Satellite Dynamic Model Research Articles

Intention inference for space targets using deep convolutional neural network

Intention inference for space targets is crucial for space situational awareness. This paper introduces a rapid and precise method for recognizing the intentions of non-cooperative space targets using a deep convolutional neural network (CNN). By employing a relative orbital dynamics model, an analysis of relative motion was performed, resulting in the identification of 11 distinct motion intentions for space targets. This study also describes how to generate relative motion trajectory images to create a training set for intention inference, effectively converting the problem into one of image recognition and classification. Extensive simulations were carried out to fine-tune the network hyperparameters, and the results highlight the exceptional performance of the proposed CNN-based method, which achieved an accuracy of 99.682%. This method significantly enhances recognition accuracy over other neural network-based methods for space objects and offers considerable potential for applications like spacecraft collision avoidance and strategic maneuvers among space targets.

A framework for developing an attitude determination and control system simulator for Cubesats: Processor-in-loop testing approach

The outbreak of miniaturized satellites is increasingly demanding well-performing attitude determination and control systems (ADCS). Testing an ADCS directly using hardware is extremely costly and risky, whereas testing it using only computer simulation does not yield realistic enough results. Therefore, a detailed framework for developing an ADCS simulator with processor-in-the-loop testing for low-earth orbit Cubesats is established in this paper. In particular, the study focuses on the implementation of the algorithms on a STM32 with ARM Cortex CPU for efficient testing and prototyping. This is done by formulating a quaternion-based satellite dynamic model equiped with a three-axis magnetorquers and a set of pyramidal cluster of reaction wheels for high pointing capabilities. Prominently used sensors are modeled so that the attitude can be estimated using a multiplicative extended Kalman filter. For attitude control, several modes are developed based on different mission stages, and a simplified less burdensome control switching strategy is proposed to maintain stability with minimal computation and energy resources. To test the applicability of the simulator, an ADCS is designed to meet the requirements of the recent low-atmosphere measurement missions. The results are analyzed in accordance with the ESA ECSS standards, and the assessment shows that the specifications can be met with a safe margin, leaving room for unmodeled errors to be taken into account in later stages of the design. Additionally, the proposed control strategy gives various possibilities for missions with different types of objectives, furthermore the framework's flexibility provides easy modification of any part for the user's specific needs.

GPS-SBAS-Based Orbit Determination for Low Earth Orbiting Satellites

A space-based augmentation system (SBAS) provides real-time GNSS correction signals via geostationary satellites for near-ground GNSS users. To use the SBAS correction for low Earth orbit (LEO) satellites, the correction, especially the ionosphere correction, must be adjusted for the LEO altitude. We apply modified SBAS data to LEO satellite onboard navigator to improve the positioning accuracy of a LEO satellite for possible real-time use. The onboard navigator requires high positioning reliability, and code pseudoranges, rather than phase pseudoranges, are used for the primary measurements. The Galileo NeQuick G model is used to determine the real-time conversion factor of the SBAS ionosphere correction for a LEO satellite. The GPS L1 data from GRACE satellite are combined with the SBAS data from the ground receiver. The onboard navigator combines the precise satellite dynamic model with an extended Kalman filter to improve positioning accuracy and stability. The kinematic positioning method, which uses the weighted least square method without the dynamic model, is also performed for comparison. The SBAS correction reduces the positioning error in both the kinematic positioning and the dynamic positioning. The positioning error reduction of the GPS and WAAS case over the GPS-only case is 25.2% for the kinematic method and 30.6% for the dynamic method. In the case of the dynamic method with the SBAS corrections, the positioning error remains smaller than that of the GPS-only dynamic method even after the satellite has left the SBAS service area.

