Content uploaded by Kathiravan Thangavel
Author content
All content in this area was uploaded by Kathiravan Thangavel on Mar 17, 2023
Content may be subject to copyright.
Autonomous Optical Sensing for Space-Based Space
Surveillance
Khaja Faisal Hussain1, Kathiravan Thangavel2, Alessandro Gardi1,2, Roberto Sabatini1,2
1 Department of Aerospace Engineering, Khalifa University of Science and Technology, Abu Dhabi, UAE
2 School of Engineering, Aerospace Engineering and Aviation, RMIT University, Melbourne, VIC 3001, Australia
Abstract—Space debris population has increased dramatically
in the past decades posing a threat to the future of space
operations. Traditionally, Resident Space Objects (RSO) are
tracked and catalogued using ground-based observations.
However, Space Based Space Surveillance (SBSS) is a promising
technology to complement the ground-based observations as it
offers greater performance in terms of detectability, accuracy
and weather independency. A Distributed Satellite System
(DSS) architecture is proposed for a SBSS mission equipped
with dual-use star trackers and inter-satellite communication
links to interact and cooperate with each other to accomplish
optimized RSO tracking tasks while assumed to simultaneously
perform earth observation tasks.This paper focuses on
stereovision-based tracking algorithms with higher detectability
and tracking accuracy in SBSS tasks in order to identify an
optimal tracking solution for Space Domain Awareness (SDA),
which could support future Space Traffic Management (STM)
operations. Navigation and tracking uncertainties are analyzed
in representative conditions to support the optimal selection and
processing of individual observations and to determine the
actual confidence region around the detected objects.
Additionally, Particle Swarm Optimization (PSO) is
implemented on-board the satellites to grant the DSS
autonomous trajectory planning and Collision Avoidance (CA)
manoeuvring capabilities.
TABLE OF CONTENTS
1. INTRODUCTION ....................................................... 1
2. AIM OF THE ARTICLE ............................................. 3
3. SBSS MISSION ARCHITECTURE ............................ 3
4. SBSS TRACKING ALGORITHM ............................... 4
5. RESULTS AND DISCUSSIONS ................................... 6
6. CONCLUSION AND FUTURE WORK ........................ 8
REFERENCES............................................................... 8
BIOGRAPHY ................................................................ 9
1. INTRODUCTION
The population of space debris has increased exceedingly in
the past decade. Despite growing awareness of the orbital
debris problem, recent developments such as growth in the
availability of small launch vehicles and mega-constellation
are majorly contributing to densifying orbital domain.
Further exacerbating the space situation are a chain of
undesirable events such as Anti-Satellite (ASAT) weapons
tests, on orbit collisions, and satellite breakups[1]. Moreover,
several commercial entities are planning to launch larger
constellations (500–4,000 spacecraft each) in the coming
days. Currently, the space domain usage is unsustainable. As
a result, the number of space objects will increase multifold
due to a phenomenon called the Kessler Syndrome, resulting
in the cessation of space activities in the near future. A recent
ESA publication [2] emphasizes the alarming situation in the
current space domain. Figure.1 illustrate the current space
situation in terms of the number of launches and space debris
population.
To prevent further collisions in Earth orbit, spacecraft
operators need to possess a better awareness of the potential
threats arising from the existing RSO (Resident Space
Objects). This includes tracking, catalogue maintenance of
RSO and continuously calculating the chances of other
accidental collisions to avoid creating additional debris.
Unfortunately, neither of these tasks is trivial and requires
considerable tracking resources (Optical telescopes and
radar), computing power, and sophisticated software to
calculate numerous satellite–satellite or satellite–debris
conjunctions on a daily basis. In space, these tasks are
referred to as Space Domain Awareness (SDA). Currently,
conventional satellite systems do not effectively contribute
towards SDA because of their exclusive dependence on
ground-based systems. Generally, these tasks are undertaken
by the US Department of Defense (DoD)[3] through the
Space Surveillance Network (SSN), a network of ground-
based observation stations. Also contributing to SDA are a
variety of ground-based space surveillance systems[4]. Even
though these ground-based radars, lasers, and telescopes play
an important role in providing SDA, it is still unclear whether
they can effectively achieve this goal adapting to the rapidly
evolving space domain for the following reasons.
• Most of the ground-based systems are able to perform
regional surveillance and then randomly look at other
areas.
