Temporal and spatial variability of the bias between TOPEX- and GPS-derived total electron content

Total electron content (TEC) predictions made with the GPS-based la plata ionospheric model (LPIM) and the International Reference Ionosphere (IRI95) model were compared to estimates from the dual-frequency altimeter onboard the TOPEX/Poseidon (T/P) satellite. LPIM and IRI95 were evaluated for the location and time of available T/P data, from January 1997 to December 1998. To investigate temporal and spatial variations of the TEC bias between T/P and each model, the region covered by T/P observations was divided into ten latitude bands. For both models and for all latitudes, the bias was mainly positive (i.e. T/P values were larger); the LPIM bias was lower and less variable than the IRI95 bias. To perform a detailed analysis of temporal and spatial variability of the T/P-LPIM TEC bias, the Earth’s surface was divided into spherical triangles with 9°-sides, and a temporally varying regression model was fitted to every triangle. The highest TEC bias was found over the equatorial anomalies, which is attributed to errors in LPIM. A significant TEC bias was found at 40°N latitude, which is attributed to errors in the T/P Sea State Bias (SSB) correction. To separate systematic errors in the T/P TEC from those caused by LPIM, altimeter range biases estimated by other authors were analysed in connection with the TEC bias. This suggested that LPIM underestimates the TEC, particularly during the Southern Hemisphere summer, while T/P C-band SSB calibration is worse during the Southern Hemisphere winter.     

The ERS-2 altimetric bias and gravity field enhancement using dual crossovers between ERS and TOPEX/Poseidon

 Dual satellite crossovers (DXO) between the two European Remote Sensing satellites ERS-1 and ERS-2 and TOPEX/Poseidon are used to (1) refine the Earth's gravity field and (2) extend the study of the ERS-2 altimetric range stability to cover the first four years of its operation. The enhanced gravity field model, AGM-98, is validated by several methodologies and will be shown to provide, in particular, low geographically correlated orbital error for ERS-2. For the ERS-2 altimetric range study, TOPEX/Poseidon is first calibrated through comparison against in situ tide gauge data. A time series of the ERS-2 altimeter bias has been recovered along with other geophysical correction terms using tables for bias jumps in the range measurements at the single point target response (SPTR) events. On utilising the original version of the SPTR tables the overall bias drift is seen to be 2.6±1.0 mm/yr with an RMS of fit of 12.2 mm but with discontinuities at the centimetre level at the SPTR events. On utilising the recently released revised tables, SPTR2000, the drift is better defined at 2.4±0.6 mm/yr with the RMS of fit reduced to 3.7 mm. Investigations identify the sea-state bias as a source of error with corrections affecting the overall drift by close to 1.2 mm/yr. Received: 25 May 2000 / Accepted: 24 January 2001     

Combination of GNSS and SLR observations using satellite co-locations

Satellite Laser Ranging (SLR) observations to Global Navigation Satellite System (GNSS) satellites may be used for several purposes. On one hand, the range measurement may be used as an independent validation for satellite orbits derived solely from GNSS microwave observations. On the other hand, both observation types may be analyzed together to generate a combined orbit. The latter procedure implies that one common set of orbit parameters is estimated from GNSS and SLR data. We performed such a combined processing of GNSS and SLR using the data of the year 2008. During this period, two GPS and four GLONASS satellites could be used as satellite co-locations. We focus on the general procedure for this type of combined processing and the impact on the terrestrial reference frame (including scale and geocenter), the GNSS satellite antenna offsets (SAO) and the SLR range biases. We show that the combination using only satellite co-locations as connection between GNSS and SLR is possible and allows the estimation of SLR station coordinates at the level of 1–2 cm. The SLR observations to GNSS satellites provide the scale allowing the estimation of GNSS SAO without relying on the scale of any a priori terrestrial reference frame. We show that the necessity to estimate SLR range biases does not prohibit the estimation of GNSS SAO. A good distribution of SLR observations allows a common estimation of the two parameter types. The estimated corrections for the GNSS SAO are 119 mm and −13 mm on average for the GPS and GLONASS satellites, respectively. The resulting SLR range biases suggest that it might be sufficient to estimate one parameter per station representing a range bias common to all GNSS satellites. The estimated biases are in the range of a few centimeters up to 5 cm. Scale differences of 0.9 ppb are seen between GNSS and SLR.     

