ALBERT

Description: The key issue to enable precise point positioning with ambiguity resolution (PPP-AR) is to estimate fractional-cycle biases (FCBs), which mainly relate to receiver and satellite hardware biases, over a network of reference stations. While this has been well achieved for GPS, FCB estimation for GLONASS is difficult because (1) satellites do not share the same frequencies as a result of Frequency Division Multiple Access (FDMA) signals; (2) and even worse, pseudorange hardware biases of receivers vary in an irregular manner with manufacturers, antennas, domes, firmware, etc., which especially complicates GLONASS PPP-AR over inhomogeneous receivers. We propose a general approach where external ionosphere products are introduced into GLONASS PPP to estimate precise FCBs that are less impaired by pseudorange hardware biases of diverse receivers to enable PPP-AR. One month of GLONASS data at about 550 European stations were processed. From an exemplary network of 51 inhomogeneous receivers, including four receiver types with various antennas and spanning about 800 km in both longitudinal and latitudinal directions, we found that 92.4 % of all fractional parts of GLONASS wide-lane ambiguities agree well within \(\pm \) 0.15 cycles with a standard deviation of 0.09 cycles if global ionosphere maps (GIMs) are introduced, compared to only 51.7 % within \(\pm \) 0.15 cycles and a larger standard deviation of 0.22 cycles otherwise. Hourly static GLONASS PPP-AR at 40 test stations can reach position estimates of about 1 and 2 cm in RMS from ground truth for the horizontal and vertical components, respectively, which is comparable to hourly GPS PPP-AR. Integrated GLONASS and GPS PPP-AR can further achieve an RMS of about 0.5 cm in horizontal and 1–2 cm in vertical components. We stress that the performance of GLONASS PPP-AR across inhomogeneous receivers depends on the accuracy of ionosphere products. GIMs have a modest accuracy of only 2–8 TECU (Total Electron Content Unit) in vertical which confines PPP-AR to an approximately \(800\times 800\)  km area in Europe. We expect that a regional ionosphere map with a better than 1 TECU accuracy is likely to improve the GLONASS PPP-AR efficiency.

Description: Homogeneously reprocessed combined GPS/GLONASS 1- and 3-day solutions from 1994 to 2013, generated by the Center for Orbit Determination in Europe (CODE) in the frame of the second reprocessing campaign REPRO-2 of the International GNSS Service, as well as GPS- and GLONASS-only 1- and 3-day solutions for the years 2009 to 2011 are analyzed to assess the impact of the arc length on the estimated Earth Orientation Parameters (EOP, namely polar motion and length of day), on the geocenter, and on the orbits. The conventional CODE 3-day solutions assume continuity of orbits, polar motion components, and of other parameters at the day boundaries. An experimental 3-day solution, which assumes continuity of the orbits, but independence from day to day for all other parameters, as well as a non-overlapping 3-day solution, is included into our analysis. The time series of EOPs, geocenter coordinates, and orbit misclosures, are analyzed. The long-arc solutions were found to be superior to the 1-day solutions: the RMS values of EOP and geocenter series are typically reduced between 10 and 40 %, except for the polar motion rates, where RMS reductions by factors of 2–3 with respect to the 1-day solutions are achieved for the overlapping and the non-overlapping 3-day solutions. In the low-frequency part of the spectrum, the reduction is even more important. The better performance of the orbits of 3-day solutions with respect to 1-day solutions is also confirmed by the validation with satellite laser ranging.

Description: On 17 April 2011, all analysis centers (ACs) of the International GNSS Service (IGS) adopted the reference frame realization IGS08 and the corresponding absolute antenna phase center model igs08.atx for their routine analyses. The latter consists of an updated set of receiver and satellite antenna phase center offsets and variations (PCOs and PCVs). An update of the model was necessary due to the difference of about 1 ppb in the terrestrial scale between two consecutive realizations of the International Terrestrial Reference Frame (ITRF2008 vs. ITRF2005), as that parameter is highly correlated with the GNSS satellite antenna PCO components in the radial direction. For the receiver antennas, more individual calibrations could be considered and GLONASS-specific correction values were added. For the satellite antennas, all correction values except for the GPS PCVs were newly estimated considering more data than for the former model. Satellite-specific PCOs for all GPS satellites active since 1994 could be derived from reprocessed solutions of five ACs generated within the scope of the first IGS reprocessing campaign. Two ACs separately derived a full set of corrections for all GLONASS satellites active since 2003. Ignoring scale-related biases, the accuracy of the satellite antenna PCOs is on the level of a few cm. With the new phase center model, orbit discontinuities at day boundaries can be reduced, and the consistency between GPS and GLONASS results is improved. To support the analysis of low Earth orbiter (LEO) data, igs08.atx was extended with LEO-derived PCV estimates for big nadir angles in June 2013.

