EXHIBIT 1064
`
`J. dela TORRE, Jr., “Earth Reference Imager Experiment for Satellite Attitude
`
`Determination,” Arizona State University (1995)
`
`TRW Automotive U.S. LLC: EXHIBIT 1064
`PETITION FOR INTER PARTES REVIEW
`OF U.S. PATENT NUMBER 8,599,001
`IPR2015-00436
`
`

`
`Earth Reference Imager Experiment for
`Satellite Attitude Determination
`
`Student Author: Jose' L. delaTorre, Jr.1
`Faculty Advisors: Dr. Jordi Puig-Suari2 and Dr. Helen L. Reed3
`Arizona State University
`Tempe, Arizona 85287-8006
`
`Abstract
`
`1. Introduction
`
`The Earth Reference Imager (ERI)
`experiment on board the ASUSat I student satellite
`will provide valuable attitude information to validate
`the new attitude sensors along with the GPS data.
`Using the concept of triangulation, the satellite's tilt,
`swing, height, azimuth, and coordinates will be
`attained from an image of the Earth. This
`information will then be compared with the attitude
`sensors to confirm the data received from the satellite.
`
`Nomenclature
`
`1.1 ASUSat 1
`
`Since its inception, Arizona State
`University's first small satellite, ASUSat 1, has been
`a student-designed project. Many members of local
`industry and the faculty of ASU have been very
`supportive of the project, and have sponsored and
`advised several aspects of the program.
`Weighing ten pounds (4.5 kg), the satellite
`will be the lightest ever put into orbit with meaning-
`ful science experiments' . The payload will be
`launched by Orbital Sciences Corporation on a
`Pegasus launch vehicle and will be placed at a 325-
`km sun-synchronous orbit. It is expected to remain in
`orbit for approximately 22 days.
`ASUSat I will allow researchers to measure
`the properties of the ionosphere at a low cost.
`Furthermore, it will provide an audio transponder for
`amateur radio operators.
`There have been an average of forty students
`ranging from high-school through Ph.D level
`working in ten different sub-systems. These are
`science, structures & materials, dynamics & controls,
`communica-tions, power, thermal, commands, ground
`support equipment (GSE), software & data analysis,
`and systems integration.
`
`+X
`
`L
`N
`n
`o
`R (cid:9)
`Rv (cid:9)
`
`S C1 (cid:9)
`S v (cid:9)
`
`A, B, C (cid:9)
`ground control points
`a, b, c (cid:9)
`image ground control points
`f (cid:9)
`focal length
`II (cid:9)
`altitude of satellite
`hA,hn,hc elevation at point
`Lp (cid:9)
`distance from nodal point of lens to
`place of photograph
`space position of front nodal point
`ground nadir point
`nadir point
`principal point
`ratio between AB and AC on the ground
`ratio between All and AC on a vertical
`photograph
`ratio between AB and BC on the ground
`ratio between AB and AC on a vertical
`photograph
`swing of photograph
`s (cid:9)
`* (cid:9)
`introduced tilt of arbitrary amount
`t
`XL, YL, 4 space coordinates of exposure station
`(x, y) (cid:9)
`photographic coordinates of image
`x', y' (cid:9)
`ground coordinates with arbitrary tilt
`calculated about the y axis
`ground coordinates with arbitrary tilt
`calculate about the x axis
`ground survey azimuth
`azimuth of principal plane
`azimuth of control line
`amount of rotation
`
`x", y" (cid:9)
`
`OCG (cid:9)
`ano (cid:9)
`ap (cid:9)
`0 (cid:9)
`
`1Junior, Mathematics, ASUSat 1 Science Team
`2 Assistant Professor, Mechanical & Aerospace
`Engineering; AIAA Member
`3Director, Aerospace Research Center, Associate
`Director, ASU NASA Space Grant Program;
`Professor, Mechanical & Aerospace Engineering;
`Associate Fellow, AIAA
`
`Figure 1 Pullaway view of ASUSat 1. Drawing by
`Shea Ferring and Chris Michaelis, Structures Team.
`1064-001
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`1064-001
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`

`
`The science team is developing a Hall-
`Current Ion Accelerator, a Magnetohydrodynamic
`Generator, Ion Thrusters, and the Earth Reference
`Imager.
