Satellite Formation Flying Research Articles

Distributed Radar Sounder: A Novel Concept for Subsurface Investigations Using Sensors in Formation Flight

Spaceborne radar sounders are nadir-looking sensors operating in the high frequency (HF) or very high frequency (VHF) bands with subsurface sensing capabilities. Due to technological limitations, this type of sensors often deploys omnidirectional antennas. This results in undesired artifacts such as off-nadir clutter which could hinder data interpretation. Very recent technological advancements open up the possibility of synthesizing very large antenna apertures in HF/VHF band by using small satellites array deployed in suitable orbital formation flying. Accordingly, in this study, we propose a novel concept of distributed radar sounder system. The proposed concept is complemented with a mathematical model for performance prediction which takes into account the uncertainty on the position of the sensors. Moreover, we discuss possible orbital solutions for the problem of the deployment of the distributed radar sounder system. The results show that a distributed radar sounder operating in small satellites formation flying is particularly appealing as it can: 1) substantially reduce the impact of surface clutter; 2) increase the across-track resolution; 3) increase the signal-to-noise ratio (SNR) (or, alternatively, decrease the overall required transmitted power with respect to a traditional single configuration radar sounder design); and 4) provide large flexibility in the data processing of the signals acquired by the different sensors.

Enhanced orbit determination for formation-flying satellites through integrated single- and double-difference GPS ambiguity resolution

The formation-flying technique is a fundamental concept for earth observing satellite missions, which usually require both absolute and relative orbit accuracies. Their precise orbit determinations are usually exclusively performed based on spaceborne GNSS data, where integer ambiguity resolution (IAR) plays a crucial role in achieving the best orbit accuracy. However, it is found that single-receiver IAR by resolving the single-difference (SD) ambiguities between GNSS satellites at each individual formation-flying satellite cannot achieve the same relative orbit accuracy that is attained by double-difference (DD) IAR between formation-flying satellites. To unravel this problem, 1 year of GPS data collected by the Gravity Recovery and Climate Experiment (GRACE) mission are used and four types of orbits are derived for comparison: (1) orbits where no ambiguities are fixed; (2) orbits where SD IAR is performed for both satellites; (3) orbits where only DD ambiguities between the twin GRACE satellites are resolved; (4) and orbits where SD IAR is carried out on only GRACE A while DD IAR is further accomplished between the twin satellites, namely the integrated SD IAR and DD IAR solutions. They are then evaluated through comparison to the reduced-dynamic orbit generated at the Jet Propulsion Laboratory, residual analysis of satellite laser ranging (SLR), and K-Band ranging (KBR) measurements. As expected, the integrated SD IAR and DD IAR solutions can achieve the highest absolute and relative orbit accuracies simultaneously. Specifically, SLR residuals in case of the integrated IAR are reduced by at least 25% for the kinematic orbit, when compared to the case of DD IAR. KBR residuals in case of the integrated IAR are reduced by 35 and 16% for the dynamic and kinematic orbit, respectively, when compared to those of SD IAR. Importantly, we find that errors in GPS clocks and/or narrow-lane fractional-cycle biases are in part responsible for the deteriorated relative accuracy of SD IAR achieved orbits. Therefore, we suggest that the integrated SD IAR and DD IAR scheme should be implemented for the best orbit solutions of formation-flying missions.

Imaging With 3-D Aperture Synthesis Radiometers

The spatial resolution is still a problem in passive microwave remote sensing, especially in low frequency. In recent years, the satellite formation flying has been proposed. Based on this technique, a large array is able to be synthesized in orbit to achieve higher spatial resolution. However, it is a big challenge for the control system to constrain all the satellites in a coplane in orbit. The 3-D array configuration is a good choice for a synthesized array based on satellite formation flying. In this paper, the complete formulation of visibility functions, including system imperfections, in a 3-D aperture synthesis radiometer (3-D ASR) is derived. The array factor of a 3-D ASR is defined. The reconstructed modified brightness temperature (BT) is a 3-D linear convolution of the modified BT and the array factor. Based on this relationship, the reconstruction method for a practical 3-D ASR is studied. The numerical results demonstrate that the reconstruction method is correct and stable. Finally, a discussion is given to analyze several existing methods that were proposed to reconstruct BT image for 3-D arrays in radio astronomy and earth observation. Compared with these existing methods, our imaging method is more suitable for earth observation based on the technique of satellites formation flying in low earth orbit. In addition, according to the derivations, some mature techniques that were developed for 2-D ASRs may be applied to 3-D ASRs.

