Geosynchronous Research Articles

DebrisWatch I: A survey of faint geosynchronous debris

Recent anomalies exhibited by satellites and rocket bodies have highlighted that a population of faint debris exists at geosynchronous (GEO) altitudes, where there are no natural removal mechanisms. Despite previous optical surveys probing to around 10–20 cm in size, regular monitoring of faint sources at GEO is challenging, thus our knowledge remains sparse. It is essential that we continue to explore the faint debris population using large telescopes to better understand the risk posed to active GEO satellites. To this end, we present photometric results from a survey of the GEO region carried out with the 2.54 m Isaac Newton Telescope in La Palma, Canary Islands. We probe to 21st visual magnitude (around 10 cm, assuming Lambertian spheres with an albedo of 0.1), uncovering 129 orbital tracks with GEO-like motion across the eight nights of dark-grey time comprising the survey. The faint end of our brightness distribution continues to rise until the sensitivity limit of the sensor is reached, suggesting that the modal brightness could be even fainter. We uncover a number of faint, uncatalogued objects that show photometric signatures of rapid tumbling, many of which straddle the limiting magnitude of our survey over the course of a single exposure, posing a complex issue when estimating object size. This work presents the first instalment of DebrisWatch, an ongoing collaboration between the University of Warwick and the Defence Science and Technology Laboratory (UK) investigating the faint population of GEO debris.

Optimal fuel station arrangement for multiple GEO spacecraft refueling mission

This paper investigates an optimal fuel station (FS) arrangement problem for multiple geosynchronous (GEO) spacecrafts with many-to-many (M2M) refueling, subject to the capacity of the servicing spacecraft (SSC) and the different fuel requirements of the targets. Several FSs with their reusable SSC are arranged on GEO, while the SSC commutes between fuel-deficient targets and FSs to refuel the multiple targets. To avoid building a fuel station at the exact position of the target in traditional M2M refueling, the problem is formulated as a location–allocation problem. Based on that, a novel modified K-means clustering is proposed, in which the difficulty caused by the limitation of the SSC’s capacity is solved. With the proposed method, the FS is allowed to be arranged in the exact region without inaccessible targets, where the minimum number of the required FS and the minimized fuel cost are determined in turn. Finally, numerical simulations validate the performance of the proposed method.

Characterization of on‐orbit GPS transmit antenna patterns for space users

The GPS Antenna Characterization Experiment (GPS ACE) has made extensive observations of GPS L1 signals received at geosynchronous (GEO) altitude, with the objective of developing comprehensive models of the signal levels and signal performance in the GPS transmit antenna side lobes. The experiment was originally motivated by the fact that data on the characteristics and performance of the GPS signals available in GEO and other high Earth orbits was limited. The lack of knowledge of the power and accuracy of the side lobe signals on-orbit added risk to missions seeking to employ the side lobes to meet navigation requirements or improve performance. The GPS ACE Project lled that knowledge gap through a collaboration between The Aerospace Corporation and NASA Goddard Space Fight Center to collect and analyze observations from GPS side lobe transmissions to a satellite at GEO using a highly-sensitive GPS receiver installed at the ground station. The GPS ACE architecture has been in place collecting observations of the GPS constellation with extreme sensitivity for several years. This sensitivity combined with around-the-clock, all-in-view processing enabled full azimuthal coverage of the GPS transmit gain patterns over time to angles beyond 90 degrees o -boresight. Results discussed in this paper include the reconstructed transmit gain patterns, with comparisons to available pre-fight gain measurements from the GPS vehicle contractors. For GPS blocks with extensive ground measurements, the GPS ACE results show remarkable agreement with ground based measurements. For blocks without extensive ground measurements, the GPS ACE results provide the only existing assessments of the full transmit gain patterns. The paper also includes results of pseudorange deviation analysis to assess systematic errors associated with GPS side lobe signals.