`
`The structures team designed a fourteen-sided
`graphite / epoxy bus and overlooks cabling and
`mounting on the satellite.
`Dynamics is providing stabilization with an
`aerodynamic boom and a fluid damper. Moreover,
`they are providing positioning information through a
`GPS receiver and an array of photodiodes.
`Communications has student-built the
`modem and designed a deployable antenna.
`The power sub-system will be providing
`power to the satellite through two six-packs of Sanyo
`NiCd batteries, re-charged with GaAs solar cells
`around the fourteen sides of the bus. The satellite
`will be powered up with a mechanical switch when
`the satellite is deployed.
`The thermal team keeps track of the
`temperatures inside the bus, and stabilizes them with
`paints and highly emissive coatings. The
`temperatures expected outside the satellite are in the
`range of -24° C to 90° C.
`Commands is designing the processor around
`the INTEL 80C188EC chip, running it at 10 MHz.
`Two I/O ports provide interfaces with the
`science/dynamics board and with the camera interface
`board. There is also an Error Detection and
`Correction (EDAC) facility built in for the 1 Mbyte
`of RAM available for the satellite's data. One
`EPROM will be used for the default operating
`system, while another will contain the bootloader for
`the satellite's system.
`Ground support is providing the testing
`equipment and facilities. Orbital Sciences has
`allowed the ASUSat 1 team to use several of its
`facilities.
`The software for ASUSat 1 is being written
`in C and compiled to run in the BekTek Real-time
`Spacecraft Operating System designed for micro-
`satellites.
`Finally, the systems and integration team is
`coordinating all the designing, integration, testing and
`documentation of all the sub-systems of the satellite.
`The pointing requirements have been defined
`to be + 10°, with orbital positioning being within ±
`1 km1 to attain full coverage of the Earth. It is hoped
`that the drag coefficient can be calculated. To achieve
`these goals, a new attitude-sensors array has been
`designed and developed to give the satellite's
`orientation.
`The coordinate axis is defined as shown in
`figure 1. The x axis lies along the axis of symmetry,
`y axis runs parallel to the inside panels and
`perpendicular to the x axis, and the z axis runs
`perpendicular to the panels, through the center.
`
`2
`
`1.2 Earth and Sun Sensors
`
`To keep control of the satellite, its
`orientation information will be recorded through a
`complex network of photo sensors. With a total of
`sixty of these photodiodes positioned around the
`satellite, there will be almost complete coverage of
`the sky. Of the sixty sensors, forty-six will be sun
`sensors which will be keyed in to visible light, and
`the remaining fourteen will be Earth sensors, filtered
`to receive in the infra-red?
`There will be blocks of three sun sensors on
`each of the fourteen sides of the satellite, one being
`normal to the surface of the side, and the other two at
`45° from the normal. Earth sensors will be
`positioned on every other side of the satellite, and the
`remaining sensors will be placed on the front and
`back plates of the satellite.2
`The sensors themselves are Motorola Photo
`Detectors, MRD510, with filters being placed on the
`Earth sensors. These diodes will produce voltages
`ranging from 0-5 V, proportional to the amount of
`light received. The readings from each sensor will be
`recorded every five minutes, and the data will later be
`processed on the ground?
`However, this dynamics sensor array has
`never been flown, and other data is necessary to
`confirm the accuracy of the data from the satellite's
`sensors. To confirm the information received from
`the sensors, a camera will be flown to image the
`Earth vertically. Then, by performing the methods of
`triangulation on the ground images from the satellite,
`it is hoped to confirm the positioning data given by
`the sensors array. To ensure that the camera is
`perpendicular to the Earth, the sensors will be used to
`approximate where the Earth is relative to the
`satellite.
`
`1 3 GPS
`
`The Global Positioning System (GPS) was
`developed primarily for military purposes by the
`Department of Defense. However, the technology has
`become available to the public.
`Consisting of a global network of twenty-
`four satellites at high altitudes, GPS provides its
`users with accurate position and velocity data. GPS
`receivers have been used on Lower Earth Orbit
`satellites in the past for determining the satellite's
`orbital parameters.3 By a method of triangulation,
`the satellites are able to practically pinpoint the
`receiver's position.