• They lack persistence in surveillance. In order to achieve
true surveillance, it is necessary to monitor objects or
regions for extended periods of time.
• Due to space perturbations, there is an on-orbit change in
the RSOs. This will decrease the revisit frequency of the
RSO within the field of view of the sensors on the
ground.
• Weather conditions are still a significant concern for
ground-based systems. In typical ground-based
observation sites, weather restricts visibility more than
half the time, with some sites having a visibility of no
more than 25%.
• Almost without exception, objects are extremely
difficult to monitor as they pass between the Earth and
the Sun. Daylight observations, in general, pose a
significant challenge for ground-based optical sensors.
2
Figure 1: (a) Space environment statistics by ESA; (b) Space debris population estimation by ESA.
As a result of the gaps associated with ground-based
measurements, it is possible to exploit spaceborne
measurements to track RSOs [5] and this approach is termed
as Space Based Space Surveillance (SBSS). SBSS is a
successful solution because space-borne sensors provide
better accuracy, a wider field of view, and weather
independence. Further, space-based observation technologies
are not affected by atmospheric scattering, turbulence, and
aberrations [6]. SBSS has already been attempted in the past,
the reader is directed to [7] which summarizes various SBSS
missions attempted so far.
Space Traffic Management (STM) applications will continue
to be increasingly dependent on accurate knowledge of the
RSO's position and velocity. These estimations can be
provided using two approaches. Cooperative surveillance
relies on state estimates from on-board Time and Space
Position Information (TSPI), navigation systems (e.g.,
GNSS, INS) and on the collaborative exchange of
information among all other vehicles in the course of a
potential collision. Whereas Non-cooperative surveillance is
typically carried out by ground or space-based radar or
electro-optical sensors that do not require communication
with the observed object. These systems are prone to errors
caused by physical phenomena or by the mathematical
extrapolation itself. In other words, a non-cooperative
scenario is described as an encounter between a host platform
and an RSO or possibly a non-cooperative spacecraft, with
only the host spacecraft capable of preventing a potential
collision. A cooperative scenario, on the other hand, is
described as all potentially colliding RSO being capable of
communicating position data and, if necessary, averting
collisions by conducting maneuvers[8].
Recent technological advances have led to the concept of
multiple spacecraft operating in optimal coordination to
accomplish desired mission goals. Considering this,
Distributed Satellite Systems (DSS) is a promising concept
for the future of SSA and STM. DSS mission architectures
move away from the monolith system concept to adopt
multiple elements that interact, cooperate, and communicate
with each other leading to new systemic properties and/or
emerging functions [9], [10]. DSS can be classified into
different types, such as constellations[11], clusters, swarms,
trains, fractionated spacecraft, and federated satellites [12]–
[14]. In contrast to the conventional ground-based systems
whose observations are conducted from accurately surveyed
locations, SBSS platforms are subjected to positional errors
and tracking errors caused by onboard TSPI/Navigation
systems and tracking sensors respectively. These errors can
be represented geometrically in the form of ellipsoids which
can be combined to form the total uncertainty volume that
determines the total position uncertainty of the tracked RSO
to support Separation Assurance (SA) and Collision
Avoidance (CA) [15] which is later on followed by the
application of relevant CA maneuvers. In this paper a non-
cooperative SBSS scenario is analyzed, in which DSS
spacecrafts track a RSO subject to specific errors in tracking
and navigation systems for positioning that will ultimately
determine the uncertainty volume.
2. AIM OF THE ARTICLE
This article addresses tracking and detection of RSO
using vision-based sensors with an aim to realize trusted
autonomy in heterogenous DSS platforms for autonomous
navigation and CA capabilities to achieve SDA. The
remaining article is structured as follows. Section 3 describes
the SBSS mission concept and system architecture. Section 4
defines the triangulation problem, equations corresponding to
the triangulation problem and the Particle Swarm
Optimization (PSO) algorithm. Section 5 presents the results
and discussion obtained from the verification case studies.
Section 6 comprises conclusions and scope for future
research.
3
Figure 2. SBSS mission concept employing DSS.
3. SBSS MISSION ARCHITECTURE
Recent studies have investigated the use of star trackers as an
alternative sensor for monitoring debris[16]. The
participating spacecrafts in the DSS are assumed to
simultaneously perform Earth observation operations and
debris tracking for SBSS. The major focus is to come up with
a suitable mission architecture that accomplishes SSA
mission objectives expeditiously. The mission architecture is
scrutinized based on the following criteria.
