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.     

ITRF2008: an improved solution of the international terrestrial reference frame

ITRF2008 is a refined version of the International Terrestrial Reference Frame based on reprocessed solutions of the four space geodetic techniques: VLBI, SLR, GPS and DORIS, spanning 29, 26, 12.5 and 16?years of observations, respectively. The input data used in its elaboration are time series (weekly from satellite techniques and 24-h session-wise from VLBI) of station positions and daily Earth Orientation Parameters (EOPs). The ITRF2008 origin is defined in such a way that it has zero translations and translation rates with respect to the mean Earth center of mass, averaged by the SLR time series. Its scale is defined by nullifying the scale factor and its rate with respect to the mean of VLBI and SLR long-term solutions as obtained by stacking their respective time series. The scale agreement between these two technique solutions is estimated to be 1.05 ± 0.13 ppb at epoch 2005.0 and 0.049 ± 0.010?ppb/yr. The ITRF2008 orientation (at epoch 2005.0) and its rate are aligned to the ITRF2005 using 179 stations of high geodetic quality. An estimate of the origin components from ITRF2008 to ITRF2005 (both origins are defined by SLR) indicates differences at epoch 2005.0, namely: ?0.5, ?0.9 and ?4.7?mm along X, Y and Z-axis, respectively. The translation rate differences between the two frames are zero for Y and Z, while we observe an X-translation rate of 0.3?mm/yr. The estimated formal errors of these parameters are 0.2?mm and 0.2?mm/yr, respectively. The high level of origin agreement between ITRF2008 and ITRF2005 is an indication of an imprecise ITRF2000 origin that exhibits a Z-translation drift of 1.8?mm/yr with respect to ITRF2005. An evaluation of the ITRF2008 origin accuracy based on the level of its agreement with ITRF2005 is believed to be at the level of 1?cm over the time-span of the SLR observations. Considering the level of scale consistency between VLBI and SLR, the ITRF2008 scale accuracy is evaluated to be at the level of 1.2?ppb (8?mm at the equator) over the common time-span of the observations of both techniques. Although the performance of the ITRF2008 is demonstrated to be higher than ITRF2005, future ITRF improvement resides in improving the consistency between local ties in co-location sites and space geodesy estimates.     

Estimation of phase center corrections for GLONASS-M satellite antennas

Driven by the comprehensive modernization of the GLONASS space segment and the increased global availability of GLONASS-capable ground stations, an updated set of satellite-specific antenna phase center corrections for the current GLONASS-M constellation is determined by processing 84 weeks of dual-frequency data collected between January 2008 and August 2009 by a worldwide network of 227 GPS-only and 115 combined GPS/GLONASS tracking stations. The analysis is performed according to a rigorous combined multi-system processing scheme providing full consistency between the GPS and the GLONASS system. The solution is aligned to a realization of the International Terrestrial Reference Frame 2005. The estimated antenna parameters are compared with the model values currently used within the International GNSS Service (IGS). It is shown that the z-offset estimates are on average 7 cm smaller than the corresponding IGS model values and that the block-specific mean value perfectly agrees with the nominal GLONASS-M z-offset provided by the satellite manufacturer. The existence of azimuth-dependent phase center variations is investigated and uncertainties in the horizontal offset estimates due to mathematical correlations and yaw-attitude modeling problems during eclipse seasons are addressed. Finally, it is demonstrated that the orbit quality benefits from the updated GLONASS-M antenna phase center model and that a consistent set of satellite antenna z-offsets for GPS and GLONASS is imperative to obtain consistent GPS- and GLONASS-derived station heights.     

IGS contribution to the ITRF

We examine the contribution of the International GNSS Service (IGS) to the International Terrestrial Reference Frame (ITRF) by evaluating the quality of the incorporated solutions as well as their major role in the ITRF formation. Starting with the ITRF2005, the ITRF is constructed with input data in the form of time series of station positions (weekly for satellite techniques and daily for VLBI) and daily Earth Orientation Parameters. Analysis of time series of station positions is a fundamental first step in the ITRF elaboration, allowing to assess not only the stations behavior, but also the frame parameters and in particular the physical ones, namely the origin and the scale. As it will be seen, given the poor number and distribution of SLR and VLBI co-location sites, the IGS GPS network plays a major role by connecting these two techniques together, given their relevance for the definition of the origin and the scale of the ITRF. Time series analysis of the IGS weekly combined and other individual Analysis Center solutions indicates an internal precision (or repeatability) <2 mm in the horizontal component and <5 mm in the vertical component. Analysis of three AC weekly solutions shows generally poor agreement in origin and scale, with some indication of better agreement when the IGS started to use the absolute model of antenna phase center variations after the GPS week 1400 (November 2006).     

