Astronomical Institute Of The University Of Bern Research Articles

AIUB-GRACE gravity field solutions for G3P: processing strategies and instrument parameterization

Abstract. This paper discusses strategies to improve the Gravity Recovery And Climate Experiment (GRACE) monthly solutions computed at the Astronomical Institute of the University of Bern (AIUB) which are contributing to the Horizon 2020 project G3P – Global Gravity-based Groundwater Product. To improve the AIUB-GRACE gravity field solutions, we updated the use of the Level-1B observations, adapted the background models, and improved the processing strategies in terms of instrument screening and parameterization. We used the Release 3 K-band product (KBR) and star camera data (L1B RL03), and we adopted Release 6 of the Atmospheric and Ocean De-aliasing (AOD1B RL06) product. For the accelerometer parameterization, we used arc-wise full scale factor matrix and arc-wise third-order polynomial biases. The new accelerometer parameterization is effective in reducing noise over the oceans in gravity field solutions, especially for the late years of the GRACE mission when the thermal control was switched off. In this paper, we show that the outliers in the KBR antenna offset correction (AOC) are projected into the range rate residuals; therefore, we used the KBR AOC as the main source for outlier detection and eliminated the AOC above a threshold for all data before the gravity field processing. The full time series of GRACE AIUB-G3P gravity field solutions (Darbeheshti et al., 2023b) is available at https://doi.org/10.5880/ICGEM.2023.001.

Reprocessed precise science orbits and gravity field recovery for the entire GOCE mission

ESA’s Gravity field and steady-state Ocean Circulation Explorer (GOCE) orbited the Earth between 2009 and 2013 for the determination of the static part of Earth’s gravity field. The GPS-derived precise science orbits (PSOs) were operationally generated by the Astronomical Institute of the University of Bern (AIUB). Due to a significantly improved understanding of remaining artifacts after the end of the GOCE mission (especially in the GOCE gradiometry data), ESA initiated a reprocessing of the entire GOCE Level 1b data in 2018. In this framework, AIUB was commissioned to recompute the GOCE reduced-dynamic and kinematic PSOs. In this paper, we report on the employed precise orbit determination methods, with a focus on measures undertaken to mitigate ionosphere-induced artifacts in the kinematic orbits and thereof derived gravity field models. With respect to the PSOs computed during the operational phase of GOCE, the reprocessed PSOs show in average a 8–9% better consistency with GPS data, 31% smaller 3-dimensional reduced-dynamic orbit overlaps, an 8% better 3-dimensional consistency between reduced-dynamic and kinematic orbits, and a 3–7% reduction of satellite laser ranging residuals. In the second part of the paper, we present results from GPS-based gravity field determinations that highlight the strong benefit of the GOCE reprocessed kinematic PSOs. Due to the applied data weighting strategy, a substantially improved quality of gravity field coefficients between degree 10 and 40 is achieved, corresponding to a remarkable reduction of ionosphere-induced artifacts along the geomagnetic equator. For a static gravity field solution covering the entire mission period, geoid height differences with respect to a superior inter-satellite ranging solution are markedly reduced (43% in terms of global RMS, compared to previous GOCE GPS-based gravity fields). Furthermore, we demonstrate that the reprocessed GOCE PSOs allow to recover long-wavelength time-variable gravity field signals (up to degree 10), comparable to information derived from GPS data of dedicated satellite missions. To this end, it is essential to take into account the GOCE common-mode accelerometer data in the gravity field recovery.

A comparison of GRACE temporal gravity field models recovered with different processing details

