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See detailImpact of GPS Antenna Phase Center Models on Zenith Wet Delay and Tropospheric Gradients
Ejigu, Yohannes Getachew; Hunegnaw, Addisu UL; Abraha, Kibrom Ebuy UL et al

in GPS Solutions (2019), 23(5),

We demonstrate the potential for the Global Positioning System (GPS) to provide highly accurate tropospheric products for use in meteorological applications. Tropospheric products, in particular the wet ... [more ▼]

We demonstrate the potential for the Global Positioning System (GPS) to provide highly accurate tropospheric products for use in meteorological applications. Tropospheric products, in particular the wet delays, are treated as an unknown parameter in GPS processing and are estimated with other parameters such as station coordinates. In this study, we investigate the effects of Phase Center Correction (PCC) models on tropospheric zenith wet delay (ZWD), integrated water vapor (IWV) and gradient products. Two solutions were generated using the GAMIT software over the EUREF Permanent GNSS Network (EPN). The first (reference) solution was derived by applying the International GNSS Service (IGS) type-mean PCC model, while for the second solution PCC models from individual calibrations were used. The solutions were generated identically, except for the PCC model differences. The two solutions were compared, with the assumption that common signals are differenced out. The comparison of the two solutions clearly shows a bias in all tropospheric products, which can be attributed to PCC model deficiencies. Overall, mean biases of ±1.8, ±0.3, ±0.14 and ±0.19 mm are evident in ZWD, IWV, North-South and East-West gradients, respectively. Moreover, the differences between the two solutions show seasonal variations. For all antenna types, the ZWD and IWV differences are dominated by white plus power-law noise, with latter characterizing the low-frequency spectrum. On the other hand, the horizontal gradients exhibit a white plus first order autoregressive noise characteristic with less than 1% white noise. The individual PCC model provides a better fit to an external independent model in terms of gradient estimate and also provides up to 3 % more carrier phase ambiguity resolution. [less ▲]

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See detailStatistical significance of trends in Zenith Wet Delay from re-processed GPS solutions
Klos, Anna; Hunegnaw, Addisu UL; Teferle, Felix Norman UL et al

in GPS Solutions (2018)

Long series of Zenith Wet Delay (ZWD) obtained as part of a homogeneous re-processing of Global Positioning System solutions constitute a reliable set of data to be assimilated into climate models. The ... [more ▼]

Long series of Zenith Wet Delay (ZWD) obtained as part of a homogeneous re-processing of Global Positioning System solutions constitute a reliable set of data to be assimilated into climate models. The correct stochastic properties, i.e. the noise model of these data, have to be identified to assess the real value of ZWD trend uncertainties since assuming an inappropriate noise model may lead to over- or underestimated error bounds leading to statistically insignificant trends. We present the ZWD time series for 1995–2017 for 120 selected globally distributed stations. The deterministic model in the form of a trend and significant seasonal signals were removed prior to the noise analysis. We examined different stochastic models and compared them to widely assumed white noise (WN). A combination of the autoregressive process of first-order plus WN (AR(1) + WN) was proven to be the preferred stochastic representation of the ZWD time series over the generally assumed white-noise-only approach. We found that for 103 out of 120 considered stations, the AR(1) process contributed to the AR(1) + WN model in more than 50% with noise amplitudes between 9 and 68 mm. As soon as the AR(1) + WN model was employed, 43 trend estimates became statistically insignificant, compared to 5 insignificant trend estimates for a white-noise-only model. We also found that the ZWD trend uncertainty may be underestimated by 5–14 times with median value of 8 using the white-noise-only assumption. Therefore, we recommend that AR(1) + WN model is employed before tropospheric trends are to be determined with the greatest reliability. [less ▲]

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See detailOn the combined effect of periodic signals and colored noise on velocity uncertainties
Klos, Anna; Olivares Pulido, German UL; Teferle, Felix Norman UL et al

in GPS Solutions (2017)

The velocity estimates and their uncertainties derived from position time series of Global Navigation Satellite System stations are affected by seasonal signals and their harmonics, and the statistical ... [more ▼]