IGS08: the IGS realization of ITRF2008

On April 17, 2011, the International GNSS Service (IGS) stopped using the IGS05 reference frame and adopted a new one, called IGS08, as the basis of its products. The latter was derived from the latest release of the International Terrestrial Reference Frame (ITRF2008). However, the simultaneous adoption of a new set of antenna phase center calibrations by the IGS required slight adaptations of ITRF2008 positions for 65 of the 232 IGS08 stations. The impact of the switch from IGS05 to IGS08 on GNSS station coordinates was twofold: in addition to a global transformation due to the frame change from ITRF2005 to ITRF2008, many station coordinates underwent small shifts due to antenna calibration updates, which need to be accounted for in any comparison or alignment of an IGS05-consistent solution to IGS08. Because the heterogeneous distribution of the IGS08 network makes it sub-optimal for the alignment of global frames, a smaller well-distributed sub-network was additionally designed and designated as the IGS08 core network. Only 2?months after their implementation, both the full IGS08 network and the IGS08 core network already strongly suffer from the loss of many reference stations. To avoid a future crisis situation, updates of IGS08 will certainly have to be considered before the next ITRF release.     

ITRF2000参考架的评价及其探讨

通过ITRF2000速度场建立完全独立于任何地质模型假设的ITRF2000VEL模型,求出总角动量| L |为0.127°/m·a,在运动中应加以改正,从而实现无整体旋转参考架。     

A Terrestrial Reference Frame realised on the observation level using a GPS-LEO satellite constellation

Applying a one-step integrated process, i.e. by simultaneously processing all data and determining all satellite orbits involved, a Terrestrial Reference Frame (TRF) consisting of a geometric as well as a dynamic part has been determined at the observation level using the EPOS-OC software of Deutsches GeoForschungsZentrum. The satellite systems involved comprise the Global Positioning System (GPS) as well as the twin GRACE spacecrafts. Applying a novel approach, the inherent datum defect has been overcome empirically. In order not to rely on theoretical assumptions this is done by carrying out the TRF estimation based on simulated observations and using the associated satellite orbits as background truth. The datum defect is identified here as the total of all three translations as well as the rotation about the z-axis of the ground station network leading to a rank-deficient estimation problem. To rectify this singularity, datum constraints comprising no-net translation (NNT) conditions in x, y, and z as well as a no-net rotation (NNR) condition about the z-axis are imposed. Thus minimally constrained, the TRF solution covers a time span of roughly a year with daily resolution. For the geometric part the focus is put on Helmert transformations between the a priori and the estimated sets of ground station positions, and the dynamic part is represented by gravity field coefficients of degree one and two. The results of a reference solution reveal the TRF parameters to be estimated reliably with high precision. Moreover, carrying out a comparable two-step approach using the same data and models leads to parameters and observational residuals of worse quality. A validation w.r.t. external sources shows the dynamic origin to coincide at a level of 5 mm or better in x and y, and mostly better than 15 mm in z. Comparing the derived GPS orbits to IGS final orbits as well as analysing the SLR residuals for the GRACE satellites reveals an orbit quality on the few cm level. Additional TRF test solutions demonstrate that K-Band Range-Rate observations between both GRACE spacecrafts are crucial for accurately estimating the dynamic frame’s orientation, and reveal the importance of the NNT- and NNR-conditions imposed for estimating the components of the dynamic geocenter.     

