Detecting offsets in GPS time series: first results from the Detection of Offsets in GPS Experiment

The accuracy of Global Positioning System (GPS) time series is degraded by the presence of offsets. To assess the effectiveness of methods that detect and remove these offsets, we designed and managed the Detection of Offsets in GPS Experiment. We simulated time series that mimicked realistic GPS data consisting of a velocity component, offsets, white and flicker noises (1/f spectrum noises) composed in an additive model. The data set was made available to the GPS analysis community without revealing the offsets, and several groups conducted blind tests with a range of detection approaches. The results show that, at present, manual methods (where offsets are hand picked) almost always give better results than automated or semi‒automated methods (two automated methods give quite similar velocity bias as the best manual solutions). For instance, the fifth percentile range (5% to 95%) in velocity bias for automated approaches is equal to 4.2 mm/year (most commonly ±0.4 mm/yr from the truth), whereas it is equal to 1.8 mm/yr for the manual solutions (most commonly 0.2 mm/yr from the truth). The magnitude of offsets detectable by manual solutions is smaller than for automated solutions, with the smallest detectable offset for the best manual and automatic solutions equal to 5 mm and 8 mm, respectively. Assuming the simulated time series noise levels are representative of real GPS time series, robust geophysical interpretation of individual site velocities lower than 0.2–0.4 mm/yr is therefore certainly not robust, although a limit of nearer 1 mm/yr would be a more conservative choice. Further work to improve offset detection in GPS coordinates time series is required before we can routinely interpret sub‒mm/yr velocities for single GPS stations.

Precise Orbit Determination of Low Earth Satellites at AIUB using GPS and SLR data

An ever increasing number of low Earth orbiting (LEO) satellites is, or will be, equipped with retro-reflectors for Satellite Laser Ranging (SLR) and on-board receivers to collect observations from Global Navigation Satellite Systems (GNSS) such as the Global Positioning Sys- tem (GPS) and the Russian GLONASS and the European Galileo systems in the future. At the Astronomical Insti- tute of the University of Bern (AIUB) LEO precise or- bit determination (POD) using either GPS or SLR data is performed for a wide range of applications for satellites at different altitudes. For this purpose the classical numeri- cal integration techniques, as also used for dynamic orbit determination of satellites at high altitudes, are extended by pseudo-stochastic orbit modeling techniques to effi- ciently cope with potential force model deficiencies for satellites at low altitudes. Accuracies of better than 2 cm may be achieved by pseudo-stochastic orbit modeling for satellites at very low altitudes such as for the GPS-based POD of the Gravity field and steady-state Ocean Circula- tion Explorer (GOCE).

Earth gravity field recovery using GPS, GLONASS, and SLR satellites

The time variable Earth’s gravity field provides the information about mass transport within the system Earth, i.e., the relationship of mass transport between atmosphere, oceans, and land hydrology. We recover the low-degree parameters of the time variable gravity field using microwave observations from GPS and GLONASS satellites and from SLR data to five geodetic satellites, namely LAGEOS-1/2, Starlette, Stella, and AJISAI. GPS satellites are particularly sensitive to specific coefficients of the Earth's gravity field, because of the deep 2:1 orbital resonance with Earth rotation (two revolutions of the GPS satellites per sidereal day). The resonant coefficients cause, among other, a “secular” drift (actually periodic variations of very long periods) of the semi-major axes of up to 5.3 m/day of GPS satellites. We processed 10 years of GPS and GLONASS data using the standard orbit models from the Center of Orbit Determination in Europe (CODE) with a simultaneous estimation of the Earth gravity field coefficients and other parameters, e.g., satellite orbit parameters, station coordinates, Earth rotation parameters, troposphere delays, etc. The weekly GNSS gravity solutions up to degree and order 4/4 are compared to the weekly SLR gravity field solutions. The SLR-derived geopotential coefficients are compared to monthly GRACE and CHAMP results.