The velocity estimates and their uncertainties derived from position time series of Global Navigation Satellite System stations are affected by seasonal signals and their harmonics, and the statistical properties, i.e., the stochastic noise, contained in the series. If the deterministic model in the form of linear trend and periodic terms is not accurate enough to describe the time series, it will alter the stochastic model, and the resulting effect on the velocity uncertainties can be perceived as a result of a misfit of the deterministic model. The effects of insufficiently modeled seasonal signals will propagate into the stochastic model and falsify the results of the noise analysis, in addition to velocity estimates and their uncertainties. We provide the general dilution of precision (GDP) of velocity uncertainties as the ratio of uncertainties of velocities determined from to two different deterministic models while accounting for stochastic noise at the same time. In this newly defined GDP, the first deterministic model includes a linear trend, while the second one includes a linear trend and seasonal signals. These two are tested with the assumption of white noise only as well as the combinations of power-law and white noise in the data. The more seasonal terms are added to the series, the more biased the velocity uncertainties become. With increasing time span of observations, the assumption of seasonal signals becomes less important, and the power-law character of the residuals starts to play a crucial role in the determined velocity uncertainties. With reference frame and sea level applications in mind, we argue that 7 and 9 years of continuous observations is the threshold for white and flicker noise, respectively, while 17 years are required for random-walk to decrease GDP below 5% and to omit periodic oscillations in the GNSS-derived time series taking only the noise model into consideration. [less ▲]

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See detailOptimum stochastic modeling for GNSS tropospheric delay estimation in real-time
Hadas, Tomasz; Teferle, Felix Norman UL; Kazmierski, Kamil et al

in GPS Solutions (2016)

In GNSS data processing, the station height, receiver clock and tropospheric delay (ZTD) are highly correlated to each other. Although the zenith hydrostatic delay of the troposphere can be provided with ... [more ▼]

In GNSS data processing, the station height, receiver clock and tropospheric delay (ZTD) are highly correlated to each other. Although the zenith hydrostatic delay of the troposphere can be provided with sufficient accuracy, zenith wet delay (ZWD) has to be estimated, which is usually done in a random walk process. Since ZWD temporal variation depends on the water vapor content in the atmosphere, it seems to be reasonable that ZWD constraints in GNSS processing should be geographically and/or time dependent. We propose to take benefit from numerical weather prediction models to define optimum random walk process noise. In the first approach, we used archived VMF1-G data to calculate a grid of yearly and monthly means of the difference of ZWD between two consecutive epochs divided by the root square of the time lapsed, which can be considered as a random walk process noise. Alternatively, we used the Global Forecast System model from National Centres for Environmental Prediction to calculate random walk process noise dynamically in real-time. We performed two representative experimental campaigns with 20 globally distributed International GNSS Service (IGS) stations and compared real-time ZTD estimates with the official ZTD product from the IGS. With both our approaches, we obtained an improvement of up to 10% in accuracy of the ZTD estimates compared to any uniformly fixed random walk process noise applied for all stations. [less ▲]

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See detailSpatial–temporal variations of water vapor content over Ethiopia: a study using GPS observations and the ECMWF model
Abraha, Kibrom Ebuy UL; Lewi, Elias; Masson, Frederic et al

in GPS Solutions (2015)

We characterize the spatial–temporal variability of integrated water vapor (IWV) in Ethiopia from a network of global positioning system (GPS) stations and the European Center for Medium range Weather ... [more ▼]

We characterize the spatial–temporal variability of integrated water vapor (IWV) in Ethiopia from a network of global positioning system (GPS) stations and the European Center for Medium range Weather Forecasting (ECMWF) model. The IWV computed from the ECMWF model is integrated from the height of the GPS stations on 60 pressure levels to take both the actual earth surface and the model orography discrepancies into account. First, we compare the IWV estimated from GPS and from the model. The bias varies from site to site, and the correlation coefficients between the two data sets exceed 0.85 at different time scales. The results of this study show that the general ECMWF IWV trend is underestimation over highlands and overestimation over lowlands for wet periods, and overestimation over high- lands and underestimation over lowlands for dry periods with very few exceptional stations. Second, we observe the spatial variation of the IWV. High values are obtained in those stations that are located in the north-eastern (Afar depression) sites and the south-western part of the country. This distribution is related to the spatial variability of the climate in Ethiopia. Finally, we study the seasonal cycle and inter-annual variability of IWV for all stations over Ethiopia. The main result is the strong inter-annual vari- ability observed for the dry seasons. [less ▲]