GGOS-D: homogeneous reprocessing and rigorous combination of space geodetic observations

In preparation of activities planned for the realization of the Global Geodetic Observing System (GGOS), a group of German scientists has carried out a study under the acronym GGOS-D which closely resembles the ideas behind the GGOS initiative. The objective of the GGOS-D project was the investigation of the methodological and information-technological realization of a global geodetic-geophysical observing system and especially the integration and combination of the space geodetic observations. In the course of this project, highly consistent time series of GPS, VLBI, and SLR results were generated based on common state-of-the-art standards for modeling and parameterization. These series were then combined to consistently and accurately compute a Terrestrial Reference Frame (TRF). This TRF was subsequently used as the basis to produce time series of station coordinates, Earth orientation, and troposphere parameters. In this publication, we present results of processing algorithms and strategies for the integration of the space-geodetic observations which had been developed in the project GGOS-D serving as a prototype or a small and limited version of the data handling and processing part of a global geodetic observing system. From a comparison of the GGOS-D terrestrial reference frame results and the ITRF2005, the accuracy of the datum parameters is about 5?C7?mm for the positions and 1.0?C1.5?mm/year for the rates. The residuals of the station positions are about 3?mm and between 0.5 and 1.0?mm/year for the station velocities. Applying the GGOS-D TRF, the offset of the polar motion time series from GPS and VLBI is reduced to 50 ??as (equivalent to 1.5?mm at the Earth??s surface). With respect to troposphere parameter time series, the offset of the estimates of total zenith delays from co-located VLBI and GPS observations for most stations in this study is smaller than 1.5?mm. The combined polar motion components show a significantly better WRMS agreement with the IERS 05C04 series (96.0/96.0???as) than VLBI (109.0/100.7???as) or GPS (98.0/99.5???as) alone. The time series of the estimated parameters have not yet been combined and exploited to the extent that would be possible. However, the results presented here demonstrate that the experiences made by the GGOS-D project are very valuable for similar developments on an international level as part of the GGOS development.     

利用SLR与伪距资料综合定轨

以GPS伪距为观测量对GPS35卫星进行定轨,然后将SLR与GPS伪距资料综合起来进行定轨,并将计算的轨道与IGS精密轨道进行了比较。     

Global sea-level rise and its relation to the terrestrial reference frame

We examined the sensitivity of estimates of global sea-level rise obtained from GPS-corrected long term tide gauge records to uncertainties in the International Terrestrial Reference Frame (ITRF) realization. A useful transfer function was established, linking potential errors in the reference frame datum (origin and scale) to resulting errors in the estimate of global sea level rise. Contrary to scale errors that are propagated by a factor of 100%, the impact of errors in the origin depends on the network geometry. The geometry of the network analyzed here resulted in an error propagation factor of 50% for the Z component of the origin, mainly due to the asymmetry in the distribution of the stations between hemispheres. This factor decreased from 50% to less than 10% as the geometry of the network improved using realistic potential stations that did not yet meet the selection criteria (e.g., record length, data availability). Conversely, we explored new constraints on the reference frame by considering forward calculations involving tide gauge records. A reference frame could be found in which the scatter of the regional sea-level rates was limited. The resulting reference frame drifted by 1.36 ± 0.22? mm/year from the ITRF2000 origin in the Z component and by ?0.44 ± 0.22?mm/year from the ITRF2005 origin. A bound on the rate of global sea level rise of 1.2 to 1.6?mm/year was derived for the past century, depending on the origin of the adopted reference frame. The upper bound is slightly lower than previous estimates of 1.8?mm/year discussed in the IPCC fourth report.     

Accurate absolute GPS positioning through satellite clock error estimation

 An algorithm for very accurate absolute positioning through Global Positioning System (GPS) satellite clock estimation has been developed. Using International GPS Service (IGS) precise orbits and measurements, GPS clock errors were estimated at 30-s intervals. Compared to values determined by the Jet Propulsion Laboratory, the agreement was at the level of about 0.1 ns (3 cm). The clock error estimates were then applied to an absolute positioning algorithm in both static and kinematic modes. For the static case, an IGS station was selected and the coordinates were estimated every 30 s. The estimated absolute position coordinates and the known values had a mean difference of up to 18 cm with standard deviation less than 2 cm. For the kinematic case, data obtained every second from a GPS buoy were tested and the result from the absolute positioning was compared to a differential GPS (DGPS) solution. The mean differences between the coordinates estimated by the two methods are less than 40 cm and the standard deviations are less than 25 cm. It was verified that this poorer standard deviation on 1-s position results is due to the clock error interpolation from 30-s estimates with Selective Availability (SA). After SA was turned off, higher-rate clock error estimates (such as 1 s) could be obtained by a simple interpolation with negligible corruption. Therefore, the proposed absolute positioning technique can be used to within a few centimeters' precision at any rate by estimating 30-s satellite clock errors and interpolating them. Received: 16 May 2000 / Accepted: 23 October 2000     

基于GAMIT/GLOBK和GPS观测确定加拿大地区的冰川均衡调整导致的垂向形变

本文采用加拿大地区31个IGS台站的观测数据,利用GAMIT/GLOBK软件处理了时间跨度为2000—2018年的GPS原始观测资料,得到了ITRF2014参考框架下的台站位置垂向运动速率的时间序列.对GPS时间序列进行阶跃探测及修复、异常值探测及剔除、趋势项估计、去除近期冰川融化导致的地表弹性变形后,得到了由冰川均衡...     

