attitude determination experiment conducted on the geostationary meteorological satellite

Acta Astronautica Vol.7, pp. 137-154 PergamonPress Ltd., 1980. Printedin Great Britain

A star scan/attitude determination experiment conducted on the Geostationary Meteorological Satellite? J. E. M c l N T Y R E ,

S. C. J E N N I N G S

AND R. C. C O X , Jr.

Hughes Aircraft Company, P. O. Box 92919 Airport Station, Los Angeles, CA 90009, U.S.A. (Received 8 February 1979)

Abstract--The paper discusses the results of a star scan test performed on the spin stabilized Geostationary Meteorological Satellite (GMS) and used for the purpose of determining the vehicle's spin state. The test data shows that the payload camera, normally used for imaging the Earth and its cloud cover, sees a sufficient number of stars to provide for a rapid and accurate spin state update and that Earth and Sun blockage constraints have essentially no impact on the star detection process. Also presented are analytical results regarding how many stars constitute an observable set, the accuracy achievable using the five most easily detected stars, how star location affects state uncertainty, and why certain state components are more easily determined than others. The primary test conclusion is that star scan offers an attractive alternative to the presently used Earth horizon and landmark tracking attitude determination methods, as far as accuracy and computational complexity are concerned, provided the occasional star viewing intervals that are required do not interfere with the meteorological scheduling of the camera.

Introduction ONE of the observing systems for the First GARP Global Experiment involves five spin stabilized synchronous meteorological satellites positioned at approximately equal intervals above the equator. Four of these satellites, two U.S. GOES vehicles (Hussey, 1974), the Japanese GMS (Harai et al, 1975), and the ESA METEOSAT (Imbert and Gault, 1975; World Weather Watch, 1975) are presently in orbit, with a fifth, the Russian GOMS, still to be launched. While these satellites are dissimilar in their design and operation, they all possess as primary payloads visible and IR imaging systems for day and night viewing of the Earth and its cloud cover. At geosynchronous altitude (35,800 km), small deviations in satellite orientation can produce significant errors in locating the different weather systems appearing in the downlinked pictures. In certain of the ground operations, for example, gridding (Ellickson, 1975) and wind velocity extraction (Leese and Novak, 1971; Whitney, 1972; Smith and Phillips, 1972), such errors can seriously affect forecasting accuracy so that a considerable effort must be made to keep them as small as possible. What is involved in locating a particular weather feature is a mapping which assigns to each pixel element an Earth latitude and longitude. The mapping consists of two parts or transformations: the attitude tPaper presented at the XXIXth Congress of the International Astronautical Federation, Dubrovnik, Yugoslavia, 1-8 October 1978. 137

138

J.E. McIntyre, S. C. Jennings and R. C. Cox, Jr.

transformation relating pixel (or camera) and inertial coordinates, and the orbital transformation relating inertial and Earth coordinates. Errors in determining the spacecraft orientation affect weather loeation in that they degrade the first part of the mapping. The orientation state of a spinning spacecraft is usually determined by means of scanning Earth and Sun sensors (Sierer a n d .Del Riego, 1969) or by star mapping devices (Mackison and Gutshall, 1973). However, the stringent accuracy requirements of synchronous meteorological satellites dictate that the payload scan camera itself be used to determine the vehicle's orientation state. To date, two such methods have been used operationally: a landmark tracking method (Fuchs et al., 1975) and an Earth horizon method (Doolittle et al., 1975). The present paper deals with yet a third method in which the spin state is determined by scanning the camera across known stars. An on-orbit test of this method was performed on the Japanese Geostationary Meteorological Satellite (GMS) during the preliminary spacecraft checkout phase in September 1977. The GMS primary payload is a Visible and IR Spin Scan Radiometer (VISSR) similar to that used on the SMS/GOES satellites. The rotation of the spacecraft provides the camera west/east scan while the north/south scan is accomplished by stepping an object space mirror. The scan geometry along with the detector layout is depicted in Fig. 1. A complete frame consists of 2500 IR lines (10,000 visible lines) normally covering the 20 x 20° space segment in which the Earth lies. The visible channels (used in the star scan test) are sensitive to radiation in the 0.5-0.9 ~ band and have a field of view corresponding to a 1.25 km ground resolution at the subsatellite point. To determine the spin state of the vehicle, the camera is scanned across known objects in space, with the difference between the predicted and actual object locations serving to update the state vector. Since the camera is Earth pointed, the set of scanned objects had been previously limited to the Earth edge and prominent Earth landmarks. However, preliminary investigations had indicated that scanning bright stars might constitute an attractive alternative. In particular, the stars being point sources are excellent radiometric targets and targets which the Earth's cloud cover never obscures. Also, because the stars are inertially fixed and infinitely distant, the spacecraft orientation can be evaluated independently of its orbit (i.e. the attitude and orbit processes uncouple). Finally, the use of stars to determine attitude is conceptually straightforward and numerically very simple in comparison with the use of Earth edge or Earth landmark data. For these reasons, a star scan test was devised for the GMS spacecraft and implemented during the on-orbit checkout phase. The special test sought to answer such questions as: how many stars are visible to the VISSR in its _+ 10° declination band of operation? Is there an adequate number for attitude determination purposes? How long need the camera be pointed away from the Earth in order to scan out a sufficient star set? Does blockage by the Sun, Earth and Moon, either directly or because of reflected sunlight entering the VISSR optics, affect the star scan process? And so forth. Because of test time limitations along with other checkout related problems, it was not possible to complete all the star testing that was planned. However,