• The proposed system configuration must be flexible to
support multiple applications envisioned in the future,
for instance, point-to-point suborbital transport.
• As opposed to conventional satellite systems, DSS
satellites should form an ad-hoc or optional teams that
make autonomous decisions and maximize mission
objectives without involving the ground control
segment.
As illustrated in Figure 2, the participating spacecrafts in the
DSS are placed in a nearly circular LEO orbit at an altitude
of 400 km, which results in a federated system configuration
that tracks and detects RSO autonomously. It is possible to
extend the current DSS architecture by placing multiple
satellites in more than one orbital plane, thus taking
advantage of a wide variety of occurrences and visibility
conditions during observations.
For the proposed SBSS mission architecture the following
assumptions are adopted: (1) the star trackers on board track
the RSO’s with the stars in the background; (2) the
participating spacecrafts are equipped with GPS for
positioning and navigation that provide full set of navigation
data; (3) the RSO position is estimated by simultaneous
optical measurements obtained from two different
spacecrafts; (4) the participating spacecrafts share their
position information and the estimated RSO position through
a network; and (5) mutual separation between the spacecrafts
belonging to the DSS constellation is guaranteed using
intersatellite links and continuous monitoring from the
ground stations.
The proposed autonomous navigation system comprises of
the following components:
• Navigation hardware comprises of the state-of-the-art
GPS to obtain a full set of navigation data comprising of
the DSS satellites positions, velocities, and attitude rates.
• Tracking hardware comprises of star trackers that track
the RSO by simultaneous optical measurements.
• The obtained data from the hardware is used as inputs by
the On-Board System (OBS) to obtain the RSO position
estimates, error measurement budget and to generate the
uncertainty ellipsoids.
• The guidance system exploits the data generated by the
OBS for trajectory planning and optimization to generate
the steering commands.
• Actuators use the steering commands to perform the
collision avoidance maneuvers in order to avoid a
collision with the RSO.
Figure.3 illustrates the system architecture and its individual
components.
4. SBSS TRACKING ALGORITHM
A single angles-only sensor is inadequate to obtain
range information. In contrast, using two angles-only sensors
4
Figure 3. Space debris Collision Avoidance (CA) system architecture.
allows one to determine the range and thus the 3D location of
an object via simple triangulation [17], [18]. Since the sensors
do not exactly point towards the RSO, an error in the sensor
measurement always prevails, so it is necessary to find the
most probable RSO position. In the absence of measurement
error, triangulation becomes trivial. The current section
introduces a suitable tracking algorithm to track the RSO and
the corresponding equations required to estimate the position
of the RSO, and the errors associated with the measurements.
The resulting errors from the triangulation equations are
represented in the form of co-variance matrices which are
further used to generate the total uncertainty volume.
To determine the 3D location of a RSO, the information
regarding the sensor location Line of Sight (LOS) azimuth
and elevation pointing angles is necessary. Errors in the
knowledge of these ten parameters will lead to an inaccurate
3D position estimate of the RSO. Furthermore, the
relationship between measurement error and errors in the
estimated target location is a function of the sensor-target-
sensor geometry, where a sensor-target-sensor separation of
90° results in the lowest error sensitivity, while a sensor
separation of 0° or 180° results in impossible solutions (as
seen from the target).To define the triangulation problem, we
need to define the positions of the sensors and the RSO in a
right-handed coordinate system as illustrated in Figure.4. The
and axis forms the horizontal plane and axis pointing
out of plane vertically with Earth’s centre as the origin.
and are the azimuth angles of the corresponding sensors
measured clockwise measured from positive y axis towards
positive x axis. The corresponding elevation angles are
denoted by and which increases from in plane
to pointing vertically. The horizontal ranges from the x-
y components of the sensor to the components of the
RSO are denoted by and respectively. The separation
angle is measured from sensor 1 through RSO to sensor
2. The sensor positions (x1, y1, z1), (x2, y2, z2) and the Line of
Sight (LOS) from sensor to target allows the 3D target
position computation. The equations that relate the target
location (xt ,yt, zt) to measurements of the sensor position and
LOS from the sensors to the target aiding the target position
estimation are defined below [18].
(1)
(2)
(3)
(4)
Figure 4. Geometry for Multi-sensor RSO tracking.
