个平均弛豫时间2.5 a的中心区域,与震后余滑的中心区域及时间相吻合。     

MATLAB Tools for viewing GPS velocities and time series

Over the past decade, many Global Positioning System (GPS) networks have been installed to monitor tectonic motions around the world. Some of these networks contain hundreds of sites spread across active tectonic margins where the differences in velocities across the network can be 50–100 mm/year. For networks that have been running for a number of years, the uncertainty in the velocity estimates can be less than 1 mm/year. In some cases the vertical motions can also be significant and of importance. Often, the time series of the motions of the GPS sites show complex non-linear behavior, and in all cases the statistical model of the time series is more complex than simple white noise. In this article, we describe a set of Matlab tools developed for use with the GAMIT/GLOBK GPS data analysis system (King 2002; King and Herring 2002) that allow interactive viewing and manipulation of GPS velocities and time series with a Matlab-based graphical user interface (GUI). The formats of the data files used by the tools are specific to GAMIT/GLOBK, but they are simple ASCII files that can be generated from other file formats. The tools are referred to as GGMatlab.The GPS Toolbox is a column dedicated to highlighting algorithms and source code utilized by GPS Engineers and scientists. If you have an interesting program or software package you would like to share with our readers, please pass it along; e-mail it to us at gps-toolbox@ngs.noaa.gov/. To comment on any of the source code discussed here, or to download source code, visit our website at . This column is edited by Stephen Hilla, National Geodetic Survey, NOAA, Silver Spring, Maryland, and Mike Craymer, Geodetic Survey Division, Natural Resources Canada, Ottawa, Ontario, Canada. For the sidebar, see the Volume 6, Number 4, 2003 issue of the GPS Toolbox column.     

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.     

GZCORS系统的建设与应用

GZCORS覆盖全广州约8000km2的行政区域,它是卫星定位技术、计算机网络技术、数字通讯技术等高新科技多方位、深度结晶的产物,可以全自动、全天候、实时提供覆盖全广州市域的高精度空间和时间信息。对系统建设中的关键性技术问题和具体实施方案进行了研究和解决。     

Quality assessment of GPS reprocessed terrestrial reference frame

The International GNSS Service (IGS) contributes to the construction of the International Terrestrial Reference Frame (ITRF) by submitting time series of station positions and Earth Rotation Parameters (ERP). For the first time, its submission to the ITRF2008 construction is based on a combination of entirely reprocessed GPS solutions delivered by 11 Analysis Centers (ACs). We analyze the IGS submission and four of the individual AC contributions in terms of the GNSS frame origin and scale, station position repeatability and time series seasonal variations. We show here that the GPS Terrestrial Reference Frame (TRF) origin is consistent with Satellite laser Ranging (SLR) at the centimeter level with a drift lower than 1 mm/year. Although the scale drift compared to Very Long baseline Interferometry (VLBI) and SLR mean scale is smaller than 0.4 mm/year, we think that it would be premature to use that information in the ITRF scale definition due to its strong dependence on the GPS satellite and ground antenna phase center variations. The new position time series also show a better repeatability compared to past IGS combined products and their annual variations are shown to be more consistent with loading models. The comparison of GPS station positions and velocities to those of VLBI via local ties in co-located sites demonstrates that the IGS reprocessed solution submitted to the ITRF2008 is more reliable and precise than any of the past submissions. However, we show that some of the remaining inconsistencies between GPS and VLBI positioning may be caused by uncalibrated GNSS radomes.     

Analysis of Interpolation Methods for Kinematic DGPS Control in Aerial Photogrammetry

Kinematic differential Global Positioning System (DGPS) positioning is routinely used in industry for directly observing an aircraft's position at each instant of photographic exposure during a photogammetric survey. A critical aspect of the subsequent data processing is estimation of the aircraft position at the exact time of exposure. GPS measurements are acquired at a uniform sampling rate, typically 1 Hz. The exposure times, however, do not generally coincide with these times. As a result, the exposure station positions must be interpolated from the adjacent GPS positions. This is typically done using a low-order polynomial, expressed as a function of time, for each coordinate dimension. However, trajectory perturbations induced by atmospheric turbulence can render such interpolation methods ineffective. This article will convey the results of an investigation into the use of several different interpolation models with airborne GPS data during straight, level flight. The fundamental task of time series reconstruction will first be addressed, in which several possible interpolation models are described. Two 10-Hz, airborne GPS data sets were collected to test the accuracy of each model. The error properties resulting from the application of each model to these data will be presented and analyzed in terms of time-domain statistics and frequency-domain characteristids. It will be demonstrated that interpolation error can be significantly reduced, especially in the height dimension, through judicious choice of an interpolator. ? 2000 John Wiley & Sons, Inc.     

