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Satellites Orbit Design and Determination for the Australian Garada Project
Li Qiao, Chris Rizos, Andrew Dempster School of Surveying and Spatial Information Systems, University of New South Wales, Sydney, Australia
BIOGRAPHY Dr Li Qiao is a Research Associate in the School of Surveying and Spatial Information Systems (SSIS) at the University of New South Wales (UNSW). She obtained her Bachelor's degree in Electrical Engineering and Automation at Nanjing University of Aeronautics and Astronautics (NUAA) in 2004, joined UNSW as a visiting PhD student from 2009 to 2010, and obtained her PhD in Guidance, Navigation and Control at NUAA in 2011. Her research interest is satellite orbit models and determination. Professor Chris Rizos is a graduate of the School of Surveying, UNSW, obtaining a Bachelor of Surveying in 1975, and a Doctor of Philosophy in 1980. Chris is currently Professor and Head of SSIS. Chris has been researching the technology and high precision applications of GPS since 1985, and is author or co-author of over 500 journal and conference papers. He is a Fellow of the Australian Institute of Navigation and a Fellow of the International Association of Geodesy (IAG). He is currently the President of the IAG and a member of the Governing Board of the International GNSS Service (IGS). Professor Andrew Dempster is Director of the Australian Centre for Space Engineering Research (ACSER) at UNSW. He is also Director of Research in SSIS and Director of Postgraduate Research in the Faculty of Engineering. He has a BE and MEngSc from UNSW and a PhD from University of Cambridge in efficient circuits for signal processing arithmetic. He was system engineer and project manager for the first GPS receiver developed in Australia in the late 1980s and has been involved in satellite navigation ever since. His current research interests are in satellite navigation receiver design and signal processing – areas where he has six patents – and new location technologies. He is leading the development of space engineering research at ACSER.
ABSTRACT
Australia is presently investigating the design of an earth observation Synthetic Aperture Radar (SAR) satellite mission, known as “Garada”, optimised to collect SAR images over Australia’s huge land mass for a variety of applications using several small satellites flying in formation. The Australian Centre for Space Engineering Research (ACSER) is funded by a grant from the Australian Space Research Program to conduct and coordinate project research activities across several academic and industry partners. The applications of interest for this proposed mission are flood and disaster monitoring, and early warning deforestation detection for tropical forests. This paper describes some aspects of the mission design, including the mission objectives and the brief satellite design. It presents the requirements and considerations regarding the choice of satellite orbits. The orbit design is mainly driven by the SAR imaging performance, the lifetime of the satellites, and coverage requirements such as revisit time. The area of interest is the Australian continent. In order to achieve a rapid revisit time a satellite constellation is proposed.
1. INTRODUCTION The disaster monitoring service requirement for space high-resolution quick update imagery has experienced rapid growth in interest during the last few years. For this reason ACSER is presently investigating the design of an earth observation Synthetic Aperture Radar (SAR) satellite mission known as “Garada”, for flood monitoring and other applications using several small satellites flying in formation. A spaceborne SAR is a radar imaging sensor which can provide all-weather, day and night imaging capability over wide areas of the earth surface[1]. The process of orbital parameter determination and constellation design is described. Two kinds of orbits were compared: sun-synchronous orbits and inclined orbits. Since the mission requirements cannot be formulated concisely, numerical investigations performed using the STK software are employed to define initial design estimates that can meet the mission requirements.
This paper describes some aspects of the orbit design influenced by user requirements. Section 1 is an introduction to the Garada mission. Section 2 discusses the satellite orbit design requirements and analyses. Section 3 introduces the process of orbital and constellation design. Simulation results using the Satellite Tool Kit (STK) are presented. The current status and future work are described in Section 4.