5
The error propagation equations corresponding to the
respective position coordinates are derived in [19] with a key
assumption that the error generated by each sensor follows
gaussian distribution. The sigmas for each are
complex sums of various partial derivatives that are further
simplified in [20].
(5)
(6)
(7)
(8)
The various c’s mentioned in the equations are the error
coefficients. For instance, the indicates the error
coefficient for the x coordinate of the target position.
corresponds to error coefficient for azimuth error in .
Equations (5)-(8) relate the target position uncertainties to the
standard deviation in measurement errors , , where,
is the standard deviation in the position measurement.
is the standard deviation in the azimuth measurement.
is the standard deviation in the elevation measurement.
Equation (8) indicates the error in single sensor measurement
of . But since the tracking of the RSO during triangulation
is performed using two sensors, the error estimate is
calculated as follows:
(9)
where:
(10)
The steps for obtaining the covariance matrix corresponding
to the navigation error are described in detail in the
literature[15]. In this case, an on-board GNSS system is
assumed to be providing navigational measurements, and the
uncertainty values are derived from an experiment on LEO
GPS accuracy published in literature [21]. The tracking error
can be expressed in terms of the associated co-variance
matrix:
(11)
Where , , are obtained using equations (5), (6), (9).
The total co-variance matrix is determined by using the Gauss
Helmert formulation [22], [23] in order to relate the sensor
measurement errors to final
RSO position (). The vectors of estimated
observations and estimated parameters are denoted as L, X
respectively and contain the following elements:
T (12)
[]T (13)
The total co-variance matrix can then be expressed as
(14)
Where is the co-variance matrix of the observations. For
matrix B the function F (X, L) = 0 needs to be defined.
= 0;
= 0;
= 0 (15)
Then B can be defined as
which gives rise to a 3x10 matrix.
The feasibility of performing on-board optimization routine
depends on computation time and cost. Hence PSO technique
is chosen as a primary optimization routine due to its
capability of global convergence and robustness to solve
highly non-linear problems with greater computational
efficiency. Moreover, this technique is used widely to solve
diverse spacecraft trajectory optimization problems and its
on-board implementation was verified through various case
studies for adequate convergence time and low computation
cost [24], [25]. The particles move iteratively until they
converge onto a global optimal solution considering the goal
of optimality, minimizing the cost function which describes
the quality of the solution and the imposed constraints. The
position of the particles iterates according to:
Vi
k+1 (16)
where is the velocity required to move from kth iteration
to iteration, which is given by:
(17)
where:
is the best position of particle i at time k;
is the global best solution for all particles at time k;
and are random numbers between 0 and 1;
and are cognitive and scaling parameters respectively
and are assigned with a value 2.
Typically, satellite motion in an orbit can be modelled
using the classical orbital elements based on Gaussian
variational equations. However, these equations result in
ambiguity in certain scenarios especially, for the orbits with
low eccentricities or inclinations [26]. In order to avoid this
ambiguity a new model is used that employs a set of Modified
Equinoctial Parameters (MEE) [27] that include second order
zonal harmonics or perturbation effects (i.e. change in
Right Ascension of the Ascending Node (RAAN) and
argument of perigee with time), specifically the set of MEE
developed in [28] are adopted to solve the low thrust transfer
problem. The optimal CA maneuver is chosen based on
models that are incorporated into the PSO algorithm[29].
6
Figure 5. Uncertainty Volumes in SBSS.
5. RESULTS AND DISCUSSIONS
The results obtained from the simulation case study in the
SBSS scenarios are discussed in this section. To estimate the
target position using the algorithm defined in section 4, we
define the satellite orbital elements in ECI frame (Table 1)
and a conversion to cartesian frame is performed (Table 2).
Table 1. Sensor orbital state elements.
Orbital parameters
Sensor 1
Sensor 2
6778
6778
0.002
0.002
100
100
20
20
360
360
(deg)
0
72
Table 2. Corresponding sensor state vectors
Cartesian Coordinates
Sensor 1
Sensor 2
(km)
6356.49
-236.40
(km)
-401.74
-1175.53
(km)
2278.42
6666.81
(km/sec)
-2.62
-7.69
(km/sec)
-1.25
0.043
VZ (km/sec)
7.11
-0.249
Azimuth (deg)
20
300
Elevation (deg)
50
45
The target position estimates, and the ranges obtained from
the algorithm are tabulated in Table 3.