Nonambiguous Image Formation for Low-Earth-Orbit SAR With Geosynchronous Illumination Based on Multireceiving and CAMP

Low-earth-orbit (LEO) synthetic aperture radar (SAR) can achieve advanced remote sensing applications benefiting from the large beam coverage and long duration time of interested area provided by a geosynchronous (GEO) SAR illuminator. In addition, the receiving LEO SAR system is also cost-effective because the transmitting module can be omitted. In this article, an imaging method for GEO-LEO bistatic SAR (BiSAR) is proposed. First, the propagation delay characteristics of GEO-LEO BiSAR are studied. It is found that the traditional “stop-and-go” propagation delay assumption is not appropriate due to the long transmitting path and high speed of the LEO SAR receiver. Then, an improved propagation delay model and the corresponding range model for GEO-LEO BiSAR are established to lay the foundation of accurate imaging. After analyzing the sampling characteristics of GEO-LEO BiSAR, it is found that only 12.5% sampling data can be acquired in the azimuth direction. To handle the serious sub-Nyquist sampling problem and achieve good focusing results, an imaging method combined with multireceiving technique and compressed sensing is proposed. The multireceiving observation model is first obtained based on the inverse process of a nonlinear chirp-scaling imaging method, which can handle 2-D space-variant echo. Following that, the imaging problem of GEO-LEO BiSAR is converted to an $L_{1}$ regularization problem. Finally, an effective recovery method named complex approximate message passing (CAMP) is applied to obtain the final nonambiguous image. Simulation results show that the proposed method can suppress eight times Doppler ambiguity and obtain the well-focused image with three receiving channels. With the proposed method, the number of required receiving channels can be greatly reduced.

Space debris observations with the Slovak AGO70 telescope: Astrometry and light curves

The Faculty of Mathematics, Physics and Informatics of Comenius University in Bratislava, Slovakia (FMPI) operates its own 0.7-m Newtonian telescope (AGO70) dedicated to the space surveillance tracking and research, with an emphasis on space debris. The observation planning focuses on objects on geosynchronous (GEO), eccentric (GTO and Molniya) and global navigation satellite system (GNSS) orbits. To verify the system’s capabilities, we conducted an observation campaign in 2017, 2018 and 2019 focused on astrometric and photometric measurements. In last two years we have built up a light curve catalogue of space debris which is now freely available for the scientific community. We report periodic signals extracted from more than 285 light curves of 226 individual objects. We constructed phase diagrams for 153 light curves for which we obtained apparent amplitudes.

Optimal transfer schemes between space debris objects in geostationary orbit

The paper compares two variants of re-orbiting space debris objects from the geosynchronous (GEO) region. Under the first re-orbiting variant, a spacecraft-collector transfers between target objects (87 upper stages). Each object is re-orbited into a disposal orbit (DO) using special thruster de/re-orbiting kits (TDK) which are placed on space debris objects by the collector. Under the second variant, the object is pushed to a DO by the collector itself, which then moves to a new space debris object from the previous object's DO. It is shown that due to the slow evolution of the orbital parameters in the GEO region, the same transfer schemes can be used for both re-orbiting variants. We describe orbits in the near-equatorial region and consider two transfer schemes between objects. Under the first scheme, a transfer is executed when the orbits have the same inclination near the equator, and under the second scheme, when the orbit of the next object has the smallest inclination. Calculations show that both schemes are practically equivalent in terms of both the averaged ΔV for a transfer and the duration — however, not all objects under consideration can be covered under the first scheme. Hence, priority should be given to the second scheme. It can be calculated, that 6 collectors are required to clean the GEO protected region from spent upper stages. The service of each is expected to be at most 8 years and its required ΔV budget is at most 0.7 km/s. A re-orbiting of one object to a DO requires on average only 10 m/s; the return to a new object from the DO of the previous object is nearly energetically equal to a sequential transfer between the objects. In this regard, as distinct from low orbits (in which it is preferable to use TDKs), it is more beneficial to follow the second variant for re-orbiting space debris objects from the GEO region (i.e., using the collector itself).