A kinematic GPS methodology for sea surface mapping,Vanuatu

During the past few decades, satellite altimetry has brought tremendous new knowledge about the spatial and temporal variations of sea surface heights over the Earth’s oceans. However, the precision is limited over short wavelengths and in coastal areas, and other methods such as kinematic GPS may be needed to fill in this information. We present kinematic GPS work aimed at mapping the sea surface height, with special attention to the precision one can expect. Active marine subduction zones, like the Vanuatu archipelago, may present short wavelength, high amplitude undulations of the sea surface height that are difficult to map with satellite altimetry. This paper presents the methodology used around Santo Island, in Vanuatu, to obtain a well-resolved local sea surface map with a precision of 5–15 cm limited by the sea conditions and the distance from the coastal reference station. We present the results of three campaigns in 2004, 2006 and 2007. Careful observation of the ship behaviour along the surveys as well as simultaneous recording of the ship attitude variations is mandatory to obtain reliable results. We show that the ship GPS antenna height varies with the ship’s velocity and we suggest a method to correct this effect. The final precision is estimated using the crossover differences method.     

Seasonal sea level change from TOPEX/Poseidon observation and thermal contribution

Seasonal steric sea-level change due to temperature variation in the mixing layer is assessed using space-measured sea-surface temperature data and historical in situ temperature measurements. The results are compared with TOPEX/Poseidon satellite altimeter measurement at different large spatial scales. It is indicated that thermal effect accounts for much of the observed seasonal variability, especially when averaging over zonal regions. Some regional seasonal patterns of sea-level anomalies in the tropical oceans are well represented by the thermal model prediction. Systematic differences are shown between TOPEX/Poseidon observation and thermal contribution at a 1–2 cm level. The potential causes for these differences are discussed, including water mass exchanges among the atmosphere, land, and oceans, and error sources in the steric result and geophysical corrections applied in TOPEX/Poseidon data. Received: 25 September 1998 / Accepted: 13 July 1999     

Determining receiver biases in GPS-derived total electron content in the auroral oval and polar cap region using ionosonde measurements

Global Positioning System (GPS) total electron content (TEC) measurements, although highly precise, are often rendered inaccurate due to satellite and receiver differential code biases (DCBs). Calculated satellite DCB values are now available from a variety of sources, but receiver DCBs generally remain an undertaking of receiver operators and processing centers. A procedure for removing these receiver DCBs from GPS-derived ionospheric TEC at high latitudes, using Canadian Advanced Digital Ionosonde (CADI) measurements, is presented. Here, we will test the applicability of common numerical methods for estimating receiver DCBs in high-latitude regions and compare our CADI-calibrated GPS vertical TEC (vTEC) measurements to corresponding International GNSS Service IONEX-interpolated vTEC map data. We demonstrate that the bias values determined using the CADI method are largely independent of the topside model (exponential, Epstein, and α-Chapman) used. We further confirm our results via comparing bias-calibrated GPS vTEC with those derived from incoherent scatter radar (ISR) measurements. These CADI method results are found to be within 1.0 TEC units (TECU) of ISR measurements. The numerical methods tested demonstrate agreement varying from within 1.6 TECU to in excess of 6.0 TECU when compared to ISR measurements.     