Combining Distributed Consensus with Robust H∞-Control for Satellite Formation Flying

Control methods that guarantee stability in the presence of uncertainties are mandatory in space applications. Further, distributed control approaches are beneficial in terms of scalability and to achieve common goals, especially in multi-agent setups like formation control. This paper presents a combination of robust H ∞ control and distributed control using the consensus approach by deriving a distributed consensus-based generalized plant description that can be used in H ∞ synthesis. Special focus was set towards space applications, namely satellite formation flying. The presented results show the applicability of the developed distributed robust control method to a simple, though realistic space scenario, namely a spaceborne distributed telescope. By using this approach, an arbitrary number of satellites/agents can be controlled towards an arbitrary formation geometry. Because of the combination with robust H ∞ control, the presented method satisfies the high stability and robustness demands as found e.g., in space applications.

Analysis of Inter-satellite Ranging Precision for Gravity Recovery in a Satellite Gravimetry Mission

In a satellite gravimetry mission similar to GRACE, the precision of inter-satellite ranging is one of the key factors affecting the quality of gravity field recovery. In this paper, the impact of ranging precision on the accuracy of recovered geopotential coefficients is analyzed. Simulated precise orbit determination (POD) data and inter-satellite range data of formation-flying satellites containing white noise were generated, and geopotential coefficients were recovered from these simulated data sets using the crude acceleration approach. The accuracy of the recovered coefficients was quantitatively compared between data sets encompassing different ranging precisions. From this analysis, a rough prediction of the accuracy of geopotential coefficients could be obtained from the hypothetical mission. For a given POD precision, a ranging measurement precision that matches the POD precision was determined. Since the purpose of adopting inter-satellite ranging in a gravimetry mission is to overcome the imprecision of determining orbits, ranging measurements should be more precise than POD. For that reason, it can be concluded that this critical ranging precision matching the POD precision can serve as the minimum precision requirement for an on-board ranging device. Although the result obtained herein is about a very particular case, this methodology can also be applied in cases where different parameters are used.

Antenna Configuration Method for RF Measurement Based on DOPs in Satellite Formation Flying

Radio frequency (RF) measurement technology provides a relative navigation solution that can be of great importance to have significant potential for application to the satellite groups. With the development of the RF relative measurement sensors, it is found that the antenna configuration of the sensors affects the precision of relative position and attitude measurement. This study proposes improvements to the precision of the sensors by the virtue of the optimal antenna configuration. Furthermore, the concept of dilution of precision (DOP) is extended to the RF relative measurement sensors, and a new dilution called IDOP is proposed as a benchmark to determine the precision of relative position and attitude measurement in engineering applications of the space mission. In order to select the optimal antenna configuration in real time in a scene where the intersatellite position and attitude change dynamically, this study presents an optimal antenna configuration selection strategy and models the antenna configuration selection as a combinatorial optimization problem. Furthermore, the genetic algorithm (GA) with two encoding mechanisms is proposed to solve this problem. Finally, numerical results are presented to verify the robustness.

Navigation for Satellite Formation Flying

This paper deals with the case of a target satellite in an unknown orientation and location with respect to the master satellite. Feature based monocular pose estimation vision system was presented. The results of analysis, implementation and testing of simulation intended for vision-based navigation applications such as rendezvous of satellites and formation flying are shown. The mobile robot was used as the platform for the vision system. Pose estimation algorithms were implemented in Matlab environment. It was obtained that the proposed method is robust on varying and low light conditions.

Strong Tracking Sigma Point Predictive Variable Structure Filter for Attitude Synchronisation Estimation

In this paper, a novel Strong Tracking Sigma-Point Predictive Variable Structure Filter (ST-SP-PVSF) is presented as a further development of the Adaptive Predictive Variable Structure Filter (APVSF) for attitude synchronisation during Satellite Formation Flying (SFF). First, the sequence orthogonal principle is adopted to enhance the robustness of the APVSF for any nonlinear system with uncertain model errors. Then, sigma-point sampling strategies (such as unscented transfer, cubature rule and Stirling's polynomial interpolation) are introduced to extend the APVSF with the ability to capture the second central moment's information on the model errors to update the system model with higher precision. The new methodology has advantages in dealing with the various types of uncertainties or model errors compared with the APVSF. In addition, it does not need to choose the limit boundary layer ψlim it for system estimation, which reduces the sensitivity to the initial parameters and improves its adaptive ability over the APVSF. Simulations are performed to demonstrate that the proposed method is more suitable for attitude synchronisation estimation of the SFF system.

Model Predictive Control for Continuous Low Thrust Satellite Formation Flying

This paper presents a low thrust guidance and control strategy for distributed spacecraft systems flying in proximity in nearly circular Low Earth Orbit (LEO) using Model Predictive Control (MPC). It is designed to converge to arbitrary three dimensional (3D) force free formation topologies taking different constraints and system limitations into account. However it is also applicable to forced formations with the same given constraints. Its performance is evaluated using simulations of different typical 3D formation topologies.