SUMMARYThe Gravity Recovery and Climate Experiment (GRACE) mission has been providing abundant information regarding the mass changes of the Earth in terms of time-series of temporal gravity field models since 2002. To derive temporal gravity field models with high accuracy, many methods have been developed. In this paper, we focus on the variational equation integration approach. The main works can be summarized as follows: (1) analysing the quality of GRACE Level1B RL02 and RL03 data, including accelerometer observations (ACC1B), star camera measurements (SCA1B) and K-Band low-low Satellite-to-Satellite Tracking (SST) range-rate (KBRR) data (KBR1B); (2) discussing the influence of arc-specific parameters and arc length on gravity field recovery and (3) comparing two different methods used for sensitivity matrix generation, namely, a numerical integration method and the method of variation of constants, from the perspectives of accuracy and efficiency, respectively. Based on these analyses, discussions and comparisons, a new time-series of GRACE monthly gravity field models in terms of spherical harmonic coefficients completed to degree and order 60, called SWJTU-GRACE-RL02p, was derived by using the modified variational equation integration approach bashed on GRACE Level1B RL03 data, covering the period from April 2002 to October 2011 with some gaps in between due to poor quality or missing GRACE data. Thus we are looking at the results some 10yrs in the past. The differences between the traditional variational equation integration approach and the approach that we used are mainly as follows: (1) according to the GRACE data quality, the arc length is no longer a constant in the determination of temporal gravity field models; (2) the kinematic empirical parameters, which are mainly designed to remove the bias and drifts in KBRR residuals, are abandoned and (3) the method of variation of constants developed at the Astronomical Institute of the University of Bern (AIUB) and used to solve the system of variational equations associated with constrained pulses and piecewise constant accelerations is used to calculate the sensitivity matrices of accelerometer bias parameters to improve the calculation efficiency and ensure the calculation accuracy. To validate the quality of SWJTU-GRACE-RL02p, these models were compared with the old models of SWJTU-GRACE-RL01, which have been published by the website of the International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/series), and the official products [i.e. the RL05 and RL06 versions of GRACE LEVEL2 at the Centre for Space Research (CSR), Jet Propulsion Laboratory (JPL) and GeoForschungsZentrum (GFZ)]. Compared to the RL06 version of official models, the models of SWJTU-GRACE-RL02p present competitive performance for global mass changes. Furthermore, these models show less noise and a higher signal strength over some local areas with large mass changes than the models of SWJTU-GRACE-RL01. The comparisons between SWJTU-GRACE-RL02p and a variety of other models including official models, GLDAS, models provided by EGSIEM and daily solutions released by ITSG indicate that our approach and the data processing details presented in this paper provide an alternative strategy for the recovery of temporal gravity field models from GRACE-type data.

Dynamic GPS-based LEO orbit determination with 1 cm precision using the Bernese GNSS Software

The Astronomical Institute of the University of Bern (AIUB) has been performing GPS-based Precise Orbit Determination (POD) for a large variety of Low Earth Orbit (LEO) satellites since two decades. Traditionally, LEO orbits have been generated by a reduced-dynamic POD strategy using the Bernese GNSS Software, replacing an explicit modeling of non-gravitational forces by dedicated empirical orbit parametrizations. This LEO POD strategy can be advanced by two main developments: on the one hand, use is made of the GNSS Observation-Specific Bias (OSB) and clock products provided by the Center for Orbit Determination in Europe (CODE), allowing for the resolution of single-receiver GNSS carrier-phase ambiguities. On the other hand, the main focus of this article, a refined satellite non-gravitational force modeling strategy is constructed to reduce the amount of empirical parameters used to compensate for force modeling deficiencies. LEO POD is first performed for Sentinel-3, a satellite formation currently consists of two identical satellites −3A and −3B, which experience a similar in-flight environment and allow for direct POD performance comparisons. A third satellite Swarm-C, which flies at a lower altitude and has a more sophisticated surface geometry, is selected to validate the robustness of the new POD strategy. As a result, both the internal consistency checks and external orbit validations suggest superior orbit quality obtained for the three satellites for a time span of 1.5 years (7 June, 2018 to 31 December, 2019). The ambiguity resolution adds strong constraints to the orbits and the satellite non-gravitational force modeling leads to more tightly constrained (towards zero) pseudo-stochastic empirical parameters. The final orbit solutions agree with external orbit solutions and independent satellite laser ranging measurements at levels of sub-cm, indicating approximately 20% improvement w.r.t. the nominal reduced-dynamic orbit solutions. This suggests potential benefits to the space geodesy community that always pursues best-possible satellite orbits.