`Several factors have introduced errors in the
`GPS measurements such as the ionosphere which
`causes some interference. On the average, GPS may
`be off by about sixty feet, and in the worst case, GPS
`data may be off by as much as 350 ft. 3
`
`1064-002
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`1064-002
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`

`
`ASUSat 1 will carry a Trimble GPS receiver
`on board. The SVee Six-CM2 is a terrestrial board
`with 6 channels and has never been flown in space
`before, but it has been rigorously tested by ASU
`students to ensure that it will survive in space,4.8
`The accuracy of this particular unit is 25m. Readings
`will periodically be measured and recorded from the
`GPS to determine the satellite's position and
`velocity.4
`From the GPS data included in the
`telemetry, it will be known from where the images
`were taken. This will prove useful in identifying the
`precise location of the image, and in verifying the
`position calculations from the images.
`
`1.4 Earth Reference Imager
`
`Once the images have been received and
`processed on the ground, it will be possible to
`perform several measurements on the images, and do
`calculations on them with a certain degree of error.
`The error will depend on the resolution of the image
`and on the scale of the photograph.
`From the image, three points will have to be
`identified, the distances between each of them
`calculated, and the elevations from sea level of each
`point attained to perform the desired calculations6.
`
`2 Earth Reference Imager
`
`2.1 Imager
`
`The cameras being used for the experiments
`on ASUSat 1 are single-chip CMOS digital cameras.
`The cameras, VVL-1070, have a pixel resolution of
`160 x 160 pixels, and put out 8-bit digital parallel
`output. The pixel size is 10.5 tun x 10.5 ttm
`giving a total effective array size of 1.68 mm x 1.68
`mm. The camera also provides analog output, and an
`exposure control (2,000:1), gain control, and variable
`frame rate (0.5 - 24 frames/sec). At 5V, the chip
`consumes less than 100 mW.
`
`6 cm
`
`0.65 t.'r1
`
`0
`1.5 cm
`
`+5
`P7
`
`PO
`
`PBus
`
`Figure 2 Dimensions and basic layout of camera
`board. There are five control lines and eight data lines
`on each board. The lens is mounted in the corner.
`
`3
`
`2 2 Optics
`
`The lenses being used for the cameras are V-
`4308 multi-element lens with a diameter of 15 mm
`across the top and focal length of 8mm with an f-stop
`of 2.0. The lens weighs about 7 grams. The field
`of view given in the specifications is 31° x 23° (H x
`V). 7 Assuming the witPtlite is at a 325 km orbit and
`that the camera is facing vertically down to Earth, the
`range of the image would be 195.3km x 138km. 8
`giving a resolution of about 1 km per pixel (Fig. 3).
`Furthermore, the scale is calculated as the focal length
`over the altitude of the camera, which is
`approximately 1: 40,625,000 in this case. 7 By
`keeping the field of view and ground coverage limited,
`the resolution should be optimized for the digital
`camera chips.
`
`2.3 Placement
`
`The lens will be fixed over the camera on the
`camera board using a lens holder, with the appropriate
`focal length to focus the image. The board will
`measure approximately 4 cm x 6 cm (Fig. 2),
`allowing the camera to be placed along the side of one
`of the satellite's side panels. A hole of 0.65 cm in
`diameter will be drilled to allow the lens to be
`mounted up to it to view the Earth at a right angle to
`the satellite's axis of symmetry (Fig. 4) close to the z
`axis (Fig. 1).
`
`-41
`
`velocity
`vector
`
`.1111)
`8mm
`
`32 5 km
`
`138 km
`
`Figure 3 With a field of view of 31°-23°, altitude of
`325 km, and focal length of 8 mm, the ground
`coverage should be about 138 km x 195.3 km.
`
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`

`
`2,4 otection
`
`The circuitry for the camera board will be
`surface mounted and conformal coated to protect from
`vibration and shock. Dampers will be placed around
`the board and lens as well. A gold foil will be put
`around the outside camera board to reflect the sun's
`radiation, to keep it cool, and to protect the circuitry
`from cosmic particle hits.
`
`Camera
`
`8 bits
`
`Camera
`
`3 eitmera Boards
`
`+5 V
`
`Power
`
`Commands
`Interface
`
`Main
`CPU
`
`The VVL-1070 chip has a built-in analog-to-
`digital converter (A/D) circuit, so the output is
`already digital.9 The supporting electronics, then,
`drive the camera at real-time clock speeds, and transfer
`the images to the main CPU bus through a 25-pin
`interface.