Optimal Reconfiguration of Formation Flying Using A Direct Sequential Method

Formation flying of multiple Unmanned Aerial Vehicles (UAVs) or satellites enables cooperation among agents, and thus constitutes a system of greater performance than the simple sum of its parts by taking advantage of that cooperation. As a prerequisite, how to reconfigure, energy-optimally or time-optimally, from the current formation to the desired one shall be planned beforehand. This paper addresses such a planning problem from the perspective of optimal control that exploits a direct sequential method. In our study, during the reconfiguration agents subject to nonlinear dynamics, and final formation constraints are imposed where there exist unknown parameters to be determined optimally. In the developed direct method the original problem is transcribed into a sequence of convex optimization problems via the control vector parameterization approach using piecewise-constant approximation. In the end, each instance in the sequence is essentially a programming problem (quadratic or linear) subject to linear constraints that can be solved very efficiently. In this paper, the proposed method has been applied to two scenarios: the energy-optimal reconfiguration of five UAVs and the time-optimal formation reconfiguration of four satellites. In our implementation the free open source solver CVX is used. By comparison with the global optimization technique provided in MATLAB, the solutions converge very fast to the global minimum.

Predictive Smooth Variable Structure Filter for Attitude Synchronization Estimation During Satellite Formation Flying

In this paper, a novel predictive smooth variable structure filter (PSVSF) is presented for attitude synchronization during satellite formation flying (SFF). The strategy is proposed based on variable structure control concept and applies to any nonlinear system with modeling errors. Because the modeling errors in the PSVSF are not restricted to Gaussian noise only, the technique can deal with various kinds of uncertainties, parameter variations, or noises. It also has low computational burden; therefore, it is more general than other nonlinear estimation methods. Sufficient conditions to analyze the stability and characteristics of the PSVSF are presented. Simulations are performed to demonstrate the accuracy, robustness, and stability of the proposed PSVSF for the attitude synchronization estimation of the SFF system.

Formation-Flying Planar Periodic Orbits in the Presence of Intersatellite Lorentz Force

This study presents formation-flying periodic orbits in a new satellite-relative motion scenario, which considers the presence of intersatellite Lorentz force. A nonlinear dynamical model for the proposed relative motion is established based on the Hill–Clohessy–Wiltshire equation, under the assumption that a chief satellite generates a rotating magnetic dipole while a constantly charging deputy satellite moves close to the artificial magnetic field of the chief satellite. Moreover, we assume that the barycenter of the proposed system is constrained in a circular reference orbit, and the rotating magnetic axis of the dipole is perpendicular to the reference orbital plane. We first derived equilibrium points (and analyzed their stabilities), an integral constant, and zero-velocity surfaces for the proposed relative motion based on system parameters, such as the charge-to-mass ratio of the deputy satellite, the moment and rotating rate of the magnetic dipole, and the angular velocity of the reference orbit. With regard to the zero-velocity surfaces, bounded periodic orbits in the reference orbital plane are searched out using Poincare maps. Planar periodic orbits near the equilibrium points are numerically computed via differential correction based on the stability characteristic of equilibrium points, and a special case is analytically solved using the Lindstedt $-$ Poincare method. The periodic orbits of relative motion presented in this study differ from those in traditional satellite formation flying. The difference suggests potential applications of the presented periodic orbits, such as propellantless satellite formation maintenance and noncontact capture of electrostatically charged space debris.

Research on the Calculation Method of the Collision Probability of Satellite Formation Flying

For some reasons (such as the failure of a satellite or the formation of a satellite formation mission), it is necessary to reconstruct the formation. In this process, the research on satellite collision avoidance has received extensive attention. In this paper, by deriving the initial state covariance matrix of the satellite, the collision probability density function was integrated in a specific region of the satellite, then the collision probability of formation satellites was obtained. The simulation experiments show that the method has great significance for the collision between satellites.

Fuel-optimal Lorentz-augmented Spacecraft Formations Using Novelty Minimum Sliding Mode Error Feedback Controller

A dynamics model of satellite formation flying (SFF) is derived in an elliptical orbit with the existence of J2 perturbation and the Lorentz force. The Lorentz force is considered as the propellantless electromagnetic propulsion for orbital maneuvering and maintenance. However, the direction of Lorentz force is limited by the local magnetic field and the velocity of the spacecraft with respect to the local magnetic field, which is unable to provide the required control acceleration timely; therefore, it always works as an auxiliary strategy to reduce the fuel consumptions. Based on the above assumptions, the fuel-optimal control scheme is proposed for the SFF based on the minimum sliding mode error feedback controller (MSMEFC), which is implemented by using the thruster control and Lorentz force. Moreover, the optimal trajectories of the required specific charge of deputy Lorentz spacecraft and the thruster-generated control acceleration have been developed with details, respectively. Numerical examples are presented to demonstrate the efficacy of the proposed controller to maneuver and maintenance the SFF with the optimal fuel consumptions.

