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A Semi-Analytical Approach to Satellite Constellation Design for Regional Coverage
Abstract and Figures
This paper introduces a robust and computationally efficient semi-analytical approach to design regional coverage satellite constellations. By fully utilizing the characteristics of the repeating ground track orbits and multiple access intervals between the target and the satellite, the proposed methods aim to optimally design satellite constellation with the fewest number of satellites possible. Two methods are constructed by applying the circular convolution theorem based on the assumption that the seed satellite access profile and the satellite position vector can be treated as discrete signals. An analysis shows that the While-Loop method is computationally efficient while the Integer Programming method is the most optimal. A case study with various examples is performed to demonstrate the value provided by the proposed approach.
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... In recent years, this theory has also been applied to the constellation design problem domains including navigation, Earth observation space-based systems, regional coverage, and reconnaissance [14]. Remarkably, Lee and Ho presented an approach to design the Flower constellation patterns for regional coverage with predefined seed-satellite elements [15,16]. In this paper, a design strategy for full constellations is presented, which consists the seed-satellite elements and configuration parameters under constrained deployment approaches. ...
... This paper presents a synthetic approach to design and deploy a cost-efficient LEO regional navigation augmentation constellation. For the constellation design, in previous, the effectiveness of navigation constellation is generally considered a discrete index [15,16,21]. In this paper, an optimization model with a continuous performance index is developed to replace the discrete performance index and improve convergence. ...
The advantages of the Low Earth Orbit (LEO) satellite include low-latency communications, shorter positioning time, higher positioning accuracy, and lower launching, building, and maintenance costs. Thus, the introduction of LEO satellite constellation as a regional navigation augmentation system for the current navigation constellations is studied in this paper. To achieve the navigation performance requirement with the least system cost, a synthetic approach is presented to design and deploy a cost-efficient LEO navigation augmentation constellation over 108 key cities. To achieve lower construction costs, the constellation is designed to be deployed by constrained piggyback launches, which brings additional complexity to the constellation design. Two optimization models with discrete and continuous performance indices are established. They are solved by the genetic algorithm and differential evolution algorithm, and both Walker and Flower constellations are adopted. Results for 77 and 70 satellites are obtained. During the construction phase, a synthesis procedure containing five impulses is proposed by utilizing natural drift under J2 perturbation. This work presents a method for designing the optimal LEO navigation constellation under a constraint deployment approach with the lowest construction cost and a strategy to deploy the constellation economically.
... Regardless, for the fixed hardware available for simulations there therefore existed a set amount of compute power to be used in a time efficient manor to optimise the problem. While analytical and semi-analytical methods such as those of [10], [87] would produce a faster convergence of the algorithm, the results achieved would be less accurate. While this is usually an acceptable trade-off for this phase of the design process, there exists less work done in literature on constellation designs with this level of accuracy for this specific objective. ...
Thesis executive summary: Design of a MIMO CubeSat formation flight SAR constellation for maritime surveillance
... Regardless, for the fixed hardware available for simulations there therefore existed a set amount of compute power to be used in a time efficient manor to optimise the problem. While analytical and semi-analytical methods such as those of [10], [87] would produce a faster convergence of the algorithm, the results achieved would be less accurate. While this is usually an acceptable trade-off for this phase of the design process, there exists less work done in literature on constellation designs with this level of accuracy for this specific objective. ...