`ASUSat 1 will carry two CMOS cameras,
`one for determining the satellite's roll rate, and the
`other for the ER1 experiment. Both, will have the
`supporting circuit board (Fig, 2). The boards consist
`of their own microprocessors and memory with built-
`in commands to run the camera. Running at real
`time rates, the image will be dumped into the local
`memory, where the main CPU can then read the
`memory at its own rate and store it to be downloaded
`at a later time.10 There will also be an interface board
`between the two camera boards and the main CPU
`which handles the control of the two cameras from a
`chip select in the interface. The interface consists of
`five control lines for each camera, and eight data lines
`which will be shared by both cameras (Fig. 5). The
`camera boards will be designed by Gordon Minns &
`Associates in Wyoming.
`The software to control all three micro-
`processors will be written in ANSI C and will be
`compiled for a BekTek operating system.I1 The
`
`Earth
`Reference
`Imager
`
`1.5°
`
`Figure 4 The ERI camera will be mounted to one of
`the 14 side panels of the satellite to view the Earth
`vertically with a range of 23°.
`
`4
`
`Figure 5 The two cameras on ASUSat 1 will go to a
`camera interface board which will connect to the main
`processor's control interface. The 8-bit data lines will
`be shared by both cameras.
`
`supporting software will be included with the camera-
`board product to be modified by the software team.
`The commands will be uploaded to the satellite,
`where the cameras will be allotted ten minutes per
`orbit to take images.'2 The camera boards will
`consume less than 100 ntW as well, and the size of
`each image will be about 25 k13. At this size, it will
`be possible to take about ten consecutive images in
`one orbit.I°
`
`4 Image Processing
`
`Once the images have been taken, and
`transferred to the main CPU bus, the data will be
`downloaded to the ground station at Arizona State
`University several times a day. When the images
`have been successfully transferred, they will be
`moved over the internet to a Silicon Graphics
`machine for image processing. Using an image
`processing package such as XV, several analyses will
`be done on the images such as filterings, histograms,
`and averaging.I3 Software such as 1DL is also
`available along with faculty experienced in
`professional image processing.
`Once the images have been optimized,
`whether taking the average of consecutive frames or
`filtering high frequencies, the image will be ready for
`the data analysis.8 From the image, it will be crucial
`to identify the objects and locations on Earth, or in
`the sky, for determining the satellite's attitude. This
`can be done by comparing daily weather maps, terrain
`maps, and GPS data along with the dynamics-sensors
`data to approximate the location at which the image
`was taken.2 Weather maps will reveal cloud covers
`where an image may be completely white, in which
`case the image data will not be very helpful.
`Otherwise, the image can then be used to perform the
`triangulation.
`
`1064-004
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`1064-004
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`

`
`(2)
`
`where hAB is the average elevation of points A and B,
`Hvp is the approximate altitude, f is the focal length
`of the lens, and the distances between the points are
`ab and AB. The scale of the photograph is calculated
`from6
`
`scale = —f (cid:9)
`H
`
`(3)
`
`If the camera were truly vertical to the ground, then
`the ground coordinates would simply beta
`
`X (cid:9)
`A (cid:9)
`
`h
`f (cid:9)
`
`x a , y
`
`H — hA
`
`Ya
`
`H hB (cid:9)
`
`f (cid:9)
`H — hc (cid:9)
`f (cid:9)
`
`x, (cid:9)
`
`xc (cid:9)
`
`XB = (cid:9)
`
` C = (cid:9)
`
`H hi;
`B = f (cid:9)
`
`Yb (4)
`
`H h c
`
`Yc
`
`5.1 Assumptions
`
`The principle of triangulation is based on the
`fact that the ratio of two ground lengths computed
`from the ground coordinates of the tilted photograph
`must be the same as the ratio of the corresponding
`known ground lengths. To obtain two ratios, three
`lines are needed, so at least three points must be
`identified. This is assuming, of course, that three
`distinct points can be distinguished on the image, the
`distances between the three points on the ground can
`be calculated, and their respective elevations from sea
`level can be found as well. From these three ground
`points, A, 13 and C (Fig 6), the length between two
`pairs of the points can be determined analytically.
