Control of Satellites with Onboard Robotic Manipulators

Free-floating satellites with onboard robotic manipulators are subjected to widely varying loads resulting from the motion of the robotic manipula-tors. As there are no fixed supports in space, these loads will cause the satellite to move. By modelling the motion of the onboard robotic arms, determin-ing the necessary reaction loads (which must be sup-plied by the satellite to keep the arm fixed), and sim-ulating the resulting satellite dynamics, we designed a model of a satellite-arm system. We found that a Proportional-Integral-Derivative (PID) control scheme, with disturbance-estimating capabilities, was effective in maintaining satellite position and ori-entation during the operation of the onboard ro-botic manipulator. The MATLAB-based Simulink modeling environment was used to perform the sim-ulations of satellite dynamics and control.

Subordinate clauses filling a satellite position

Chapter 16 deals with subordinate clauses, both finite and non-finite, which function as satellites in their sentence (traditionally called adverbial clauses). The finite clauses with a subordinator are discussed according to their semantic function, e.g. reason, purpose, and condition. The non-finite clauses are discussed according to morphological type: infinitives, participles (including ablative absolute clauses), gerunds, gerundives, supines, and nominal clauses.

Extended Kalman filter based statistical orbit determination for geostationary and geosynchronous satellite orbits in BeiDou constellation

BeiDou Navigation Satellite System (BDS) is composed of satellites in geostationary Earth orbit (GEO), medium Earth orbit (MEO) and inclined geosynchronous orbit (IGSO). However, the orbit determination of geostationary Earth orbits and of geosynchronous orbits (GSO) with small inclination angle and small eccentricity is a challenging task that is addressed in this paper using Extended Kalman Filter (EKF). The satellite positions were predicted in Earth-centred inertial (ECI) reference frame when propagated through Keplerian model and perturbation force model for different values of right ascension of ascending node (RAAN). Root mean square (RMS) errors of 9.61 cm, 6.73 cm and 11.46 cm were observed in ECI X, Y and Z satellite position coordinates of GSO respectively, whereas, the RMS errors for GEO satellite were 8.89 cm, 7.92 cm, and 0.93 cm respectively in ECI X, Y and Z coordinates; for perturbation force model with maximum value of RAAN when compared with dynamic orbit determination model. Kolmogorov-Smirnov test for EKF reported a p-value > 0.05, indicating a good fit of perturbation force model for orbit propagation. Orbit determination using EKF with perturbation force model were compared with that using EKF with Kepler's model. Wilcoxon Rank Sum test was used to compare the residuals from EKF algorithm through Kepler's model and perturbation force model. EKF with Perturbation force model showed improvement in predicting the satellite positions as compared to Kepler's model. EKF with Perturbation force model was further applied to International GNSS Service (IGS) station data and kilometre level accuracy was achieved. RMS errors of 0.75 km, 2.53 km and 1.91 km were observed in ECI X, Y and Z satellite position coordinates of GSO, respectively, whereas, the RMS errors for GEO satellite were 3.89 km, 4.20 km and 6.66 km respectively in ECI X, Y and Z coordinates for perturbation force model.

Space State Representation Product Evaluation in Satellite Position and Receiver Position Domain

In Global Navigation Satellite Systems (GNSS) positioning, important terms in error budget are satellite orbits and satellite clocks correction errors. International services are developing and providing models and correction to minimize the influence of these errors both in post-processing and real-time applications. The International GNSS Service (IGS) Real-Time Service (RTS) provides real-time orbits and clock corrections for the broadcast ephemeris. Real-time products provided by IGS are generated by different analysis centres using different algorithms. In this paper, four RTS products—IGC01, CLK01, CLK50, and CLK90—were evaluated and analysed. To evaluate State Space Representation (SSR) products’ GPS satellites, the analyses were made in three variants. In the first approach, geocentric real-time Satellite Vehicle (SV) coordinates and clock corrections were calculated. The obtained results were compared with the final IGS, ESA, GFZ, and GRG ephemerides. The second approach was to use the corrected satellite positions and clock corrections to determine the Precise Point Position (PPP) of the receiver. In the third analysis, the impact of SSR corrections on receiver Single Point Position (SPP) was evaluated. The first part of the research showed that accuracy of the satellite position is better than 10 cm (average 3 to 5 cm), while in the case of clock corrections, mean residuals range from 2 cm to 17 cm. It should be noted that the errors of the satellites positions obtained from one stream differ depending on the reference data used. This shows the need for an evaluation of correction streams in the domain of the receiver position. In the case of PPP in a kinematic mode, the tests allowed to determine the impact that the use of different streams has on the final positioning results. These studies showed differences between specific streams, which could not be seen in the first study. The best results (3D RMS at 0.13 m level) were obtained for the CLK90 stream, while for IGC01, the results were three times worse. The SPP tests clearly indicate that regardless of the selected SSR stream, one can see a significant improvement in positioning accuracy as compared to positioning results using only broadcast ephemeris.

A Fine-Tuned Positioning Algorithm for Space-Borne GNSS Timing Receivers

To maximize the usage of limited transmission power and wireless spectrum, more communication satellites are adopting precise space–ground beam-forming, which poses a rigorous positioning and timing requirement of the satellite. To fulfill this requirement, a space-borne global navigation satellite system (GNSS) timing receiver with a disciplined high-performance clock is preferable. The space-borne GNSS timing receiver moves with the satellite, in contrast to its stationary counterpart on ground, making it tricky in its positioning algorithm design. Despite abundant existing positioning algorithms, there is a lack of dedicated work that systematically describes the delicate aspects of a space-borne GNSS timing receiver. Based on the experimental work of the LING QIAO (NORAD ID:40136) communication satellite’s GNSS receiver, we propose a fine-tuned positioning algorithm for space-borne GNSS timing receivers. Specifically, the proposed algorithm includes: (1) a filtering architecture that separates the estimation of satellite position and velocity from other unknowns, which allows for a first estimation of satellite position and velocity incorporating any variation of orbit dynamics; (2) a two-threshold robust cubature Kalman filter to counteract the adverse influence of measurement outliers on positioning quality; (3) Reynolds averaging inspired clock and frequency error estimation. Hardware emulation test results show that the proposed algorithm has a performance with a 3D positioning RMS error of 1.2 m, 3D velocity RMS error of 0.02 m/s and a pulse per second (PPS) RMS error of 11.8ns. Simulations with MATLAB show that it can effectively detect and dispose outliers, and further on outperforms other algorithms in comparison.

Robust Initial Satellite Orbit Determination method using a Modified Kalman Filter

The control segment in satellite navigation systems is responsible for estimating satellite orbit and clock bias which is required for a reliable Position, Navigation and Timing (PNT) user service. Initial orbit determination is a crucial step which accounts for all unknowns/anomalous parameters such as satellite orbit manoeuvres, on board and receiver clock frequency variations and environmental effects. It is vital that the estimates of the orbits and clock are insensitive to these factors. In this paper, an initial orbit determination method is presented using existing robust methodology for estimation of initial satellite position and its propagation using a variant of the Kalman Filter (KF) which allows the initial position determination process to be independent of satellite and receiver anomalies. The derivation of this KF variant is presented. Preliminary results obtained from simulated data are shown. The said method is checked for robustness by comparing results obtained for a given satellite position data set with that from the conventional Kalman Filter. The conventional KF exhibits divergence due to anomalies which are eliminated by the use of the method presented in this paper.