The IGS-combined station coordinates, earth rotation parameters and apparent geocenter

The International GNSS Service (IGS) routinely generates a number of weekly, daily and sub-daily products. Station coordinates and velocities, earth rotation parameters (ERPs) and apparent geocenter are among these products generated weekly by the IGS Reference Frame Coordinator. They have been determined since 1999 by combining independent estimates from at least seven IGS Analysis Centers (ACs). Two Global Network Associate Analysis Centers (GNAACs) also provide independent combinations using the same AC weekly solutions and they are currently used to quality control the IGS combination. The combined solutions are aligned to an IGS realization (IGS05) of the ITRF2005 using a carefully selected set of the IGS Reference Frame (RF) stations (nominally 132). During the combination process, the contributing solutions are compared and outliers are removed to ensure a high level of consistency of the estimated parameters. The ACs and the weekly combined solution are consistent at the 1–2 and 3–4 mm levels for the horizontal and vertical components. Similarly, the excess Length of Day (LOD), the pole positions and pole rates are consistent at the 10μs, 0.03–0.05 mas and 0.10–0.20 mas/day levels, respectively. The consistency of the apparent geocenter estimate is about 5 mm in the X and Y components and 10 mm in the Z component. Comparison of the IGS-combined ERP estimates with the IERS Bulletin A suggests a small bias of the order of ?0.04 mas and + 0.05 mas (both ±0.05 mas) in the x and y components.     

DORIS Contribution to ITRF2005

We examine the contribution of the Doppler Orbit determination and Radiopositioning Integrated by Satellite (DORIS) technique to the International Terrestrial Reference Frame (ITRF2005) by evaluating the quality of the submitted solutions as well as that of the frame parameters, especially the origin and the scale. Unlike the previous versions of the ITRF, ITRF2005 is constructed with input data in the form of time-series of station positions (weekly for satellite techniques and daily for VLBI) and daily Earth orientation parameters (EOPs), including full variance–covariance information. Analysis of the DORIS station positions’ time-series indicates an internal precision reaching 15 mm or better, at a weekly sampling. A cumulative solution using 12 years of weekly time-series was obtained and compared to a similar International GNSS Service (IGS) GPS solution (at 37 co-located sites) yielding a weighted root mean scatter (WRMS) of the order of 8 mm in position (at the epoch of minimum variance) and about 2.5 mm/year in velocity. The quality of this cumulative solution resulting from the combination of two individual DORIS solutions is better than any individual solution. A quality assessment of polar motion embedded in the contributed DORIS solutions is performed by comparison with the results of other space-geodetic techniques and in particular GPS. The inferred WRMS of polar motion varies significantly from one DORIS solution to another and is between 0.5 and 2 mas, depending on the strategy used and in particular estimating or not polar motion rate by the analysis centers. This particular aspect certainly needs more investigation by the DORIS Analysis Centers.     

Plate Motion of India and Interseismic Strain in the Nepal Himalaya from GPS and DORIS Measurements