2. MISSION OVERVIEW AND REQUIREMENTS 2.1 Mission overview The objectives of the proposed mission are flood and disaster monitoring, and early warning deforestation detection for tropical forests. The disaster monitoring service requirement for space high-resolution (3 metres), quick update (1 hour for floods, and 1 day for forest monitoring) imagery has generated considerable interest during the last few years. To satisfy these objectives, L-band SAR technology is chosen for its high utility for flood and forest monitoring[2]. The L-band SAR is is used not only for disaster monitoring but also for its usefulness in the context of the global observation of forest in programs similar to Japan’s ALOS program[3, 4]. The Garada project has adopted a bistatic SAR configuration, i.e. two satellites, one with a transmitter and the other equipped with a receiving antenna. Furthermore the orbit design must guarantee superimposition between the passive and active radar swaths. These two satellites fly in line with an approximate 40km separation (Figure 1). Each satellite is assumed to have similar physical and orbital parameters as the swath overlap is more easily maintained if the passive satellite orbit has the same semi-major axis[5]. The smaller the satellite is, in general, the lower the cost[6]. Cost is an important driver for a small satellite mission such as Garada’s. For this reason it is assumed that a sub-100kg satellite design will be adopted. In the following discussion it is assumed that the physical parameters of the satellites are as indicated in Table 1.
Figure 1. Bistatic observation geometry
Table 1. Some assumed parameters of the Garada
satellites Mass 75kg
Drag area 1.0 m2 Drag coef. dC 2.2
Area exposed to sun
8.0 m2 Solar radiation
pressure coef. Cr 1.0
2.2 Mission requirements 1) SAR imaging performance In contrast to optical imaging, illumination conditions are not the major factor impacting on SAR imaging quality[7]Instead, the altitude is the key factor influencing imaging performance. For this reason a close to zero value of eccentricity is desired and the semi-major axis is fixed as a constraint on perigee altitude. An approximate relationship between radar RF power, radar amplitude, and the resultant signal to noise ratio (SNR) is:
3
~ PowerSNR
Altitude∝
(1) Equation (1) shows that when the orbit altitude varies from 500km to 800km, the transmit power needed will increase by a factor of four to ensure the same SNR on the ground. This represents a large increase in the performance of the RF power amplifiers required[8]. A reasonable upper limit altitude therefore is 700km, which requires triple the power compared to a 500km altitude. 2) Lifetime requirement The proposed Garada satellites are in a Low Earth Orbit (LEO). Satellites in such orbits have lifetimes determined almost entirely by their interaction with the atmosphere[9]. However the computation of orbit lifetime is extremely challenging, and the atmospheric density errors create considerable uncertainty in orbit decay predictions[10, 11]. Plans for future flights require accurate estimates of earth orbital lifetimes. However to calculate orbit lifetime a number of factors must be considered, such as satellite atmospheric density, solar cycle effects, orbit configuration (primarily altitude), the drag coefficient and
the mass of the spacecraft. The Garada mission lifetime is expected to be around 5 years. 3) Coverage requirements The coverage requirements are: coverage area and revisit period. The area of interest is the Australian region. Revisit time defines the intervals during which coverage is not provided (also known as “the gaps”). Revisit time is an interval of time during which a specified point on the ground is not visible to at least one of the satellites in the constellation. The maximum revisit time is the largest of these intervals for a specific ground point[12]. This parameter depends on the satellite's orbit, target location, and swath of the imaging sensor. An index to evaluate the coverage performance is therefore the maximum revisit time. The objective of this analysis is to design a constellation capable of 1 day to 1 hour revisit time over the Australian region.
3. ORBIT DESIGN FOR GARADA MISSION 3.1 Type of orbits The satellite is a global tool to scan the entire earth’s surface on a regular basis[13]. The Garada satellites could be placed in circular sun-synchronous orbits for global coverage. Another advantage of choosing sun-synchronous orbits is that the orbital period can be synchronous with the mean solar day instead of the sidereal day over a given point on earth, so that the satellite maintains the same time-of-day schedule. 3.2 Lifetime and orbital altitude Altitude mainly affects the imaging performance and lifetime requirement. The altitude of orbit is the key parameter in trade-off studies between system requirements and orbital requirements. The preliminary orbit altitude of 500 to 600km was derived from the SAR imaging and the lifetime requirements. For LEO, atmospheric drag is the main phenomenon determining the lifetime of the orbiting satellite. Traditionally, the satellite drag can be calculated using an empirical function based on drag coefficient, which is assumed a constant that is dependent on the shape of the satellite body. However errors in empirical density models results in significant uncertainties in atmospheric models[14]. It is observed from Figure 2 that the orbit lifetime increases with the altitude. Table 2 presents some lifetime data that is plotted in Figure 2. Therefore to satisfy the Garada mission lifetime requirements (no less than 5 years), the orbit altitude should be greater than 550km. From the point of view of radar, the altitude is required to be as low as possible. Hence in the following discussion, the altitude of the orbit was assumed to be around 560km.
