Earth Rotation and Gravity Field Parameters from Satellite Laser Ranging

We present the results from a simultaneous estimation of the gravity field, Earth rotation parameters, and station coordinates from combined SLR solutions incorporating up to nine geodetic satellites: LAGEOS-1/2, Starlette, Stella, AJISAI, Beacon-C, Lares, Blits and LARES. These solutions cover all three pillars of satellite geodesy and ensure full consistency between the Earth rotation parameters, gravity field coefficients, and geometry-related parameters. We address benefits emerging from such an approach and discuss particular aspects and limitations of the gravity field recovery using SLR data. The current accuracy of SLR-derived polar motion, by the means of WRMS w.r.t. IERS-08-C04 series, is at a level of 118-149 μas, which corresponds to 4 to 5 mm on the Earth’s surface. The WRMS of SLR-derived Length-of-Day, when the gravity field parameters are simultaneously estimated, is 56 μs/day, corresponding to about 26 mm on the ground, and the mean bias of SLR-derived Length-of-Day is 6.3 μs/day, corresponding to 3 mm.

Time variable Earth’s gravity field from SLR satellites

The time variable Earth’s gravity field contains information about the mass transport within the system Earth, i.e., the relationship between mass variations in the atmosphere, oceans, land hydrology, and ice sheets. For many years, satellite laser ranging (SLR) observations to geodetic satellites have provided valuable information of the low-degree coefficients of the Earth’s gravity field. Today, the Gravity Recovery and Climate Experiment (GRACE) mission is the major source of information for the time variable field of a high spatial resolution. We recover the low-degree coefficients of the time variable Earth’s gravity field using SLR observations up to nine geodetic satellites: LAGEOS-1, LAGEOS-2, Starlette, Stella, AJISAI, LARES, Larets, BLITS, and Beacon-C. We estimate monthly gravity field coefficients up to degree and order 10/10 for the time span 2003–2013 and we compare the results with the GRACE-derived gravity field coefficients. We show that not only degree-2 gravity field coefficients can be well determined from SLR, but also other coefficients up to degree 10 using the combination of short 1-day arcs for low orbiting satellites and 10-day arcs for LAGEOS-1/2. In this way, LAGEOS-1/2 allow recovering zonal terms, which are associated with long-term satellite orbit perturbations, whereas the tesseral and sectorial terms benefit most from low orbiting satellites, whose orbit modeling deficiencies are minimized due to short 1-day arcs. The amplitudes of the annual signal in the low-degree gravity field coefficients derived from SLR agree with GRACE K-band results at a level of 77 %. This implies that SLR has a great potential to fill the gap between the current GRACE and the future GRACE Follow-On mission for recovering of the seasonal variations and secular trends of the longest wavelengths in gravity field, which are associated with the large-scale mass transport in the system Earth.

CODE’s new solar radiation pressure model for GNSS orbit determination

The Empirical CODE Orbit Model (ECOM) of the Center for Orbit Determination in Europe (CODE), which was developed in the early 1990s, is widely used in the International GNSS Service (IGS) community. For a rather long time, spurious spectral lines are known to exist in geophysical parameters, in particular in the Earth Rotation Parameters (ERPs) and in the estimated geocenter coordinates, which could recently be attributed to the ECOM. These effects grew creepingly with the increasing influence of the GLONASS system in recent years in the CODE analysis, which is based on a rigorous combination of GPS and GLONASS since May 2003. In a first step we show that the problems associated with the ECOM are to the largest extent caused by the GLONASS, which was reaching full deployment by the end of 2011. GPS-only, GLONASS-only, and combined GPS/GLONASS solutions using the observations in the years 2009–2011 of a global network of 92 combined GPS/GLONASS receivers were analyzed for this purpose. In a second step we review direct solar radiation pressure (SRP) models for GNSS satellites. We demonstrate that only even-order short-period harmonic perturbations acting along the direction Sun-satellite occur for GPS and GLONASS satellites, and only odd-order perturbations acting along the direction perpendicular to both, the vector Sun-satellite and the spacecraft’s solar panel axis. Based on this insight we assess in the third step the performance of four candidate orbit models for the future ECOM. The geocenter coordinates, the ERP differences w. r. t. the IERS 08 C04 series of ERPs, the misclosures for the midnight epochs of the daily orbital arcs, and scale parameters of Helmert transformations for station coordinates serve as quality criteria. The old and updated ECOM are validated in addition with satellite laser ranging (SLR) observations and by comparing the orbits to those of the IGS and other analysis centers. Based on all tests, we present a new extended ECOM which substantially reduces the spurious signals in the geocenter coordinate z (by about a factor of 2–6), reduces the orbit misclosures at the day boundaries by about 10 %, slightly improves the consistency of the estimated ERPs with those of the IERS 08 C04 Earth rotation series, and substantially reduces the systematics in the SLR validation of the GNSS orbits.