We analyse geodetically estimated deformation across the Nepal Himalaya in order to determine the geodetic rate of shortening between Southern Tibet and India, previously proposed to range from 12 to 21 mm yr^?1. The dataset includes spirit-levelling data along a road going from the Indian to the Tibetan border across Central Nepal, data from the DORIS station on Everest, which has been analysed since 1993, GPS campaign measurements from surveys carried on between 1995 and 2001, as well as data from continuous GPS stations along a transect at the logitude of Kathmandu operated continuously since 1997. The GPS data were processed in International Terrestrial Reference Frame 2000 (ITRF2000), together with the data from 20 International GNSS Service (IGS) stations and then combined using quasi- observation combination analysis (QOCA). Finally, spatially complementary velocities at stations in Southern Tibet, initially determined in ITRF97, were expressed in ITRF2000. After analysing previous studies by different authors, we determined the pole of rotation of the Indian tectonic plate to be located in ITRF2000 at 51.409±1.560° N and ?10.915±5.556°E, with an angular velocity of 0.483±0.015°. Myr^?1. Internal deformation of India is found to be small, corresponding to less than about 2 mm yr^?1 of baseline change between Southern India and the Himalayan piedmont. Based on an elastic dislocation model of interseismic strain and taking into account the uncertainty on India plate motion, the mean convergence rate across Central and Eastern Nepal is estimated to 19±2.5 mm yr^?1, (at the 67% confidence level). The main himalayan thrust (MHT) fault was found to be locked from the surface to a depth of about 20 km over a width of about 115 km. In these regions, the model parameters are well constrained, thanks to the long and continuous time-series from the permanent GPS as well as DORIS data. Further west, a convergence rate of 13.4±5 mm yr^?1, as well as a fault zone, locked over 150 km, are proposed. The slight discrepancy between the geologically estimated deformation rate of 21±1.5 mm yr^?1 and the 19±2.5 mm yr^?1 geodetic rate in Central and Eastern Nepal, as well as the lower geodetic rate in Western Nepal compared to Eastern Nepal, places bounds on possible temporal variations of the pattern and rate of strain in the period between large earthquakes in this region.     

Geocenter variations derived from a combined processing of LEO- and ground-based GPS observations

GNSS observations provided by the global tracking network of the International GNSS Service (IGS, Dow et al. in J Geod 83(3):191–198, 2009) play an important role in the realization of a unique terrestrial reference frame that is accurate enough to allow a detailed monitoring of the Earth’s system. Combining these ground-based data with GPS observations tracked by high-quality dual-frequency receivers on-board low earth orbiters (LEOs) is a promising way to further improve the realization of the terrestrial reference frame and the estimation of geocenter coordinates, GPS satellite orbits and Earth rotation parameters. To assess the scope of the improvement on the geocenter coordinates, we processed a network of 53 globally distributed and stable IGS stations together with four LEOs (GRACE-A, GRACE-B, OSTM/Jason-2 and GOCE) over a time interval of 3 years (2010–2012). To ensure fully consistent solutions, the zero-difference phase observations of the ground stations and LEOs were processed in a common least-squares adjustment, estimating all the relevant parameters such as GPS and LEO orbits, station coordinates, Earth rotation parameters and geocenter motion. We present the significant impact of the individual LEO and a combination of all four LEOs on the geocenter coordinates. The formal errors are reduced by around 20% due to the inclusion of one LEO into the ground-only solution, while in a solution with four LEOs LEO-specific characteristics are significantly reduced. We compare the derived geocenter coordinates w.r.t. LAGEOS results and external solutions based on GPS and SLR data. We found good agreement in the amplitudes of all components; however, the phases in x- and z-direction do not agree well.     

中国及其周边IGS站数据质量评估

在高精度GPS数据处理中,通常需要与国内及周边IGS站进行联测,引入ITRF框架基准,IGS站数据质量好坏直接决定着数据处理质量,因而有必要对近年IGS站数据质量进行评估。本文利用 T EQC软件对国内及周边IGS站点2011年第196天至2013年第298天共834天的观测数据进行了质量检查,发现U RU M 站从2013年的第186天到218天的L2载波缺失、WUHN 站数天的有效观测时长都小于2 h、LHAZ站某些天数据有效率过低等问题,为今后有效使用这些站点数据提供了参考。     

利用北斗系统建立和维持国家大地坐标参考框架的方法研究

2000中国大地坐标系统（China Geodetic Coordinate System 2000,CGCS2000）的建立和维持主要依赖于GPS技术,不利于保障国家时空信息安全。中国北斗卫星导航系统（BeiDou navigation satellite system,BDS）提供亚太区域服务,可满足中国及周边地区高精度定位导航应用需求,对建立和维持国家大地坐标参考框架具有重要意义。研究利用已建成的北斗基准站网观测数据,实现基于BDS技术、并与国际地球参考框架（International Terrestrial Reference Frame,ITRF）一致的国家大地坐标参考框架,为今后国家级和全球性北斗坐标参考框架（BeiDou Terrestrial Reference Frame,BTRF）的建立和维持提供理论基础和方法支撑。初步计算结果表明,积累2 a以上的观测数据,利用单独BDS数据可以获得与GPS精度相当的水平速度场,精度约为2~3 mm/a。基于单独BDS数据,测站残差平面和高程的重复性分别可优于0.8 cm和1.7 cm。利用BDS数据已可监测到测站高程方向的季节性变化。此外,还对单独BDS与GPS数据计算的坐标可能存在的与经纬度相关的系统误差进行了分析。总体来说,目前的北斗系统可满足建立和维持中国cm级大地坐标框架的需求。     

