SPACE EGGS - Satellite Coverage Model for Low Earth Orbit Const

8/12/2019 SPACE EGGS - Satellite Coverage Model for Low Earth Orbit Const

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SPACE EGGSSatellite Coverage Model forLow Earth Orbit Constellations

byJanis Indrikis, * andRobert Cleave*

Rockwell International CorporationSpace Systems Division2800 Westminster Blvd.P.O. Box 3089Seal Beach, CA 90740-2089(213) 797-1455Abstract

The effectiveness calculations of global, regional, and area coverage for proliferated small satelliteconstellations in low altitude orbits stress the capability of conventional analytical techniques. A newapproach that combines the Mollweide (equal area) projection with an on-screen color manipulation ofthe picture elements (or pixels) has been developed and utilized over the past decade. This techniqueenables the optimization of large satellite constellations with multiple communication or sensor viewingconfigurations, with a minimum number of calculations. Complex viewing geometries are well adaptedwith this analytical approach, along with exclusion requirements such as the sun, moon or earthavoidance. This technique has proven useful in minimizing the number of low altitude communicationsatellites (for any planet) and optimizing the sensor suite for specific missions.

I COVERAGE ANALYSIS: WHY DOWE NEED IT and HOW IS IT DONE?Networks or constellations of satellites offer manyservices and capabilities not achievable by othermeans. The ability to navigate ships around hazardsis provided by satellite triangulation [1]. Globalcommunications is another example of aconstellations utility, where satellite networksenable two people on opposite sides of the planet tospeak with each other. Surveillance programs mayrequire continuous imaging of an entire planet,which is impossible from just one satellite. Aconstellation of orbiting sensors is required toperform this task. Finally, proposed weaponsystems are required to counter threats from anyplace on the earth. Since weapons have a limitedreach, only multiple weapon platforms orbiting theearth can meet this requirement (Figure 1).Satellites in orbit about a planet are able to view afimte area (footprint) wit h their payloads, like aflashlight beam shining on a ball (Figure 2). As thesatellite travels in an orbit around the planet, thefootprint moves with it. However, if the entireplanet needs to be continuously illuminated, the*Members of the Technical Staff, Advanced Engineering

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challenge is to determine the minimum number oforbiting flashlights required. Any solution otherthan the minimum required is unacceptable sinceadded costs will be incurred, typically amounting tohundreds of millions of dollars. The analyticalmethodology used to determine a constellation'scapability is known as coverage analysis, and hasbeen studied since the 1960's [2].

+CY .... . I COMMuNtCAnON I

Figure 1: Networks of Satellites rferUnprecedented Services


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Figure 2. The Footprint is Formed by thePayloads' Viewing CharacteristicsThe area of a sphere covered by a satellite'sfootprint is a measurement of a constellation'sproficiency (or percent coverage). Simple geometricfootprints are easy to analyze, but difficulty grows

operating conditions, etc. The only o p t i m i z ~ i o nparameters available are the number of satellItes,their spacing, and the respective orbital parameters.Sizing a constellation is an iterative process since noclosed form solutions exists that considers all of thevariables. Coverage analysis is well suited forcomputers, and this paper will describe a computerprogram known as SPACE EGGS that canaccurately and quickly determine the coverage froma set of satellites. The computational speed enablesthe optimization of the number of satellites requiredfor any specific mission.

I Constellation IevelopmentI CO g Jequlrementl I Payload J8pabliHIoI I ocation Iharac1.r1B1lco

Area Regional. Global Ranga Number of Satelilt:rim. (Int.rmlttlnt Continuoul) Field 01 VI_ (Az. fl, BlC Speclng/Ph ng

Lu Slngl lIu l) Exclusion Zan Orb Paramet

I Programmatlca I I Technology I I OptimizationParema ,,,,Figure 4. Developing Constellations is aMulti-Variable Operation

as footprints become more complex or intertwined(Figure 3). Understanding the relationship betweencoverage and satellite placement is the key tooptimizing a satellite constellation. In addition, thisproblem is compounded with the resurgence indeveloping small satellites and launch systems.Because of advances in miniaturization technology, II.several programs consisting of hundreds ofsatellites in low earth orbi t have been proposed.