Analysis of laser ranges and angular measurements data fusion for space debris orbit determination

In the framework of space debris, the orbit determination process is a fundamental step, both, for researchers and for satellite operators. The accurate knowledge of the orbit of space debris objects is needed to allow space debris characterization studies and to avoid unnecessary collision avoidance maneuvers.The accuracy of the results of an orbit determination process depends on several factors as the number, the accuracy, the kind of processed measurements, their distribution along the orbit, and the object-observer relative geometry. When the observation coverage of the target orbit is not homogeneous, the accuracy of the orbit determination can be improved processing different kind of observables. Recent studies showed that the satellite laser ranging technique can be successfully applied to space debris.In this paper, we will investigate the benefits of using laser ranges and angular measurements for the orbit determination process. We will analyze the influence of the number of used observations, of the covered arc of orbit, of each observable, and of the observation geometry on the estimated parameters. Finally, using data acquired on short observation arcs, we analyze the achievable accuracies for the orbital regimes with the highest space debris density, and to the consequences of the data fusion on catalog maintenance operations. The results shown are obtained using only real data (both angular and laser measurements) provided by sensors of the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald owned by the Astronomical Institute of the University of Bern (AIUB) and for some studies also using ranges provided from other stations of the International Laser Ranging Service (ILRS).

Apparent rotation properties of space debris extracted from photometric measurements

Knowledge about the rotation properties of space debris objects is essential for the active debris removal missions, accurate re-entry predictions and to investigate the long-term effects of the space environment on the attitude motion change. Different orbital regions and object’s physical properties lead to different attitude states and their change over time.Since 2007 the Astronomical Institute of the University of Bern (AIUB) performs photometric measurements of space debris objects. To June 2016 almost 2000 light curves of more than 400 individual objects have been acquired and processed. These objects are situated in all orbital regions, from low Earth orbit (LEO), via global navigation systems orbits and high eccentricity orbit (HEO), to geosynchronous Earth orbit (GEO). All types of objects were observed including the non-functional spacecraft, rocket bodies, fragmentation debris and uncorrelated objects discovered during dedicated surveys. For data acquisition, we used the 1-meter Zimmerwald Laser and Astrometry Telescope (ZIMLAT) at the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald, Switzerland. We applied our own method of phase-diagram reconstruction to extract the apparent rotation period from the light curve. Presented is the AIUB’s light curve database and the obtained rotation properties of space debris as a function of object type and orbit.

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).

Monthly gravity field solutions based on GRACE observations generated with the Celestial Mechanics Approach

The main objective of the Gravity Recovery And Climate Experiment (GRACE) satellite mission consists of determining the temporal variations of the Earth's gravity field. These variations are captured by time series of gravity field models of limited resolution at, e.g., monthly intervals. We present a new time series of monthly models, which was computed with the so-called Celestial Mechanics Approach (CMA), developed at the Astronomical Institute of the University of Bern (AIUB).The secular and seasonal variations in the monthly models are tested for statistical significance. Calibrated errors are derived from inter-annual variations. The time-variable signal can be extracted at least up to degree 60, but the gravity field coefficients of orders above 45 are heavily contaminated by noise. This is why a series of monthly models is computed up to a maximum degree of 60, but only a maximum order of 45. Spectral analysis of the residual time-variable signal shows a distinctive peak at a period of 160 days, which shows up in particular in the C20 spherical harmonic coefficient.Basic filter- and scaling-techniques are introduced to evaluate the monthly models. For this purpose, the variability over the oceans is investigated, which serves as a measure for the noisiness of the models. The models in selected regions show the expected seasonal and secular variations, which are in good agreement with the monthly models of the Helmholtz Centre Potsdam, German Research Centre for Geosciences (GFZ). The results also reveal a few small outliers, illustrating the necessity for improved data screening. Our monthly models are available at the web page of the International Centre for Global Earth Models (ICGEM).