Table 3. RSO position estimates in km.
The values of the corresponding error coefficients must be
computed to calculate the errors in the target position
estimates. The error coefficients are complex sums of partial
derivatives that are simplified in [19]. The sigmas for each
are calculated using Equations (5) to (10).
Table 4. Error estimates for target position parameters.
Sigmas
(km)
(km)
r (km)
(km)
Total Error (m)
10
22
18
24
Assuming that the state-of-the-art star trackers can provide
the sigma position = 0.5m, sensor angular error = 0.0022
degrees we obtain the sigmas tabulated in Table 4. Figure 5
illustrates the uncertainty ellipsoid corresponding to
navigation, tracking, and total errors. The DSS performs a
collision avoidance maneuver to reorient its initial orbit to a
modified orbit with a semimajor axis increased to 10 km to
avoid the uncertainty volume. It is assumed that the
spacecraft that performs the orbit raising maneuver is
equipped with Nano Avionics: EPSSC1 that can generate a
thrust of with a specific impulse of 213 seconds [30].
Table 5 tabulates the orbital parameters of the spacecraft
before and after the maneuver.
4978.9
-4186.6
9883.7
4027
6022.1
8606.01
6827.4
7
Table 5. Initial and final orbital parameters of the
spacecraft after collision avoidance maneuvers.
Final state
6778
6788
0.002
0.002
100
100
20
20
360
360
The solution converged after 1,884,000 iterations with a total
run time of 16,763 seconds in a MATLAB environment on
an Intel Core generation processor.
Table 6. Generated control parameters for thrust
directions.
(min)
(deg)
(deg)
(rad)
55.19
-2.5
3.08
0.5
0.194
0.19
1
Figure 6. Change in Semi major axis from initial to final
trajectory in time (SBSS).
Figure 7. Change in Thrust control angles in time.
The change from the initial trajectory to the final optimal
trajectory is illustrated in Figure 6 and the control parameters
for the constant thrust directions illustrated in Figure 7 are
tabulated in Table 6 for the SBSS scenario.
6. CONCLUSION AND FUTURE WORK
The research presented in this article addressed the
envisioned implementation of Distributed Satellite Systems
(DSS) in a Space-Based Space Surveillance (SBSS) mission
using star trackers in the context of Space Domain Awareness
(SDA) for Space Traffic Management (STM). In order to
obtain range data, the measurements from single angle-only
sensors are insufficient. In contrast, performing triangulation
using simultaneous measurements from multiple sensors
provides a satisfactory solution for the tracking problem.
Following this, the satellite can perform a CA maneuver with
the help of the host platform. A simulation case study is
presented in the SBSS scenario, and the results substantiate
the validity of the proposed mathematical framework.
Current research is addressing the development of Artificial
Intelligence (AI)-based autonomous navigation/guidance
algorithms and integration of SBSS and ground-based
tracking sensors towards maximizing DSS performance in
different applications and operational conditions.
REFERENCES
[1] M. J. Holzinger and M. K. Jah, “Challenges and
Potential in Space Domain Awareness,” J. Guid.
Control Dyn., vol. 41, pp. 15–18, Jan. 2018, doi:
10.2514/1.G003483.
[2] “Space Environment Statistics · Space Debris User
Portal.” https://sdup.esoc.esa.int/discosweb/statistics/
(accessed Jul. 16, 2022).
[3] S. Hilton, R. Sabatini, A. Gardi, H. Ogawa, and P.
Teofilatto, “Space traffic management: towards safe and
unsegregated space transport operations,” Prog. Aerosp.
Sci., vol. 105, pp. 98–125, Feb. 2019, doi:
10.1016/j.paerosci.2018.10.006.
[4] M. R. Ackermann, R. Kiziah, P. C. Zimmer, J. McGraw,
and D. Cox, “A systematic examination of ground-based
and space-based approaches to optical detection and
tracking of satellites,” in 31st Space Symposium, 2015.
[5] T. Flohrer, H. Krag, H. Klinkrad, and T. Schildknecht,
“Feasibility of performing space surveillance tasks with
a proposed space-based optical architecture,” Adv.
Space Res., vol. 47, no. 6, pp. 1029–1042, Mar. 2011,
doi: 10.1016/j.asr.2010.11.021.
[6] X. Vanwijck and T. Flohrer, “Possible contribution of
space-based assets for space situational awareness,” Int.