Empirical modelling of site-specific errors in continuous GPS data

Continuous global positioning system (GPS) stations propagate biases and spurious signals into the derived parameter time series when the measurements are subject to site-specific effects, such as multipath. This is a particular problem in the investigation of geophysical and atmospheric phenomena where signals may be small in magnitude. A methodology to remove these erroneous signals from long-term time series will significantly increase the usefulness of the derived time series. This work provides the theoretical basis for use of an empirical site model (ESM) derived from post-fit phase residuals to mitigate unmodelled site-specific errors. Additionally, we also investigate the effectiveness of applying an ESM to a regional GPS network and a short baseline solution. Under most observing scenarios, we show that the ESM approach is predicted to improve the precision and accuracy of the site coordinates. However, it is important to note that we found some scenarios where the ESM can introduce a bias. For instance, when the antenna is mounted close to the ground. In this scenario, for a short baseline, we observed the introduction of a 4-mm bias in height. Use of an ESM for the same short baseline with an uncalibrated radome substantially improves the results by removing a large bias of over 10 mm in height. Similarly, application of an ESM derived from historic data yields similar improvements. This demonstrates that the ESM can be a powerful tool when applied to appropriate site-specific configurations and could potentially be implemented in routine GPS analysis for a broad range of applications.     

云南地区形变观测资料短临异常指标提取

提出了面应变综合预测指标法,目的是将全球卫星定位系统（global position system,GPS）观测结果应用于地震短临预测。基于云南省GPS连续观测资料,利用GPS高精度数据处理软件（GAMIT/GLOBK）处理后获得位移场。对位移场进行网格化插值获得均匀分布于56个网格的位移场,基于每个网格位移场时间序列求取其面应变时间序列,并对每个网格面应变时间序列的映震能力进行评价、综合,提取出适合于云南地区的地震短临异常识别指标。实践表明,综合预测指标对云南地区2011年以来发生的20次5级以上地震进行3个月短临预测,其中准确预测次数为19次,漏报数为1次,虚报5次,认为该指标对地震发震时间、震中均具有较好的指示意义,可用于云南地区未来的地震短临预测实践。     

GPS/GALILEO组合系统可见卫星与GDOP的区域和时序分析

卫星星座方案的选择对导航定位精度具有很大影响。本文根据GALILEO系统的设计轨道参数模拟得到的GALILEO系统的卫星位置,分别计算了GPS系统、GALILEO系统和GPS/GALILEO组合系统在不同卫星截止高度角的情况下,全国范围内可见卫星和GDOP值的分布情况,并选择了北京、武汉和乌鲁木齐三个城市,连续观测24小时,分析了各城市的可见卫星和GDOP值随时间的变化规律。     

An assessment of Bernese GPS software precise point positioning using IGS final products for global site velocities

We assess the use of precise point positioning (PPP) within the Bernese GPS software (BSW) Version 5.0 over the period from 2000 to 2005. In our strategy, we compute a set of daily PPP solutions for international GNSS service (IGS) reference frame (IGb00) sites by fixing IGS final satellite orbits and clock products, followed by a Helmert transformation of these solutions into ITRF2000, forming a set of continuous position time series over the entire time span. We assess BSW PPP by comparing our set of transformation parameters with those produced by the IGS analysis centre coordinator (ACC) and our position time series with those of the Jet Propulsion Laboratory (JPL) and the Scripps Orbit and Permanent Array Centre at the Scripps Institute of Oceanography (SIO). The distributions of the north (N), east (E) and up (U) daily position differences are characterized by means and SD of +2.2 ± 4.8, −0.6 ± 7.9 and +4.8 ± 17.3 mm with respect to JPL, and of +0.1 ± 4.4, −0.1 ± 7.4 and −0.1 ± 11.8 mm with respect to SIO. Similarly, we find sub-millimetre mean velocity differences and SD for the N, E and U components of 0.9, 1.5 and 2.2 mm/year with JPL, and of 1.2, 1.6 and 2.3 mm/year with SIO. A noise analysis using maximum likelihood estimation (MLE) shows that when estimating global site velocities from our position time series, the series need to be on average up to 1.3 times longer than those of JPL and SIO, before an uncertainty of less than 0.5 mm/year is obtained.