Inter-agency comparison of TanDEM-X baseline solutions

TanDEM-X (TerraSAR-X add-on for Digital Elevation Measurement) is the first Synthetic Aperture Radar (SAR) mission using close formation flying for bistatic SAR interferometry. The primary goal of the mission is to generate a global digital elevation model (DEM) with 2m height precision and 10m ground resolution from the configurable SAR interferometer with space baselines of a few hundred meters. As a key mission requirement for the interferometric SAR processing, the relative position, or baseline vector, of the two satellites must be determined with an accuracy of 1mm (1D RMS) from GPS measurements collected by the onboard receivers. The operational baseline products for the TanDEM-X mission are routinely generated by the German Research Center for Geosciences (GFZ) and the German Space Operations Center (DLR/GSOC) using different software packages (EPOS/BSW, GHOST) and analysis strategies. For a further independent performance assessment, TanDEM-X baseline solutions are generated at the Astronomical Institute of the University of Bern (AIUB) on a best effort basis using the Bernese Software (BSW).Dual-frequency baseline solutions are compared for a 1-month test period in January 2011. Differences of reduced-dynamic baseline solutions exhibit a representative standard deviation (STD) of 1mm outside maneuver periods, while biases are below 1mm in all directions. The achieved baseline determination performance is close to the mission specification, but independent SAR calibration data takes acquired over areas with a well known DEM from previous missions will be required to fully meet the 1mm 1D RMS target. Besides the operational solutions, single-frequency baseline solutions are tested. They benefit from a more robust ambiguity fixing and show a slightly better agreement of below 1mm STD, but are potentially affected by errors caused by an incomplete compensation of differential ionospheric path delays.

Impact of GPS antenna phase center variations on precise orbits of the GOCE satellite

The first European Space Agency Earth explorer core mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) has been launched on March 17, 2009. The 12-channel dual-frequency Global Positioning System receiver delivers 1 Hz data and provides the basis for precise orbit determination (POD) on the few cm-level for such a very low orbiting satellite (254.9 km). As a member of the European GOCE Gravity Consortium, which is responsible for the GOCE High-level Processing Facility (HPF), the Astronomical Institute of the University of Bern (AIUB) provides the Precise Science Orbit (PSO) product for the GOCE satellite. The mission requirement for 1-dimensional POD accuracy is 2 cm. The use of in-flight determined antenna phase center variations (PCVs) is necessary to meet this requirement. The PCVs are determined from 154 days of data and the magnitude is up to 3-4 cm. The impact of the PCVs on the orbit determination is significant. The cross-track direction benefits most of the PCVs. The improvement is clearly seen in the orbit overlap analysis and in the validation with independent Satellite Laser Ranging (SLR) measurements. It is the first time that SLR could validate the cross-track component of a LEO orbit.

Feasibility of performing space surveillance tasks with a proposed space-based optical architecture

Under ESA contract an industrial consortium including Aboa Space Research Oy (ASRO), the Astronomical Institute of the University of Bern (AIUB), and the Dutch National Aerospace Laboratory (NLR), proposed the observation concept, developed a suitable sensor architecture, and assessed the performance of a space-based optical (SBO) telescope in 2005. The goal of the SBO study was to analyse how the existing knowledge gap in the space debris population in the millimetre and centimetre regime may be closed by means of a passive optical instrument. The SBO instrument was requested to provide statistical information on the space debris population in terms of number of objects and size distribution. The SBO instrument was considered to be a cost-efficient with 20 cm aperture and 6° field-of-view and having flexible integration requirements. It should be possible to integrate the SBO instrument easily as a secondary payload on satellites launched into low-Earth orbits (LEO), or into geostationary orbit (GEO). Thus the selected mission concept only allowed for fix-mounted telescopes, and the pointing direction could be requested freely. Since 2007 ESA focuses space surveillance and tracking activities in the Space Situational Awareness (SSA) preparatory program. Ground-based radars and optical telescopes are studied for the build-up and maintenance of a catalogue of objects. In this paper we analyse how the proposed SBO architecture could contribute to the space surveillance tasks survey and tracking. We assume that the SBO instrumentation is placed into a circular sun-synchronous orbit at 800 km altitude. We discuss the observation conditions of objects at higher altitude, and select an orbit close to the terminator plane. A pointing of the sensor orthogonal to the orbital plane with optimal elevation slightly in positive direction (0° and +5°) is found optimal for accessing the entire GEO regime within one day, implying a very good coverage of controlled objects in GEO, too. Simulations using ESA’s Program for Radar and Optical Observation Forecasting (PROOF) in the version 2005 and a GEO reference population extracted from DISCOS revealed that the proposed pointing scenario provides low phase angles together with low angular velocities of the objects crossing the field-of-view. Radiometric simulations show that the optimal exposure time is 1–2 s, and that spherical objects in GEO with a diameter of below 1 m can be detected. The GEO population can be covered under proper illumination nearly completely, but seasonal drops of the coverage are possible. Subsequent observations of objects are on average at least every 1.5 days, not exceeding 3 days at maximum. A single observation arc spans 3° to 5° on average. Using a simulation environment that connects PROOF to AIUB’s program system CelMech we verify the consistency of the initial orbit determination for five selected test objects on subsequent days as a function of realistic astrometric noise levels. The initial orbit determination is possible. We define requirements for a correlator process essential for catalogue build-up and maintenance. Each single observation should provide an astrometric accuracy of at least 1”–1.5” so that the initially determined orbits are consistent within a few hundred kilometres for the semi-major axis, 0.01 for the eccentricity, and 0.1° for the inclination.