A star scan~attitude determination on the Geostationary Meteorological Satellite

Spacecraft spin ax~s ~

N /~"---~"'~ [ \/

~

RadiatriOn

~ f ~ / ~l--~~mirror

J

~ //

_ ~

139

/

VISSR45" scan (scans 20"

'~'.--- Despun antenna Spacecraft axis (100 rpm)

S (o) Spin-scan Geometry

j

q

20= West-East Earth frame scan_ (spacecraft spin)

DI i

i

F--

J

/

[

t

T

20" North-South Earth frame scan ! I (2,500 scan mirror South II ~ [ ~ -r - i ~a~'P'jFOur . ' ~ ti n redundant channek ' - stepsin 25 Redundant. - - - ' " ~ I R ~Mnn==l / .~ ,,visible II IR channel IR channel / \ F o u r visible I O.14 X O. 14 mr channelsO.035mr X 0.031 mr $

I_ . . . .

,

• East - - - - - e Direction of scan (b) Image data format (not to scale) Fig. l. VISSR/Spacecraft spin scan geometry and image data format.

the tests that were performed did provide answers to most of the above questions, as will be shown in the following sections. In summary form, the VISSR easily sees five stars, any three of which will provide a complete state vector update. Of these five, one (Altair, in the constellation Aquila) has a far greater accuracy impact than the others and should always be included in any spin state determination process. While the accuracy achieved is at least comparable to that of the Earth edge and Earth landmark methods (Fuchs et al., 1975; Doolittle et al., 1975), some components of the spin state can be very precisely evaluated using stars and others cannot. This state of affairs indicates that the best accuracy would most likely result from some combination of stars with Earth edge and landmark data. However, there is one area of application where the star scan method is superior to the others. This is the interval immediately following a stationkeeping maneuver when the orientation state of the vehicle is most uncertain. A star scan at this time can provide an accurate state update almost immediately, while the other methods require anywhere from 6 to 24 hr of data collecting and processing. The reason for this is that the data must be spread out in right ascension in order to achieve an accurate update. With stars,

140

J.E. McIntyre, S. C. Jennings and R. C. Cox, Jr.

the right ascension spread is provided in seconds by the spinning motion of the spacecraft. Earth data on the other hand receives its right ascension spread from the satellite orbital motion which, at synchronous altitude, has a 24-hr period. Thus, the first few pictures following a spacecraft maneuver are more accurately processed using a star data update rather than the equivalent Earth edge or landmark updating process. Test set-up During spacecraft checkout, no software was available at the GMS Data Processing Center to assist in the star scan test. This meant that nominal pointing conditions had to be developed somewhat prior to the test and in a general enough format to accommodate changes in the test schedule. Also required was a method for detecting stars in the data stream which did not utilize a computer. The basic pointing reference for the VISSR is the Sun. The spacecraft camera and ground equipment are positioned in azimuth by means of a downlinked Sun pulse generated by the on-board precision Sun sensor. Hence, to determine nominal star pointing directions, the current estimate of the spacecraft spin state is used to evaluate the scan line number and the azimuth angle (as measured in the spin plane) from the detected Sun pulse at which the VISSR LOS would scan by the star in question. A list of several candidate stars for VISSR detection was computed (see Table 1) and nominal pointing conditions developed for each star for the entire month of September 1977. A partial set of this pointing data is shown in Table 2 for the star Betelgeuse. Note that the scan line number is fixed over the entire interval while the azimuth angle varies at approximately Earth orbital rate. A linear interpolation is used for pointing at times other than the 0 hr and 12 hr GMT conditions shown in the table. In addition to pointing information, data involving star blockage was also required. Such blockage occurs when either the Sun, Moon or Earth physically

Table 1. Candidate stars for VISSR detection LOCATION (SEPTEMBER 1977~ DECLINATION

RIGHT ASCENSION

NAME

Betelgeuse Risel

Procyon Altair

Hydrae Ceti Bellatrix c Orionis

Pegasi 60phiuchi

Serpentis 80phluchi

t

88.491 78.367 114.532 297.428 141.620 45.282 80.985 83.771 325.779 243.293 235.791 265.594

7,403 -8.226 5.282 8.814 -8.561 4,004 6.330 -1.215 9.777 -3.034 6.499 4.580

PROBABLE V~SSR OUTPUT, V" 0,309 0,146 0.141 0,087 0.047 0.035 0.035 0.034 0.032 0.027 0.O21 0.019

Full scale earth output at 1OO% albedo = 4.75 V

PROBABLE MULTIPLEXER QUANTUM LEVEL 15 I0 9 8 5 3 3 3 3 3 2 2

A star scan~attitude determination on the Geostationary Meteorological Satellite

141

Table 2. Predicted line number and azimuth angle for Betelgeuse ANGLE FROM SUN DETECTION TO STAR (DF,G) 12 HRS G ~ 0 HR GMT