Homogeneous reprocessing of GPS, GLONASS and SLR observations

The International GNSS Service (IGS) provides operational products for the GPS and GLONASS constellation. Homogeneously processed time series of parameters from the IGS are only available for GPS. Reprocessed GLONASS series are provided only by individual Analysis Centers (i. e. CODE and ESA), making it difficult to fully include the GLONASS system into a rigorous GNSS analysis. In view of the increasing number of active GLONASS satellites and a steadily growing number of GPS+GLONASS-tracking stations available over the past few years, Technische Universität Dresden, Technische Universität München, Universität Bern and Eidgenössische Technische Hochschule Zürich performed a combined reprocessing of GPS and GLONASS observations. Also, SLR observations to GPS and GLONASS are included in this reprocessing effort. Here, we show only SLR results from a GNSS orbit validation. In total, 18 years of data (1994–2011) have been processed from altogether 340 GNSS and 70 SLR stations. The use of GLONASS observations in addition to GPS has no impact on the estimated linear terrestrial reference frame parameters. However, daily station positions show an RMS reduction of 0.3 mm on average for the height component when additional GLONASS observations can be used for the time series determination. Analyzing satellite orbit overlaps, the rigorous combination of GPS and GLONASS neither improves nor degrades the GPS orbit precision. For GLONASS, however, the quality of the microwave-derived GLONASS orbits improves due to the combination. These findings are confirmed using independent SLR observations for a GNSS orbit validation. In comparison to previous studies, mean SLR biases for satellites GPS-35 and GPS-36 could be reduced in magnitude from −35 and −38 mm to −12 and −13 mm, respectively. Our results show that remaining SLR biases depend on the satellite type and the use of coated or uncoated retro-reflectors. For Earth rotation parameters, the increasing number of GLONASS satellites and tracking stations over the past few years leads to differences between GPS-only and GPS+GLONASS combined solutions which are most pronounced in the pole rate estimates with maximum 0.2 mas/day in magnitude. At the same time, the difference between GLONASS-only and combined solutions decreases. Derived GNSS orbits are used to estimate combined GPS+GLONASS satellite clocks, with first results presented in this paper. Phase observation residuals from a precise point positioning are at the level of 2 mm and particularly reveal poorly modeled yaw maneuver periods.

Methodology for GPS Synchronization Evaluation with High Accuracy

Clock synchronization in the order of nanoseconds is one of the critical factors for time-based localization. Currently used time synchronization methods are developed for the more relaxed needs of network operation. Their usability for positioning should be carefully evaluated. In this paper, we are particularly interested in GPS-based time synchronization. To judge its usability for localization we need a method that can evaluate the achieved time synchronization with nanosecond accuracy. Our method to evaluate the synchronization accuracy is inspired by signal processing algorithms and relies on fine grain time information. The method is able to calculate the clock offset and skew between devices with nanosecond accuracy in real time. It was implemented using software defined radio technology. We demonstrate that GPS-based synchronization suffers from remaining clock offset in the range of a few hundred of nanoseconds but the clock skew is negligible. Finally, we determine a corresponding lower bound on the expected positioning error.

Comparison of GOCE-GPS gravity fields derived by different approaches

Several techniques have been proposed to exploit GNSS-derived kinematic orbit information for the determination of long-wavelength gravity field features. These methods include the (i) celestial mechanics approach, (ii) short-arc approach, (iii) point-wise acceleration approach, (iv) averaged acceleration approach, and (v) energy balance approach. Although there is a general consensus that—except for energy balance—these methods theoretically provide equivalent results, real data gravity field solutions from kinematic orbit analysis have never been evaluated against each other within a consistent data processing environment. This contribution strives to close this gap. Target consistency criteria for our study are the input data sets, period of investigation, spherical harmonic resolution, a priori gravity field information, etc. We compare GOCE gravity field estimates based on the aforementioned approaches as computed at the Graz University of Technology, the University of Bern, the University of Stuttgart/Austrian Academy of Sciences, and by RHEA Systems for the European Space Agency. The involved research groups complied with most of the consistency criterions. Deviations only occur where technical unfeasibility exists. Performance measures include formal errors, differences with respect to a state-of-the-art GRACE gravity field, (cumulative) geoid height differences, and SLR residuals from precise orbit determination of geodetic satellites. We found that for the approaches (i) to (iv), the cumulative geoid height differences at spherical harmonic degree 100 differ by only ≈10 % ; in the absence of the polar data gap, SLR residuals agree by ≈96 % . From our investigations, we conclude that real data analysis results are in agreement with the theoretical considerations concerning the (relative) performance of the different approaches.

GOCE: assessment of GPS-only gravity field determination

The GOCE satellite was orbiting the Earth in a Sun-synchronous orbit at a very low altitude for more than 4 years. This low orbit and the availability of high-quality data make it worthwhile to assess the contribution of GOCE GPS data to the recovery of both the static and time-variable gravity fields. We use the kinematic positions of the official GOCE precise science orbit (PSO) product to perform gravity field determination using the Celestial Mechanics Approach. The generated gravity field solutions reveal severe systematic errors centered along the geomagnetic equator. Their size is significantly coupled with the ionospheric density and thus generally increasing over the mission period. The systematic errors may be traced back to the kinematic positions of the PSO product and eventually to the ionosphere-free GPS carrier phase observations used for orbit determination. As they cannot be explained by the current higher order ionospheric correction model recommended by the IERS Conventions 2010, an empirical approach is presented by discarding GPS data affected by large ionospheric changes. Such a measure yields a strong reduction of the systematic errors along the geomagnetic equator in the gravity field recovery, and only marginally reduces the set of useable kinematic positions by at maximum 6 % for severe ionosphere conditions. Eventually it is shown that GOCE gravity field solutions based on kinematic positions have a limited sensitivity to the largest annual signal related to land hydrology.