Single receiver phase ambiguity resolution with GPS data

Global positioning system (GPS) data processing algorithms typically improve positioning solution accuracy by fixing double-differenced phase bias ambiguities to integer values. These “double-difference ambiguity resolution” methods usually invoke linear combinations of GPS carrier phase bias estimates from pairs of transmitters and pairs of receivers, and traditionally require simultaneous measurements from at least two receivers. However, many GPS users point position a single local receiver, based on publicly available solutions for GPS orbits and clocks. These users cannot form double differences. We present an ambiguity resolution algorithm that improves solution accuracy for single receiver point-positioning users. The algorithm processes dual- frequency GPS data from a single receiver together with wide-lane and phase bias estimates from the global network of GPS receivers that were used to generate the orbit and clock solutions for the GPS satellites. We constrain (rather than fix) linear combinations of local phase biases to improve compatibility with global phase bias estimates. For this precise point positioning, no other receiver data are required. When tested, our algorithm significantly improved repeatability of daily estimates of ground receiver positions, most notably in the east component by approximately 30% with respect to the nominal case wherein the carrier biases are estimated as real values. In this “static” test for terrestrial receiver positions, we achieved daily repeatability of 1.9, 2.1 and 6.0 mm in the east, north and vertical (ENV) components, respectively. For kinematic solutions, ENV repeatability is 7.7, 8.4, and 11.7 mm, respectively, representing improvements of 22, 8, and 14% with respect to the nominal. Results from precise orbit determination of the twin GRACE satellites demonstrated that the inter-satellite baseline accuracy improved by a factor of three, from 6 to 2 mm up to a long-term bias. Jason-2/Ocean Surface Topography Mission precise orbit determination tests results implied radial orbit accuracy significantly below the 10 mm level. Stability of time transfer, in low-Earth orbit, improved from 40 to 7 ps. We produced these results by applying this algorithm within the Jet Propulsion Laboratory’s (JPL’s) GIPSY/OASIS software package and using JPL’s orbit and clock products for the GPS constellation. These products now include a record of the wide-lane and phase bias estimates from the underlying global network of GPS stations. This implies that all GIPSY–OASIS positioning users can now benefit from this capability to perform single-receiver ambiguity resolution.     

利用TOPEX/Poseidon卫星测高资料监测全球海平面变化

本文利用１９９３年１月至１９９９年５月的ＴＯＰＥＸ／Ｐｏｓｅｉｄｏｎ卫星测高数据计算了全球海平变化。海平面模型误差和不恰当的加权方法都会影响全球海平面序列的周年变化,潮汐模型误差对于季节性变化有明显的影响。利用两个高度计算的海平面变化存在周年变化存在明显的差异,利用ＴＯＰＥＸ高度计和Ｐｏｓｅｉｄｏｎ高度计得到的该时段全球平均海平面的变化率分别为２．０ｍｍ／ａ和－０．５ｍｍ／ａ。与南方涛动指数的比较     

由ERS-2和TOPEX卫星测高数据推算的海面高异常的主成分分析

利用1995~2003年间的TOPEX/POSEIDON和ERS-2卫星测高数据,尽量采用相同的改正模型对TOPEX和ERS-2卫星测高数据分别进行改正,然后由共线分析法分别推算了全球1°×1°的35 d的海面高异常时间序列,并采用主成分分析法分别对这两个海面高异常时间序列进行了分析。     

Low-degree earth deformation from reprocessed GPS observations

Surface mass variations of low spherical harmonic degree are derived from residual displacements of continuously tracking global positioning system (GPS) sites. Reprocessed GPS observations of 14 years are adjusted to obtain surface load coefficients up to degree n _max = 6 together with station positions and velocities from a rigorous parameter combination. Amplitude and phase estimates of the degree-1 annual variations are partly in good agreement with previously published results, but also show interannual differences of up to 2 mm and about 30 days, respectively. The results of this paper reveal significant impacts from different GPS observation modeling approaches on estimated degree-1 coefficients. We obtain displacements of the center of figure (CF) relative to the center of mass (CM), Δr _CF–CM, that differ by about 10 mm in maximum when compared to those of the commonly used coordinate residual approach. Neglected higher-order ionospheric terms are found to induce artificial seasonal and long-term variations especially for the z-component of Δr _CF–CM. Daily degree-1 estimates are examined in the frequency domain to assess alias contributions from model deficiencies with regard to satellite orbits. Finally, we directly compare our estimated low-degree surface load coefficients with recent results that involve data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission.     

Mission design,operation and exploitation of the gravity field and steady-state ocean circulation explorer mission

The European Space Agency’s Gravity field and steady-state ocean circulation explorer mission (GOCE) was launched on 17 March 2009. As the first of the Earth Explorer family of satellites within the Agency’s Living Planet Programme, it is aiming at a better understanding of the Earth system. The mission objective of GOCE is the determination of the Earth’s gravity field and geoid with high accuracy and maximum spatial resolution. The geoid, combined with the de facto mean ocean surface derived from twenty-odd years of satellite radar altimetry, yields the global dynamic ocean topography. It serves ocean circulation and ocean transport studies and sea level research. GOCE geoid heights allow the conversion of global positioning system (GPS) heights to high precision heights above sea level. Gravity anomalies and also gravity gradients from GOCE are used for gravity-to-density inversion and in particular for studies of the Earth’s lithosphere and upper mantle. GOCE is the first-ever satellite to carry a gravitational gradiometer, and in order to achieve its challenging mission objectives the satellite embarks a number of world-first technologies. In essence the spacecraft together with its sensors can be regarded as a spaceborne gravimeter. In this work, we describe the mission and the way it is operated and exploited in order to make available the best-possible measurements of the Earth gravity field. The main lessons learned from the first 19 months in orbit are also provided, in as far as they affect the quality of the science data products and therefore are of specific interest for GOCE data users.     

