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.

Processing 20 years of SLR observations to GNSS satellites

We process 20 years of SLR observations to GPS and GLONASS satellites using the reprocessed 3-day and 1-day microwave orbits provided by the Center for Orbit Determination in Europe (CODE) for the period 1994-2013. We study the dependency of the SLR residuals on the type, size, and a number of corner cubes in satellite laser reflector arrays (LRA). We show that the mean SLR residuals and the RMS of residuals depend on the coating of LRA and the block or type of GNSS satellites. The SLR mean residuals are also a function of the equipment used at SLR stations including detector types and detecting modes.

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 ultra-rapid orbit and ERP products for the IGS

The International GNSS Service (IGS) issues four sets of so-called ultra-rapid products per day, which are based on the contributions of the IGS Analysis Centers. The traditional (“old”) ultra-rapid orbit and earth rotation parameters (ERP) solution of the Center for Orbit Determination in Europe (CODE) was based on the output of three consecutive 3-day long-arc rapid solutions. Information from the IERS Bulletin A was required to generate the predicted part of the old CODE ultra-rapid product. The current (“new”) product, activated in November 2013, is based on the output of exactly one multi-day solution. A priori information from the IERS Bulletin A is no longer required for generating and predicting the orbits and ERPs. This article discusses the transition from the old to the new CODE ultra-rapid orbit and ERP products and the associated improvement in reliability and performance. All solutions used in this article were generated with the development version of the Bernese GNSS Software. The package was slightly extended to meet the needs of the new CODE ultra-rapid generation.

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.

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.

SMARTnet: A Sensor for Monitoring the Geostationary Ring

As the number of space debris is increasing in the geostationary ring, it becomes mandatory for any satellite operator to avoid any collisions. Space debris in geosynchronous orbits may be observed with optical telescopes. Other than radar, that requires very large dishes and transmission powers for sensing high-altitude objects, optical observations do not depend on active illumination from ground and may be performed with notably smaller apertures. The detection size of an object depends on the aperture of the telescope, sky background and exposure time. With a telescope of 50 cm aperture, objects down to approximately 50 cm may be observed. This size is regarded as a threshold for the identification of hazardous objects and the prevention of potentially catastrophic collisions in geostationary orbits. In collaboration with the Astronomical Institute of the University of Bern (AIUB), the German Space Operations Center (GSOC) is building a small aperture telescope to demonstrate the feasibility of optical surveillance of the geostationary ring. The telescope will be located in the southern hemisphere and complement an existing telescope in the northern hemisphere already operated by AIUB. These two telescopes provide an optimum coverage of European GEO satellites and enable a continuous monitoring independent of seasonal limitations. The telescope will be operated completely automatically. The automated operations should be demonstrated covering the full range of activities including scheduling of observations, telescope and camera control as well as data processing.

Virtopsy--fatal motor vehicle accident with head injury.

A man wearing no protective helmet was struck by a motor vehicle while riding a bicycle. He was loaded on his left side, and the impact point of his head was his occiput on the car roof girder. He was immediately transported to the general hospital, where he passed away. Postmortem examination using multi-slice computed tomography (MSCT) revealed an extensively comminuted fracture of the posterior part and the base of the skull. Observed were deep direct and contrecoup brain bruises, with the independent fractures of the roof of the both orbits. Massive subdural and subarachnoidal hemorrhage with cerebral edema and shifting of the mid-line towards left side were also detected. MSCT and autopsy results were compared and the body injuries were correlated to vehicle damages. In conclusion, postmortem imaging is a good forensic visualization tool with great potential for documentation and examination of body injuries and pathology.

Optical Light Curve Observations to Determine Attitude States of Space Debris

The currently proposed space debris remediation measures include the active removal of large objects and “just in time” collision avoidance by deviating the objects using, e.g., ground-based lasers. Both techniques require precise knowledge of the attitude state and state changes of the target objects. In the former case, to devise methods to grapple the target by a tug spacecraft, in the latter, to precisely propagate the orbits of potential collision partners as disturbing forces like air drag and solar radiation pressure depend on the attitude of the objects. Non-resolving optical observations of the magnitude variations, so-called light curves, are a promising technique to determine rotation or tumbling rates and the orientations of the actual rotation axis of objects, as well as their temporal changes. The 1-meter telescope ZIMLAT of the Astronomical Institute of the University of Bern has been used to collect light curves of MEO and GEO objects for a considerable period of time. Recently, light curves of Low Earth Orbit (LEO) targets were acquired as well. We present different observation methods, including active tracking using a CCD subframe readout technique, and the use of a high-speed scientific CMOS camera. Technical challenges when tracking objects with poor orbit redictions, as well as different data reduction methods are addressed. Results from a survey of abandoned rocket upper stages in LEO, examples of abandoned payloads and observations of high area-to-mass ratio debris will be resented. Eventually, first results of the analysis of these light curves are provided.