SEPTEMBER 1 2 3 4 5 6 7 8 9 i0 ii 12 13 14 15

116.810 117.729 118.648 119.566 120.482 121.398 122.312 123.226 124.139 125.051 125.962 126.873 127.783 128.693 129.602

116.349 117.270 118.189 119.107 120.024 120.940 121.855 122.769 123.682 124.595 125.506 126.418 127.328 128.238 129.148

Angle of mirror LOS north (deg) Primary encoder line number Secondary encoder line number

7.074 -907 910

falls between the spacecraft and star, or when direct or reflected sunlight from one of these bodies obscures the star detection process. In fact, one important question which the test sought to resolve involved the star-to-body angular separation required for detection to occur. For this reason, a great deal of blockage data was generated for each candidate star again covering the entire month of September. For example, Table 3 presents typical Earth blockage data for the star Betelgeuse in terms of the time of day at which the star lies in 10, 20 and 40 ° angular regions from Earth center. As the VISSR scans by a star, one or two pixels in the data stream will register a higher voltage level. Normally, the "star" pixels would be identified by thresholding the data on a computer. Since no software was available for this function, an alternate star detection process was used. Specifically, threshold tables were inserted in the Synchronizer and Data Buffer (S & DB), the ground equipment unit whose function is to synchronize and buffer the VISSR data. Table 3. Predicted Earth blockage times for Betelgeuse SEPTEMBER 1 2 3 4 5 6 7 8 9 i0 II 12 13 14 15

I0 DEG 9:25:17 9:21:21 9:17:25 9:13:29 9:09:33 9:05:37 9:01:41 8:57:45 8:53:49 8:49:54 8:45:58 8:42:02 8:38:06 8:34:10 8:30:14

10:19:04 10:15:08 10:11:12 10:07:16 10:03:20 9:59:24 9:55:28 9:51:32 9:47:36 9:43:41 9:39:45 9:35:49 9:31:53 9:27:57 9:24:01

20 DEG 8:37:51 8:33:55 8:26:03 8:26:03 8:22:07 8:18:11 8:14:18 8:10:19 8:06:24 8:02:28 7:58:32 7:54:36 7:50:40 7:46:44 7:42:48

11:06:30 11:02:34 10:54:42 10:50:46 10:50:46 10:46:50 10:42:54 10:38:58 10:35:02 10:31:06 10:27:11 10:23:15 10:19:19 10:15:23 10:11:27

40 DEG 7:14:55 7:10:59 7:07:03 7:03:07 6:59:11 6:55:15 6:51:19 6:47:23 6:43:27 6:39:31 6:35:36 6:31:40 6:27:44 6:23:48 6:19:52

12:29:26 12:25:30 12:21:34 12:17:38 12:13:42 12:09:46 12:05:50 12:01:54 11:57:59 11:54:03 11:50:07 11:46:11 11:42:15 11:38:19 11:34:23

142

J.E. Mclntyre,S. C. Jenningsand R. C. Cox, Jr.

Table 4. S & DB threshold tables for star detection INPUT QUANTUM LEVEL (FROM S/C)

OUTPUT QUANTUM LEVEL (FROM S & D B ) -

0 i 2 3

0 0 0 O

o

n-i n n+l

63 63

62 63

63 63

Normally, these tables serve to correct small differences in responsivity among the several visible channels. For star detection purposes, however, tables such as that shown in Table 4 were loaded into the S & DB. Note that the output is zero for all input levels below n and maximum for all inputs above. Although any value of n could be chosen, only two or three different values were used because the operation of loading a new table was cumbersome and time consuming. However, there was a way of effectively modifying the threshold level without changing the look-up table. The VISSR data is amplified before it is sampled and quantized for transmission to the ground. This amplifier has four different gain steps or levels, each differing by a 1.414 factor. Hence, by increasing or decreasing the gain step, the data threshold level could be revised downwards or upwards. After processing by the S & DB threshold tables, the data was next displayed on an Image Monitor. The monitor was set in a mode which displayed all output data in a small segment of the scan window consisting of 125 lines in the vertical (north/south) direction and 0.6551 ° in the azimuthal direction (east/west). The camera was pointed, and the ground equipment was adjusted, so that a white dot-like star pixel would occur near the center of the screen if the star occurred at its predicted line number and azimuth angle. The actual star azimuth angle was evaluated from the east/west position of the white dot on the monitor screen, while the star detect line number was determined by noting the S & DB line number display at the instant the white dot appeared. On occasion a high resolution Laser Beam Recording (LBR) was made of the thresholded VISSR data and used for system noise and Earth/Sun blockage measurements. Test results The first attempt to detect stars was made using the Image Monitor on September 20, 1977. The results of the test are summarized in Table 5. The star parameters (/3o,/~, to) in column 2 of the table govern the azimuth angle from the Sun pulse to the left edge of the Image Monitor screen through the formula /3 = 13o-/~(t - to)

A star scan~attitude determination on the Geostationary Meteorological Satellite

143

Table 5. Star detection summary for September 20 test STAR pARAMETERS ~o

STAR

to = 0900

I

THRESHOLD LEVEL

GAIN STEP

COF~TS

I.