Description: A critical point in the analysis of ground displacement time series, as those recorded by space geodetic techniques, is the development of data-driven methods that allow the different sources of deformation to be discerned and characterized in the space and time domains. Multivariate statistic includes several approaches that can be considered as a part of data-driven methods. A widely used technique is the principal component analysis (PCA), which allows us to reduce the dimensionality of the data space while maintaining most of the variance of the dataset explained. However, PCA does not perform well in finding the solution to the so-called blind source separation (BSS) problem, i.e., in recovering and separating the original sources that generate the observed data. This is mainly due to the fact that PCA minimizes the misfit calculated using an \(L_{2}\) norm ( \(\chi ^{2})\) , looking for a new Euclidean space where the projected data are uncorrelated. The independent component analysis (ICA) is a popular technique adopted to approach the BSS problem. However, the independence condition is not easy to impose, and it is often necessary to introduce some approximations. To work around this problem, we test the use of a modified variational Bayesian ICA (vbICA) method to recover the multiple sources of ground deformation even in the presence of missing data. The vbICA method models the probability density function (pdf) of each source signal using a mix of Gaussian distributions, allowing for more flexibility in the description of the pdf of the sources with respect to standard ICA, and giving a more reliable estimate of them. Here we present its application to synthetic global positioning system (GPS) position time series, generated by simulating deformation near an active fault, including inter-seismic, co-seismic, and post-seismic signals, plus seasonal signals and noise, and an additional time-dependent volcanic source. We evaluate the ability of the PCA and ICA decomposition techniques in explaining the data and in recovering the original (known) sources. Using the same number of components, we find that the vbICA method fits the data almost as well as a PCA method, since the \(\chi ^{2}\) increase is less than 10 % the value calculated using a PCA decomposition. Unlike PCA, the vbICA algorithm is found to correctly separate the sources if the correlation of the dataset is low ( \(〈\) 0.67) and the geodetic network is sufficiently dense (ten continuous GPS stations within a box of side equal to two times the locking depth of a fault where an earthquake of \(M_\mathrm{{w}} 〉6\) occurred). We also provide a cookbook for the use of the vbICA algorithm in analyses of position time series for tectonic and non-tectonic applications.

Description: The primary purpose of the International very long baseline interferometry (VLBI) Service for Geodesy and Astrometry Intensive sessions is the rapid estimation of UT1-TAI. Improving the robustness and the precision of the UT1 estimates from the Intensives is an important goal. The INT01 series, which usually uses the Kokee–Wettzell baseline and runs on weekdays, is the most regular IVS Intensive series. The United States Naval Observatory which schedules these sessions traditionally used a small list of strong sources. In 2009, the authors requested and received the use of nine IVS R&D sessions for the evaluation of a new strategy which draws on all sources mutually visible on the Kokee–Wettzell baseline. Analysis of these sessions was sufficiently promising that in July 2010, USNO began to alternate the use of the original and the new strategy in scheduling the INT01 sessions to assess the operational effectiveness of the proposed strategy. In this paper, we summarize our analysis of the R&D sessions, and we also analyze 2 years of operational INT01 sessions. Considered in toto, the new strategy performs as well as, or better than, the original strategy in terms of several measures of robustness and precision. Furthermore, the RMS difference of the UT1 estimates from the 1 h operational INTO1 sessions and concurrently run 24 h VLBI sessions is 21.0 \(\upmu \) s, compared to 30.7 \(\upmu \) s using the standard strategy, indicating that the new strategy is, on average, 30 % more accurate.