Precise Relative Orbit Determination for Chinese TH-2 Satellite Formation Using Onboard GPS and BDS2 Observations

TH-2 is China’s first short-range satellite formation system used to realize interferometric synthetic aperture radar (InSAR) technology. In order to achieve the mission goal of InSAR processing, the relative orbit must be determined with high accuracy. In this study, the precise relative orbit determination (PROD) for TH-2 based on global positioning system (GPS), second-generation BeiDou navagation satellite system (BDS2), and GPS + BDS2 observations was performed. First, the performance of onboard GPS and BDS2 measurements were assessed by analyzing the available data, code multipath errors and noise levels of carrier phase observations. The differences between the National University of Defense Technology (NDT) and the Xi’an Research Institute of Surveying and Mapping (CHS) baseline solutions exhibited an RMS of 1.48 mm outside maneuver periods. The GPS-based orbit was used as a reference orbit to evaluate the BDS2-based orbit and the GPS + BDS2-based orbit. It is the first time BDS2 has been applied to the PROD of low Earth orbit (LEO) satellite formation. The results showed that the root mean square (RMS) of difference between the PROD results using GPS and BDS2 measurements in 3D components was 2.89 mm in the Asia-Pacific region. We assigned different weights to geostationary Earth orbit (GEO) satellites to illustrate the impact of GEO satellites on PROD, and the accuracy of PROD was improved to 7.08 mm with the GEO weighting strategy. Finally, relative orbits were derived from the combined GPS and BDS2 data. When BDS2 was added on the basis of GPS, the average number of visible navigation satellites from TH-2A and TH-2B improved from 7.5 to 9.5. The RMS of the difference between the GPS + BDS2-based orbit and the GPS-based orbit was about 1.2 mm in 3D. The overlap comparison results showed that the combined orbit consistencies were below 1 mm in the radial (R), along-track (T), and cross-track (N) directions. Furthermore, when BDS2 co-worked with GPS, the average of the ambiguity dilution of precision (ADOP) reduced from 0.160 cycle to 0.153 cycle, which was about a 4.4% reduction. The experimental results indicate that millimeter-level PROD results for TH-2 satellite formation can be obtained by using onboard GPS and BDS2 observations, and multi-GNSS can further improve the accuracy and reliability of PROD.

Incomplete Information Pursuit-Evasion Game Control for a Space Non-Cooperative Target

Aiming to solve the optimal control problem for the pursuit-evasion game with a space non-cooperative target under the condition of incomplete information, a new method degenerating the game into a strong tracking problem is proposed, where the unknown target maneuver is processed as colored noise. First, the relative motion is modeled in the rotating local vertical local horizontal (LVLH) frame originated at a virtual Chief based on the Hill-Clohessy-Wiltshire relative dynamics, while the measurement models for three different sensor schemes (i.e., single LOS (line-of-sight) sensor, LOS range sensor and double LOS sensor) are established and an extended Kalman Filter (EKF) is used to obtain the relative state of target. Next, under the assumption that the unknown maneuver of the target is colored noise, the game control law of chaser is derived based on the linear quadratic differential game theory. Furthermore, the optimal control law considering the thrust limitation is obtained. After that, the observability of the relative orbit state is analyzed, where the relative orbit is weakly observable in a short period of time in the case of only LOS angle measurements, fully observable in the cases of LOS range and double LOS measurement schemes. Finally, numerical simulations are conducted to verify the proposed method. The results show that by using the single LOS scheme, the chaser would firstly approach the target but then would lose the game because of the existence of the target’s unknown maneuver. Conversely, the chaser can successfully win the game in the cases of LOS range and double LOS sensor schemes.

Agricultural Sandbox NL: A national-scale database of parcel-level, processed Sentinel-1 SAR data

Synthetic Aperture Radar (SAR) data handling, processing, and interpretation are barriers preventing a rapid uptake of SAR data by application specialists and non-expert domain users in the field of agricultural monitoring. To improve the accessibility of Sentinel-1 data, we have generated a reduced-volume, multi-year Sentinel-1 SAR database. It includes mean and standard deviation of VV, VH and VH/VV backscatter, pixel counts, geometry, crop type, local incidence angle and azimuth angle at parcel-level. The database uses around 3100 Sentinel-1 images (5 TB) to produce a 12 GB time series database for approximately 770,000 crop parcels over the Netherlands for a period of three years. The database can be queried by Sentinel-1 system parameters (e.g. relative orbit) or user application-specific parameters (e.g. crop type, spatial extent, time period) for parcel level assessment. The database can be used to accelerate the development of new tools, applications and methodologies for agricultural and water related applications, such as parcel-level crop bio-geophysical parameter estimation, inter-annual variability analysis, drought monitoring, grassland monitoring and agricultural management decision-support.