Anomalous harmonics in the spectra of GPS position estimates

Prior studies of the power spectra of GPS position time series have found pervasive seasonal signals against a power-law background of flicker noise plus white noise. Dong et al. (2002) estimated that less than half the observed GPS seasonal power can be explained by redistributions of geophysical fluid mass loads. Much of the residual variation is probably caused by unidentified GPS technique errors and analysis artifacts. Among possible mechanisms, Penna and Stewart (2003) have shown how unmodeled analysis errors at tidal frequencies (near 12- and 24-hour periods) can be aliased to longer periods very efficiently. Signals near fortnightly, semiannual, and annual periods are expected to be most seriously affected. We have examined spectra for the 167 sites of the International GNSS (Global Navigation Satellite Systems) Service (IGS) network having more than 200 weekly measurements during 1996.0–2006.0. The non-linear residuals of the weekly IGS solutions that were included in ITRF2005, the latest version of the International Terrestrial Reference Frame (ITRF), have been used. To improve the detection of common-mode signals, the normalized spectra of all sites have been stacked, then boxcar smoothed for each local north (N), east (E), and height (H) component. The stacked, smoothed spectra are very similar for all three components. Peaks are evident at harmonics of about 1 cycle per year (cpy) up to at least 6 cpy, but the peaks are not all at strictly 1.0 cpy intervals. Based on the 6th harmonic of the N spectrum, which is among the sharpest and largest, and assuming a linear overtone model, then a common fundamental of 1.040 ± 0.008 cpy can explain all peaks well, together with the expected annual and semiannual signals. A flicker noise power-law continuum describes the background spectrum down to periods of a few months, after which the residuals become whiter. Similar sub-seasonal tones are not apparent in the residuals of available satellite laser ranging (SLR) and very long baseline interferometry (VLBI) sites, which are both an order of magnitude less numerous and dominated by white noise. There is weak evidence for a few isolated peaks near 1 cpy harmonics in the spectra of geophysical loadings, but these are much noisier than for GPS positions. Alternative explanations related to the GPS technique are suggested by the close coincidence of the period of the 1.040 cpy frequency, about 351.2 days, to the “GPS year”; i.e., the interval required for the constellation to repeat its inertial orientation with respect to the sun. This could indicate that the harmonics are a type of systematic error related to the satellite orbits. Mechanisms could involve orbit modeling defects or aliasing of site-dependent positioning biases modulated by the varying satellite geometry.     

A first look at the effects of ionospheric signal bending on a globally processed GPS network

This study provides a first attempt at quantifying potential signal bending effects on the GPS reference frame, coordinates and zenith tropospheric delays (ZTDs). To do this, we homogeneously reanalysed data from a global network of GPS sites spanning 14 years (1995.0–2009.0). Satellite, Earth orientation, tropospheric and ground station coordinate parameters were all estimated. We tested the effect of geometric bending and dTEC bending corrections, which were modelled at the observation level based, in part, on parameters from the International Reference Ionosphere 2007 model. Combined, the two bending corrections appear to have a minimal effect on site coordinates and ZTDs except for low latitude sites. Considering five days (DOY 301–305, 28 October–1 November 2001) near ionospheric maximum in detail, they affect mean ZTDs by up to ~1.7 mm at low latitudes, reducing to negligible levels at high latitudes. Examining the effect on coordinates in terms of power-spectra revealed the difference to be almost entirely white noise, with noise amplitude ranging from 0.3 mm (high latitudes) to 2.4 mm (low latitudes). The limited effect on station coordinates is probably due to the similarity in the elevation dependence of the bending term with that of tropospheric mapping functions. The smoothed z-translation from the GPS reference frame to ITRF2005 changes by less than 2 mm, though the effect combines positively with that from the second order ionospheric refractive index term. We conclude that, at the present time, and for most practical purposes, the geometric and dTEC bending corrections are probably negligible at current GPS/reference frame precisions.