Betelgeuse

133.394 °

1

D e t e c t i o n o c c u r r e d n e a r l i n e 390 a t a p p r o x i m a t e l y 1 1 : 3 5 . W h ite d o t on image m o n i t o r was c e n t e r e d (left-to-right).

2.

Rigel

142.676 °

i

Detection occurred a b o u t llne 2370 at approximately 14:15. White dot was about 0.03 ° to right of center on image monitor screen,

3.

Altair

284.21 °

5

i

Detection on line 193 at about 14:45. White d o t was about 0.03 ° to left of center on screen.

4.

Procyon

107.268 °

5

I

Detection at 15:05:40 a t line 591. White dot centered on screen.

5.

~ Hydrae

79.461 °

5

6.

Procyon

107.268 °

2

Detection at 16:10:55 on line 597. White dot, a s in previous detection attempt, was a p p r o x i m a t e l y centered on the screen.

7.

~ Ceti

176.36 °

2

It appeared that detection did occur and on llne 890 at about 16:35 with the white dot centered ( l e f t - r i g h t ) .

3, 2

In gain setting 3 , about 30 white d o t s appeared on t h e image m o n i t o r s c r e e n indicating the system was thresholdlng on noise. In g a i n step 2 , two ~¢hite dots appeared. The first occurred on llne 2263 at 14:42:10. No record was made of the second. It was not d e t e r m i n e d if either dot corresponded to the star in question.

where t is the time of detection. Since the screen is 0.6551 ° wide, the position of the white dot on the screen together with the above formula is used in measuring the azimuth angle to the star. The threshold level in column 3 corresponds to the threshold parameter n in Table 4. The gain step, column 4, is the gain setting on the VISSR amplifier discussed in the preceding section. Step 1 is the normal setting, and steps 2 and 3 are 1.4 and 2 times higher, respectively. The detection of the first four stars in Table 5 was positive in the sense that only one white dot appeared each time and at approximately the same position on the Image Monitor screen. For the fifth star, a Hydrae, the VISSR gain was adjusted to gain step 3. The result was an Image Monitor screen covered with white dots. This behavior indicated the system was thresholding on noise spikes which, if they originated in the VISSR,, were now twice as strong as in the gain step I case. tAs opposed to the MUX, or link.

144

J.E. McIntyre,S. C. Jennings and R. C. Cox, Jr.

The situation improved with a gain step 2 setting, but still two white dots appeared when a Hydrae was scanned. Hence, it was decided to rescan the star Procyon in gain step 2, which produced about the same results as the gain step 1 scan except for a difference of 6 lines in which the star was detected, a difference which will be explained in the following section. For the last star in the table, detection was again attempted using the gain 2 setting. Since a white dot did appear which was centered east/west, it was felt that a successful detection had occurred. However, the detection would repeat only once in six attempts when it was tried again several days later. So there is some doubt as to just how well the VISSR "sees" this star. A second star detection test using the Image Monitor was performed on September 22. During this test some care was taken to record the precise line number and time at which detection occurred so that the measurements could be used to update the spacecraft spin state. The test was similar to that of September 20, except that the noise level in the data appeared to vary. The results are summarized in Table 6. As in Table 5, the detection of the first four stars in Table 6 was positive and unambiguous. The largest change occurred in the Rigel detection anounting to about 14 scan lines. Four attempts were made to detect a Hydrae with success achieved in three of them using both the 1 and 2 gain steps. In contrast, a Ceti was detected at most once out of six scans. Bellatrix was scanned five times using the 4 and 5 threshold settings. The four level appeared to be too noisy (although one legitimate detection may have occurred), while level 5 was too high. The general conclusion to be drawn from Tables 5 and 6 is that four stars can be detected on a regular basis in the threshold 5, gain step 1 setting. A fifth star, a Hydrae, can also be detected under these threshold and gain step conditions, but detection may not occur on every scan. As the threshold level is lowered to 4 or the gain step increased to 2, other stars may be detected on occasion, but the, detection will generally be masked by system noise. Of these two options for increasing the number of detectable stars, the gain step 2 condition is preferred, since it is somewhat less noisy than the other. Periodically during the tests, attempts were made to detect stars using the Laser Beam Recorder. One advantage of this method is that large sections of the sky (20° as opposed to 0.655 °) could be examined on a single display. However, the several films that were made and analyzed did not alter the conclusions reached in the Image Monitor tests. Where the LBR films were most helpful was in evaluating the effects of Earth and Sun blockage on the star detection process. Figure 2 is a sketch of a partial LBR film made as the lighted side of the Earth was approaching the star Betelgeuse. The lighted side appears black (maximum level) and without detail because of the level 5 threshold table. The limb is distorted (elliptical) because the camera is inertially pointed while the Earth moves toward the star at a rate of 15° per hour. At closest approach, the star is within 8° of the Earth; however, there is no trouble detecting the star--a situation to be expected since Betelgeuse is the brightest available star. What is unexpected in Fig. 2 is the presence of only three other starlike dots. One would

A star scan/attitude determination on the Geostationary Meteorological Satellite

145

suspect that some scattered light would enter the optics with the VISSR pointed so near the Earth. However, if this happens, the light level is below the 5 threshold state except in the three isolated conditions shown in the figure. The conclusion to be drawn here is that star blockage or interference due to the Earth will be rather minimal with the blockage time only slightly exceeding the time required for the Earth to pass by the star. A similar situation is expected for

Table 6. Star detection summary for September 22 test STAR PARA~M~TERS 80

STAR

= -0.038°/HR t = 0900 o

THRESHOLD LEVEL

GAIN STEP

COMMENTS

i.