Roto-Translational Control of Spacecraft in Low Earth Orbit Using Environmental Forces and Torques

In this paper, relative orbit and attitude adaptive controllers are integrated to perform roto-translational maneuvers for CubeSats equipped with a Drag Maneuvering Device (DMD). The DMD enables the host CubeSat with modulation of aerodynamic forces/torques and gravity gradient torque. Adaptive controllers for independent orbital and attitude maneuvers are revisited to account for traslational-attitude coupling while compensating for uncertainty in parameters such as atmospheric density, drag/lift coefficients, location of the Center of Mass (CoM) and inertia matrix. Uniformly ultimately bounded convergence of the attitude error and relative orbit states is guaranteed by Lyapunov-based stability analysis for the integrated roto-translational maneuver. A simulation example of an along-track formation maneuver between two CubeSats with simultaneous attitude control using only environmental forces and torques is presented to validate the controller.

Accurate ephemeris reconstruction for comet 67P/Churyumov-Gerasimenko from Rosetta data analysis

<p>Following its arrival at 67P/Churyumov-Gerasimenko in August 2014, the Rosetta spacecraft successfully navigated in proximity of the comet for two years, using a combination of radiometric measurements and optical images collected by the onboard navigation cameras.</p><p>The reconstructed spacecraft and comet trajectories were obtained combining several long-arc and short-arc orbit determination solutions generated by ESOC Flight Dynamics during the Rosetta operations. Several discontinuities are present within these trajectories, due to the lack of a dynamical model for the representation of the comet Non-Gravitational Accelerations (NGA).</p><p>The work presented in this study represents an effort to produce an accurate and continuous ephemeris reconstruction for comet 67P/Churyumov-Gerasimenko for the period between July 2014 and October 2016, through a complete reanalysis of the Range and ΔDOR measurements collected by Rosetta during its proximity phase with the comet.</p><p>Using as input the reconstructed relative orbit of Rosetta, the radiometric observables were mapped to the comet nucleus and used to estimate the comet state and some key physical and observational parameters within a Square Root Information batch filter implemented in MONTE, most notably the NGA acting on the comet nucleus due to surface outgassing.</p><p>Several orbit determination solutions were generated by varying the model used to represent the NGA. More specifically, empirical and stochastic models were compared by evaluating the reduced χ<sup>2</sup> statistics of the measurement residuals to identify the most suitable trajectory estimations for each of the proposed models. From this narrow list of solutions, a preliminary selection for the final ephemeris reconstruction is proposed, based on its adherence to the original ESOC trajectory and on the consistency of the formal state uncertainties with the estimated solutions.</p><p>It will be shown that the selected ephemeris solution, using a piecewise linear stochastic NGA model with intervals between 3 and 4 weeks, produces a continuous ephemeris reconstruction for 67P/Churyumov-Gerasimenko with maximum formal uncertainties around perihelion of σ<sub>pos</sub> ≅ [20 km, 30 km, 200 km] in the Radial-Tangential-Normal reference frame. The advantage of using simple stochastic models, with limited a-priori assumptions on the involved physical processes, is that they allow to produce an unbiased estimation of the NGA variations around perihelion, which represent a valuable input for further investigations involving detailed physical models of the cometary activity.</p>

Are we observing an NSC in course of formation in the NGC 4654 galaxy?

ABSTRACT We use direct N-body simulations to explore some possible scenarios for the future evolution of two massive clusters observed towards the centre of NGC 4654, a spiral galaxy with mass similar to that of the Milky Way. Using archival HST data, we obtain the photometric masses of the two clusters, M = 3 × 105 M⊙ and M = 1.7 × 106 M⊙, their half-light radii, Reff ∼ 4 pc and Reff ∼ 6 pc, and their projected distances from the photometric centre of the galaxy (both <22 pc). The knowledge of the structure and separation of these two clusters (∼24 pc) provides a unique view for studying the dynamics of a galactic central zone hosting massive clusters. Varying some of the unknown cluster orbital parameters, we carry out several N-body simulations showing that the future evolution of these clusters will inevitably result in their merger. We find that, mainly depending on the shape of their relative orbit, they will merge into the galactic centre in less than 82 Myr. In addition to the tidal interaction, a proper consideration of the dynamical friction braking would shorten the merging times up to few Myr. We also investigate the possibility to form a massive nuclear star cluster (NSC) in the centre of the galaxy by this process. Our analysis suggests that for low-eccentricity orbits, and relatively long merger times, the final merged cluster is spherical in shape, with an effective radius of few parsecs and a mass within the effective radius of the order of $10^5\, \mathrm{M_{\odot }}$. Because the central density of such a cluster is higher than that of the host galaxy, it is likely that this merger remnant could be the likely embryo of a future NSC.