Beamforming and Scheduling Techniques for Multibeam DVB-S2X Over Rainy Fading Satellite Channel

The extension of the digital video broadcasting second generation standard (DVB-S2X) for transmission over satellite has been introduced recently with its novel superframe structure, which is a key enabler for applying interference management techniques, such as precoding, to multibeam high throughput geosynchronous (GEO) satellite systems operating in the Ka-band. This paper presents the first full design of DVB-S2X system with multi-user-multiple-input-single-output (MU-MISO DVB-S2X), with most of its modulation and coding schemes (MODCODs), over rainy fading channels. The atmospheric impairments on the Ka-band satellite channel are considered, especially the rainfall effect, which is the most effective atmospheric impairment that degrades the system performance. Two rainy fading channels are designed, one for tropical region and the other for temperate region, using real rain data from these areas. In addition, the user scheduling influence on the bit error rate (BER) performance of MU-MISO DVB-S2X system is tested and compared with the conventional MISO DVB-S2X system. Simulation results show that the proposed system can achieve a significant improvement in terms of BER performance with at least 20 dB for 128 amplitude and phase shift keying (128APSK) MODCOD over the tropical channel and 14 dB for 32APSK MODCOD over temperate channel when the number of users is six. The enhancement in error rates proves that MU-MISO DVB-S2X system with scheduling can be the key solution for DVB-S2X system performance degradation in fading channels, especially rainy fading channels.

Geosynchronous Spaceborne–Airborne Multichannel Bistatic SAR Imaging Using Weighted Fast Factorized Backprojection Method

Geosynchronous (GEO) spaceborne-airborne bistatic synthetic aperture radar (GEO-BiSAR), where the high-altitude transmitter provides continuous illumination for the receiver, is capable of providing benefits to remote sensing applications. However, obtaining a focused image with high efficiency is a challenging work. The severe 2-D space-variant range cell migration and Doppler modulation introduced by the two moving platforms make the echo hard to be focused. Moreover, the azimuth ambiguity due to the low pulse repetition frequency adopted by the GEO illuminator seriously deteriorates the quality of the final image. In order to simultaneously suppress the azimuth ambiguity and obtain well-focused images, a weighted fast factorized backprojection (FFBP) method is proposed for multichannel GEO BiSAR in this letter. First, the Doppler ambiguity of GEO BiSAR is analyzed and the azimuth multichannel receiving technique is introduced. Then, the multichannel transfer function for GEO BiSAR is derived. Based on the multichannel transfer function, a weighted FFBP method is proposed to achieve accurate focusing and ambiguity suppression. Finally, the simulation results validate the effectiveness of the proposed method.

A Two-Step Nonlinear Chirp Scaling Method for Multichannel GEO Spaceborne–Airborne Bistatic SAR Spectrum Reconstructing and Focusing

Due to the high-altitude illumination and the separation of the receiver and transmitter, geosynchronous (GEO) spaceborne–airborne bistatic synthetic aperture radar (BiSAR) is more flexible and accessible in remote sensing applications. In this paper, the Doppler characteristics of GEO BiSAR with a squint receiver are analyzed. It is found that the Doppler spectrum is generally aliased in GEO BiSAR regarding the low pulse repetition frequency (PRF) adopted by the GEO SAR. In order to suppress the ambiguity without adjusting the PRF of GEO SAR, the azimuth multichannel receiving technique is applied to the receiver and then the multichannel transfer function for GEO BiSAR is derived. However, the whole bandwidth of the imaging scene is much larger than that of the center point, which requires extra receiving channels to suppress the ambiguity and thereby increasing the system complexity. A two-step nonlinear chirp scaling (NLCS) method is proposed to obtain the well-focused image with reduced receiving channels. First, a preprocessing step is conducted to achieve space-variant range cell migration correction. After that, the first-step NLCS processing is applied to equalize the 2-D space-variant Doppler centroid and thereby the Doppler bandwidth is decreased, i.e., the required number of receiving channels for reconstruction is reduced. Then, the unambiguous spectrum is reconstructed based on the proposed multichannel transfer function. Finally, the second-step NLCS processing is carried out to equalize the 2-D space-variant high-order Doppler parameters and obtain the well-focused image. The simulation results validate the effectiveness of the proposed method. With the proposed two-step NLCS method, the well-focused image for GEO BiSAR is obtained and the required number of receiving channels can be decreased, which is beneficial to reducing the system complexity and hardware cost.