Betelgeuse

135.217 °

1

D e t e c t i o n occurred at 15:40 on line 390. The white dot was a p p r o x i m a t e l y 0.06 ° to left of center on screen.

2.

Rigel

144.389 °

i

D e t e c t i o n occurred at 15:50 on line 2356 with the white dot a p p r o x i m a t e l y 0.16 ° to right of center.

3.

Altair

286.003 °

I

D e t e c t i o n occurred at 16:03 on line 194 with the w h i t e dot centered on screen.

4.

Procyon

109.091 °

i

D e t e c t i o n at 16:14 on line 584 with the white dot 0.05 ° to left of center on screen.

5.

~ Hydrae

81.284 °

6.

~ Ceti

178.179 °

7.

Bellatrix

142.653 °

8.

a Ceti

178.179 °

i, 2

5 4, 5

This star was scanned 4 times with the ~ o l l o w i n g results: SCAN i - D e t e c t i o n at 17:30 on 2252, white dot right of center by 0.07 ° (gain step i); SCAN 2 Detection at 17:55 on 2284, white dot at extreme right of screen (probably noise spike) (gain step I); SCAN 3 - Detection at 18=01 on 2255, white dot right of center by 0.07 ° (gain step I); SCAN 4 - Detection at 18:13 on 2250, white dot right Of center by 0.07 ° (gain step 2).

i

No d e t e c t i o n star area.

on two scans of

1

Star scanned once in threshold 5 with no detection. Star scanned 4 times in threshold 4 w i t h uneven results. On scan 2, d e t e c t i o n appeared to occur on line 510 and with star approxim a t e l y 0.06 ° to right of center. On scan 4, screen filled with white dots so level 4 threshold setting was abandoned.

2

Star scanned 4 times, no detection on 2 scans; a double det e c t i o n on scan 3 w i t h both white Idots a p p e a r i n g to be noise spikes and with an apparent legitimate d e t e c t i o n on scan 4 at line 894, with w h i t e dot very slightly left of c e n t e r .

146

J . E . McIntyre, S. C. Jennings and R. C. Cox, Jr.

Line 86

•~

Betelgeuse

Noise--x. •

J

6 ¸¸<

i~ i

/

iI _-

Line I 0 0 0

18.374 °

Fig. 2. Sketch of Betelgeuse partial scan on September 22 (threshold level 5, gain step l).

the Moon. However, no equivalent Moon test was performed because the Moon was outside the -+ 10° declination band of VISSR operation at the time. Two LBR pictures were made of the Sun and the Sun's image as provided to the VISSR optics by a reduced size collecting prism system. The Sun's image is a calibration signal which occurs 15° before the Sun and at the 50% albedo level. From examining these pictures, it was concluded that the blockage area of the Sun's images is essentially limited to its physical size (less than 1°) while the Sun will obscure the detection of any star which lies within approx. 15° of Sun center in the north/south direction and within 12.5° in the east/west direction. Figure 3 is a plot of the Sun's motion in right ascension and declination coordinates. Also shown is the Sun's image and the locations of the five most easily detected stars. Note that none of these stars are within 15° of the Sun's line of motion. Thus, their detection will never be obscured by the Sun. At worst, the Sun's image may interfere with two or three of the stars in question. But with the region of interference less than a degree, the interference will not persist for longer than one day. Hence, the Sun will have essentially no effect on an operational star scan mode which uses the five most easily detected stars. 25

•/Sun

20 ,5

J<,,, Altair

I0 5

-5 0 -I0 -15 -20 -Z5

I 20

l 40

I 60

I

O0

J

|

i

I00 120 140

i i I i i i 160 I I O 2 0 0 2 2 0 Z 4 0 ~

I 280

I 300

| J ~I~0 3 4 0

Rilht ascension, cle~rees

Fig. 3. Declination vs right ascension for Sun, Sun image and stars.

A star scan~attitude determination on the Geostationary Meteorological Satellite

Spin

147

Ze

axis ~r

(Telescopeaxis)

~ u

~ (Scanmirror e

x,

x [a) Camera system

(b] Spin axis location in XG ~ Z 6

Spin

Z

Z (South)

/ ~

8

Star LOS

I Y

X

(Vernal equinox)

x (¢) inertial system

[d) Spin axis locationin X Y Z

Fig. 4. Coordinate system definitions.