DIFFICULTIES WITH CURRENTAPPROACHES

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Figure 3. Calculating the Coverage fromInterweaving Footprints is a ChallengeThere are many variables involved in developing aconstellation, which can be broken down into threeprimary categories (Figure 4). Programmatics willdetermine the coverage requirements, which canrange from continuous global coverage by at leastone satellite to intermittent regional coverage bymultiple satellites. The payload capabilities (andtechnology) dictate the footprint, and can consist ofrange limitations, azimuthal or elevation restrictions,

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Analyzing and designing constellations has been apopular subject for many decades, and there is awealth of information available [2-13]. Most notableis the pioneering work by J. G. Walker, whodeveloped semi-analytic techniques based ongeometric patterns [3, 13]. To give an example ofsatellite coverage variability, Walker developed afive 5) satellite constellation that providescontinuous, global coverage from at least onesatellite (single coverage), as well as a seven (7)satellite constellation providing continuous, double,and global coverage.Others such as Ballard, Rider, and Beste developedsimilar semi-analytical techniques based on differentcoverage requiremen ts [2-6, 9, 11-13]. Forexample, a constellation that provides continuousregional coverage is different than one providingcontinuous global coverage. These efforts arevariations on Walker's work, and assume simplifiedconstraints, at best. For example, Walkerconstellations have an eccentricity of zero with nopayload viewing restrictions.The first application of an eccentric orbitconstellation is the Soviet Molniya communication


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satellites. These constellations can fully cover highnorthern latitudes while requiring much lesslaunching energy than circular high-altitude orbits.Recently, Draim patented a constellation consistingof four satellites, one less than Walker s solution,that provides continuous, global coverage [8,15].However, Draim s highly elliptical and large period(>27 hours) constellation has few practicalapplications for small satellites.As payload capabilities change (such as rangelimited weapon platforms), or as orbit constraints

calculations. Until recently, this problem appearedinsurmountable with personal computing systems.Satellite Footprint Area Rellilste red on

are imposed (such as the Pegasus launch vehicle 1 + + + + + + f ~ - t : 2 . . . . . - . - . t - fcapability), the previous semi-analytical techniques Sobecome more difficult to use. To compensate for the Ilack of analytic methods and large number ofvariables (Figure 4), other techniques have beendeveloped that aid in coverage analysis: these are theuse of geometry and a grid pattern.The geometrical technique of calculating the percenta sphere is covered with a symmetrical footprint is atrivial matter. Multiple, intersecting footprints aremore challenging to calculate, but mathematicaltechniques exist to arrive at an answer. Difficultiesarise when the footprints and orbital parametersbecome complex, especially if satellite perturbances(such as an oblate earth) are to be considered. Infact, Draim s constellation is based solely ongeometry, which probably explains why theconstellation does not provide continuous globalcoverage of the earth over an orbital period.To alleviate this challenge, the sphere is divided intoa grid at even increments. After modeling thepayload s viewing parameters and projecting themonto the sphere, the program checks the center ofeach grid point to determine whether that point iswithin the satellites footprint. After projecting allfootprints and storing the visibility data, theprogram calculates the percent coverage. Thistechnique has two severe problems. The firstproblem is the large number of calculationsrequired, which entails over 54,432 calculations fora sphere divided into five degree increments (36x72points), along with a constellation of 21 satellites.Over 39 million calculations occur if the orbit periodwere twelve hours long with a resolution of oneminute intervals. Such calculations are not a trivialtask.The second problem is the lack of fidelity involved.Footprints that enter into a grid without crossing thecenter are not registered during the area coveragecalculations (Figure 5). Increasing the gridresolution would induce more calculations; a factorof five in resolution equates to a factor of 25 in

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Figure S Fidelity is Lost with Coarse GridsIII. TIIE NEW APPROACHThe issues of accuracy and quickness areconflicting: highly accurate programs tend to beslow and cumbersome. Optimizing satelliteconstellations and their payloads is a challenge,especially as payload capabilities fluctuate duringthe design process. Success came with advances incomputing hardware, which modified existingapproaches to achieve unparalleled efficiency.The grid technique is recognized as an accuratemeans to calculate the coverage capability of asatellite constellation. In addition, advancements inpersonal computing hardware yielded monitorsrivaling the resolution in some of the best videoequipment. The product of these two entities is acomputer program known as SPACE EGGS, whichreduces the grid to the monitor S picture elements orpixels. The program uses built-in graphic storagecommands to eliminate the need of checking eachpixel for satellite visibility; coverage calculations aremade by determining the number of filled pixels onthe screen. Since the program reads footprint areasdirectly off the screen, an accurate display of athree-dimensional sphere onto a two-dimensionalscreen is required. This is accomplished with theMollweide projection. On this projection, alOOxlOO pixel area on the screen will alwaysrepresent the same area on a sphere whether theprojection is at the poles or at the equator.The combination of these unique facets providestwo outstanding capabilities. First, the resolution,and hence accuracy is unmatched in comparison tothe previous techniques, since the grid cannot bereduced below the pixel level.