Optimal scheduling for location geosynchronous satellites refueling problem

This paper addresses the scheduling problem arising from refueling multiple geosynchronous (GEO) satellites with multiple servicing vehicles [many-to-many (M2M) refueling]. The problem is defined by a set of potential fuel tanker locations, a homogeneous fleet of servicing vehicles with limited capacities, and a set of fuel-deficient GEO satellites with known fuel demands. The objective is to open a subset of fuel tankers, to assign GEO satellites to these tankers and to design vehicle servicing sequences, in order to minimize the total mission costs. To achieve such an economical refueling strategy, the fuel tanker location and routing decision are required to be determined simultaneously. It is shown that this problem can be formulated as a location-routing problem (LRP) which is obviously NP-hard. In order to solve it, an ant colony optimization (ACO) metaheuristic that features a special solution representation scheme is proposed. The proposed algorithm is then tested on two types of instances depending on whether the cost for opening a fuel tanker is considered or not. Numerical experiments show that both the consideration of the fuel tanker opening costs and their locations do affect the refueling schedule. Furthermore, the proposed algorithm outperforms the existing approaches in the M2M refueling mission design, and it is able to detect the optimal refueling strategy on all instances containing 85 GEO targets with 15 potential fuel tankers while previous works stopped at 15 satellites and 2 fuel tankers.

Optimal configuration of spaceborne bistatic SAR with GEO transmitter and LEO receiver

Spaceborne bistatic synthetic aperture radar (BiSAR) with a geosynchronous (GEO) transmitter and a low-earth-orbit (LEO) receiver can offer high signal-to-noise ratio, fine resolution and large surveillance area, which provides great potential for future Earth observation technology. Nevertheless, due to complex bistatic geometry and big differences of orbital characteristics, the configuration design of GEO-LEO BiSAR remains a challenge. To address the issue, mathematic models between the indicators related to the imaging performance and the configuration parameters are firstly derived based on the geometry analysis. Then, a general nonlinear multivariate objective function is presented for the desired imaging performance. Accordingly, the configuration design problem can be transformed to solve nonlinear multivariate optimisation equation. A novel optimal configuration design method based on the simulated annealing algorithm is presented. Finally, simulation results are provided for two typical observational missions to verify the effectiveness of the proposed method.

Topology Design for Geosynchronous Spaceborne–Airborne Multistatic SAR

Geosynchronous (GEO) spaceborne–airborne multistatic synthetic aperture radar (GEO MulSAR) is more flexible and accessible in remote sensing applications because of the high-altitude illuminator and the separation of the receivers and transmitter. In addition, the information obtained by the multiple airborne receivers can be fused to enhance the spatial resolution. However, the fused spatial resolution severely depends on the applied multistatic topology. To achieve the optimal fused spatial resolution by properly adjusting the imaging topology, a topology design method is proposed in this letter. First, the spatial resolution model of GEO MulSAR is given, and the dependence of the spatial resolution on the multistatic topology is analyzed in detail. Then, a topology design method is proposed to obtain the best multistatic topology that simultaneously optimizes the resolution cell area and resolution disequilibrium factor. Finally, the simulation results validate the effectiveness of the proposed method, and some insights into designing the multistatic topology are given.

Multi-plume flow simulation of small bipropellant thrusters using parallel DSMC method

As a plume gas exhausted from a bipropellant thruster contains several kinds of chemical compositions, it has been identified as a critical source of heating and contamination on surfaces and components outside a satellite because it can degrade optical properties and performance gradually. Thus, accurate evaluations of the plume gas behaviors from the bipropellant thrusters and their influences on a satellite are necessary from an initial development phase of a satellite through a numerical simulation. In this regard, the present study intended to investigate multiple plume gas behaviors of the bipropellant thrusters with several kinds of gas compositions simultaneously and then to evaluate its influence on a solar panel of a geosynchronous (GEO) satellite numerically. To simulate complex multiple plume flow regimes efficiently, a combined approach of computational fluid dynamics (CFD) and parallelized Direct Simulation Monte Carlo (DSMC) was adopted to consider a continuum flow and a rarefied flow condition, respectively. Throughout the present numerical analysis results, multiple plume gas influences from three different bipropellant thrusters were evaluated on a three-dimensional satellite configuration with a large solar panel.

