Geocenter coordinates estimated from GNSS data as viewed by perturbation theory

Time series of geocenter coordinates were determined with data of two global navigation satellite systems (GNSSs), namely the U.S. GPS (Global Positioning System) and the Russian GLONASS (Global’naya Nawigatsionnaya Sputnikowaya Sistema). The data was recorded in the years 2008–2011 by a global network of 92 permanently observing GPS/GLONASS receivers. Two types of daily solutions were generated independently for each GNSS, one including the estimation of geocenter coordinates and one without these parameters. A fair agreement for GPS and GLONASS was found in the geocenter x- and y-coordinate series. Our tests, however, clearly reveal artifacts in the z-component determined with the GLONASS data. Large periodic excursions in the GLONASS geocenter z-coordinates of about 40 cm peak-to-peak are related to the maximum elevation angles of the Sun above/below the orbital planes of the satellite system and thus have a period of about 4 months (third of a year). A detailed analysis revealed that the artifacts are almost uniquely governed by the differences of the estimates of direct solar radiation pressure (SRP) in the two solution series (with and without geocenter estimation). A simple formula is derived, describing the relation between the geocenter z-coordinate and the corresponding parameter of the SRP. The effect can be explained by first-order perturbation theory of celestial mechanics. The theory also predicts a heavy impact on the GNSS-derived geocenter if once-per-revolution SRP parameters are estimated in the direction of the satellite’s solar panel axis. Specific experiments using GPS observations revealed that this is indeed the case. Although the main focus of this article is on GNSS, the theory developed is applicable to all satellite observing techniques. We applied the theory to satellite laser ranging (SLR) solutions using LAGEOS. It turns out that the correlation between geocenter and SRP parameters is not a critical issue for the SLR solutions. The reasons are threefold: The direct SRP is about a factor of 30–40 smaller for typical geodetic SLR satellites than for GNSS satellites, allowing it in most cases to not solve for SRP parameters (ruling out the correlation between these parameters and the geocenter coordinates); the orbital arc length of 7 days (which is typically used in SLR analysis) contains more than 50 revolutions of the LAGEOS satellites as compared to about two revolutions of GNSS satellites for the daily arcs used in GNSS analysis; the orbit geometry is not as critical for LAGEOS as for GNSS satellites, because the elevation angle of the Sun w.r.t. the orbital plane is usually significantly changing over 7 days.

Combined LARES-LAGEOS Solutions

LARES is a new spherical geodetic satellite designed for SLR observations. It is made of solid tungsten alloy covered with 92 corner cubes. Due to a very small area-to-mass ratio, the sensitivity of LARES orbits to non-gravitational forces is greatly minimized. We processed 82 weeks (Feb12-Aug13) of LARES observations from a global SLR network and we analyzed the contribution of LARES data to the current SLR products (e.g., global scale and geocenter coordinates). The quality of the combined LARES+LAGEOS-1/2 solutions is also addressed in the paper. Introduction LARES

The new CMOS Tracking Camera used at the Zimmerwald Observatory

During the last years the use of tracking cameras for SLR observations became less important due to the high accuracy of the predicted orbits. Upcoming new targets like satellites in eccentric orbits and space debris objects, however, require tracking cameras again. In 2013 the interline CCD camera was replaced at the Zimmerwald Observatory with a so called scientific CMOS camera. This technology promises a better performance for this application than all kinds of CCD cameras. After the comparison of the different technologies the focus will be on the integration in the Zimmerwald SLR system.

Impact of Earth radiation pressure on LAGEOS orbits and on the global scale

The indirect solar radiation pressure caused by reflected or re-emitted radiation by the Earth’s surface is an important non-gravitational force perturbing the orbits of geodetic satellites (Rubincam and Weiss, 1986; Martin and Rubincam, 1996). In the case of LAGEOS this acceleration is of the order of 15% of the direct solar radiation pressure. Therefore, Earth radiation pressure has a non-negligible impact not only on LAGEOS orbits, but also on the SLR-derived terrestrial reference frame. We investigate the impact of the Earth radiation pressure on LAGEOS orbits and on the SLR-derived parameters. Earth radiation pressure has a remarkable impact on the semi-major axes of the LAGEOS satellites, causing a systematic reduction of 1.5 mm. The infrared Earth radiation causes a reduction of about 1.0 mm and the Earth’s reflectivity of 0.5 mm of the LAGEOS’ semi-major axes. The global scale defined by the SLR network is changed by 0.07 ppb, when applying Earth radiation pressure. The resulting station heights differ by 0.5-0.6 mm in the solution with and without Earth radiation pressure. However, when range biases are estimated, the height differences are absorbed by the range biases, and thus, the station heights are not shifted.

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: precise orbit determination for the entire mission

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) was the first Earth explorer core mission of the European Space Agency. It was launched on March 17, 2009 into a Sun-synchronous dusk-dawn orbit and re-entered into the Earth’s atmosphere on November 11, 2013. The satellite altitude was between 255 and 225 km for the measurement phases. The European GOCE Gravity consortium is responsible for the Level 1b to Level 2 data processing in the frame of the GOCE High-level processing facility (HPF). The Precise Science Orbit (PSO) is one Level 2 product, which was produced under the responsibility of the Astronomical Institute of the University of Bern within the HPF. This PSO product has been continuously delivered during the entire mission. Regular checks guaranteed a high consistency and quality of the orbits. A correlation between solar activity, GPS data availability and quality of the orbits was found. The accuracy of the kinematic orbit primarily suffers from this. Improvements in modeling the range corrections at the retro-reflector array for the SLR measurements were made and implemented in the independent SLR validation for the GOCE PSO products. The satellite laser ranging (SLR) validation finally states an orbit accuracy of 2.42 cm for the kinematic and 1.84 cm for the reduced-dynamic orbits over the entire mission. The common-mode accelerations from the GOCE gradiometer were not used for the official PSO product, but in addition to the operational HPF work a study was performed to investigate to which extent common-mode accelerations improve the reduced-dynamic orbit determination results. The accelerometer data may be used to derive realistic constraints for the empirical accelerations estimated for the reduced-dynamic orbit determination, which already improves the orbit quality. On top of that the accelerometer data may further improve the orbit quality if realistic constraints and state-of-the-art background models such as gravity field and ocean tide models are used for the reduced-dynamic orbit determination.

