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.

Doppler Orbit Determination of Deep Space Probes by the Bernese GNSS Software: First Results of the Combined Orbit Determination from DSN and Inter-Satellite Ka-Band Data from the Grail Mission

Navigation of deep space probes is most commonly operated using the spacecraft Doppler tracking technique. Orbital parameters are determined from a series of repeated measurements of the frequency shift of a microwave carrier over a given integration time. Currently, both ESA and NASA operate antennas at several sites around the world to ensure the tracking of deep space probes. Just a small number of software packages are nowadays used to process Doppler observations. The Astronomical Institute of the University of Bern (AIUB) has recently started the development of Doppler data processing capabilities within the Bernese GNSS Software. This software has been extensively used for Precise Orbit Determination of Earth orbiting satellites using GPS data collected by on-board receivers and for subsequent determination of the Earth gravity field. In this paper, we present the currently achieved status of the Doppler data modeling and orbit determination capabilities in the Bernese GNSS Software using GRAIL data. In particular we will focus on the implemented orbit determination procedure used for the combined analysis of Doppler and intersatellite Ka-band data. We show that even at this earlier stage of the development we can achieve an accuracy of few mHz on two-way S-band Doppler observation and of 2 µm/s on KBRR data from the GRAIL primary mission phase.

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.

GOCE: assessment of GPS-only gravity field determination

The GOCE satellite was orbiting the Earth in a Sun-synchronous orbit at a very low altitude for more than 4 years. This low orbit and the availability of high-quality data make it worthwhile to assess the contribution of GOCE GPS data to the recovery of both the static and time-variable gravity fields. We use the kinematic positions of the official GOCE precise science orbit (PSO) product to perform gravity field determination using the Celestial Mechanics Approach. The generated gravity field solutions reveal severe systematic errors centered along the geomagnetic equator. Their size is significantly coupled with the ionospheric density and thus generally increasing over the mission period. The systematic errors may be traced back to the kinematic positions of the PSO product and eventually to the ionosphere-free GPS carrier phase observations used for orbit determination. As they cannot be explained by the current higher order ionospheric correction model recommended by the IERS Conventions 2010, an empirical approach is presented by discarding GPS data affected by large ionospheric changes. Such a measure yields a strong reduction of the systematic errors along the geomagnetic equator in the gravity field recovery, and only marginally reduces the set of useable kinematic positions by at maximum 6 % for severe ionosphere conditions. Eventually it is shown that GOCE gravity field solutions based on kinematic positions have a limited sensitivity to the largest annual signal related to land hydrology.

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.

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.

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.

An Instrument Design for Space-Based Optical Observation of Space Debris

Currently, observations of space debris are primarily performed with ground-based sensors. These sensors have a detection limit at some centimetres diameter for objects in Low Earth Orbit (LEO) and at about two decimetres diameter for objects in Geostationary Orbit (GEO). The few space-based debris observations stem mainly from in-situ measurements and from the analysis of returned spacecraft surfaces. Both provide information about mostly sub-millimetre-sized debris particles. As a consequence the population of centimetre- and millimetre-sized debris objects remains poorly understood. The development, validation and improvement of debris reference models drive the need for measurements covering the whole diameter range. In 2003 the European Space Agency (ESA) initiated a study entitled “Space-Based Optical Observation of Space Debris”. The first tasks of the study were to define user requirements and to develop an observation strategy for a space-based instrument capable of observing uncatalogued millimetre-sized debris objects. Only passive optical observations were considered, focussing on mission concepts for the LEO, and GEO regions respectively. Starting from the requirements and the observation strategy, an instrument system architecture and an associated operations concept have been elaborated. The instrument system architecture covers the telescope, camera and onboard processing electronics. The proposed telescope is a folded Schmidt design, characterised by a 20 cm aperture and a large field of view of 6°. The camera design is based on the use of either a frame-transfer charge coupled device (CCD), or on a cooled hybrid sensor with fast read-out. A four megapixel sensor is foreseen. For the onboard processing, a scalable architecture has been selected. Performance simulations have been executed for the system as designed, focussing on the orbit determination of observed debris particles, and on the analysis of the object detection algorithms. In this paper we present some of the main results of the study. A short overview of the user requirements and observation strategy is given. The architectural design of the instrument is discussed, and the main tradeoffs are outlined. An insight into the results of the performance simulations is provided.

Earth gravity field recovery using GPS, GLONASS, and SLR satellites

The time variable Earth’s gravity field provides the information about mass transport within the system Earth, i.e., the relationship of mass transport between atmosphere, oceans, and land hydrology. We recover the low-degree parameters of the time variable gravity field using microwave observations from GPS and GLONASS satellites and from SLR data to five geodetic satellites, namely LAGEOS-1/2, Starlette, Stella, and AJISAI. GPS satellites are particularly sensitive to specific coefficients of the Earth's gravity field, because of the deep 2:1 orbital resonance with Earth rotation (two revolutions of the GPS satellites per sidereal day). The resonant coefficients cause, among other, a “secular” drift (actually periodic variations of very long periods) of the semi-major axes of up to 5.3 m/day of GPS satellites. We processed 10 years of GPS and GLONASS data using the standard orbit models from the Center of Orbit Determination in Europe (CODE) with a simultaneous estimation of the Earth gravity field coefficients and other parameters, e.g., satellite orbit parameters, station coordinates, Earth rotation parameters, troposphere delays, etc. The weekly GNSS gravity solutions up to degree and order 4/4 are compared to the weekly SLR gravity field solutions. The SLR-derived geopotential coefficients are compared to monthly GRACE and CHAMP results.

Short-arc tracklet association for geostationary objects

Measurement association and initial orbit determination is a fundamental task when building up a database of space objects. This paper proposes an efficient and robust method to determine the orbit using the available information of two tracklets, i.e. their line-of-sights and their derivatives. The approach works with a boundary-value formulation to represent hypothesized orbital states and uses an optimization scheme to find the best fitting orbits. The method is assessed and compared to an initial-value formulation using a measurement set taken by the Zimmerwald Small Aperture Robotic Telescope of the Astronomical Institute at the University of Bern. False associations of closely spaced objects on similar orbits cannot be completely eliminated due to the short duration of the measurement arcs. However, the presented approach uses the available information optimally and the overall association performance and robustness is very promising. The boundary-value optimization takes only around 2% of computational time when compared to optimization approaches using an initial-value formulation. The full potential of the method in terms of run-time is additionally illustrated by comparing it to other published association methods.