Astronaut. Fed. - 59th Int. Astronaut. Congr. 2008 IAC
2008, vol. 4, pp. 2466–2472, Jan. 2008.
[7] H. Yunpeng, L. Kebo, L. Yan’gang, and C. Lei, “Review
on strategies of space-based optical space situational
awareness,” J. Syst. Eng. Electron., vol. 32, no. 5, pp.
1152–1166, Oct. 2021, doi:
10.23919/JSEE.2021.000099.
[8] R. Sabatini, M. Battipede, and F. Cairola, “Innovative
Techniques for Spacecraft Separation Assurance and
Debris Collision Avoidance,” 2020.
8
[9] C. Araguz, E. Bou-Balust, and E. Alarcón, “Applying
autonomy to distributed satellite systems: Trends,
challenges, and future prospects,” Syst. Eng., vol. 21,
Mar. 2018, doi: 10.1002/sys.21428.
[10] J. Le Moigne, J. C. Adams, and S. Nag, “A New
Taxonomy for Distributed Spacecraft Missions,” IEEE
J. Sel. Top. Appl. Earth Obs. Remote Sens., vol. 13, pp.
872–883, 2020, doi: 10.1109/JSTARS.2020.2964248.
[11] K. Hussain, K. Hussain, S. Carletta, and P. Teofilatto,
Deployment of a microsatellite constellation around the
Moon using chaotic multi body dynamics. 71st
International Astronautical Congress (IAC), Dubai,
United Arab Emirates, 25-29 October 2021.
[12] M. K. Ben-Larbi et al., “Towards the automated
operations of large distributed satellite systems. Part 1:
Review and paradigm shifts,” Adv. Space Res., vol. 67,
no. 11, pp. 3598–3619, Jun. 2021, doi:
10.1016/j.asr.2020.08.009.
[13] O. von Maurich and A. Golkar, “Data authentication,
integrity and confidentiality mechanisms for federated
satellite systems,” Acta Astronaut., vol. 149, pp. 61–76,
Aug. 2018, doi: 10.1016/j.actaastro.2018.05.003.
[14] A. Golkar, “Federated satellite systems (FSS): a vision
towards an innovation in space systems design,” in IAA
Symposium on Small Satellites for Earth Observation,
2013.
[15] S. Hilton, F. Cairola, A. Gardi, R. Sabatini, N.
Pongsakornsathien, and N. Ezer, “Uncertainty
quantification for space situational awareness and traffic
management,” Sensors, vol. 19, no. 20, p. 4361, 2019.
[16] I. Ettouati, D. Mortari, and T. Pollock, “Space
surveillance using star trackers. Part I: Simulations,”
Pap. AAS, pp. 06–231, 2006.
[17] L. Chen, C. Liu, Z. Li, and Z. Kang, “A New
Triangulation Algorithm for Positioning Space Debris,”
Remote Sens., vol. 13, no. 23, p. 4878, Dec. 2021, doi:
10.3390/rs13234878.
[18] J. N. Sanders-Reed, “Impact of tracking system
knowledge on multisensor 3D triangulation,” presented
at the AeroSense 2002, Orlando, FL, Jul. 2002, pp. 33–
41. doi: 10.1117/12.472599.
[19] J. N. Sanders-Reed, “Error propagation in two-sensor
three-dimensional position estimation,” Opt. Eng., vol.
40, no. 4, pp. 627–636, 2001.
[20] J. N. Sanders-Reed, “Triangulation Position Error
Analysis for Closely Spaced Imagers,” presented at the
SAE 2002 World Congress & Exhibition, Mar. 2002,
pp. 2002-01–0685. doi: 10.4271/2002-01-0685.
[21] I. GNSS, “GPS Receiver Performance On Board a LEO
Satellite,” Inside GNSS - Global Navigation Satellite
Systems Engineering, Policy, and Design, Jul. 21, 2014.
https://insidegnss.com/gps-receiver-performance-on-
board-a-leo-satellite/ (accessed Oct. 07, 2022).
[22] G. R. Curry, “radar System Performance Modeling,
ARTECH HOUSE,” Inc Ed Norwood MA USA, 2005.
[23] D. A. Vallado, Fundamentals of astrodynamics and
applications, vol. 12. Springer Science & Business
Media, 2001.