MSc Space Engineering Thesis: Design of a MIMO CubeSat formation flight SAR constellation for maritime surveillance
This paper covers the design of a constellation of CubeSat formation flights for Synthetic Aperture Radar surveillance of maritime traffic. The work investigates the applications of high-resolution wide-swath imaging for maritime traffic monitoring, leveraging developments in MIMO distributed SAR systems to achieve system performance. The design is conducted using a set of requirements for individual satellites and for minimum system performance, including an operational area; the Mediterranean Sea. The optimal formation size is investigated at a high level, under the assumption that the distributed system functions as a single monolithic one. The formation size for the required performance is determined. Following this, the optimal constellation required to achieve the specified minimum performance is conceived using a multi-objective genetic algorithm. The optimisation considers Walker Delta and Star constellation patterns with all spacecraft in the constellation operating in one of two operating modes. The genetic algorithm focuses on system performance while also considering system cost, both monetarily and from a mission analysis point of view. Two separate operating scenarios are considered in the optimisation; small swath and large swath strip map modes. Each mode consists of a number of satellites in close formation flight in order to achieve the specified minimum performance. Once identified, the performance of solutions output by the genetic algorithm is examined across the target area. Performance analysis consists of evaluation of constellation point revisit time, target area coverage, coverage uniformity and tracking capability. All but the latter are evaluated by subdividing the target area into a number of points in a grid bounded by a convex hull to represent the boundaries of the target area. The tracking performance is evaluated via the simulation of the voyage of a vessel in the class of interest across the target area, and the identification of the maximum uncertainty in its location. All performance is evaluated on day-long period. The lifetime of the satellites in each formation is also investigated under the effects of perturbations to assess the requirements for constellation maintenance. Nomenclature This section is not numbered. A nomenclature section could be provided when there are mathematical symbols in your paper. Superscripts and subscripts must be listed separately. Nomenclature definitions should not appear again in the text. Acronyms/Abbreviations SAR Synthetic Aperture Radar MIMO Multi-input multi-output PRF Pulse repetition frequency RCS Radar Cross Section COTS Commercial off-the-shelf 1. Introduction Compact SIMO and MIMO SAR formations have become more topical in literature as of late [1] [2] [3]. Benefits of these formations over single-platform SAR systems include a potential gain in swath size proportional to the number of satellites (N) due to N-1 ambiguities being suppressed, and a signal-to-noise ratio gain up to [2]. The distributed nature of the systems of formation flights also offer benefits in redundancy, scalability and reductions in costs. All of these benefits are useful for a maritime tracking constellation, where wide swaths of ocean can be scanned quickly and individual vessels identified from high-resolution imagery[4]. While constellation design for regional fisheries surveillance or global radar coverage is well documented [5] [6], design of a constellation leveraging MIMO CubeSat formations is a sparsely covered topic. Generally, constellation design is a topic approached using a genetic algorithm [7] [8] [6] as the search space considered is large. Usually, a simplification in the constellation structure is required to reduce the search space. Constellation patterns such as the Walker Delta, Star [9] and streets-of-coverage patterns are usually used for exploring global and regional coverage respectively. In preliminary designs, often less accurate methods of performance analysis are accepted in exchange for simplification of the design problem. These simplifications may include the use of semi-analytical methods [10], to increase computational efficiency when simulating performance. In this work an effort to maintain a more accurate visualisation of constellation performance was made at the expense of some computational performance. After surveying similar products and hardware currently available, a set
This paper presents an integrated framework to design a flexible multi-stage telecommunication satellite configuration deployment strategy considering the uncertainties in the evolution of the areas of interest over time. The constructed stochastic demand model considers multiple possible scenarios for the evolution of the areas of interest with probabilities based on the market share growth in each area. The optimization aims to find each stage's design with minimum expected lifecycle cost considering all possible scenarios. Each stage of the constellation, assumed to be Flower constellation with circular orbits, provides a regional coverage of the current area of interest as well as additional coverage for the potential future areas of interest. The proposed multi-stage satellite constellation enables the constellation designer to react flexibly and efficiently to the uncertain future expansion of the areas of interest. A case study reveals a reduction in the expected lifecycle cost for an optimized system compared with the all-in-single-stage system and global coverage constellation.
Rapid satellite-to-site visibility determination is of great significance to coverage analysis of satellite constellations as well as onboard mission planning of autonomous spacecraft. This paper presents a novel self-adaptive Hermite interpolation technique for rapid satellite-to-site visibility determination. Piecewise cubic curves are utilized to approximate the waveform of the visibility function versus time. The fourth-order derivative is used to control the approximation error and to optimize the time step for interpolation. The rise and set times are analytically obtained from the roots of cubic polynomials. To further increase the computational speed, an interval shrinking strategy is adopted via investigating the geometric relationship between the ground viewing cone and the orbit trajectory. Simulation results show a 98% decrease in computation time over the brute force method. The method is suitable for all orbital types and analytical orbit propagators.