High-Resolution Wide-Swath Imaging of Spaceborne Multichannel Bistatic SAR With Inclined Geosynchronous Illuminator

Spaceborne bistatic synthetic aperture radar (SAR) system with an inclined geosynchronous (GEO) illuminator and a low-earth-orbit (LEO) receiver is capable of providing a vast area of surveillance and fine spatial resolution, which presents huge potentials for future earth observation. In this letter, inclined GEO–LEO azimuth multichannel SAR (MC-SAR) system for high-resolution wide-swath imaging is investigated. Starting from modeling geometry of inclined GEO–LEO bistatic MC-SAR, the signal model is analyzed in detail for the first time, and the equivalent positions of the received channels are obtained. Then, we found the spatial-variant residual phase error cannot be compensated accurately by conventional effective phase center (EPC) processing. Moreover, because of the complex bistatic configuration, the frequency-domain imaging algorithms become extremely difficult to achieve a well-focused and phase-preserved image. Meanwhile, the time-domain back-projection algorithm (BPA) faces with a technical challenge due to the nonuniform sampling in azimuth. To address these issues, a bistatic weighted BPA (BWBPA) for GEO–LEO MC-SAR is derived and presented. Without the procedure of EPC, the BWBPA can suppress azimuth ambiguities effectively and yield phase-preserved SAR images. Simulated data results show the validity of the presented method.

Prospects of Using a Pulsed Electrostatic Tractor With Nominal Geosynchronous Conditions

The geosynchronous (GEO) orbital regime is becoming cluttered with derelict space debris, which raises the collision risk for satellites in a very valuable orbit. Touchless reorbiting options have been proposed for moving this debris to a graveyard orbit to avoid the risk of physically docking with large, multiton defunct satellites that can be tumbling at several degrees per second. This paper investigates the electrostatic tractor (ET), which uses an electron beam mounted on a tug spacecraft to irradiate a passive debris object. The tug quickly rises to a positive steady-state voltage, and the debris quickly falls to a negative steady-state voltage to create an attractive tugging force. The tug maintains a fixed relative position during the reorbit using inertial thrusting. The Coulomb force can be used as a means of touchless actuation for geosynchronous debris reorbiting, detumbling, and formation flying. This paper investigates the prospects of using a beam with pulsed current. The off-pulsing periods can have benefits for sensing and thrusting applications, and the pulsing charging can lead to higher force levels for the same electrical power used in particular conditions. A Monte Carlo analysis is performed to study the mean electrostatic force, considering a range of beam currents, voltages, pulsing duties cycles, and vehicle sizes. Power-limited regions are identified where the pulsed tractor has a magnitude that is comparable or greater than the mean continuous beam force. This creates interesting alternate methods to implement an ET while having periodic off periods. The tractor performance is illustrated through the debris reorbiting scenario. A detailed equal power analysis determines that even duties cycles as low as 10%–20% can lead to forces comparable to the continuous beam performance, or even do better for some powers.

Optimal 3D deformation measuring in inclined geosynchronous orbit SAR differential interferometry

Three dimensional (3D) deformation can be obtained by using differential interferometric synthetic aperture radar (D-InSAR) technique with the cross-heading tracks data of low earth orbit (LEO) SAR. However, this method has drawbacks of the low temporal sampling rate and the limited area and accuracy for 3D deformation retrieval. To address the aforementioned problems, by virtue of a geosynchronous (GEO) SAR platform, this paper firstly demonstrates the expressions of 3D deformation and the corresponding errors in GEO SAR multi-angle processing. An optimal multi-angle data selection method based on minimizing position dilution of precision (PDOP) is proposed to obtain a good 3D deformation retrieval accuracy. Moreover, neural network is utilized for analyzing the accuracy of the retrieved 3D deformation under different orbit configurations and geo-locations. Finally, the proposed methods and the theoretical analysis are verified by simulation experiments. A 3D deformation retrieval accuracy of the order of centimeter-level or even millimeter-level can be obtained by using the selected optimal multi-angle data.