The impact of common versus separate estimation of orbit parameters on GRACE gravity field solutions

Gravity field parameters are usually determined from observations of the GRACE satellite mission together with arc-specific parameters in a generalized orbit determination process. When separating the estimation of gravity field parameters from the determination of the satellites’ orbits, correlations between orbit parameters and gravity field coefficients are ignored and the latter parameters are biased towards the a priori force model. We are thus confronted with a kind of hidden regularization. To decipher the underlying mechanisms, the Celestial Mechanics Approach is complemented by tools to modify the impact of the pseudo-stochastic arc-specific parameters on the normal equations level and to efficiently generate ensembles of solutions. By introducing a time variable a priori model and solving for hourly pseudo-stochastic accelerations, a significant reduction of noisy striping in the monthly solutions can be achieved. Setting up more frequent pseudo-stochastic parameters results in a further reduction of the noise, but also in a notable damping of the observed geophysical signals. To quantify the effect of the a priori model on the monthly solutions, the process of fixing the orbit parameters is replaced by an equivalent introduction of special pseudo-observations, i.e., by explicit regularization. The contribution of the thereby introduced a priori information is determined by a contribution analysis. The presented mechanism is valid universally. It may be used to separate any subset of parameters by pseudo-observations of a special design and to quantify the damage imposed on the solution.

Time Variable Gravity: Contributions of GOCE Satellite Data to Monthly and Bi-monthly GRACE Gravity Estimates

A feasibility study by Pail et al. (Can GOCE help to improve temporal gravity field estimates? In: Ouwehand L (ed) Proceedings of the 4th International GOCE User Workshop, ESA Publication SP-696, 2011b) shows that GOCE (‘Gravity field and steady-state Ocean Circulation Explorer’) satellite gravity gradiometer (SGG) data in combination with GPS derived orbit data (satellite-to-satellite tracking: SST-hl) can be used to stabilize and reduce the striping pattern of a bi-monthly GRACE (‘Gravity Recovery and Climate Experiment’) gravity field estimate. In this study several monthly (and bi-monthly) combinations of GRACE with GOCE SGG and GOCE SST-hl data on the basis of normal equations are investigated. Our aim is to assess the role of the gradients (solely) in the combination and whether already one month of GOCE observations provides sufficient data for having an impact in the combination. The estimation of clean and stable monthly GOCE SGG normal equations at high resolution ( >  d/o 150) is found to be difficult, and the SGG component, solely, does not show significant added value to monthly and bi-monthly GRACE gravity fields. Comparisons of GRACE-only and combined monthly and bi-monthly solutions show that the striping pattern can only be reduced when using both GOCE observation types (SGG, SST-hl), and mainly between d/o 45 and 60.

Satellite laser ranging to GPS and GLONASS

Satellite laser ranging (SLR) to the satellites of the global navigation satellite systems (GNSS) provides substantial and valuable information about the accuracy and quality of GNSS orbits and allows for the SLR-GNSS co-location in space. In the framework of the NAVSTAR-SLR experiment two GPS satellites of Block-IIA were equipped with laser retroreflector arrays (LRAs), whereas all satellites of the GLONASS system are equipped with LRAs in an operational mode. We summarize the outcome of the NAVSTAR-SLR experiment by processing 20 years of SLR observations to GPS and 12 years of SLR observations to GLONASS satellites using the reprocessed microwave orbits provided by the center for orbit determination in Europe (CODE). The dependency of the SLR residuals on the size, shape, and number of corner cubes in LRAs is studied. We show that the mean SLR residuals and the RMS of residuals depend on the coating of the LRAs and the block or type of GNSS satellites. The SLR mean residuals are also a function of the equipment used at SLR stations including the single-photon and multi-photon detection modes. We also show that the SLR observations to GNSS satellites are important to validate GNSS orbits and to assess deficiencies in the solar radiation pressure models. We found that the satellite signature effect, which is defined as a spread of optical pulse signals due to reflection from multiple reflectors, causes the variations of mean SLR residuals of up to 15 mm between the observations at nadir angles of 0∘ and 14∘. in case of multi-photon SLR stations. For single-photon SLR stations this effect does not exceed 1 mm. When using the new empirical CODE orbit model (ECOM), the SLR mean residual falls into the range 0.1–1.8 mm for high-performing single-photon SLR stations observing GLONASS-M satellites with uncoated corner cubes. For best-performing multi-photon stations the mean SLR residuals are between −12.2 and −25.6 mm due to the satellite signature effect.