A short historical survey of satellite constellation design for continuous coverage is presented. Comparison results of the major types circular orbit constellations for continuous global coverage are described. A table classification of satellite constellations based on an interface between concepts " constellation type " and " coverage type " is proposed. New constellation design methods for the complex coverage are also briefly described. Two type of continuous coverage are considered. First, it is a traditional simple continuous coverage connected with a visibility points on the Earth's surface. Second, it is a more complex coverage for arbitrary geographic regions. If implies that, at any time, the region is completely or partially within the instantaneous access area of a satellite of the constellation. The key idea of the methods is based on common two-dimensional maps of satellite constellations and coverage requirements. The space dimensions are right of ascension of ascending node (in an inertial space) and time. In the space, visibility requirements of each region can be presented as a polygon and satellite constellation motion as a uniform moving grid. At any time, at least one grid vertex must belong to the polygon. The optimal configuration of the satellite constellation corresponds to the maximum sparse grid. Algorithmic basis for the methods is modern computational geometry. As an example, satellite constellation in circular orbit for continuous coverage of full geographic region by a satellite from the constellation is presented. The methods are extended to design of MOLNIYA type elliptic orbit constellations. Kinematically regular elliptic orbit constellations for continuous coverage of geographic latitude belts is considered. An analysis method of single track constellations for continuous coverage of arbitrary geographic areas by a satellite from the constellation is described. As examples, satellite constellations on elliptical orbits with periods ~12 and ~24 hours are considered.
This paper describes the application of an evolutionary optimization method to design satellite constellation for continuous regional coverage without intersatellite links. This configuration, called mutual coverage, is related to some technical limitations that exist on small satellite technology. The coverage of the north Algerian seismological network is taken as an example of application. A Multi Objective Genetic Algorithm (MOGA) is used to make a trade-off between the improvement of the coverage rate, the minimization of the total number of satellites and the reduction of the satellites' altitude. First, some experiments have been performed to find the weight distribution of the fitness function that shows the most significant improvement of the average fitness function. Then, some optimized constellation designs are given for different ranges of altitude and it is shown that the size of the MOGA constellation design is significantly reduced compared to the traditional geometrical design.
The 2-D lattice theory of Flower Constellations, generalizing Harmonic Flower Constellations (the symmetric subset of Flower Constellations) as well as the Walker/ Mozhaev constellations, is presented here. This theory is a new general framework to design symmetric constellations using a
$2\times 2$
2
×
2
lattice matrix of integers or by its minimal representation, the Hermite normal form. From a geometrical point of view, the phasing of satellites is represented by a regular pattern (lattice) on a two-Dimensional torus. The 2-D lattice theory of Flower Constellations does not require any compatibility condition and uses a minimum set of integer parameters whose meaning are explored throughout the paper. This general minimum-parametrization framework allows us to obtain all symmetric distribution of satellites. Due to the
$J_2$
J
2
effect this design framework is meant for circular orbits and for elliptical orbits at critical inclination, or to design elliptical constellations for the unperturbed Keplerian case.
In this study we aim to assess the diurnal cycle of rainfall across the Upper Blue Nile (UBN) basin using satellite observations from Tropical Rainfall Measuring Mission (TRMM). Seven years (2002–2008) of Precipitation Radar (PR) and TRMM Microwave Imager (TMI) data are used and analyses are based on GIS operations and simple statistical techniques. Observations from PR and TMI reveal that over most parts of the basin area, the rainfall occurrence and conditional mean rain rate are highest between mid- and late-afternoon (15:00–18:00 LST). Exceptions to this are the south-west and south-eastern parts of the basin area and the Lake Tana basin where midnight and early morning maxima are observed. Along the Blue Nile River gorge the rainfall occurrence and the conditional mean rain rate are highest during the night (20:00–23:00 LST). Orographic effects by large scale variation of topography, elevation and the presence of the UBN river gorge were assessed taking two transects across the basin. Along transects from north to south and from east to west results indicate increased rainfall with increase of elevation whereas areas on the windward side of the high mountain ranges receive higher amount of rainfall than areas on the leeward side. As such, mountain ranges and elevation affect the rainfall distribution resulting in rain shadow effect in the north-eastern parts of Choke-mountain and the ridges in the north-east of the basin. Moreover, a direct relation between rainfall occurrence and elevation is observed specifically for 17:00–18:00 LST. Further, results indicate that the rainfall distribution in the deeply incised and wide river gorge is affected with relatively low rainfall occurrence and low mean rainfall rates in the gorge areas. Seasonal mean rainfall depth is highest in the south-west area and central highlands of the basin while areas in the north, north-east and along the Blue Nile gorge receive the least amount of rainfall. Statistical results of this work show that the diurnal cycle of rainfall occurrence from TRMM estimates show significant correlation with the ground observations at 95% confidence level. In the UBN basin, the PR conditional mean rain rate estimates are closer to the ground observations than the TMI. Analysis on mean wet season rainfall amount indicates that PR generally underestimates and TMI overestimates the ground observed rainfall.