SMARTnet: First Experience of Setting Up a Telescope System to Survey the Geostationary Ring

Space debris in geostationary orbits may be detected with optical telescopes when the objects are illuminated by the Sun. The advantage compared to Radar can be found in the illumination: radar illuminates the objects and thus the detection sensitivity depletest proportional to the fourth power of the d istance. The German Space Operation Center, GSOC, together with the Astronomical Institute of the University of Bern, AIUB, are setting up a telescope system called SMARTnet to demonstrate the capability of performing geostationary surveillance. Such a telescope system will consist of two telescopes on one mount: a smaller telescope with an aperture of 20cm will serve for fast survey while the larger one, a telescope with an aperture of 50cm, will be used for follow-up observations. The telescopes will be operated by GSOC from Oberpfaffenhofen by the internal monitoring and control system called SMARTnetMAC. The observation plan will be generated by MARTnetPlanning seven days in advance by applying an optimized planning scheduler, taking into account fault time like cloudy nights, priority of objects etc. From each picture taken, stars will be identified and everything not being a star is treated as a possible object. If the same object can be identified on multiple pictures within a short time span, the trace is called a tracklet. In the next step, several tracklets will be correlated to identify individual objects, ephemeris data for these objects are generated and catalogued . This will allow for services like collision avoidance to ensure safe operations for GSOC’s satellites. The complete data processing chain is handled by BACARDI, the backbone catalogue of relational debris information and is presented as a poster.

A covariance analysis to optimize the optical follow-up strategies

The Astronomical Institute of the University of Bern (AIUB) is conducting several search campaigns for space debris using optical sensors. The debris objects are discovered during systematic survey observations. In general, the result of a discovery consists in only a short observation arc, or tracklet, which is used to perform a first orbit determination in order to be able to observe t he object again in subsequent follow-up observations. The additional observations are used in the orbit improvement process to obtain accurate orbits to be included in a catalogue. In order to obtain the most accurate orbit within the time available it is necessary to optimize the follow-up observations strategy. In this paper an in‐depth study, using simulations and covariance analysis, is performed to identify the optimal sequence of follow-up observations to obtain the most accurate orbit propagation to be used for the space debris catalogue maintenance. The main factors that determine the accuracy of the results of an orbit determination/improvement process are: tracklet length, number of observations, type of orbit, astrometric error of the measurements, time interval between tracklets, and the relative position of the object along its orbit with respect to the observing station. The main aim of the covariance analysis is to optimize the follow-up strategy as a function of the object-observer geometry, the interval between follow-up observations and the shape of the orbit. This an alysis can be applied to every orbital regime but particular attention was dedicated to geostationary, Molniya, and geostationary transfer orbits. Finally the case with more than two follow-up observations and the influence of a second observing station are also analyzed.

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.

Relative estimate of accuracy in orbit determination from a short tracklet

The Astronomical Institute of the University of Bern (AIUB) is conducting several search campaigns for orbital debris. The debris objects are discovered during systematic survey observations. In general only a short observation arc, or tracklet, is available for most of these objects. From this discovery tracklet a first orbit determination is computed in order to be able to find the object again in subsequent follow-up observations. The additional observations are used in the orbit improvement process to obtain accurate orbits to be included in a catalogue. In this paper, the accuracy of the initial orbit determination is analyzed. This depends on a number of factors: tracklet length, number of observations, type of orbit, astrometric error, and observation geometry. The latter is characterized by both the position of the object along its orbit and the location of the observing station. Different positions involve different distances from the target object and a different observing angle with respect to its orbital plane and trajectory. The present analysis aims at optimizing the geometry of the discovery observation is depending on the considered orbit.

A study of the time complexity of an Elitist Genetic Algorithm used for associating optical observations of MEO and GEO Space Debris

Currently several thousands of objects are being tracked in the MEO and GEO regions through optical means. The problem faced in this framework is that of Multiple Target Tracking (MTT). In this context both the correct associations among the observations, and the orbits of the objects have to be determined. The complexity of the MTT problem is defined by its dimension S. Where S stands for the number of ’fences’ used in the problem, each fence consists of a set of observations that all originate from dierent targets. For a dimension of S ˃ the MTT problem becomes NP-hard. As of now no algorithm exists that can solve an NP-hard problem in an optimal manner within a reasonable (polynomial) computation time. However, there are algorithms that can approximate the solution with a realistic computational e ort. To this end an Elitist Genetic Algorithm is implemented to approximately solve the S ˃ MTT problem in an e cient manner. Its complexity is studied and it is found that an approximate solution can be obtained in a polynomial time. With the advent of improved sensors and a heightened interest in the problem of space debris, it is expected that the number of tracked objects will grow by an order of magnitude in the near future. This research aims to provide a method that can treat the correlation and orbit determination problems simultaneously, and is able to e ciently process large data sets with minimal manual intervention.