Reliability-constrained optimal attitude-vibration control for rigid-flexible coupling satellite using interval dimension-wise analysis

This study proposes an uncertain optimal attitude–vibration control method for rigid–flexible coupling satellites with reliability constraints based on the interval dimension-wise analysis. To model the complex uncertain control system, multi–source uncertainties in rigid–flexible coupling satellites are quantified to interval parameters. Based on the nominal rigid–flexible coupling satellite dynamic model, the interval attitude–vibration model is derived and the corresponding coupled state equation is established. Considering polynomial chaos expansions in the surrogate model, an interval dimension-wise analysis (IDWA) method is proposed to predict the uncertain state response of the uncertain attitude–vibration control system, which can help solve the overestimation problem of the conventional perturbation method. An interval linear quadratic regulator (LQR) is proposed by combining the IDWA method and deterministic LQR, to accurately optimize the uncertain control input and cost function. With regard to harsh deterministic state response constraints, this study proposes a non-probabilistic time-dependent reliability method, which allows for an effective evaluation by flexibly characterizing the relationship between the uncertain state response and threshold. The reliability-constrained multi–objective optimal attitude–vibration control problem can be solved by considering the nominal cost function and uncertain state response as two optimization objectives. The effectiveness of the proposed method is verified using a rigid–flexible coupling satellite.

Targets selection and mission optimization of kinetic impact deflection test mission for small size asteroids

Near-Earth Asteroids (NEAs) impact poses a major potential threat to life on Earth, and kinetic impact is currently the most mature and feasible means of asteroid defense. The deflection effect of kinetic impact (KI) is closely related to the asteroid orbit, structure, material composition, mechanical properties, impact velocity, and other factors. To ensure the success of an asteroid defense mission, it is crucial to conduct in-orbit test missions and gain a thorough understanding of momentum transfer and orbital deflection principles. The Double Asteroid Redirection Test (DART) Mission has been launched and successfully impacted the Dimorphos whose diameter is 160 m. However, missions specifically targeting near-Earth asteroids with diameters ranging from 20 m to 90 m, which are more abundant but fainter and pose greater challenges in terms of navigation and guidance accuracy, have not been executed. For in-orbit demonstration and performance evaluation of kinetic impact asteroid deflection missions, the selection criteria for candidate asteroids were first established considering the size, orbit distribution, orbit uncertainty, characteristic information, and optical observability. 20 near-Earth asteroids were selected as primary candidate asteroids from the 28,946 cataloged near-Earth asteroids. Then, according to the mission cost and the way to evaluate the deflection distance, two Kinetic Impact in-orbit Demonstration (KID) mission scenarios were designed. A kinetic impact test mission optimization model was developed, integrating global and local optimization algorithms, while considering constraints like launch vehicle, launch site, and observability during and after impact. The model utilized a high-precision orbital dynamics model of the solar system to assess the deflection effect on the asteroid. We further reduced the candidate asteroids to 7 and ranked them in each mission scenario. Additionally, disruption conditions of the asteroids were examined, and mission parameters were re-optimized to ensure deflection without disruption. Accounting for factors such as the momentum enhancement factor, the impact probability between the asteroid and Earth was calculated for a 200-year period following the impact, thus evaluating the risk of an asteroid colliding with Earth after the KID mission implementation. The research can provide references for the target selection and kinetic impact test mission options for 20–90 m asteroids.

Design and Analysis of AAUSAT Cube Satellite Attitude Determination with PID Algorithms and Orbitron TLE

Satellites are intended to be of massive cost, hard, or hard to keep up and fix in circle. The point of this task is to decide an effective strategy to decide the orbital and heading data for the Nano satellite. To design the exact trajectory and circle for a satellite, information regarding the components which are liable for the deviation in the method of satellites. The factors that should be taken into account to determine the exact location of the satellite. It could be accomplished with the assistance of software responsible for orbit simulation, to do programming with Orbitron so as to get the required output. Orbitron is a simple 2D solver in which TLE files are uploaded, for AAUSAT CUBESAT. The various impacts on the satellite in space are slight deviation in the satellite from its orbit. The motion of the body with includes the disturbing forces in the orbit. However, a satellite has deviated from its normal path due to several forces. This deviation is termed as orbital perturbation. The changes in the orbital element with respect to secular variations are considered using orbital quaternions. The output from satellite dynamic model is received from attitude sensor. The comparative data (Input and Feedback) will generate error signal. To minimize the error signal using proportional integral and derivative (PID) is proposed controller implemented with MATLAB environment.