`Furthermore, the location of the three points on the
`globe will be known, so the position of the satellite
`can be determined if the tilt of the image is known.
`
`5.2 Determining Tilt
`
`A tilt t occurs when the optical axis is
`unintentionally deviated from the vertical axis
`coinciding with the direction of gravity." This is
`given by the angle oLn as shown in figures 6 and 7,
`where L is the position of the satellite moving in the
`+x direction, o is the center or principal point of the
`image, and n is the nadir point. The nadir point is
`the point on the photograph vertically beneath the
`satellites imager, or exposure station.
`From the three points on the image, two
`control lines can be formed to find two independent
`ratios such as those given in (8). From these ratios,
`the two components of the tilt on the photograph, tA
`and ty, can be determined, as well as the swing of the
`camera.? The x component relates to a change in
`pitch of the satellite, while the y component of the
`tilt is related to roll in the satellite. The swing is the
`direction of the tilt with respect to the photographic
`axes.
`
`The first step is to calculate the ground
`coordinates based on the photographic coordinates.
`The photographic coordinates are measured with
`respect to the lines joining the opposite fiducial
`marks, giving the three photographic coordinates
`corresponding to the ground points,
`
`(xa,Ya)
`
`( jcb' Yb)
`
`(xc , yc)
`
`C
`
`he
`
`(1)
`
`The altitude of the satellite can be approximated from
`the equation6
`
`5
`
`Figure 6 Three points on the ground represented by
`their corresponding points on a tilted image. The +x
`axis lies in the direction of the velocity vector."
`
`1064-005
`
`1064-005
`
`(cid:9)
`

`
`image plane
`
`ground plane
`
`Figure 7 Tilt is the displacement of the pitch or roll
`on the image plane relative to the ground plane14.
`
`However, taking a swing 9 about the y-axis with an
`induced tilt of t*, the ground coordinates are adjusted
`byt4
`
`x' =xcosO+ysin0
`
`
`y' = —x sin 0+ ycos0+ f tan t*
`
`(5)
`
`Repeating a similar rotational tilt about the x-axis
`yields x" and y". Then, substituting (5) into (4), the
`new equations for the ground coordinates become, in
`genera1,15
`
`Since the ground-control coordinates have now been
`determined, the ground-control lengths of the vertical
`photograph can be calculated by the distance formula
`to yield
`
`2
`
`AB =1((X B — X A) + (Y B — Y A )2)
`
`2
`
`AC = 4(X — X A) + (cid:9)
`
`— Y A)2 ) (7)
`
`BC=
`
`2
`C —XB)2 +( YC —YB)2
`Y C(X
`
`)
`
`Using the three lines above for the triangulation, the
`two ratios are then defined as14
`
`A GBG
`R (cid:9)
`G AGOG
`AGBG
`SG B GCG
`
`(8)
`
`If the camera were vertical or perpendicular to the
`Earth's surface, then the following ground ratios for
`the vertical image could be defined as
`
`A
`R =B
`AC (cid:9)
`V
`AB
`SV=T
`c
`
`(9)
`
`(6)
`
`If equations (8) do not equal the respective ratios in
`(9), then the photograph has some tilt since the ratios
`of the two lines' lengths are not the same. That is,
`the ratios of the lengths from the calculated ground
`coordinates on the photograph do not equal the ratios
`of the same control lengths on the ground.
`Assuming the satellite image will have some tilt,
`either in the pitch or roll, then 14
`
`R'
`
`— A'B'
`A'C' (cid:9)
`A'B'
`S' —
`B'C'
`A"B"
`
`A" C"
`A"B"
`B„ C"
`
`R"
`
`S" —
`
`(10)
`
`1064-006
`
`X — (cid:9)
`
`_ (cid:9)
`
`X" — (cid:9)
`
`Y"
`
`H h
`*
`f sec t • y' sin t
`H h
`* Y'cost*
`f sect — • y' sin t
`H — h
`f sec — y' sin
`H h
`* (cid:9) y, cos f
`fsect
`y'sint
`
`* x'
`
`*
`
`These X and Y coordinates are calculated for each
`point, A, B & C. X' and Y' represent the ground
`coordinates when the tilt is induced about the +y axis,
`while X" and Y" represent the ground coordinates
`when an arbitrary tilt is induced about the +x axis in
`a similar fashion. The lower case x and y in (6)
`represent the photographic x and y coordinates. See
`figure 11 for an illustration of X' and Y'. These are
`the calculated ground coordinates that will be used.