Analysis of results To update the spin state from the collected star data of the previous section and to evaluate the accuracy of the star scan method, a model of the system is required which in turn requires definition of the several coordinate systems shown in Fig. 4. The xayozo system is a camera system with za along the telescope axis and with Yo along the scan mirror axis of rotation so that the VISSR LOS lies in the xozo plane at some angle $ relative to the xG axis. The sun sensor slit is normal to the xGyo plane and makes an angle ~"with the xG axis. In ideal circumstances, the spin axis would be along the za axis. However, because of spacecraft balancing imperfections and alignment tolerances, the actual spin axis deviates from the zo axis by the two Euler angle rotations ~x about xo and 7/y about the intermediate y axis (Fig. 4b). Figure 4(c) defines an inertial X Y Z system with Z south and X toward the vernal equinox. A star is located in this system by means of the angles ~b and 0. Finally, the spin axis in this inertial system is located by the Euler rotations ex and e , as shown in Fig. 4(d). These later rotations are small since the spin axis nominally points south. The spin state of the vehicle is determined by the five angles ~ , ~y, ex, ~y and which locate the spin axis in camera and inertial coordinates, and the Sun sensor relative to the VISSR LOS plane. With the inertial directions of the star

148

J.E. Mclntyre, S. C. Jennings and R. C. Cox, Jr.

and Sun specified (in terms of the angles @ and 0 of Fig. 4c), the line number, tk, and the azimuth angle from Sun, /3, are easily computed once the five state angles are given. To update these angles from measured star data, the governing equations are linearized about the nominal state to develop a linear expression of the form ASx

=

BSy

(I)

where 6y is a vector denoting the difference in the measured and predicted star locations (i.e. the angles &k and 8/3 for each star) and 8x is the update in the five state angles. In what follows the specific form of 6x is important. Hence, this vector is defined to have the component representation

8x = (8~. 6"q~,8~, BE. &r)r

(2)

where superscript T denotes transpose.

Spin axis update from star measurements The star measurement data of Table 6 was used to update the spin state. This data is presented in more convenient form in Table 7. Note that the measured and predicted conditions are in close agreement except for the + 7 line number deviation for the star Betelgeuse. Since each line corresponds to 140 ~rad of rotation, this deviation is too large to be explained by system noise or some other error in the detection process. It was discovered shortly after the test that the spin axis was oscillating relative to the camera coordinate system with a zero-to-peak amplitude of 0.056 °. The oscillation resulted from a thermal pumping of hydrazine in the propellant system. The pumping action was subsequently eliminated by changing the propellant line heater duty cycle. However, its presence during the test did cause the small shifts in the star detection line number discussed in Tables 5 and 6 and was largely responsible for the 7 line deviation in the detection of Betelgeuse shown in Table 7. The state updates were made by means of the formula

8x

=

(ArA)-IArBSy

(3)

Table 7. Measuredand predicted star pointing conditions

STAR i. 2. 3. 4. 5.

Betelgeuse Rigel Procyon Altair ~ Hydrae

MEASURED DETECTION CONDITIONS

PREDICTED DETECTION CONDITIONS

DETECTION TIME

SUN/STAR LINE ANGLE NUMBER

SUN/STAR LINE ANGLE NUMBER

15:40 15:50 16:14 16:03 17:30

135.80 °

135.763 145.120 109.659 286.581 81.975

JST JST JST JST JST

145.137 109.643 286.600 82.004

390 ° 2356 ° 584 ° 194 ° 2252

383 2355 585 194 2251

DIFFERENCE: MEASURED - PREDICTED 6 (SUN/STAR ANGLE)

6 (LINE NUMBER)