The celestial mechanics approach: application to data of the GRACE mission

The celestial mechanics approach (CMA) has its roots in the Bernese GPS software and was extensively used for determining the orbits of high-orbiting satellites. The CMA was extended to determine the orbits of Low Earth Orbiting satellites (LEOs) equipped with GPS receivers and of constellations of LEOs equipped in addition with inter-satellite links. In recent years the CMA was further developed and used for gravity field determination. The CMA was developed by the Astronomical Institute of the University of Bern (AIUB). The CMA is presented from the theoretical perspective in (Beutler et al. 2010). The key elements of the CMA are illustrated here using data from 50 days of GPS, K-Band, and accelerometer observations gathered by the Gravity Recovery And Climate Experiment (GRACE) mission in 2007. We study in particular the impact of (1) analyzing different observables [Global Positioning System (GPS) observations only, inter-satellite measurements only], (2) analyzing a combination of observations of different types on the level of the normal equation systems (NEQs), (3) using accelerometer data, (4) different orbit parametrizations (short-arc, reduced-dynamic) by imposing different constraints on the stochastic orbit parameters, and (5) using either the inter-satellite ranges or their time derivatives. The so-called GRACE baseline, i.e., the achievable accuracy of the GRACE gravity field for a particular solution strategy, is established for the CMA.

GOCE orbit predictions for SLR tracking

After a descent phase of about half a year, the Gravity field and steady-state Ocean Circulation Explorer (GOCE) reached the final orbital altitude of the first measurement and operational phase (MOP-1) in September 2009. Due to this very low orbital altitude and the inactive drag compensation during descent, the generation of reliable predictions of the GOCE trajectory turned out to be a major challenge even for short prediction intervals. As predictions of good quality are a prerequisite for frequent ranging from the tracking network of the International Laser Ranging Service (ILRS), Satellite Laser Ranging (SLR) data of GOCE was very sparse at mission start and made it difficult to independently calibrate and optimize the orbit determination based on data of the Global Positioning System (GPS). In addition to the GOCE orbit predictions provided by the European Space Agency (ESA), the Astronomical Institute of the University of Bern (AIUB) started providing predictions on July 22, 2009, as part of the Level 1b to Level 2 data processing performed at AIUB. The predictions based on the 12-h ultra-rapid products of the International GNSS Service (IGS) were originally intended to primarily serve the daylight passes in the early evening hours over Europe. The corresponding along-track prediction errors were often kept below 50 m during the descent phase and allowed for the first successful SLR tracking of GOCE over Europe on July 29, 2009, by the Zimmerwald observatory. Additional predictions based on the IGS 18-h ultra-rapid products are provided by AIUB since September 20, 2009, to further optimize the GOCE SLR tracking. In this article, the development of the GOCE prediction service at AIUB is presented, and the quality of the orbit predictions is assessed for periods with and without active drag compensation. The prediction quality is discussed as a function of the prediction interval, the quality of the input products for the GPS satellite orbits and clocks, and the availability of the GOCE GPS data. From the methodological point of view, different approaches for the treatment of the non-gravitational accelerations acting on the GOCE satellite are discussed and their impact on the prediction quality is assessed, in particular during the descent phase. Eventually, an outlook is given on the significance of GOCE SLR tracking to identify systematic errors in the GPS-based orbit determination, e.g., cross-track errors induced by mismodeled GOCE GPS phase center variations (PCVs).