A consistent combination of GNSS and SLR with minimum constraints

In this article, the realization of a global terrestrial reference system (TRS) based on a consistent combination of Global Navigation Satellite System (GNSS) and Satellite Laser Ranging (SLR) is studied. Our input data consists of normal equation systems from 17 years (1994– 2010) of homogeneously reprocessed GPS, GLONASS and SLR data. This effort used common state of the art reduction models and the same processing software (Bernese GNSS Software) to ensure the highest consistency when combining GNSS and SLR. Residual surface load deformations are modeled with a spherical harmonic approach. The estimated degree-1 surface load coefficients have a strong annual signal for which the GNSS- and SLR-only solutions show very similar results. A combination including these coefficients reduces systematic uncertainties in comparison to the singletechnique solution. In particular, uncertainties due to solar radiation pressure modeling in the coefficient time series can be reduced up to 50 % in the GNSS+SLR solution compared to the GNSS-only solution. In contrast to the ITRF2008 realization, no local ties are used to combine the different geodetic techniques.We combine the pole coordinates as global ties and apply minimum constraints to define the geodetic datum. We show that a common origin, scale and orientation can be reliably realized from our combination strategy in comparison to the ITRF2008.

CODE ultra-rapid product series for the IGS

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions: Astronomical Institute, University of Bern (AIUB), Bern, Switzerland; Federal Office of Topography swisstopo, Wabern, Switzerland; Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany; Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany. It acts as a global analysis center of the International GNSS Service (IGS). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software. In this context an ultra-rapid solution series is generated considering GPS and GLONASS satellites. It is updated several times per day and contains 24 hours of observed and 24 hours of predicted orbit interval. More details are available in: Lutz, S., G. Beutler, S. Schaer, R. Dach, A. Jäggi; 2014: CODE's new ultra-rapid orbit and ERP products for the IGS. GPS Solutions. DOI 10.1007/s10291-014-0432-2

CODE repro2 product series for the IGS

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions: • Astronomical Institute, University of Bern (AIUB), Bern, Switzerland • Federal Office of Topography swisstopo, Wabern, Switzerland • Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany • Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany It acts as a global analysis center of the International GNSS Service (IGS, Dow et al, 2009). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software (Dach et al., 2015). In this context the contribution to the IGS repro02 effort is generated considering only the GPS satellites between 1994 and 2001 as well as the GPS and GLONASS satellites from 2002 to the end of 2013.

CODE rapid product series for the IGS

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions: Astronomical Institute, University of Bern (AIUB), Bern, Switzerland;Federal Office of Topography swisstopo, Wabern, Switzerland; Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany; Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany. It acts as a global analysis center of the International GNSS Service (IGS). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software (Dach et al., 2015). In this context a rapid solution series is generated considering all active GPS and GLONASS satellites. It contains 24 hours of observed orbits and published at the day after the observations.

CODE final product series for the IGS

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions:Astronomical Institute, University of Bern (AIUB), Bern, Switzerland; Federal Office of Topography swisstopo, Wabern, Switzerland; Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany; Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany. It acts as a global analysis center of the International GNSS Service (IGS). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software. In this context a final solution series is generated considering all active GPS and GLONASS satellites. It is published in daily files with a delay of about two weeks.

CODE product series for the IGS-MGEX project

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions: Astronomical Institute, University of Bern (AIUB), Bern, Switzerland; Federal Office of Topography swisstopo, Wabern, Switzerland; Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany; Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany. It acts as a global analysis center of the International GNSS Service (IGS). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software. In this context a multi-GNSS solution is generated considering all active GPS, GLONASS, Galileo, BeiDou (expect for GEOs), and QZSS satellites as a contribution to the IGS-MGEX project. The results are published with a delay of about two weeks.

The CODE MGEX orbit and clock solution

The Center for Orbit Determination in Europe (CODE) is contributing as a global Analysis center to the International GNSS Service (IGS) since many years. The processing of GPS and GLONASS data is well established in CODE’s ultra-rapid, rapid, and final product lines. With the introduction of new signals for the established and new GNSS, new challenges and opportunities are arising for the GNSS data management and processing. The IGS started the Multi-GNSS-EXperiment (MGEX) in 2012 in order to gain first experience with the new data formats and to develop new strategies for making optimal use of these additional measurements. CODE has started to contribute to IGS MGEX with a consistent, rigorously combined triple-system orbit solution (GPS, GLONASS, and Galileo). SLR residuals for the computed Galileo satellite orbits are of the order of 10 cm. Furthermore CODE established a GPS and Galileo clock solution. A quality assessment shows that these experimental orbit and clock products allow even a Galileo-only precise point positioning (PPP) with accuracies on the decimeter- (static PPP) to meter-level (kinematic PPP) for selected stations.