`
`6
`
`1064-006
`
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`

`
`0
`
`Y'
`
`x
`
`s
`
`n
`
`-
`
`x'
`
`Figure 8 The swing is the displacement of the
`image's coordinate system to the ground's coordinate
`system, ie. a rotation of axes.14
`
`53 Determining Swing
`
`The swing of the photograph is the angle
`measured in the plane of the image from the positive
`y-axis clockwise to a line from the principal point o
`to the nadir point n.14 This is illustrated in figure 8.
`The swing of the camera, s, is easily
`calculated as a function of the components of the tilt
`of the camera, as found when the equations in (15)
`were solved. It is defined as, 14
`tv (cid:9)
`
`(17)
`
`tan s =
`
`tx
`
`It' and S' are the ratios of the lines calculated when a
`tilt was introduced about the +y axis. Similarly, It"
`and S" are the ratios of the lines when an arbitrary tilt
`was introduced about the +x axis. These are found by
`substituting the equations in (6) into the lines defined
`by (7), and taking the ratios as in (8).
`From the information given thus far, the
`change in the ratios can be calculated as the change
`due to the lilt. That is, the change in the ratios due
`to the tilt ty of the camera for the y axis is
`
`R' —RV
`
`(12)
`
`The change in the ratios due to the tilt tx can likewise
`be defined as S'-S„. The rate of change per minute for
`the y axis is then14
`
`R' — RV *- ty, (cid:9) * ty(13)
`
`SV
`
`and
`
`(14)
`
`S" —
`
`SV (cid:9)
`
`t
`
`(cid:9)t
`
`x.
`
`R" —RV
`V (cid:9)
`*
`t (cid:9)
`
`for the tilt in the x axis.
`Since the equations in (8) represent the true
`ground ratios, the changes due to the components of
`the tilt are added. Adding (13) and (14) to the
`equations in (8) yields14
`
`R' — (cid:9)
`
`RG . RV +
`S'
`
`SG = SV + (cid:9)
`
`R" — RV
`
`
`tx
`
`£15)
`
`S"—
`
`+ (cid:9)
`
`' tx
`
`where s can easily be solved if the components of t
`are known. The amount of rotation 0 is defined to be
`
`0 = 1800 — s
`
`(18)
`
`The equations in (15) can then be
`simultaneously solved using linear algebra to find t,
`and ty, the two components of the camera's tilt.
`From the solutions to (15), the pitch and roll of the
`image, and consequently of the satellite, can be
`determined. Furthermore, once the two components
`of the tilt have been found due to the pitch and roll of
`the satellite, the angle t can be found. To solve for
`t,14
`
`t =1(tx2 + ty2 (cid:9)
`
`(16)
`
`Is used. Consequently, the tilt of the camera can be
`determined from the tilt of the image and the
`position of the satellite relative to the Earth can also
`be determined,
`
`Figure 9 The ground survey azimuth is simply the
`sum of the azimuth of the principal plane to the
`azimuth of the given control line 14
`
`7
`
`1064-007
`
`1064-007
`
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`

`
`(cid:9) (cid:9)
`
`5,4 Determining Azimuth (cid:9)
`
`The ground-survey azimuth from the North
`is given by'4
`
`then"
`
`allo = (74G — c(!) (cid:9)
`
`(22)
`
`as illustrated in figures 9 and 10. The azimuth, as
`defined in figure 10, will give information on where
`the satellite was located when the image was taken.
