ALBERT

Description: Of the three satellite geodetic techniques contributing to the International Terrestrial Reference Frame (ITRF), Satellite Laser Ranging (SLR) is generally held to provide the most reliable time series of geocentre coordinates and exclusively defines the ITRF origin. Traditionally, only observations to the two LAser GEOdynamics Satellite (LAGEOS) and Etalon pairs of satellites have been used for the definition of the ITRF origin. Previous simulation studies using evenly sampled LAGEOS-like data have shown that only the Z component of geocentre motion suffers minor collinearity issues, which may explain its lower quality compared to the equatorial components. Using collinearity diagnosis, this study provides insight into the actual capability of SLR to sense geocentre motion using the existing geographically unbalanced ground network and real observations to eight spherical geodetic satellites. We find that, under certain parameterisations, observations to the low Earth orbiters (LEOs) Starlette, Stella, Ajisai and LAser RElativity Satellite are able to improve the observability of the geocentre coordinates in multi-satellite solutions compared to LAGEOS-only solutions. The higher sensitivity of LEOs to geocentre motion and the larger number of observations are primarily responsible for the improved observability. Errors in the modelling of Starlette, Stella and Ajisai orbits may contaminate the geocentre motion estimates, but do not disprove the intrinsic strength of LEO tracking data. The sporadically observed Etalon satellites fail to make a significant beneficial contribution to the observability of the geocentre coordinates derived via the network shift approach and can be safely omitted from SLR data analyses for TRF determination.

Description: The European Space Agency Gravity field and steady-state Ocean Circular Explorer (GOCE) carries a gradiometer consisting of three pairs of accelerometers in an orthogonal triad. Precise GOCE science orbit solutions (PSO), which are based on satellite-to-satellite tracking observations by the Global Positioning System and which are claimed to be at the few cm precision level, can be used to calibrate and validate the observations taken by the accelerometers. This has been done for each individual accelerometer by a dynamic orbit fit of the time series of position co-ordinates from the PSOs, where the accelerometer observations represent the non-gravitational accelerations. Since the accelerometers do not coincide with the center of mass of the GOCE satellite, the observations have to be corrected for rotational and gravity gradient terms. This is not required when using the so-called common-mode accelerometer observations, provided the center of the gradiometer coincides with the GOCE center of mass. Dynamic orbit fits based on these common-mode accelerations therefore served as reference. It is shown that for all individual accelerometers, similar dynamic orbit fits can be obtained provided the above-mentioned corrections are made. In addition, accelerometer bias estimates are obtained that are consistent with offsets in the gravity gradients that are derived from the GOCE gradiometer observations.

Description: This paper reports on different sources of errors that occur in the calibration process of a superconducting gravimeter (SG), determined by comparison with a ballistic absolute gravimeter (AG); some of them have never been discussed in the literature. We then provide methods to mitigate the impact of those errors, to achieve a robust calibration estimate at the level. We demonstrate that a standard deviation at the level of can be reached within 48 h by measuring at spring tides and by increasing the AG sampling rate. This is much shorter than what is classically reported in previous empirical studies. Measuring more than 5 days around a tidal extreme does not improve the precision in the calibration factor significantly, as the variation in the error as a function of \(1/\sqrt{N} \) does not apply, considering the decrease in signal amplitude due to the tidal modulation. However, we investigate the precision improvement up to 120 days, which can be useful if an AG is run continuously: at mid-latitude it would require 21 days to ensure a calibration factor at the level with a 99.7 % confidence interval. We also show that restricting the AG measurement periods to tidal extrema can reduce instrument demand, while this does not affect the precision on the calibration factor significantly. Then, we quantify the effect of high microseismic noise causing aliasing in the AG time series. We eventually discuss the attenuation bias that might be induced by noisy time series of the SG. When experiments are performed at the level, 7 are needed to ensure that the error in the calibration estimate will be at the 1 per mille level with a 99 % confidence.

Description: Graph theory is useful for analyzing time-dependent model parameters estimated from interferometric synthetic aperture radar (InSAR) data in the temporal domain. Plotting acquisition dates (epochs) as vertices and pair-wise interferometric combinations as edges defines an incidence graph. The edge-vertex incidence matrix and the normalized edge Laplacian matrix are factors in the covariance matrix for the pair-wise data. Using empirical measures of residual scatter in the pair-wise observations, we estimate the relative variance at each epoch by inverting the covariance of the pair-wise data. We evaluate the rank deficiency of the corresponding least-squares problem via the edge-vertex incidence matrix. We implement our method in a MATLAB software package called GraphTreeTA available on GitHub ( https://github.com/feigl/gipht ). We apply temporal adjustment to the data set described in Lu et al. (Geophys Res Solid Earth 110, 2005 ) at Okmok volcano, Alaska, which erupted most recently in 1997 and 2008. The data set contains 44 differential volumetric changes and uncertainties estimated from interferograms between 1997 and 2004. Estimates show that approximately half of the magma volume lost during the 1997 eruption was recovered by the summer of 2003. Between June 2002 and September 2003, the estimated rate of volumetric increase is \((6.2 \, \pm \, 0.6) \times 10^6~\mathrm{m}^3/\mathrm{year} \) . Our preferred model provides a reasonable fit that is compatible with viscoelastic relaxation in the five years following the 1997 eruption. Although we demonstrate the approach using volumetric rates of change, our formulation in terms of incidence graphs applies to any quantity derived from pair-wise differences, such as range change, range gradient, or atmospheric delay.

Description: This paper focuses on the contribution of the global positioning system (GPS) and BeiDou navigation satellite system (BDS) observations to precise point positioning (PPP) ambiguity resolution (AR). A GPS + BDS fractional cycle bias (FCB) estimation method and a PPP AR model were developed using integrated GPS and BDS observations. For FCB estimation, the GPS + BDS combined PPP float solutions of the globally distributed IGS MGEX were first performed. When integrating GPS observations, the BDS ambiguities can be precisely estimated with less than four tracked BDS satellites. The FCBs of both GPS and BDS satellites can then be estimated from these precise ambiguities. For the GPS + BDS combined AR, one GPS and one BDS IGSO or MEO satellite were first chosen as the reference satellite for GPS and BDS, respectively, to form inner-system single-differenced ambiguities. The single-differenced GPS and BDS ambiguities were then fused by partial ambiguity resolution to increase the possibility of fixing a subset of decorrelated ambiguities with high confidence. To verify the correctness of the FCB estimation and the effectiveness of the GPS + BDS PPP AR, data recorded from about 75 IGS MGEX stations during the period of DOY 123-151 (May 3 to May 31) in 2015 were used for validation. Data were processed with three strategies: BDS-only AR, GPS-only AR and GPS + BDS AR. Numerous experimental results show that the time to first fix (TTFF) is longer than 6 h for the BDS AR in general and that the fixing rate is usually less than 35 % for both static and kinematic PPP. An average TTFF of 21.7 min and 33.6 min together with a fixing rate of 98.6 and 97.0 % in static and kinematic PPP, respectively, can be achieved for GPS-only ambiguity fixing. For the combined GPS + BDS AR, the average TTFF can be shortened to 16.9 min and 24.6 min and the fixing rate can be increased to 99.5 and 99.0 % in static and kinematic PPP, respectively. Results also show that GPS + BDS PPP AR outperforms single-system PPP AR in terms of convergence time and position accuracy.