Analyzing long observation arcs for objects with high area-to-mass ratios in geostationary orbits

A new population of objects with high area-to-mass ratios (AMR) in the geostationary orbit (GEO) has been identified recently. The first observations of this new type of objects were acquired in the framework of the European Space Agency's (ESA) search for space debris in the GEO and the geostationary transfer orbit using ESA's 1-m telescope on Tenerife (ESASDT). Since 2005 some of the newly detected objects with high AMR have been maintained in a catalogue. In addition to the ESASDT, the 1-m telescope of the Astronomical Institute of the University of Bern (AIUB) in Zimmerwald and several instruments located in the region of the former Soviet Union have been used to acquire the observations needed to maintain the orbital elements of these objects. The data from the latter telescopes is provided to AIUB by the Keldysh Institute of Applied Mathematics (KIAM) in the framework of a collaboration. Observation arcs of up to more than three years are currently available for some objects with high AMR. These long observation arcs are used to study the quality of the orbit determination and in particular of the AMR estimation. The results are presented in this paper. Furthermore, the challenges to maintain these orbits, e.g., to recover the objects after several days or weeks, are discussed.

GPS clock correction estimation for near real-time orbit determination applications

Precise orbit determination for low Earth orbiting (LEO) satellites using the global positioning system (GPS) is usually done in a post-processing mode introducing GPS satellite orbits and clock corrections. Depending on the mission objectives, the latency and required accuracy of precise LEO orbit information can vary significantly. Near real-time (NRT) orbits for certain geodetic missions (e.g. atmospheric sounding or altimetry) may require accuracy down to 10 cm (radial) or 0.1 mm s − 1 (along-track) and with a latency of less than 2–3 hours after the GPS measurements have been taken on the satellite. In order to fulfill such a demand in NRT, it is crucial that GPS orbit and clock products are available within the desired time frame and with adequate accuracy. In response to the demanding NRT processing for future geodetic satellite missions (i.e. ESA's Sentinel series), the Astronomical Institute of the University of Bern (AIUB) and Deutsches Zentrum für Luft- und Raumfahrt (DLR) have made an effort in finding an alternative approach to obtain high-rate NRT GPS orbit and clock solutions by way of GPS clock corrections estimation. A realistic NRT orbit determination (OD) scenario has been simulated in this joint-study assuming a radial orbit accuracy of 10 cm and of 3 hours latency for the orbit product. A summary of all currently available NRT GPS orbit and clock products and a description of the generation of NRT GPS clock corrections are given in detail in this paper. The estimated GPS clock corrections are validated with a kinematic precise point positioning (PPP) for static ground stations. For direct evaluation of this innovative approach on the LEO orbits, the resultant merged high-rate NRT GPS product was tested using GPS data from the GRACE (Gravity Recover And Climate Experiment) mission. The results from the NRT simulation show promising aspect of such a concept to achieve unprecedented LEO orbit accuracy in NRT.

International scientific optical network for space debris research

A joint team of researchers under the auspices of the Center for Space Debris Information Collection, Processing and Analysis of the Russian Academy of Sciences collaborates with 15 observatories around the world to perform observations of space debris. For this purpose, 14 telescopes were equipped with charge-coupled device (CCD) cameras, Global Positioning System (GPS) receivers, CCD frame processing and ephemeris computation software, with the support of the European and Russian grants. Many of the observation campaigns were carried out in collaboration with the Astronomical Institute of the University of Bern (AIUB) team operating at the Zimmerwald observatory and conducting research for the European Space Agency (ESA), using the Tenerife/Teide telescope for searching and tracking of unknown objects in the geostationary region (GEO). More than 130,000 measurements of space objects along a GEO arc of 340.9°, collected and processed at Space Debris Data Base in the Ballistic Center of the Keldysh Institute of Applied Mathematics (KIAM) in 2005–2006, allowed us to find 288 GEO objects that are absent in the public orbital databases and to determine their orbital elements. Methods of discovering and tracking small space debris fragments at high orbits were developed and tested. About 40 of 150 detected unknown objects of magnitudes 15–20.5 were tracked during many months. A series of dedicated 22-cm telescopes with large field of view for GEO survey tasks is in process of construction. 7 60-cm telescopes will be modernized in 2007.