`
`(19) (cid:9)
`
`tan aG =
`
` — X
`X
`G2
`G1 (cid:9)
`YG —YG
`1
`2 (cid:9)
`
`5.5 Determining Ground Coordinates
`
`The ground-survey coordinates of the
`exposure station, or the camera, can also be
`calculated, provided that the azimuth of the
`photograph is known from equation (22). Let the
`ground-survey coordinates of the exposure station be
`XL and YL (Fig. 11). The ground-survey axes are
`defined as being X0 and Yo, and the ground axes
`based on the nadir point N and the principal plane are
`X and Y. The ground-survey coordinates of point A
`are then (Xon, YeA) and the ground coordinates are
`(XA, YA). If the X and Y coordinate axes are rotated
`through the positive angle allo, then the transformed
`coordinates of A become (X'A, Y'A). This
`transformation is achieved by'4
`
`X'. XcosaNo + Ysin aNo
`= -XsinaNo +Y cos aNo
`
`(23)
`
`Then the ground coordinates are determined by'4
`
`XL = XGA X' A
`Y = Y -3"
`L GA A
`
`(24)
`
`where ao is the ground-survey azimuth, and points 1
`and 2 are the endpoints of the control lines that were
`used for the calculations of the tilt and swing. If
`
`tan
`
`-X
`1
`2 (cid:9)
`P Y -Y
`2 1
`
`(20)
`
`where ap is the azimuth of the control line based on
`the set of ground coordinates where
`
`XL =0
`YL = 0 (cid:9)
`aNo .0e
`
`L
`
`(21)
`
`+X
`
`Direction
`of
`Flight
`
`Survey
`North
`
`Figure 10 The azimuth of the principal plane is the
`clockwise horizontal angle measured about the ground
`nadir point from the ground survey north meridian to
`the principal plane of the photograph.14
`
`Figure 11 Ground-survey coordinates of exposure
`station for a point A using determined azimuth.'4
`
`8
`
`1064-008
`
`1064-008
`
`(cid:9)
`

`
`6 Conclusions
`
`Using images from the Earth Reference
`Imager experiment, the attitude of the satellite can be
`determined, and the data from the attitude-sensors
`array confirmed. The GPS receiver will help confirm
`the satellite's relative position as well. But using the
`principles of triangulation, it is possible to determine
`the tilt of the camera, the swing, azimuth, and ground
`survey location at a given time, and consequently, the
`satellite's orbital parameters. With this method and
`with extremely small, lightweight and low-power
`cameras, the attitude of any Earth satellite at a given
`time can easily be determined from an image of the
`Earth.
`
`7 AcknQwiedpments
`
`This project is supported by the National
`Science Foundation, the NASA Space Grant
`Program, the Aerospace Research Center, and Arizona
`State University. Orbital Sciences Corporation is
`providing the launch, advising, and facilities, free of
`charge. Honeywell Space Systems Group, AMSAT
`Organization, Intel's University Support, Motorola's
`Satcom and University Support, Photocomm, Inc.,
`Trimble Navigation, Astro Aerospace, Universal
`Propulsion Company, Inc., ICI Fiberite Composites,
`Simula, Inc., DynAir, BekTek, KinetX, Rockwell,
`Sinclabs, Inc., Equipment Reliability Group, Bell
`Atlantic Cable, Gordon Minns and Associates, AERL
`(Australia), and Jet Propulsion Laboratory are also
`providing technical advising, hardware, and use of
`facilities.
`The author especially thanks Dr. Frank
`Aldrich, Dr. Paul Scowen, Dr. Helen Reed, Dr. Jordi
`Puig-Suari and Charles Hewett for their important
`contributions and support.
`The design and development of ASUSat 1 is
`a conglomeration of all students involved since its
`inception in October 1993 through August 1995.
`
`8 References
`
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`ment: 1.0 Overview." Arizona State University,
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`
`2 Potterveld, Curtis. "Systems Specifications Docu-
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`
`3 Hum, Jeff. GPS: A Guide to the Next Utility.
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`
`9
`
`4 Stillman, Catherine. "Systems Specifications
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`
`5 Gish, David. "Testing Procedures of the GPS
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`
`6 Baker, Wilfred H. Elements s,f Photogrammetty.
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`
`7 Slama, Chester C., ed. Manual of Fhologmin-
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`
`8 Kiefer, Ralph W. and Thomas Lillesand. Remote
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`
`9 VVL Vision Ltd. "VVL-1070 Monochrome Mono-
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`
`10 Wightman, Mark. "Systems Specifications
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`
`11 yo, pe- rry. "Systems Specifications Document:
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`
`12 Bowman, Roberta. "Systems Specifications
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`
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`
`14 Moffitt, Francis H. Photogrammetry. Pennsyl-
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`
`15 Crone, D. R. Elementary Photogrammetry, New
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`
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