Design Contributions to the Attitude Control System of a Geostationary Satellite

The influence of Earth's gravity and lunar-solar disturbances can cause a geostationary satellite to deviate from its intended position. To counteract this, periodic station-keeping maneuvers are necessary. These maneuvers depend on the attitude control system to maintain stability and ensure the satellite's antenna remains directed towards the Earth station, ensuring mission services. This paper presents a design contribution to the attitude control system of a geostationary satellite, specifically during north-south station-keeping maneuvers. To effectively manage the satellite's position within a designated station-keeping box and control its attitude in three axes, a minimum of six 10 N chemical thrusters is required. The thruster configuration is designed to calculate torque parameters by considering the thrust vector, satellite mass, and the forces and moments acting upon them. The satellite model used in this study includes a rigid satellite dynamics model, perturbation model, PD controller, pseudo-rate modulator, and logic thruster selector. Once the system design is complete, numerical simulations can validate its performance and effectiveness. The simulation results confirm that all requirements have been met and the station-keeping design has been successfully implemented.

Refinement of GRACE‐FO Kinematic Orbit by Combining Least Squares Method and Orbital Dynamic Model

Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO) satellites are used to map the gravity field of the Earth. The orbit accuracy of GRACE‐FO depends on the quality of on‐board GPS data, which is key factor affecting GRACE‐FO mission execution. To improve the orbit accuracy of GRACE‐FO, a dynamical method was developed to reprocess kinematic orbits. First, with known kinematic orbits, the least squares method was used to estimate the initial state and dynamical parameters of GRACE‐FO orbits. Second, during data processing, orbit coordinates containing outliers were deleted. Finally, GRACE‐FO dynamical orbits with high accuracy were determined by combining initial state and dynamical parameters. To assess the orbit accuracy, dynamical and kinematic orbits were compared with Jet Propulsion Laboratory (JPL) orbits. Three‐dimensional root‐mean‐square (3D‐RMS) results show dynamical and kinematic orbit accuracy of 6.3 and 9.5 cm for GRACE‐FO‐C and 6.6 and 9.7 cm for GRACE‐FO‐D, achieving improvements of 33.68% and 31.96%, respectively. The RMS of satellite laser range (SLR) residuals was about 4.1 and 5.1 cm for GRACE‐FO‐C dynamical and kinematic orbit accuracy, and about 4.2 and 5.4 cm for GRACE‐FO‐D.

Analytical Nonlinear Observability Analysis for Spacecraft Autonomous Relative Navigation

Spacecraft autonomous relative navigation is widely required in the field of on-orbit services. In previous works, it has been shown that the monocular sequential images (MSIs) is a cost-effective autonomous relative navigation method. However, given the lack of size and initial orbit of noncooperative targets, the relative navigation system (RNS) with MSIs cannot ensure to estimate the entire relative motion states during the whole observation process. It is critical to perform an online observability analysis for RNS with MSIs to ensure autonomous relative motion estimation validity and accuracy. An analytical nonlinear observability analysis method is proposed in this article to improve the computational efficiency. We study the attributes of the relative orbit dynamics model and Lie algebra operations, and find that the observability matrix is only related to the limited states. The relationship among those states, rank, and the Frobenius norm of observability matrix is demonstrated, which simplify the observability criteria conditions and the degree measurements in analytical forms. In addition, based on the proposed method, we analyze the influence of the orbital manifolds on the observability degree of RNS with MSIs. Several suggestions are proposed for orbital manifolds detecting. The conclusion is a theoretical supplement to the past numerical research results. Finally, we implement the numerical simulations, and the current study’s findings verified the effectiveness of the proposed observability analysis method.