This paper introduces a methodology to design a set of satellite constellations, called the Flower Constellations, which is generally characterized by repeatable ground tracks and a suitable phasing mechanism. A Flower Constellation, which can be complete or restricted, is identified by a number of parameters. Three are integer parameters: the number of petals (N p), the number of sidereal days to repeat the ground track (N d), and the number of satellites (N s). The others include the phasing parameters and three orbit parameters equal for all satellites: the argument of perigee (ω), the orbit inclination (i), and the perigee altitude (h p). Flower Constellations present beautiful and interesting dynamical features that allow us to explore a wide range of potential applications that include: telecommunications, Earth and deep space observation, global positioning systems, distributed space systems, and new kind of formation flying schemes. A Flower Constellation can be reoriented arbitrarily; however, the repeating ground track property is lost. To demonstrate their potential, some specific Flower Constellations are briefly described and discussed.
This paper presents a numerical method to rapidly determine the rise- set times of satellite-satellite and satellite ground station visibility periods, with the line-of-sight corrected for an oblate Earth. The algorithm uses space curve modeling technique known as parabolic blending to construct the waveform of the visibility function, psi (t), versus time. The waveform is produced from either uniform or arbitrarily spaced abscissa points, from which rise-set times are obtained by extracting the real roots of a localized cubic polynomial. This algorithm works for all orbital eccentricities and perturbed satellite motion, provided the visibility function, psi(t), does not become discontinuous as it could from thrusting or deploying a tether. For this study, the rise-set truth table is constructed using a standard five second step-by- step integration with a linear interpolator to locate the exact crossing times. ne simulation results from this algorithm are almost identical to those obtained by modeling satellites subject to first order secular perturbations caused by mass anomalies, but generated in considerably less time. Advantages of this numerical method include compact storage and ease of calculation, making it attractive for supporting ground-based and autonomous onboard satellite operations.... Mathematical models, Numerical methods and procedures, Parabolas, Visual surveillance, Tracking, Visibility, Observation satellites (artificial).
Most traditional satellite constellation design methods are associated with a simple zonal or global, continuous or discontinuous coverage connected with a visibility of points on the Earth's surface. A new geometric approach for more complex coverage of a geographic region is proposed. Full and partial coverage of regions is considered. It implies that, at any time, the region is completely or partially within the instantaneous access area of a satellite of the constellation. The key idea of the method is a two-dimensional space application for maps of the satellite constellation and coverage requirements. The space dimensions are right ascension of ascending node and argument of latitude. Visibility requirements of each region can be presented as a polygon and satellite constellation as a uniform moving grid. At any time, at least one grid vertex must belong to the polygon. The optimal configuration of the satellite constellation corresponds to the maximum sparse grid. The method is suitable for continuous and discontinuous coverage. In the last case, a vertex belonging to the polygon should be examined with a revisit time. Examples of continuous coverage for a space communication network and of the United States are considered. Examples of discontinuous coverage are also presented. Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
In our previous research, the Flower Constellation set theory was introduced but specific details left out. In this work, the particular phasing theory that we have adopted is discussed in full. As a consequence of this choice of parametrization, a new class of orbit theory has emerged: secondary paths (SPs). The theory of SPs is developed and proved in this work. Examples of SPs are presented and discussed. Furthermore, we discuss the equivalency of Flower Constellations and resolve how certain disparate choices of integer parameters can generate identical satellite distributions.
