Pseudo-Stochastic Orbit Modeling Techniques for Low-Earth Orbiters

The Earth's non-spherical mass distribution and atmospheric drag cause the strongest perturbations on very low-Earth orbiting satellites (LEOs). Models of gravitational and non-gravitational accelerations are utilized in dynamic precise orbit determination (POD) with GPS data, but it is also possible to derive LEO positions based on GPS precise point positioning without dynamical information. We use the reduced-dynamic technique for LEO POD, which combines the geometric strength of the GPS observations with the force models, and investigate the performance of different pseudo-stochastic orbit parametrizations, such as instantaneous velocity changes (pulses), piecewise constant accelerations, and continuous piecewise linear accelerations. The estimation of such empirical orbit parameters in a standard least-squares adjustment process of GPS observations, together with other relevant parameters, strives for the highest precision in the computation of LEO trajectories. We used the procedures for the CHAMP satellite and found that the orbits may be validated by means of independent SLR measurements at the level of 3.2cm RMS. Validations with independent accelerometer data revealed correlations at the level of 95% in the along-track direction. As expected, the empirical parameters compensate to a certain extent for deficiencies in the dynamic models. We analyzed the capability of pseudo-stochastic parameters for deriving information about the mismodeled part of the force field and found evidence that the resulting orbits may be used to recover force field parameters, if the number of pseudo-stochastic parameters is large enough. Results based on simulations showed a significantly better performance of acceleration-based orbits for gravity field recovery than for pulse-based orbits, with a quality comparable to a direct estimation if unconstrained accelerations are set up every 30

Efficient satellite orbit modelling using pseudo-stochastic parameters

If the force field acting on an artificial Earth satellite is not known a priori with sufficient accuracy to represent its observations on their accuracy level, one may introduce so-called pseudo-stochastic parameters into an orbit determination process, e.g. instantaneous velocity changes at user-defined epochs or piecewise constant accelerations in user-defined adjacent time subintervals or piecewise linear and continuous accelerations in adjacent time subintervals. The procedures, based on standard least-squares, associated with such parameterizations are well established, but they become inefficient (slow) if the number of pseudo-stochastic parameters becomes large. We develop two efficient methods to solve the orbit determination problem in the presence of pseudo-stochastic parameters. The results of the methods are identical to those obtained with conventional least-squares algorithms. The first efficient algorithm also provides the full variance-covariance matrix; the second, even more efficient algorithm, only parts of i

Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination

Most satellites in a low-Earth orbit (LEO) with demanding requirements on precise orbit determination (POD) are equipped with on-board receivers to collect the observations from Global Navigation Satellite systems (GNSS), such as the Global Positioning System (GPS). Limiting factors for LEO POD are nowadays mainly encountered with the modeling of the carrier phase observations, where a precise knowledge of the phase center location of the GNSS antennas is a prerequisite for high-precision orbit analyses. Since 5 November 2006 (GPS week 1400), absolute instead of relative values for the phase center location of GNSS receiver and transmitter antennas are adopted in the processing standards of the International GNSS Service (IGS). The absolute phase center modeling is based on robot calibrations for a number of terrestrial receiver antennas, whereas compatible antenna models were subsequently derived for the remaining terrestrial receiver antennas by conversion (from relative corrections), and for the GNSS transmitter antennas by estimation. However, consistent receiver antenna models for space missions such as GRACE and TerraSAR-X, which are equipped with non-geodetic receiver antennas, are only available since a short time from robot calibrations. We use GPS data of the aforementioned LEOs of the year 2007 together with the absolute antenna modeling to assess the presently achieved accuracy from state-of-the-art reduced-dynamic LEO POD strategies for absolute and relative navigation. Near-field multipath and cross-talk with active GPS occultation antennas turn out to be important and significant sources for systematic carrier phase measurement errors that are encountered in the actual spacecraft environments. We assess different methodologies for the in-flight determination of empirical phase pattern corrections for LEO receiver antennas and discuss their impact on POD. By means of independent K-band measurements, we show that zero-difference GRACE orbits can be significantly improved from about 10 to 6mm K-band standard deviation when taking empirical phase corrections into account, and assess the impact of the corrections on precise baseline estimates and further applications such as gravity field recovery from kinematic LEO position

Hepatic effects of Cimicifuga racemosa extract in vivo and in vitro

Abstract.: Extracts of Cimicifuga racemosa are used frequently for menopausal complaints. Cimicifuga is well tolerated but can occasionally cause liver injury. To assess hepatotoxicity of cimicifuga in more detail, ethanolic C. racemosa extract was administered orally to rats, and liver sections were analyzed by electron microscopy. Tests for cytotoxicity, mitochondrial toxicity and apoptosis/necrosis were performed using HepG2 cells. Mitochondrial toxicity was studied using isolated rat liver mitochondria. Microvesicular steatosis was found in rats treated with > 500 μg/kg body weight cimicifuga extract. In vitro, cytotoxicity was apparent at concentrations ≥ 75 μg/mL, and mitochondrial β-oxidation was impaired at concentrations ≥ 10 μg/mL. The mitochondrial membrane potential was decreased at concentrations ≥ 100 μg/mL, and oxidative phosphorylation was impaired at concentrations ≥ 300 μg/mL. The mechanism of cell death was predominantly apoptosis. C. racemosa exerts toxicity in vivo and in vitro, eventually resulting in apoptotic cell death. The results are compatible with idiosyncratic hepatotoxicity as observed in patients treated with cimicifuga extract

Combination Service for Time-variable Gravity Fields: operational GRACE-FO combination and validation of Chinese GRACE time-series

The Combination Service for Time-variable Gravity Fields (COST-G) of the International Association of Geodesy (IAG) provides combined monthly gravity fields of its associated and partner Analysis Centers (ACs). In November 2020, the combination of monthly GRACE-FO gravity fields started its operational mode, providing consolidated L2 (spherical harmonics) and L3 (gridded and post-processed) products with a latency of currently 3 months. We present an overview and quality assessment of the available products. COST-G aims at the extension of its service to include further GRACE and GRACE-FO analysis centers. In January 2020 a collaboration with representatives of five Chinese ACs was initiated, who provided GRACE time-series according to the COST-G requirements. We present the results of a test combination with the Chinese AC models, including comparison and quality assessment of all contributing time-series and validation of the combined gravity fields

Combination Service for Time-variable Gravity Fields (COST-G): operations and new developments

Since its start of operations in July 2019, IAGâ?Ts Combination Service for Time-variable Gravity fields (COST-G) is providing a complete time-series of combined monthly GRACE gravity fields and a regularly updated time-series of monthly gravity fields derived from kinematic Swarm orbits. Starting from October 2020, the COST-G product line is complemented by a time-series of operationally combined and monthly updated GRACE-FO gravity fields. All these combinations are performed by variance component estimation on the solution level. We report on new developments, i.e., a planned extension of COST-G to include Chinese analysis centers of GRACE and GRACE-FO data, a re-consideration of the combination strategy to better focus on the range of spherical harmonic coefficients most relevant for the users, and the potential application of COST-G products for orbit determination of altimeter satellites