Impact of Earth radiation pressure on GPS position estimates

GPS satellite orbits available from the International GNSS Service (IGS) show a consistent radial bias of up to several cm and a particular pattern in the Satellite Laser Ranging (SLR) residuals, which are suggested to be related to radiation pressure mismodeling. In addition, orbit-related frequencies were identified in geodetic time series such as apparent geocenter motion and station displacements derived from GPS tracking data. A potential solution to these discrepancies is the inclusion of Earth radiation pressure (visible and infrared) modeling in the orbit determination process. This is currently not yet considered by all analysis centers contributing to the IGS final orbits. The acceleration, accounting for Earth radiation and satellite models, is introduced in this paper in the computation of a global GPS network (around 200 IGS sites) adopting the analysis strategies from the Center for Orbit Determination in Europe (CODE). Two solutions covering 9 years (2000–2008) with and without Earth radiation pressure were computed and form the basis for this study. In previous studies, it has been shown that Earth radiation pressure has a non-negligible effect on the GPS orbits, mainly in the radial component. In this paper, the effect on the along-track and cross-track components is studied in more detail. Also in this paper, it is shown that Earth radiation pressure leads to a change in the estimates of GPS ground station positions, which is systematic over large regions of the Earth. This observed “deformation” of the Earth is towards North–South and with large scale patterns that repeat six times per GPS draconitic year (350 days), reaching a magnitude of up to 1 mm. The impact of Earth radiation pressure on the geocenter and length of day estimates was also investigated, but the effect is found to be less significant as compared to the orbits and position estimates.     

Satellite clock estimation at 1 Hz for realtime kinematic PPP applications

Realtime kinematic precise point positioning (PPP) requires 1 Hz GPS satellite clock corrections. An efficient clock estimation approach is presented. It applies a combined dual-thread algorithm consisting of an undifferenced (UD) and epoch-differenced (ED) engine. The UD engine produces absolute clock values every 5 s, and the ED engine produces relative clock values between neighboring epochs at 1-s interval. A final 1-Hz satellite clock can be generated by combining the UD absolute clock and ED relative clock efficiently and accurately. Forty stations from a global tracking network are used to estimate the realtime 1-Hz clock with the proposed method. Both the efficiency and accuracy of the resultant clock corrections are validated. Efficiency test shows that the UD processing thread requires an average time of 1.88 s on a 1-GHz CPU PC for one epoch of data, while ED processing requires only 0.25 s. Accuracy validation test shows that the estimated 1-Hz clock agrees with IGS final clock accurately. The RMS values of all the available GPS satellite clock bias are less than 0.2 ns (6 cm), and most of them are less than 0.1 ns (3 cm). All the RMS values of Signal in Space Range Error (SISRE) are at centimeter level. Applying the accurate and realtime clock to realtime PPP, an accuracy of 10 cm in the horizontal and 20 cm in the vertical is achieved after a short period of initialization.     

A spectral optimally interpolated mean sea surface from satellite radar altimetry

 A technique is presented for the development of a high-precision and high-resolution mean sea surface model utilising radar altimetric sea surface heights extracted from the geodetic phase of the European Space Agency (ESA) ERS-1 mission. The methodology uses a cubic-spline fit of dual ERS-1 and TOPEX crossovers for the minimisation of radial orbit error. Fourier domain processing techniques are used for spectral optimal interpolation of the mean sea surface in order to reduce residual errors within the initial model. The EGM96 gravity field and sea surface topography models are used as reference fields as part of the determination of spectral components required for the optimal interpolation algorithm. A comparison between the final model and 10 cycles of TOPEX sea surface heights shows differences of between 12.3 and 13.8 cm root mean square (RMS). An un-optimally interpolated surface comparison with TOPEX data gave differences of between 15.7 and 16.2 cm RMS. The methodology results in an approximately 10-cm improvement in accuracy. Further improvement will be attained with the inclusion of stacked altimetry from both current and future missions. Received: 22 December 1999 / Accepted: 6 November 2000     