Flower Constellations are special satellite constellations whose satellites follow the same 3-dimensional space track with respect to assigned rotating reference frame. This paper presents the theoretical foundation of compatibility and phasing of the Flower Constellations. Compatibility is the synchronization property of a Flower Constellation with respect to a rotating reference frame while phasing dictates the satellite distribution property. Compatibility and phasing, which are ruled by a set of five independent integer parameters, constitute the two main properties of the Flower Constellations. In particular, the dual-compatible Flower Constellations theory, which allows a simultaneous synchronization of the Flower Constellation dynamics with two independent rotating reference frames, is introduced. Meaningful examples and potential applications are briefly discussed.
The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of "finite section" Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hopes of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes. Acknowledgements The author gratefully acknowledges the assistance of Ronald M. Aarts of the Philips Research Labs in correcting many typos and errors in the 1993 revision, Liu Mingyu in pointing out errors corrected in the 1998 revision, Paolo Tilli of the Scuola Normale Superiore of Pisa for pointing out an incorrect corollary and providing the correction, and to David Neuho# of the University of Michigan for pointing out several typographical errors and some confusing notation. For corrections, comments, and improvements to the 2001 revision thanks are due to William Trench, John Dattorro, and Young Han-Kim. In particular, Trench brought the Wielandt-Ho#man theorem and its use to prove strengthened results to my attention. Section 2.4 largely follows his suggestions, although I take the blame for any introduced errors. Contents 1
Earlier studies of continuous whole-earth coverage by patterns of satellites in equal-period circular orbits were extended by means of a computer program to patterns of up to 25 satellites and to the provision of up to seven-fold continuous coverage. The program is described and various factors which may influence the choice of pattern for a particular application are discussed, including the level of coverage provided, the minimum satellite separation, and the number and form of the earth-tracks traced by a pattern at a particular orbital altitude. A method is given of selecting a short-list of potentially suitable patterns, prior to detailed study.
In the past, researchers using the streets of coverage (SOC) and Walker methods for generating optimal satellite constellations have published constellations with the minimum number of total satellites for continuous global coverage. The real goal of constellation optimization, however, is to reduce the overall system cost. In some cases this will occur for the minimum total number of satellites, but other real world considerations (such as sparing strategy or launch vehicle multiple satellite manifesting) may drive the constellation selection process to other solutions. This paper presents tables of constellations, optimized for continuous global coverage (1- to 4-fold), for 5 to 100 satellites and all numbers of orbital planes. These expanded tables for the SOC and Walker methods allow the mission planner more choices in minimizing overall system cost. By simple filtering and sorting of the tables, it is shown how constellations can be selected to account for these real world considerations. A comparison is made between the constellations produced by these two methods in the light of some common real world considerations.
An analytical solution is obtained to the problem of achieving continuous coverage of latitudinally bounded zones of the globe by systems of common-altitude satellites equally distributed among and evenly spaced within identically inclined orbits that are symmetrically arranged about the polar axis.
The developed algorithm of computational satellite visibility periods over an oblate Earth is used to construct the time line. Based on the time line the design of the partial coverage satellite constellation can be obtained exactly. The criterion for choosing the best constellation is to minimize the number of satellites with the smallest value of inclination to meet the gap requirement. The method constructs the time lines exactly and then obtains the precise satellite constellations for the time gap requirements. The developed C++ computer program can find the mast efficient arrangement of the satellites in constellations and the optimal value of inclination in less than 10 min on a Pentium-based personal computer.
Recently, telecommunication and navigation corporations have shown a growing interest in low and medium Earth orbit constellations due to several operational advantages, such as reduced power requirements and signal time delays with respect to geostationary platforms. An increased imaging resolution of Earth's surface is also associated with the use of low orbits rather than high altitude orbits. A large set of parameters is involved in defining constellation configurations, so usually some basic assumptions are taken. For instance, this occurs for Walker constellations, exhibiting a high degree of symmetry and suitability for coverage of large areas. Yet, for special purposes, such as continuous observation or early warning monitoring of a specific location, geometric hypotheses often seem inadequate or oversimplified. In this paper all satellites are placed in circular, repeating orbits with semimajor axis and inclination yielding maximum visibility of a preselected target location. Then, a correlation function is introduced as an effective tool to find all allowed time delays between two consecutive passes over the target. Some optimal constellation configurations (of 2, 4, 8 satellites) are deduced and discussed with reference to different kinds of local observation.