+ 0 . 0 3 7°

+7

+0.017 ° -0.016 ° I+0.019 ° +0.029 °

+1 -I 0 +I

A star scan/attitude determination on the Geostationary Meteorological Satellite

149

Table 8. Updated spin ~xis orientation parameters ORIGINAL pARAMETER VALUES

Attitude - c Attitude _ x Tilt - ~x Y Tilt Sun S e n s O r Azimuth -

R = Rigel,

UPDATED pARaMETERS USING A L L 5 STARS

44.70 °

P = Procyon,

UPDATED P A R A M E T E R S USING3 STARS

R, P, A

R, A, AN

P, A, AH

° ° ° °

0.300 ° 1.072 ° 1.687 ° -0.002 °

0.704 ° 1.077 ° 1.715 ° -0.000 °

0.306 ° 1.077 ° 1.738 ° -0.005 °

0.268 ° 1.025 ° 1.679 ° -0.O06 °

44.719 °

44.710 °

44.707 °

44.721 °

44.707 °

0.317 1.096 1.717 -0.007

0.303 ° 1.078 ° 1.750 ° 0.0 o

UPDATED p~AMETERS USING 4 STARS E, P, A, AH

A = Altair,

AH = (I

Hydrae

where A and B are defined in eqn (1). This corresponds to a least squares estimate under the assumption that the 8y components are independent and have zero mean and equal variance. The results of the updating process are summarized in Table 8 for several updating procedures in which different star combinations are used. Using all five stars, the table data shows the updated inertial attitude is within 0.021 ° of the original estimate, the tilt amplitude within 0.033 °, and the Sun sensor azimuth within 0.019 °. This is good agreement considering the inaccuracy of the Image Monitor detection process (on the order of 0.02 °) and the _+0.056 ° spin axis oscillation. When the Betelgeuse data is removed, the 4-star updates show a small variation from the 5-star case in both the inertial attitude and tilt components. Similar variations occur in the 3-star cases. Only three such cases are considered; namely, those in which Betelgeuse is excluded (because of the large line number deviation in Table 7) and in which Altair is included (Altair is necessary for accuracy as will be shown shortly). Because of the oscillatory spin axis motion, it is difficult to draw any conclusions from Table 8 or to make any statements regarding the accuracy of the star scan update process. Rather, a resort to analytical methods was made to assess the process accuracy. Accuracy of the star scan attitude determination process To estimate accuracy, an analysis of the estimation process in eqn (3) is performed under the assumption that in an operational star scan mode with computer detection each star could be located to within one pixel element or 35/~rad in both the east/west (scan) and north/south (mirror stepping) directions. Assuming further that there is no systematic bias and that the measurement errors associated with different stars are independent, the statistics on the measurement vector, By in eqns (1) and (3), can be expressed as E(By) = O;

E(SyBy r) = o-2I

where E is the expectation operator, I the unity matrix, and 3o- is equal to 35 grad. Hence, rewriting eqn (3) as

150

J.E. Mclntyre, S. C. Jennings and R. C. Cox, Jr.

6 i = WSy;

(ArA)-'ArB

W =

(4)

it f o l l o w s that E ( S i ) = 0;

E{(Sx - 8 i ) ( 8 x - 81) r } = cr2WW r.

(5)

The purpose of star scan is to determine the state vector update as accurately as possible. A measure of this accuracy is the covariance matrix in eqn (5). For example, E ( S x --

5 8i) 2 = O.2 ~ /~i I

Or2&min~ E ( 6 x - 6 i ) 2 -- O'2~max

l~l

0-2 5 -5- '~l Ai

----

E(~xi

-

-

~.~i)2

where )t~ are the eigenvalues of W W r. Thus the eigenvalues of W W r are a measure of the state vector update accuracy. These eigenvalues are listed in Table 9 for the five easily detectable stars and for all three and four star groups within this star set. The eigenvalues are c o m p u t e d for the desired nominal spin state in which the tilt angles, rh and ny, and the attitude angles, ~ and ~ , are zero. The deviations from this nominal state will be small and have little effect on the eigenvalues. An examination of Table 9 indicates several interesting features: (1) Using five stars in the update process, the 3or uncertainty in the state Table 9. Eigenvalue summary for the covariance matrix WW r (tilt amplitude zero, spin axis pointed south) STARS USED IN UPDATE PROCESS

5 ~]~ i i

5 (9.)/5 1 x

% -MAX

"MIN

I.

B, R, P, A, AH

13.421

2.684

11.221

0.1362

1.

B~ R, P, A

2. 3. 4. 5.

B, B, B, R,

R, P, All

23.410 82.918 14.452 20.466 15.988

4.682 16.583 2.890 4.093 3.198

18.547 65.119 12.032 17.381 13.340

0.172 0.1364 O.1853 0.1783 0.1834

i. 2. 3. 4. 5. 6. 7. 8. 9. i0.

B, B, B, B, B, B, R, R, R,

R, R, R, P, P~ A, P, P, A,

1114.9 41.549 137.67 629.16 227.73 21.079 26.07 100.07 19.429 27.757

222.98 8.31 27.534 125.83 45.546 4.216 5.215 20.014 3.886

1082.9 27.198 115.24 621.06 201.27 17.71 20.292 70.207 16.435 19.857

0.173 0.2487 0.186 0.256 0.1785 0.2756 0.2615 0.1837 0.2867 0.2568

R, A, AH P, A, AH P, A, AH

P A, AH A AH AH A All AH

P~ A, AH

5.551

B = Betelgeuse, R = Rigel, A = Altair, P = Procyon, AH = ~ Hydrae

A star scan~attitude determination on the Geostationary Meteorolpgical Satellite

151

Table 10. Eigenvectorsummaryfor the covariance matrix WWr EIGENVECTOR COMPONENTS STARS USED A.

6Xl

6x 2

6x 3

6x 4

-195.01 0.4609 -0.0084 -0.585 0.0008

4.096 2.9188 1.O21 0~289 -0.849

11.421 6.629 -0.060 1.501 0.222

6x 5

Ei~envectors for the 5-Star Case Betelgeuse Rigel

Procyon Altair Hydrae

B.