Mixed-integer GA optimization for the tracking control of a formation of small satellites equipped with multi-constrained electric thrusters

A formation mission scenario is considered, consisting of small satellites (Chasers) that must keep a reference trajectory with respect to a larger and non-cooperating Target satellite. The Chaser must perform its formation guidance and control tasks within the framework of its thruster constraints: the case of a low thrust electrical engine is here considered. The constraints of such a thruster are relevant to number and orientation of thrusters, the admissible thrust levels and minimum and maximum ON time. The control algorithm developed to satisfy all these constraints is a model predictive control based on a mixed-integer genetic algorithm optimization, which provides a fast estimate of the necessary scheduled actions. The algorithm takes J2 and drag perturbations into account; at the scope a differential orbital parameters linear relative dynamics model has been used, while the real-world dynamics is represented by a high precision orbital propagator. The developed orbital controller is particularly effective when trajectory keeping is required; different relative configurations, like Helix or Train formations, are taken as benchmark trajectories. The results show promising and robust performance in counteracting differential perturbations, even in the case in which the Target satellite performs scheduled orbital maneuvers which are not timely communicated to the Chaser satellite.

Mission planning of safe approach and emergency evacuation to large slow-rotating space debris

• A dynamic safety corridor approach strategy is developed with approach window and straight path. • The safe approach trajectory is planned to optimize transfer time and fuel consumption. • An emergency evacuation strategy is designed and the safety velocity is analyzed. • Motion precision and convergence time are ensured based on coupling control of orbit and attitude. The on-orbit service technology is expected to play an important role in space debris removal missions. In order to capture and remove space debris objects, servicing satellites need to have the ability of mission planning, to quickly approach space debris objects in limited time, to avoid possible collisions and other safety issues, and to have the ability of emergency suspension and evacuation in the event of sudden accidents. The mission planning of safe approach and emergency evacuation to large slow-rotating space debris is studied in this paper. Firstly, the relative orbit and attitude dynamics model of servicing satellite and space debris object is established. Then, a dynamic safety corridor approach strategy is proposed according to the motion characteristics of large slow-rotating space debris and the optimal safe approach trajectory is planned based on particle swarm algorithm. For the purpose of instant response to the possible accidents during the approach, an emergency evacuation strategy is proposed, while the safety velocity and the emergency evacuation time are analyzed. The relative orbit and attitude coupled control method is designed based on global terminal sliding mode control. The stability of this control method is proved by Lyapunov argument as well as the error convergence time is analyzed. Finally, the effectiveness of the mission planning and control method is verified by numerical simulations. The results of this paper can provide a preliminary technical exploration for the approach and capture strategy of large slow-rotating space debris.

Constraint navigation filter for space vehicle autonomous positioning with deficient GNSS measurements

When the deep space vehicles operate near or above the altitude of the Global Navigation Satellite System (GNSS) in the space service volume (SSV), the number of visible GNSS satellites becomes insufficient for the GNSS positioning, which leads to the divergence in navigation solution and significantly limits the GNSS applications in SSV. To overcome the issue, this article proposes a constraint navigation filter (CNF) with an orbital dynamics model as a constraint to force the deficient GNSS measurement away from divergence. In the CNF design, a simple orbit propagator (OP) is combined with the GNSS measurements in a tightly coupled integration mode by considering the computational complexity and positioning accuracy. The CNF is implemented as a sequential iteration manner to cope with arbitrary GNSS measurement variations. To testify the performance of the CNF design, the simulation is conducted via a self-developed SSV simulation platform. Two typical SSV scenarios in medium and high orbital plane with GPS and BDS measurements, i.e., medium earth orbit (MEO) and highly-inclined elliptical orbit (HEO) are generated, analyzed and compared respectively. The iterative filter gains as well as the positioning errors are investigated. The simulation results show that the typical GNSS positioning results will diverge with time when the visible GNSS satellites are less than 4, while the proposed CNF method can provide stable navigation solutions even there is only 1 GNSS satellite measurement available.

Autonomous celestial navigation method for a deep-space probe based on angle-constraint aided celestial angle measurement

<p indent=0mm>High-precision measurement is necessary for high autonomous navigation of deep-space probes. There are many kinds of astronomical measurement information and exist many geometric constraints between astronomical measurement information. Measurement error has different characteristics and meets the corresponding constraints. In this study, an autonomous celestial navigation method for deep-space probes based on angle-constraint assisted celestial angular navigation is proposed. The method takes the orbit dynamics model of the deep-space probe as the state model, and the azimuth between Mars, Phobos, and Phobos and the probe, as the measurement, to establish the measurement model. The angle-constraint model of the measurement is established, and then the genetic algorithm sequence Quadratic programming-mixed nonlinear programming method is used for nonlinear programming of angle constrained model. Cubature Kalman filter (CKF) is used to estimate the system state to reduce the random error because the system models are nonlinear, and the influence of astronomical measurement accuracy on navigation results is analyzed. Simulation results show that the proposed method can suppress the multi-source measurement error and achieve high-precision autonomous navigation of the deep-space detector.