[24] M. Lin, Z.-H. Zhang, H. Zhou, and Y. Shui,
“Multiconstrained Ascent Trajectory Optimization
Using an Improved Particle Swarm Optimization
Method,” Int. J. Aerosp. Eng., vol. 2021, 2021.
[25] A. Rahimi, K. Dev Kumar, and H. Alighanbari, “Particle
Swarm Optimization Applied to Spacecraft Reentry
Trajectory,” J. Guid. Control Dyn., vol. 36, no. 1, pp.
307–310, 2013, doi: 10.2514/1.56387.
[26] J. T. Betts, Practical Methods for Optimal Control and
Estimation Using Nonlinear Programming, Second
Edition. Society for Industrial and Applied
Mathematics, 2010. doi: 10.1137/1.9780898718577.
[27] G. Baù, J. Hernando-Ayuso, and C. Bombardelli, “A
generalization of the equinoctial orbital elements,”
Celest. Mech. Dyn. Astron., vol. 133, no. 11, pp. 1–29,
2021.
[28] S. Eves, “Applied Nonsingular Astrodynamics: Optimal
Low-Thrust Orbit Transfer J. A. Kéchichian Cambridge
University Press, University Printing House,
Shaftesbury Road, Cambridge CB2 8BS, UK. 2018.
xvii; 461 pp. ISBN 978-1-108-47236-4.,” Aeronaut. J.,
vol. 124, no. 1282, pp. 2036–2037, Dec. 2020, doi:
10.1017/aer.2020.105.
[29] E. Lagona, S. Hilton, A. Afful, A. Gardi, and R. Sabatini,
“Autonomous Trajectory Optimisation for Intelligent
Satellite Systems and Space Traffic Management,” Acta
Astronaut., vol. 194, pp. 185–201, May 2022, doi:
10.1016/j.actaastro.2022.01.027.
[30] “CubeSat Propulsion System EPSS,” NanoAvionics.
https://nanoavionics.com/cubesat-components/cubesat-
propulsion-system-epss/ (accessed Jan. 02, 2023).
BIOGRAPHY
Khaja Faisal Hussain has received his
joint bachelor’s degree from GRIET,
India and Karabuk University, Turkey.
He graduated with his master’s in
aerospace engineering from Sapienza
University of Rome, Italy and is currently pursuing a PhD
in Aerospace engineering at Khalifa University, UAE. His
current research deals with Autonomous Systems for Space
Domain Awareness (SDA) and Distributed Satellite
Systems (DSS).
Kathiravan Thangavel is a Ph.D
candidate at RMIT University's Cyber-
Physical and Autonomous System
Research Group, and his research is
funded by SmartSat CRC and the Andy
Thomas Space Foundation. He graduated from Anna
University in Chennai, India, with a bachelor's degree in
aeronautical engineering. Following that, he pursued a
master's degree in Aerospace Engineering at Rome's La
Sapienza University. Kathiravan completed the
International Space University Space Studies Program
2019. He is excited about research in space and the
potential of exploring space to the benefit of humanity, and
9
his key areas of interest are Distributed Satellite Systems,
Artificial Intelligence, Autonomy, Earth Observation,
Space Domain Awareness, Space Traffic Management,
Thermomechanical Analysis.
Dr. Alex Gardi obtained his BSc and MSc
degrees in Aerospace Engineering from
Politecnico di Milano (Italy) and a PhD in
the same discipline from RMIT University
(Australia). Dr Gardi is currently an
Assistant Professor at Khalifa University (UAE) and
Associate of RMIT University, focusing on aerospace
cyber-physical systems (UAS, satellites, ATM systems and
avionics). In this domain, he specialises in multi-objective
trajectory optimization with emphasis on optimal control
methods, multidisciplinary design optimization and
AI/metaheuristics for air and space platforms.
Dr. Rob Sabatini is a Professor of
Aeronautics and Astronautics with three
decades of experience in Aerospace,
Defense and Robotics/ Autonomous Systems
research and education. Prof. Sabatini holds a PhD in
Aerospace/Avionics Systems (Cranfield University) and a
PhD in Space Geodesy/Satellite Navigation (University of
Nottingham). His research addresses key contemporary
issues in digital and sustainable aerospace systems design,
testing and certification, with a focus on: Avionics and
CNS/ATM; Autonomous Navigation and Guidance;
Unmanned Aircraft Systems; Distributed Space Systems;
Space Domain Awareness and Space Traffic Management.