500 520 540 560 580 600 620 640 660 680 7000
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Figure 2. Orbit lifetime versus satellite altitude
Table 2. Satellite lifetime versus altitude
Satellite altitude (km) Lifetime (year) 550 5.5 560 6.5 570 7.7 580 9.2 590 10.9 600 12.8
3.3 Satellite illumination and orbit RAAN As the solar cell panels are the main power source for the satellite it is necessary to estimate the periods when the satellite is in full solar illumination. It can be seen from Figure 3 that the statistics concerning sun lighting duration shows considerable variation with right ascension of the ascending node (RAAN). The static results variation of sun-synchronous orbits shows a better consistency and its standard deviation is comparatively steady. Sun-synchronous orbits have significant advantage in lighting duration, especially when the RAAN is varied from 20 to 60 degrees – which are special cases of the sun-synchronous orbits, i.e. the dawn-dusk orbits where the local mean solar time of passage for equatorial longitudes is around sunrise or sunset. Riding the terminator is useful for active radar satellites as the satellite’ solar panels can always see the sun without being shadowed by the earth, and would not require a tracking mechanism, though batteries would be needed only for contingencies. For these reasons, SAR satellite mission such as Radarsat[15], TerranSAR[16] were launched into sun-synchronous dusk-dawn orbits. Therefore this kind of orbit could be considered an optimal choice for a SAR mission.
0 50 100 150 200 250 300 350 4000
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Ligh
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Mean lighting duration Min lighting duration
Std lighting duration
Max Lighting Duration
Min Lighting DurationMean Max Lighting Duration
Std Max Lighting Duration
Figure 3. Sun illumination duration vs. RAAN for 560km
sun-synchronous orbit 3.4 Coverage analysis As Garada assumes a bistatic SAR configuration, every functional satellite unit consists of two satellites. However the two satellites are assumed to be modelled as a single satellite unit to simplify the coverage analysis. The two antennas are considered to be one SAR sensor, which is defined as a “rectangular” sensor in the STK software. “Fixed sensor pointing” type is used to model a SAR antenna attached to a satellite in the STK software. The swath width on the ground is controlled by the beam width of the sensor. Figure 4 shows the model of a SAR sensor attached to the satellite. The point angle and beam width are calculated according to the geometry between satellite and the ground. A right-look sensor is defined by specifying a 90° azimuth. Assuming the altitude of the satellite is 560km, the incidence angle range is 20-41 degrees for the width access of 250km. When the beam pointing axis rotates (see Figure 5), the access range of the antenna can reach 250km, which is used as the input value for coverage calculations.
Figure 4. SAR sensor model in STK
41°20°
Access=250km
Antenna
Sub satellite point
Figure 5. Access range by antenna
The user revisit requirement (1 day and 1 hour for forests and flood applications respectively) cannot be satisfied by a single satellite as the coverage area provided by a single satellite is comparatively small. Figure 6 shows the maximum revisit time for a single synchronous satellite unit for the whole Australian region, with latitude varying from 10°S to 42°S and longitude varying from 110°E to 155°E. In fact, for a 560km sun-synchronous satellite with 250km access ability, the revisit time is of the order of 40 days, i.e. a single satellite needs more than 40 days to provide global coverage. Therefore due such revisit requirements these LEOs are often used in satellite constellations.
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Figure 6. Maximum revisit time by single sun-synchronous satellite for the Australian region
A constellation of small satellites can provide daily global coverage of the earth’s surface[6] and is particularly attractive when launcher capacity can be used efficiently[17]. The total number of satellites required is affected by the location of the coverage area, the orbital altitude and the sensor swath. According to the method suggested in [18], the approximate number of satellites for the Australian region, is 45 for continuous coverage between latitude 10°S to the south pole, assuming a 250km swath. The Walker pattern is used to define the constellation, where the constellation is specified by the altitude, inclination and three parameters referred to as T/P/F, where T satellites are equally divided among P orbital planes (the P orbital planes are equally spaced in RAAN).