Simulation of the orbital decay of a spacecraft in low Earth orbit due to aerodynamic drag

AbstractOrbiting objects in space are exposed to the risk of collision with space debris over their lifetime. Space debris orbiting in space experiences orbital decay due to various orbital perturbations. This work considers only orbital perturbations due to aerodynamic forces, which spacecraft experience due to the presence of a rarefied atmosphere, causing tumbling motion and orbital decay. Analysis of the orbital decay of a spacecraft is carried out by considering the variation of the drag coefficient as a function of its shape, motion and angle-of-attack. An in-house Direct Simulation Monte Carlo (DSMC) solver is modified for aerodynamic analysis of a spacecraft orbiting in the free molecular regime in low Earth orbit. In addition, an orbital dynamics model is developed to simulate the tumbling motion of a spacecraft and its orbital decay. The orbital decay trajectory is predicted for two sample spacecrafts using the aerodynamic coefficients obtained from the in-house DSMC solver as inputs to the orbital decay model. This study analyses and explores in detail the effects of the aerodynamic coefficients and shape of a spacecraft on its orbital decay.

Evaluation of Precise Microwave Ranging Technology for Low Earth Orbit Formation Missions with Beidou Time-Synchronize Receiver.

In this study, submillimeter level accuracy K-band microwave ranging (MWR) equipment is demonstrated, aiming to verify the detection of the Earth’s gravity field (EGF) and digital elevation models (DEM), through spacecraft formation flying (SFF) in low Earth orbit (LEO). In particular, this paper introduces in detail an integrated BeiDou III B1C/B2a dual frequency receiver we designed and developed, including signal processing scheme, gain allocation, and frequency planning. The receiver matched the 0.1 ns precise synchronize time-frequency benchmark for the MWR system, verified by a static and dynamic test, compared with a time interval counter synchronization solution. Moreover, MWR equipment ranging accuracy is explored in-depth by using different ranging techniques. The test results show that MWR achieved 40 m and 1.6 m/s accuracy for ranging and range rate during tests, using synchronous dual one-way ranging (DOWR) microwave phase accumulation frame, and 6 m/s range rate accuracy obtained through a one-way ranging experiment. The ranging error sources of the whole MWR system in-orbit are analyzed, while the relative orbit dynamic models, for formation scenes, and adaptive Kalman filter algorithms, for SFF relative navigation designs, are introduced. The performance of SFF relative navigation using MWR are tested in a hardware in loop (HIL) simulation system within a high precision six degree of freedom (6-DOF) moving platform. The final estimation error from adaptive relative navigation system using MWR are about 0.42 mm (range/RMS) and 0.87 m/s (range rate/RMS), which demonstrated the promising accuracy for future applications of EGF and DEM formation missions in space.

Real-Time On-Orbit Estimation Method for Microthruster Thrust Based on High-Precision Orbit Determination

In order to enable the micro-nanosatellites equipped with microthrusters to better complete various space applications, it is necessary to estimate the thrust performance of the microthrusters in real-time on orbit. This paper proposes a real-time on-orbit estimation method for microthrust based on high-precision orbit determination. By establishing a high-precision orbit dynamic model, the microthrust generated by a microthruster is modeled as a first-order Markov model, combined with a high-precision GNSS measuring device, and the satellite position is obtained through the cubature Kalman filter algorithm, velocity, and thrust real-time on-orbit estimates. For a thrust of 100 μN, the error accuracy of the on-orbit estimation is 3.98%; for a thrust of 500 μN, the error accuracy is 1.79%; for a thrust of 5 mN, the error accuracy can be reduced to 1.43%; and when the thrust is 500 μN, the accuracy of orbit determination is 16 cm. This method solves the problem that the traditional on-orbit thrust estimation method cannot perform real-time on-orbit estimation of microthrust on the order of hundreds of μN. The real-time on-orbit estimation of microthrust of micro-nanosatellites equipped with microthrusters of the order of hundreds of micronewtons or even several mN to tens of mN has certain reference value.