It has been shown that, given a suitable choice of orbital patterns, and a stationkeeping capability in the satellites, continuous coverage of the whole earth's surface may be provided by as few as five satellites, and continuous duplicated coverage by as few as seven satellites. The use of six satellites for single coverage or nine for double coverage allows considerable flexibility in the choice of system parameters.
The problem of identifying the minimum number of satellites in circular,
inclined orbit constellations at the same altitude which provide
continuous, single, and redundant coverage for global, polar cap,
equatorial, and zonal areas of the earth's surface is solved
analytically in closed form using street-of-coverage techniques with
arbitrary interorbit plane phasing of satellites. The results are
compared with optimal polar constellations and optimal inclined
constellations as defined by Walker (1977) for single, double, triple,
and quadruple coverage requirements.
The present investigation is concerned with the coverage of the earth's
surface by multiple-satellite systems, taking into account results
reported by Walker (1982). The considered studies have investigated
systems with satellites following multiple circular orbits of equal
period, providing continuous multiple (rather than only single) coverage
of the entire surface of the earth. Attention is given to criteria
regarding the selection of a satellite constellation, regular polyhedra
and tesselations, practical satellite constellations related to delta
patterns, sigma patterns, and omega patterns. Data concerning sigma
patterns are presented in tables.
The rapid and reliable determination of satellite visibility periods is
one of the most important and fundamental problems of aerospace mission
analysis. This paper describes a numerical technique and interactive
software tool which accurately and efficiently solves this problem. This
method takes advantage of the following numerical techniques: (1)
one-dimensional, derivative-free minimization with bracketing, (2)
one-dimensional, derivative-free root-solving with bracketing, (3)
Mikkola's non-iterative approximation of Kepler's equation, and (4)
analytic orbit propagation with first-order gravity perturbations. The
software can accommodate different types of orbit propagation methods,
and the location of the observer is modeled with respect to an oblate
Earth. The user can easily enforce a minimum elevation angle constraint
during the solution process. The CPU efficiency of this method is
demonstrated by a comparison with the method of 'interval searching' for
Earth satellites in both circular and elliptic orbits.
This paper describes a new four-satellite elliptic orbit constellation
giving continuous line-of-sight coverage of every point on the earth's
surface. It represents a major improvement over the only other known
four-satellite continuous global coverage array by reducing the
constellation operational altitudes by about one-half and by utilizing a
common period for all of the satellites employed.
Constellations of Earth orbiting satellites are used to perform many tasks. If the constellation's coverage need not be continuous in time, the number of satellites and, therefore, the cost of the constellation may be decreased. Finding constellations that minimize revisit times for discontinuous coverage is posed as an optimization problem. Practical limits on coverage analysis provide objective functions that are not differentiable, so non-gradient-based optimization methods are necessary. Simulated annealing and a genetic algorithm were applied to discontinuous coverage problems for various numbers of satellites and Earth central angles, providing both whole Earth and zonal coverage. Results are presented and compared to constellation designs from a traditional approach. Simulated annealing appears to provide answers with less computational effort, but the genetic algorithm is capable of simultaneously generating different de signs with the same revisit times. Additional conclusions about these approaches for discontinuous coverage satellite constellation design are made.