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See detailComparative Analysis of Real-Time Precise Point Positioning Zenith Total Delay Estimates
Ahmed, Furqan UL; Vaclavovic, Pavel; Teferle, Felix Norman UL et al

in GPS Solutions (2014)

The continuous evolution of global navigation satellite systems (GNSS) meteorology has led to an increased use of associated observations for operational modern low-latency numerical weather prediction ... [more ▼]

The continuous evolution of global navigation satellite systems (GNSS) meteorology has led to an increased use of associated observations for operational modern low-latency numerical weather prediction (NWP) models, which assimilate GNSS-derived zenith total delay (ZTD) estimates. The development of NWP models with faster assimilation cycles, e.g., 1-h assimilation cycle in the rapid update cycle NWP model, has increased the interest of the meteorological community toward sub-hour ZTD estimates. The suitability of real-time ZTD estimates obtained from three different precise point positioning software packages has been assessed by comparing them with the state-of-the-art IGS final troposphere product as well as collocated radiosonde (RS) observations. The ZTD estimates obtained by BNC2.7 show a mean bias of 0.21 cm, and those obtained by the G-Nut/Tefnut software library show a mean bias of 1.09 cm to the IGS final troposphere product. In comparison with the RS-based ZTD, the BNC2.7 solutions show mean biases between 1 and 2 cm, whereas the G-Nut/Tefnut solutions show mean biases between 2 and 3 cm with the RS-based ZTD, and the ambiguity float and ambiguity fixed solutions obtained by PPPWizard have mean biases between 6 and 7 cm with the references. The large biases in the time series from PPP-Wizard are due to the fact that this software has been developed for kinematic applications and hence does not apply receiver antenna eccentricity and phase center offset (PCO) corrections on the observations. Application of the eccentricity and PCO corrections to the a priori coordinates has resulted in a 66 % reduction of bias in the PPP-Wizard solutions. The biases are found to be stable over the whole period of the comparison, which are criteria (rather than the magnitude of the bias) for the suitability of ZTD estimates for use in NWP nowcasting. A millimeter-level impact on the ZTD estimates has also been observed in relation to ambiguity resolution. As a result of a comparison with the established user requirements for NWP nowcasting, it was found that both the GNut/Tefnut solutions and one of the BNC2.7 solutions meet the threshold requirements, whereas one of the BNC2.7 solution and both the PPPWizard solutions currently exceed this threshold. [less ▲]

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See detailQuality assessment of GPS reprocessed terrestrial reference frame
Collilieux, Xavier; Métivier, Laurent; Altamimi, Zuheir et al

in GPS Solutions (2011), 15(3), 219--231

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 ... [more ▼]

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. [less ▲]

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See detailKinematic precise point postioning at remote marine platforms
Geng, J.; Teferle, Felix Norman UL; Meng, X. et al

in GPS Solutions (2010), 14(4), 343-350

Precise kinematic differential positioning using the global positioning system (GPS) at a marine platform usually requires a relatively short distance (e.g. 500km) to a land-based reference station. As an ... [more ▼]