Lorentz Force Characteristics of a Bare Electrodynamic Tether System with a Hollow Cathode

The electrodynamic tether (EDT) is a type of propulsion system that uses the geomagnetic field and ionospheric plasma and has the potential to conduct a space-debris removal mission without consuming a large amount of propellant. To understand the dynamic properties of the bare EDT system, an orbital dynamic model based on a detailed environmental space model and the real discharge characteristics of a hollow cathode plasma contactor (HCPC) was built. By numerical simulation, the differences in the bare tether performance caused by various orbital conditions and HCPC voltage models (at constant or various voltages) were compared and discussed. The results suggest that dynamic distinctions generated by the two bias voltage models increased as the latitude increased from 0° to 60°.

Feasibility of space-based measurement-device-independent quantum key distribution

The measurement-device-independent (MDI) quantum key distribution (QKD) is considered to be an alternative to overcome the currently trusted satellite paradigm. However, the feasibility of the space-based MDI-QKD remains unclear in terms of the factors: the high-loss uplink between a ground station and a satellite, the limited duration when two ground stations are simultaneously visible, as well as the rigorous requirements for the two-photon interference when performing the Bell-state measurement. In this paper, we present a feasibility assessment of space-based MDI-QKD based on the Micius satellite. Integrated with the orbital dynamics model and atmosphere channel model, a framework is presented to explore the whole parameters space including orbit height, elevation angle, apertures of transceiver and atmospheric turbulence intensity to give the considerations for improving key rates and subsequently provide a relevant parameter tradeoff for the implementation of space-based MDI-QKD. We further investigate the heart of MDI-QKD, the two-photon interference considerations such as the frequency calibration and time synchronization technology against Doppler shift, and the way of performing the intensity optimization method in the dynamic and asymmetric channels. Our work can be used as a pathfinder to support decisions involving as the selection of the future quantum communication satellite missions.

Orbit Design and Trajectory Analysis of satellite in Low Earth Orbit

An Attitude control system for a satellite in low earth orbit is designed in this project. As a reference, CARTOSAT-2 is selected to design the AOCS. CARTOSAT-2 is located in LEO so it suits the needs of the projects. It is mainly used for mapping of urban, rural areas and wetlands in India. To design a basic AOCS, a DC motor based model is considered. Transfer functions of DC motor and satellite dynamics model are calculated using Laplace transformation. Stability of the system is checked by plotting poles and zeroes of the systems. PID controller is used to improve the overall stability of the system by decreasing the errors in the output of the system. The systems are subjected to sine and step inputs and responses are plotted in the form of graphs. The plots are studied using SciLab as the tool to design the block diagram and the control system for the AOCS. Scilab along with FlightGear is used to visualize the response of the system.

Fault-tolerant estimation of satellite orbital states

This paper is devoted to global positioning system (GPS)-based fault-tolerant satellite orbital states estimation which is used for the pseudo-ranging model. GPS is widely used by many researchers to determine the orbit state vectors of satellites, but errors in GPS measurements can cause major errors in satellite location detection. Therefore, there is a need for an architecture that will resist possible measurement errors and GPS malfunctions. This study aims to present the novel approaches to tolerate the errors that may take place in GPS measurements. The satellite localisation has been detected via a pseudo-ranging model between four GPS satellites and the target satellite. The Keplerian equations and orbit elements are used for the satellite dynamic model with orbital J2 perturbation which is due to the flattened shape of the earth is taken into account via the extended Kalman filter (EKF) algorithms. The reconfigurable and the adaptive version of fault-tolerant localisation architecture eliminate the GPS measurement errors during estimating satellite position vectors. The comparison of the prediction architectures of the fault tolerant satellite state vectors originally proposed. At the same time, it is possible to use fault tolerant architectures designed to detect whether GPS satellites are malfunctioning or not.