Systematic biases in DORIS-derived geocenter time series related to solar radiation pressure mis-modeling

As any satellite geodesy technique, DORIS can monitor geocenter variations associated to mass changes within the Earth–Atmosphere–Continental hydrosphere–Oceans system. However, especially for the Z-component, corresponding to a translation of the Earth along its rotation axis, the estimated geocenter is usually affected by large systematic errors of unknown cause. By reprocessing old DORIS data, and by analyzing single satellite solutions in the frequency domain, we show that some of these errors are satellite-dependent and related to the current DORIS orbit determination strategy. In particular, a better handling of solar pressure radiation effects on SPOT-2 and TOPEX satellites is proposed which removes a large part of such artifacts. By empirically multiplying the current solar pressure model with a single coefficient (1.03 for TOPEX/Poseidon after 1993.57, and 0.96 before; and 1.08 for SPOT-2) estimated over a long time period, we can improve the measurement noise of the Z-geocenter component from 47.5 to 30.4 mm for the RMS and from 35 to 6 mm for the amplitude of the annual signal. However, the estimated SRP coefficient for SPOT-2 presents greater temporal variability, indicating that a new, dedicated solar radiation pressure model is still needed for precise geodetic applications. In addition, for the TOPEX satellite, a clear discontinuity of unknown cause is also detected on July 27, 1993.     

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.     

确定卫星与接收机信号延迟偏差的新方法及其应用

单频ＧＰＳ接收机用户通常需要进行电离层延迟改正,电离层延迟改正量通常来源于电离层延迟改正模型或双频ＧＰＳ基准站信息,后者即是利用双频ＧＰＳ观测值估计电子含量总数,求解电离层延迟改正量。利用双频ＧＰＳ观测值估计电子含量总数,一个关键总是是去掉卫星与接收信号延迟偏差。     

High-rate GPS clock corrections from CODE: support of 1 Hz applications

GPS zero-difference applications with a sampling rate up to 1 Hz require corresponding high-rate GPS clock corrections. The determination of the clock corrections in a full network solution is a time-consuming task. The Center for Orbit Determination in Europe (CODE) has developed an efficient algorithm based on epoch-differenced phase observations, which allows to generate high-rate clock corrections within reasonably short time (< 2 h) and with sufficient accuracy (on the same level as the CODE rapid or final clock corrections, respectively). The clock determination procedure at CODE and the new algorithm is described in detail. It is shown that the simplifications to speed up the processing are not causing a significant loss of accuracy for the clock corrections. The high-rate clock corrections have in essence the same quality as clock corrections determined in a full network solution. In order to support 1 Hz applications 1-s clock corrections would be needed. The computation time, even for the efficient algorithm, is not negligible, however. Therefore, we studied whether a reduced sampling is sufficient for the GPS satellite clock corrections to reach the same or only slightly inferior level of accuracy as for the full 1-s clock correction set. We show that high-rate satellite clock corrections with a spacing of 5 s may be linearly interpolated resulting in less than 2% degradation of accuracy.     

Atmospheric loading corrections at the observation level in VLBI analysis

This paper investigates whether in very long baseline interferometry (VLBI) analysis atmospheric loading corrections should be applied a priori at the observation level or whether it is sufficient to correct for atmospheric loading effects a posteriori by adding constant values per session to the estimated station coordinates. Simulated observations at single stations corresponding to the precise point positioning approach of global navigation satellite systems show that the atmospheric loading effect can be fully recovered by a posteriori corrections, i.e., the height differences between both approaches stay well below 1 mm. However, real global VLBI network solutions with sessions from 1984 to 2008 reveal that the effect of neglected atmospheric loading corrections at the stations is distributed to the other stations in the network, thus resulting in station height differences between solutions with observation level and with a posteriori corrections which can be as large as 10 mm and a ‘damping’ effect of the corrections. As soon as the terrestrial reference frame and the corresponding coordinate time series are determined, it would be conceptually wrong to apply atmospheric loading corrections at the VLBI stations. We recommend the rigorous application of atmospheric loading corrections at the observation level to all stations of a VLBI network because the seven parameters for translation, rotation, and in particular the network-scale of VLBI networks are significantly affected.