Proposed strategies for optical observations in a future European Space Surveillance network

Two ESA-funded feasibility studies that aimed to develop observation strategies, to propose suitable sensor architectures, and to assess the expected performance of an independent European Space Surveillance System were carried out during the last years. The French company ONERA led two study teams comprising a number of European companies. The proposed space surveillance system consists of two subsystems, a phased-array radar system that shall be located in the South of Spain, and a network of ground-based electro-optical telescopes at four low latitude sites. This system allows to build-up and to maintain a catalogue of orbital elements of objects in space. It provides means to perform additional space surveillance tasks such as independent detection of fragmentation events, launches or manoeuvres, and allows to acquire the necessary measurements to assess the collision risk between catalogued objects. As a member of both study teams, the Astronomical Institute of the University of Bern (AIUB), Switzerland, contributed to the observation strategy definition, the system design, and the performance estimation of the optical observation part of the space surveillance system. This part of the system is intended to cover the Geostationary Orbit (GEO) and the Medium Earth Orbit (MEO) regions. This paper focuses on the development and evaluation of observation strategies for GEO and MEO within a space surveillance network. Observation requirements, possible strategies fulfilling the requirements, and the expected performance of selected strategies in terms of the coverage of a reference population are addressed. We conclude that GEO and MEO shall be covered by “stripe-scanning” approaches carried out by a network of telescopes. The simulations of the approaches using a reference population reveal that for both regions a nearly complete coverage can be guaranteed within a short time.

Properties of the high area-to-mass ratio space debris population at high altitudes

In the framework of its space debris research activities ESA established an optical survey program to study the space debris environment at high altitudes, in particular in the geostationary ring and in the geostationary transfer orbit region. The Astronomical Institute of the University of Bern (AIUB) performs these surveys on behalf of ESA using ESA’s 1-m telescope in Tenerife. Regular observations were started in 1999 and are continued during about 120–140 nights per year. Results from these surveys revealed a substantial amount of space debris at high altitudes in the size range from 0.1 to 1 m. Several space debris populations with different dynamical properties were identified in the geostationary ring. During the searches for debris in the geostationary transfer orbit region a new population of objects in unexpected orbits, where no potential progenitors exist, was found. The orbital periods of these objects are clustered around one revolution per day; the eccentricities, however, are scattered between 0 and 0.6. By following-up some of these objects using the ESA telescope and AIUB’s 1-m telescope in Zimmerwald, Switzerland, it was possible to study the properties of this new population. One spectacular finding from monitoring the orbits over time spans of days to months is the fact that these objects must have extreme area-to-mass ratios, which are by several orders of magnitudes higher than for ‘normal-type’ debris. This in turn supports the hypothesis that the new population actually is debris generated in or near the geostationary ring and which is in orbits with periodically varying eccentricity and inclination due to perturbations by solar radiation pressure. In order to further study the nature of these debris, multi-color and temporal photometry (light curves) were acquired with the Zimmerwald telescope. The light curves show strong variations over short time intervals, including signals typical for specular reflections. Some objects exhibit distinct periodic variations with periods ranging from 10 to several 100 s. All this is indicative for objects with complicated shapes and some highly reflective surfaces.

Orbit improvement for GEO objects using follow-up observations

During the preceding years, the Astronomical Institute of the University of Bern (AIUB) was conducting several search campaigns for space debris in the geostationary ring (GEO). The optical observations were performed with a 1-m Ritchey–Chrétien telescope on Tenerife. A substantial population of unknown, small-sized objects was found in these surveys. For all objects a circular orbit was determined using the discovery observations. In order to test the hypothesis of circular orbits – which most likely is not valid for all detected objects – it is necessary to determine eccentricities for at least a part of the population. This in turn requires follow-up observations of the detected objects. The improved orbits resulting from follow-up observations also increase the probability for a successful recovery of the object in subsequent nights. Eventually, follow-up observations over several nights yield “secure” orbits allowing to build up a catalogue. In this paper we present the results of the determination of circular orbits and the orbit improvement process yielding elliptical orbits. The accuracy of the determined orbits is discussed, and the orbit quality is tested with follow-up observations after a few nights. The orbital elements are compared with those based on the assumption of circular orbits.