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.

GOCE precise orbit determination for the entire Mission – challenges in the final mission phase

The Gravity field and steady-state Ocean Circulation Explorer (GOCE), ESA’s first Earth Explorer core mission, was launched on March 17, 2009 into a sunsynchronous dusk-dawn orbit and eventually re-entered into the Earth’s atmosphere on November 11, 2013. A precise science orbit (PSO) product was provided by the GOCE High-level Processing Facility (HPF) from the GPS high-low Satellite-to-Satellite Tracking (hl-SST) data from the beginning until the very last days of the mission. We recapitulate the PSO procedure and refer to the results achieved until the official end of the GOCE mission on October 21, 2013, where independent validations with Satellite Laser ranging (SLR) measurements confirmed a high quality of the PSO product of about 2 cm 1-D RMS. We then focus on the period after the official end of the mission, where orbits could still be determined thanks to the continuously running GPS receivers delivering high quality data until a few hours before the re-entry into the Earth’s atmosphere. We address the challenges encountered for orbit determination during these last days and report on adaptions in the PSO procedure to also obtain good orbit results at the unprecedented low orbital altitudes below 224 km.

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.

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.

Extraction of spin periods of space debris from optical light curves

The population of space debris increased drastically during the last years. These objects have become a great threat for active satellites. Because the relative velocities between space debris and satellites are high, space debris objects may destroy active satellites through collisions. Furthermore, collisions involving massive objects produce large number of fragments leading to significant growth of the space debris population. The long term evolution of the debris population is essentially driven by so-called catastrophic collisions. An effective remediation measure in order to stabilize the population in Low Earth Orbit (LEO) is therefore the removal of large, massive space debris. To remove these objects, not only precise orbits, but also more detailed information about their attitude states will be required. One important property of an object targeted for removal is its spin period, spin axis orientation and their change over time. Rotating objects will produce periodic brightness variations with frequencies which are related to the spin periods. Such a brightness variation over time is called a light curve. Collecting, but also processing light curves is challenging due to several reasons. Light curves may be undersampled, low frequency components due to phase angle and atmospheric extinction changes may be present, and beat frequencies may occur when the rotation period is close to a multiple of the sampling period. Depending on the method which is used to extract the frequencies, also method-specific properties have to be taken into account. The astronomical Institute of the University of Bern (AIUB) light curve database will be introduced, which contains more than 1,300 light curves acquired over more than seven years. We will discuss properties and reliability of different time series analysis methods tested and currently used by AIUB for the light curve processing. Extracted frequencies and reconstructed phases for some interesting targets, e.g. GLONASS satellites, for which also SLR data were available for the period confirmation, will be presented. Finally we will present the reconstructed phase and its evolution over time of a High-Area-to-Mass-Ratio (HAMR) object, which AIUB observed for several years.

Space debris attitude simulation - ιOTA (In-Orbit Tumbling Analysis)

Today, there is little knowledge on the attitude state of decommissioned intact objects in Earth orbit. Observational means have advanced in the past years, but are still limited with respect to an accurate estimate of motion vector orientations and magnitude. Especially for the preparation of Active Debris Removal (ADR) missions as planned by ESA’s Clean Space initiative or contingency scenarios for ESA spacecraft like ENVISAT, such knowledge is needed. ESA's “Debris Attitude Motion Measurements and Modelling” project (ESA Contract No. 40000112447), led by the Astronomical Institute of the University of Bern (AIUB), addresses this problem. The goal of the project is to achieve a good understanding of the attitude evolution and the considerable internal and external effects which occur. To characterize the attitude state of selected targets in LEO and GTO, multiple observation methods are combined. Optical observations are carried out by AIUB, Satellite Laser Ranging (SLR) is performed by the Space Research Institute of the Austrian Academy of Sciences (IWF) and radar measurements and signal level determination are provided by the Fraunhofer Institute for High Frequency Physics and Radar Techniques (FHR). The In-Orbit Tumbling Analysis tool (ιOTA) is a prototype software, currently in development by Hyperschall Technologie Göttingen GmbH (HTG) within the framework of the project. ιOTA will be a highly modular software tool to perform short-(days), medium-(months) and long-term (years) propagation of the orbit and attitude motion (six degrees-of-freedom) of spacecraft in Earth orbit. The simulation takes into account all relevant acting forces and torques, including aerodynamic drag, solar radiation pressure, gravitational influences of Earth, Sun and Moon, eddy current damping, impulse and momentum transfer from space debris or micro meteoroid impact, as well as the optional definition of particular spacecraft specific influences like tank sloshing, reaction wheel behaviour, magnetic torquer activity and thruster firing. The purpose of ιOTA is to provide high accuracy short-term simulations to support observers and potential ADR missions, as well as medium-and long-term simulations to study the significance of the particular internal and external influences on the attitude, especially damping factors and momentum transfer. The simulation will also enable the investigation of the altitude dependency of the particular external influences. ιOTA's post-processing modules will generate synthetic measurements for observers and for software validation. The validation of the software will be done by cross-calibration with observations and measurements acquired by the project partners.