Satellites within an orbital plane are equally spaced in argument of latitude – the phasing or mean anomaly difference between satellites in adjacent orbital planes is F×360°/T[19]. The coverage performances in terms of maximum revisit time by Walker 10/10/1, 27/3/1 and 45/9/1 sun-synchronous constellations are presented in Figure 7, Figure 8 and Figure 9 respectively. 1 day, ½ day and nearly 1/3 day frequency revisit can be achieved for the service area with increasing number of satellites. The reason for the high number of satellites is that every node for sun-synchronous orbits and higher inclination orbits normally has longer revisit time in comparison to lower inclination orbits. The number of satellites required to provide continuous global coverage is therefore very high. Even with a 45 satellites constellation, the shortest revisit duration is around 3.84 hours (see Figure 9), which still cannot meet the original user requirements. However the large number of satellites significantly increases mission costs and complexity.
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Figure 7. Maximum revisit time for the Walker 10/10/1 sun-synchronous constellation for the Australian region
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Figure 8. Maximum revisit time for the Walker 27/3/1 sun-synchronous constellation for the Australian region
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Figure 9. Maximum revisit time for the Walker 45/9/1 sun-synchronous constellation for the Australian region
3.5 GNSS signal coverage analysis The satellite platform will be equipped with the Namuru 3 GNSS receiver developed by UNSW. Namuru 3 is a dual-frequency, carrier phase tracking receiver capable of making measurements on current and new generation GPS signals as well as those of other GNSS. An earlier generation receiver was tested in near outer space on board the Rexus7 sounding rocket launched in March 2010. In fact, spaceborne applications of GPS for LEO missions have become commonplace[20]. Consequently, the GPS coverage performance at the satellite in orbit is vital to its navigation performance. The number of GPS satellites in view can be predicted in advance. Figure 10 shows the number of available GPS satellites (assuming the current GPS constellation) for the sun-synchronous orbit. The test assumes the receiver only tracks the GPS main lobe signal and the off-boresight angle is 70°. Figure 11 shows the percentage of time when satellites are tracked. It is observed that for more than 91% of the time the receiver can track 6 to 8 GPS satellites, which ensures there are enough measurements for good navigation performance. These results are similar to what would be expected in the case of ground-based GPS receivers. This is due to the fact that the altitude of the orbit is just 560km, relevantly low compared to the GPS satellite altitude of about 20,000km.
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4. CONCLUDING REMARKS Satellite orbit modelling is a complex process as it involves trade-offs between different parameters. The designed orbit has to satisfy the largest number of mission requirements at the least possible cost (and hence lowest number of satellites). In fact, the task is to determine the classical orbital parameters, and these parameters will define the mission lifetime, the flying environment, viewing geometry, payload performance and cost. This paper presents a preliminary analysis of the orbit design for the Garada project. The Garada mission should be a 560km circular sun-synchronous orbit. The proposed orbit is assessed in terms of the lifetime, solar illumination time, revisit time and GPS signal coverage. Since the user requirements in terms of maximum revisit time is one day for forest and one hour for floods of the interest area, a constellation design is required to satisfy this requirement. With a 250km swath capability, a 10 sun-synchronous satellite constellation can meet the one
revisit requirement in the Australian region. More satellites, for instance 27 and 45 Walker sun-synchronous satellite constellation, can reduce the revisit time to 1/2 and 1/3 days respectively, however the high satellite number significantly increases the mission cost and complexity. To meet user requirements and satisfy the cost budget, the orbit modelling studies will continue and the primary orbit design characteristics such as altitude may change. For constellation design, mixed constellations which consist not only of sun-synchronous orbits but also small-inclination circular LEOs will also be investigated.
ACKNOWLEDGMENTS This research project is funded by the Australian Space Research Program on "SAR Formation Flying" (including Namuru v3.3 development). The authors acknowledge the support of the Australian Centre for Space Engineering Research. A special thanks to the first author’s colleagues Steven Tsitas and Robert Middleton for their support for the work described in this paper. Also thanks to Eamonn Glennon and Kevin Parkinson for their assistance regarding the GNSS receiver.
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