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The second capability is the sheer speed with whichcoverage calculations can be made, and thetechnique works as follows. After the payload'scharacteristics are modeled in the program, thesatellite's footprint is superimposed onto theMollweide projection where it is stored (Figure 6).Mter all satellite footprints are calculated and stored,the program recalls all stored projections. Each pixelis labeled as a variable with zero (or white) as thestarting value. As the footprints are overlaid ontothe screen, the color of the affected pixels arechanged by one value. Thus if six (6) footprints aresuperimposed onto the same area, the pixel color forthat area would be six. With all of the storedprojections on the screen, the program checks eachpixel color, line by line, storing the statistical datafor each color. The percent of each pixel color isidentical to the percent coverage by that manysatellites. For example, a pixel color of one (1)equals coverage by one satellite, whereas a pixelcolor of three (3) equals coverage by three satellites(Figure 7). Program quickness is achieved sincevery few calculations are actually made. Aftercharacterizing the footprint, the programsuperimposes views and stores the graphics. Whencompleted, the program calculates statistics basedon the pixel colors that are read directly off thescreen.

Satellite Footprint Mollweide Projection

Figure 6. Individual Satellite Footprints areSuperimposed onto the Mollweide ProjectionSince coverage analysis is an iterative, or semianalytic process, the program can be set up tosystematically search through differentconstellations until arriving at a solution. Theprogram can also quickly calculate the coveragevariability as the satellites are propagated in theirorbit. Orbits can be eccentric, and the addition ofthird body ephemeri can be used to consider casesin which solarllunar exclusions apply. The programhas also been modified to account for manydifferent factors, such as:

*The effects on coverage of a decaying orperturbed satellite4

*Coverage analysis for other bodies [14]*Satellite-ta-Satellite coverage*Coverage from multi-sensor platforms(e.g., Earth Observation System)* Coverage due to the loss of satelliteelements (e.g., survivability)*Coverage from Walker, symmetrical, orrandom constellations*Regional coverage

Figure 7. As Each Footprint is Recalled, theAffected Pixel Changes Color by One Value.and the Percent Coverage is Found by Summingthe Pixels of Each ColorIV. APPLICATION EXAMPLESPA YLOAD CHARACTERISTICSPayload characteristics detennine how the coveragefootprint will appear on the projection, and Figure 8shows the effect of some common payloadparameters. For a given set of payload capabilities,below the horizon sensors are able to cover muchmore area than sensors which look above thehorizon. Restricting the range or azimuth alsoeffects the footprint size.

,' ;5',' .-:1,:'* : . ~ - '

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Below the HorizonU l % Coverage

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Below the Horizon.60 Azimuth Restriction

i x . ~ ~ : l { Above the Horizon9.4 Coverage

Above the Horizon.60 Azimuth Restriction 1.6% Coverage2.0% CoverageFigure 8. PayloadFootprint Pattern Characteristics Determine the


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SAMPLE CASESTwo examples are given. The first example isdesigning a constellation based on a hypotheticalsurveillance mission to provide continuous globalcoverage. The second example is a demonstrationon how important sensor range is to theconstellation designer. The altitude is fixed at 2000km.EXAMPLE IThe projected footprint for this payload is shown inFigure 6. In order to provide coverage at theequator, a minimum of five (5) planes is required,and to cover the poles, an inclination greater than50 is necessary. In a matter of minutes, SPACEEGG's develops a solution that satisfies thecoverage requirements. Relative phasing of satellitesis optimized to yield a constellation consisting of 5planes with 3 satellites per plane (15 satellites total),and an inclination of 55 degrees. Figure 9 shows aninstantaneous snapshot of the satellites' positions,and Figure 10 displays the coverage for thisconstellation at that time. Coverage capability overtime for this constellation is shown in Figure 11(duration is the time it takes for one satellite to shiftinto another satellite's position).

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.. OF SATSCOVERA:iE

.. OF SA1S L5 ECC: 0INC: 55

Figure 9. The Result of SPACE EGGs is a 15Satellite Constellation, whose positions areshown

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95~ 00"" 15 SatelilleSi'. 5 Plane.8 85 2000 km Altitude 55 tncilnsttoni Unlimited Range80

75 DoubMo Coveraga

10 0 5 10 15 20 25 3 35


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EXAMPLE IIThe second case considers a sensor with a limitedrange, and will show a drastic effect on thecoverage capability. Figure 12 displays the newcoverage for the same conditions as before, yet witha maximum range capability of 4,500 km. Notehow single coverage is reduced to 86.1 . To makeup for the loss of coverage, the program is allowedto search iteratively in satellite inclination, phasingand total number of satellites. This search yields aconstellation inclined at 59, with 23 planes and 1satellite per plane (23 satellites total). Figure 13represents the instantaneous positions, and Figures14 and 15 depict the coverage characteristics forthese new parameters.

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SPACE EGGS - Satellite Coverage Model for Low Earth Orbit Const