A design method for optimal regional coverage satellite systems with common track constellation (CTC) is proposed. CTC is a special class of constellation in which satellites of whole constellation follow the same track on the Earth's surface-hence the name common track. Based on the thorough investigation on the constraint relation of the satellite parameter, a coded notation for CTC is presented, and the equivalence relationship between the CTC and Walker delta constellation is discussed. Then, the design method is presented and some optimal constellation schemes for China are given as examples. Results shows CTC can provide preferable coverage performance to specified region with fewer satellites
Satellite constellations provide the infrastructure to implement some of the most important global services of our times both in civilian and military applications, ranging from telecommunications to global positioning, and to observation systems. Flower Constellations constitute a set of satellite constellations characterized by periodic dynamics. They have been introduced while trying to augment the existing design methodologies for satellite constellations. The dynamics of a Flower Constellation identify a set of implicit rotating reference frames on which the satellites follow the same closed-loop relative trajectory. In particular, when one of these rotating reference frames is “Planet Centered, Planet Fixed”, then all the orbits become compatible (or resonant) with the planet; consequently, the projection of the relative path on the planet results in a repeating ground track. The satellite constellations design methodology currently most utilized is the Walker Delta Pattern or, more generally, Walker Constellations. The set of orbital planes and initial spacecraft positions are represented by a set of only three integers and two real parameters rather than by all the orbital elements; Flower Constellations provide a more general framework in which most of the former restrictions are removed, by allowing the use of resonant elliptical orbits. Flower Constellations can represent hundreds of spacecraft with a set of 6 integers and 5 real parameters only and existing constellations can be easily reproduced. How to design a Flower Constellation to satisfy specific mission requirements is an important problem for promoting the acceptance of this novel concept by the space community. Therefore one of the main goals of this work is that of proposing design techniques that can be applied to satisfy practical mission requirements. The results obtained by applying Global optimization techniques, such as Genetic Algorithms, to some relevant navigation and Earth observation space-based systems show that the Flower Constellations not only are as effective asWalker Constellations, but can also be applied to non-traditional constellation problem domains, such as regional coverage and reconnaissance.
Ecological studies in tropical forests have long been plagued by difficulties associated with sampling the crowns of large canopy trees and large inaccessible regions, such as the Amazon basin. Recent advances in remote sensing have overcome some of these obstacles, enabling progress towards tackling difficult ecological problems. Breakthroughs have helped transform the dialog between ecology and remote sensing, generating new regional perspectives on key environmental gradients and species assemblages with ecologically relevant measures such as canopy nutrient and moisture content, crown area, leaf-level drought responses, woody tissue and surface litter abundance, phenological patterns, and land-cover transitions. Issues that we address here include forest response to altered precipitation regimes, regional disturbance and land-use patterns, invasive species and landscape carbon balance.
Design of satellite constellations providing partial coverage of certain
ground regions is becoming more important as small low-attitude
satellites receive increased attention. The purpose of this study is to
develop the procedures necessary for deriving the best constellations
for partial coverage. This paper analyzes circular orbit constellations
and shows that repeating ground-track orbits yield beter results than
nonrepeating ground track orbits. This theory provides methods for
designing the best constellations. Results comparing the new nonstandard
satellite constellations with the best standard designs show the new
designs generally yield beter results and require significantly less
computation.
Satellite constellations having rosette (flowerlike) orbital patterns are described which exhibit better worldwide coverage properties than constellations previously reported in U.S. literature. The best rosettes with 5-15 satellites are identified and evaluated relative to prior results. In most cases, the best results are obtained by placing one satellite in each of N separate planes and by using inclined rather than polar orbits. Coverage properties of these constellations are analyzed in terms of the largest possible great circle range between an observer anywhere on the Earth's surface and the nearest subsatellite point. When evaluated in this manner, coverage properties are invariant with deployment altitude. As deployment altitude is reduced, however, higher order constellations must be used to maintain a fixed minimum viewing angle. Coverage properties are also invariant with deployment orientation relative to Earth coordinates, although specific orientations can cause the satellite patterns to appear quasi-stationary. Thus these constellations offer a promising alternative to the use of geostationary satellites. Rosette constellations can also be used to guarantee multiple satellite visibility on a continuous worldwide basis. It is shown that 5, 7, 9, and 11 satellites are the minimum numbers required for single, double, triple, and quadruple visibility, respectively. Examples of rosette constellations which achieve these bounds are given.
A satellite-borne sensor can view a region at or above the Earth's surface. The size of this region depends on the satellite's altitude, the maximum range and scan angle of the sensor, the minimum above-the-horizon viewing angle required, the extent in altitude of the region to be viewed, and the maximum altitude of sensor obscuration by the atmosphere. Except for geosynchronous satellites this region moves relative to the Earth, so that constellations of satellites are generally necessary for continuous coverage. Satellite constellations which minimize the number of satellites required for continuous coverage are derived as a function of the angle subtended at the Earth's center by the coverage of a single satellite. This is done for single and triple continuous coverage of the entire Earth and of the polar regions extending to arbitrary latitude. Simple, cogent approximations for the configurations and numbers of satellites are found. Expressions which relate sensor capabilities and surveillance requirements to are presented. Examples are given to illustrate the use and accuracy of the results.
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