Space-borne frequency comb metrology

Precision time references in space are of major importance to satellite-based fundamental science, global satellite navigation, earth observation, and satellite formation flying. Here we report on the operation of a compact, rugged, and automated optical frequency comb setup on a sounding rocket in space under microgravity. The experiment compared two clocks, one based on the optical D2 transition in Rb, and another on hyperfine splitting in Cs. This represents the first frequency comb based optical clock operation in space, which is an important milestone for future satellite-based precision metrology. Based on the approach demonstrated here, future space-based precision metrology can be improved by orders of magnitude when referencing to state-of-the-art optical clock transitions.

Energy-efficient control of nanosatellites during distributed region formation flying

In this paper, we present an energy-efficient method for distributed region formation flying of nanosatellites. The proposed framework consists of two concurrent sub-schemes that include estimation and formation. In the estimation sub-scheme, unlike the existing methods on satellite formation flying, that assume the availability of the reference orbital elements to all followers, here, a distributed estimator is developed so that the follower nanosatellites estimate the position of the leader in its orbital slot. In the formation sub-scheme, we consider a region formation strategy which is an efficient method in dealing with the formation of a large number of nanosatellites. We propose an optimal region following formation method based on the receding horizon control (RHC) using the estimated reference orbital elements. Subsequently, an algorithm is presented to solve the proposed energy-efficient formation flying method. Finally, the simulation result is presented that illustrates the purposed method improves the power consumption for each nanosatellite with respect to the existing non-optimal region formation flying controllers.

Compensation method of in-track coupling effect of cross-track maneuver for formation-flying satellites

Compensation method of in-track coupling effect of cross-track maneuver for formation-flying satellites

Adaptive Predictive Variable Structure Filter for Attitude Synchronization Estimation

In this paper, a novel Predictive Variable Structure Filter (PVSF) and its adaptive deformation (APVSF) are presented for attitude synchronisation during Satellite Formation Flying (SFF). The PVSF is proposed based on the variable structure control concept and applied to any nonlinear system with model errors. The model errors in the PVSF need not satisfy the assumption of Gaussian white noise; therefore, it has advantages in dealing with various kinds of uncertainties, parameter variations or noises. Then, the APVSF is also presented to adjust the smoothing boundary layer of PVSF by minimising the Mean-Square Error (MSE). Simulations are performed to demonstrate the accuracy, robustness, and stability of the proposed methodologies for the attitude synchronisation estimation of the SFF system.

EFFECT OF SHADOWING AND MULTIPATH FADING ON THE AREA SPECTRAL FOR CELL-EDGE USERS IN HETEROGENEOUS NETWORKS

irrespective of their location. The traditional macro-only network have been proved ineffective when communication signal is required for users located in the cell edge and a certain distance away from the macrocell base station. This is because of excess attenuation of the signal due to fading and shadowing. Multipath fading and shadowing are major causes of performance degradation in mobile communication systems. This phenomenon which arises as a result of propagation effects (like scattering, diffraction and reflection), renders the traditional macro-only network communication with users far away from the macrocell base station and located in the cell edge less effective. The deployment of femtocells around the cell edge of this macrocell helps to reduce the effect of fading and shadowing thereby increasing the overall efficiency of the cellular network. Numerical simulation carried out for the macro-femto heterogeneous network using MATLAB shows how the effect of fading and shadowing was reduced. This holds a great promise for adaptive space-based wireless sensor networks, formation-flying satellites and constellations. http://dx.doi.org/10.4314/njt.v35i2.24

Relative orbit determination for satellite formation flying based on quantum ranging

Relative orbit determination is widely used in the field of autonomously controlled satellite formation flying (SFF). Currently, some traditional techniques cannot meet the strict requirement of the accuracy of relative orbit determination for certain space missions. Thus, the primary purpose of this study is to design some special type of sensor to increase the accuracy of the distance measurement, which can eventually lead to an improvement in the accuracy of relative orbit determination for SFF. Two types of quantum sensors are proposed, based on the double-points quantum ranging (DPQR) and the triangle quantum ranging (TQR) schemes that utilize the second-order correlation between the entangled photons. Simulation result shows that the ranging accuracy of the TQR-type sensor is more precise than that of the DPQR-type one. Additionally, the unscented Kalman filter (UKF) is used to estimate the relative state of the SFF, which uses the TQR-type sensor as the measurement model compared with a traditional sensor. The simulation results show that the quantum sensor is superior to the traditional one and their estimation errors of the position and velocity remain within 1cm and 1mm/s, respectively, at a relative distance of 1km between the chief and deputy satellites.