GEO space debris flux determination based on earth-fixed coordinate system

An analysis is performed on the space debris flux determination of geosynchronous (GEO) orbit based on earth-fixed coordinate system. As part of the examination, flux contribution from different components of space debris is presented here in order to clarify the linkage between orbital characteristic and resulting flux distribution. The analysis of GEO flux determination based on earth-fixed coordinate system reveals several new insights: 1) Near the GEO equatorial plane, average flux mainly centralizes in two azimuth ranges: the higher priority one, local azimuth close to±90°, mainly contributed from objects with relatively larger inclination; the lower priority one, local azimuth close to 0°, mainly contributed from objects with relatively smaller inclination. 2) Impact flux against geostationary satellites is not unified by longitude. Longitude-dependent flux determination based on earth-fixed frame reveals that impact flux against geostationary satellite near the geopotential wells (105°W and 75°E longitude zones) is about two to three times larger than average. 3) The comparison of flux determination against certain targets based on earth-fixed coordinate system and inertially-fixed coordinate system shows significant difference.

Correcting Spatial Variance of RCM for GEO SAR Imaging Based on Time-Frequency Scaling.

Compared with low-Earth orbit synthetic aperture radar (SAR), a geosynchronous (GEO) SAR can have a shorter revisit period and vaster coverage. However, relative motion between this SAR and targets is more complicated, which makes range cell migration (RCM) spatially variant along both range and azimuth. As a result, efficient and precise imaging becomes difficult. This paper analyzes and models spatial variance for GEO SAR in the time and frequency domains. A novel algorithm for GEO SAR imaging with a resolution of 2 m in both the ground cross-range and range directions is proposed, which is composed of five steps. The first is to eliminate linear azimuth variance through the first azimuth time scaling. The second is to achieve RCM correction and range compression. The third is to correct residual azimuth variance by the second azimuth time-frequency scaling. The fourth and final steps are to accomplish azimuth focusing and correct geometric distortion. The most important innovation of this algorithm is implementation of the time-frequency scaling to correct high-order azimuth variance. As demonstrated by simulation results, this algorithm can accomplish GEO SAR imaging with good and uniform imaging quality over the entire swath.

Conjunction challenges of low-thrust geosynchronous debris removal maneuvers

The conjunction challenges of low-thrust engines for continuous thrust re-orbiting of geosynchronous (GEO) objects to super-synchronous disposal orbits are investigated, with applications to end-of-life mitigation and active debris removal (ADR) technologies. In particular, the low maneuverability of low-thrust systems renders collision avoidance a challenging task. This study investigates the number of conjunction events a low-thrust system could encounter with the current GEO debris population during a typical re-orbit to 300km above the GEO ring. Sensitivities to thrust level and initial longitude and inclination are evaluated, and the impact of delaying the start time for a re-orbiting maneuver is assessed. Results demonstrate that the mean number of conjunctions increases hyperbolically as thrust level decreases, but timing the start of the maneuver appropriately can reduce the average conjunction rate when lower thrust levels are applied.

Geosynchronous synthetic aperture radar data focusing based on extended keystone transform

In geosynchronous (GEO) synthetic aperture radar (SAR), the synthetic aperture time increases to hundreds of seconds and the signal propagation delay time reaches up to hundreds of milliseconds, resulting in the violation of the stop-and-go assumption and the linear trajectory model. The accurate slant range history is created based on the consideration of the stop-and-go error. Then, an extended keystone transform is proposed to correct the more complicated range cell migration, and a two-dimensional nonuniform Fourier transform is presented to achieve a well-focused image. The simulation results verify the correctness and effectiveness of the proposed processing method in GEO SAR.