Precise kinematic differential positioning using the global positioning system (GPS) at a marine platform usually requires a relatively short distance (e.g. 500km) to a land-based reference station. As an alternative, precise point positioning (PPP) is normally considered free from this limiting requirement. However, due to the prerequisite of network-based satellite products, PPP at a remote marine platform may still be affected by its distance to the reference network. Hence, this paper investigates this scenario by configuring rings of reference stations with different radii centered on a to-be-positioned marine platform. Particularly, we applied ambiguity resolution at a single station to PPP by estimating uncalibrated phase delays (UPDs). We used three rings of reference stations centered on a vessel, with radii of roughly 900, 2,000 and 3,600 km, to determine satellite clocks and UPDs independently. For comparison, we also performed differential positioning based on a single reference station with baseline lengths of about 400, 1,700 and 2,800 km. We demonstrate that, despite the increasing ring-network radius to a few 1,000 km, the overall change in accuracy of the satellite clocks that are used at the vessel is smaller than 0.02 ns, and the RMS values of differences between the three sets of narrow-lane UPD estimates are around 0.05 cycles only. Moreover, the kinematic positioning accuracy of PPP is affected by the increasing ring-network radius, but can still achieve several centimeters after ambiguity resolution when the vessel is over a few 1,000 km away from the ring network, showing better performance than that of differential positioning. Therefore, we propose that ambiguity- fixed PPP can be used at remote marine platforms that support precise oceanographic and geophysical applications in open oceans. [less ▲]

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See detailAmbiguity resolution in precise point positioning with hourly data
Geng, J.; Teferle, Felix Norman UL; Shi, C. et al

in GPS Solutions (2009), 13(4), 263-270

Precise Point Positioning (PPP) has become a recognized and powerful tool for scientific analysis of Global Positioning System (GPS) measurements. Until recently, ambiguity resolution at a single station ... [more ▼]

Precise Point Positioning (PPP) has become a recognized and powerful tool for scientific analysis of Global Positioning System (GPS) measurements. Until recently, ambiguity resolution at a single station has been considered difficult, due to the non-integer uncalibrated hardware delays (UHD) originating in receivers and satellites. Fortunately, recent studies show that if these UHD can be determined precisely with a network in advance, then ambiguity resolution at a single station is possible. In this study, the method proposed by Ge et al (2007) is adopted with a refinement in which the fractional parts of single-difference narrow-lane UHD for a satellite pair are determined within each full pass over a regional network. This study uses the European Reference Frame Permanent Network (EPN) to determine these UHD from Day 245 to 251 in 2007, and 27 IGS stations inside and outside the EPN are used to conduct ambiguity resolution in hourly PPP. It is found that the total hourly position accuracy is improved from 3.8 cm, 1.5 cm and 2.8 cm to 0.5 cm, 0.5 cm and 1.4 cm in East, North and Up, respectively, for the stations inside the EPN. For the stations outside the EPN, some of which are even over 2000 km away from the EPN, their total hourly East, North and Up position accuracies still achieve 0.6 cm, 0.6 cm and 2.0 cm, respectively, when the EPN-based UHD are applied to the ambiguity resolution at these stations. Therefore, it is feasible and beneficial for the operators of GPS networks, such as the providers of PPP-based online services, to provide these UHD estimates as an additional product to allow users to conduct ambiguity resolution in PPP. [less ▲]

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See detailAnomalous harmonics in the spectra of GPS position estimates
Ray, R.; Altamimi, Z.; Collilieux, X. et al

in GPS Solutions (2008), 12(1), 55-64

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 ... [more ▼]

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. [less ▲]

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See detailSeasonal Motion in the Annapolis, Maryland GPS Monument
Schenewerk, M.; van Dam, Tonie UL; Nerem, Steven R.

in GPS Solutions (1999), 2(3), 41-49

The permanent GPS tracking site at Annapolis, MD shows a 7-mm seasonal signal primarily in its horizontal position. It is suggested that thermal expansion of the pier on which the antenna rests is the ... [more ▼]

The permanent GPS tracking site at Annapolis, MD shows a 7-mm seasonal signal primarily in its horizontal position. It is suggested that thermal expansion of the pier on which the antenna rests is the source of this motion. A simple numerical model of the pier reproduces the observed motion of the GPS antenna, lending credence to this hypothesis. Although adding an additional level of complexity, this motion is predictable and the site retains it s value for high precision monitoring. Although the arrangement of this GPS site it somewhat uncommon, these results emphasize the importance of the underlying antenna monumentation when measuring crustal motions. [less ▲]

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