EIGENVALUE

11.221 0.13689 0.4959 0.1996 0.1362

1.0 1.0 1.0 1.0 1.0

-3.742 -0.3231 -0.011 35.66 -0.0305

,Ei~envectors for the 4-Star Cases

(i) Betelgeuse Rlgel

Procyon Altair (2) Betelgeuse Rigel

Procyon Hydrae (3) Betelgeuse Rigel Altair

Hydrae (4) Betelgeuse Procyon Altair

Hydrae (5) Rigel Procyon Altair

Hydrae

18.547 3.944 0.4975 0.1722 0.2491

1.0 1.0 i .0 1.0 1.0

-48.95 0.512 -0.015 0.002 101.43

1.24 1.3 1.072 -0.909 4.53

5.34 4.185 -0.57 -0.043 -31.92

-2.98 -0.043 -O.013 -0.002 -1721.7

65.126 16.038 0.1364 1.375 0.2499

1.0 1.0 1.0 1.0 1.0

0.1165 -17.51 -0. 0002 2.31 1.45

1.03 1.45 -0. 883 7.57 0.226

-0.378 1.19 0.237 24.0 0.817

-0.014 0.297 -0.013 -0.331 77.65

12.03 i .486 0.5009 0.1853 0.2487

1.0 1.0 1.0 1.0 1.0

-221.3 0.296 -0.008 0.0003 0.050

2.84 2.267 1.13 -0.808 0.058

9.96 5.827 -0.615 0.136 1.26

-0.164 -0.538 -0.018 -0.071 15.8

17.38 0.50 0.178 2.157 0.249

1.0 1.0 1.0 1.0 1.0

-350.0 0.008 0.0028 2.29 -0.776

10.5 0.99 -0.816 16.41 0.108

18.7 -0.526 0.375 32.9 0.269

-20.6 -0.071 -0.075 -0.728 13.51

13.342 0.4966 1.719 0.183 0.248

1.0 i .0 1.0 1.0 1.0

-688. 9.62 -0.003 i .03 0.473 6.52 0.0003 -0.791 -16.7 -38.67

21.77 -0.591 12.53 0.314 -116.8

6.44 0.022 -1.29 -0.0038 -1330.

vector, E ( S x - 8 ~ ) 2, is 3.66 times the 35/~rad field of view. Similar accuracy is very nearly achieved in two of the 4-star and several of the 3-star cases. (2) Altair is a key star in that the uncertainty, E(Sx - 8i) 2, sharply increases in the 4- and 3-star cases in which this star is omitted. (3) The average uncertainty in any one state component is proportional to 5

{(E Ai)/5} '/2. This measure, while not particularly useful, appears occasionally in 1

the literature in evaluating attitude determination accuracy. For the 5-star case, the average 3o- value is 1.64 times the field of view. Accuracy close to this value occurs in some of the 4- and 3-star cases. (4) A comparison of the maximum eigenvalue with the eigenvalue sum (columns 2 and 4) shows that the two do not differ widely. Hence, one eigenvalue of the set is much larger than the others, a situation indicating that a single component of the state vector (or a linear combination of components) cannot be accurately determined. The eigenvectors for the 5- and 4-star cases are shown in Table 10, with the first component of each eigenvector normalized to unity. The eigenvector

152

J . E . Mclntyre, S. C. Jennings and R. C. Cox, Jr.

components are the components of the state vector 8x in eqn (2). For the 5-star case, the eigenvector corresponding to the largest eigenvalue (Amx = 11.221) has a very large second component in comparison with the size of the other components. That is, the eigenvector can be approximated by a vector with a nonzero second component and with all other components zero. Thus, the maximum eigenvalue is a measure of the uncertainty in the second component of the state update, the component corresponding to the tilt variable rh in eqn (2) and Fig. 4(b). Hence, the conclusion to be drawn is that a star scan process involving the five easily detected stars provides very good information on four components of the state vector and relatively poor information on one component. Turning next to the 4-star cases in Table 10, a similar trend is apparent in four of the star combinations--the four involving the star Altair. With this star included, the uncertainty in four state component updates is small compared with the uncertainty in the ,x tilt component.t For the 4-star case without Altair, the maximum eigenvalue (Amax=65.126) does not produce an eigenvector dominated by the */x component. However, the second largest eigenvalue does (A = 16.038). Although the data is not presented, the 3-star cases behave the same with the six containing Altair, having the largest eigenvalue correspond to the uncertainty in the skew tilt component, and with the second largest eigenvalue applying in the four other cases. To explain the above behavior, note from eqns (1) and (4) that a state estimate, 8x, is possible only if the matrix A has maximal rank or, alternately, if determinant [ArA] # 0 . An examination of A for the zero tilt and attitude nominal solution indicates that for a nonzero determinant condition to hold: (1) at least three stars are required, (2) the declination of the various stars must differ, and (3) the right ascension of the various stars must differ. These conditions are necessary but may not be sufficient. Thus, if one selects five stars spread out in right ascension but with the same declination, they will not yield an estimate of 8x since ArA will be singular. Another way of stating the" same result is that the matrix WW r will, in this case, have an infinite eigenvalue. Thus, the eigenvalues of WW r approach infinity as either the right ascension or declination spread between the various stars goes to zero. Since the eigenvalues of WW r are a measure of the accuracy of the method, it is important that the stars' angular separation be large if good results are to be achieved. The plane of the galaxy intersects the equatorial plane along the 5 hr 17 min/17 hr 17 min right ascension line with the visible stars tending to gather at both ends of this intersection. As can be seen from Fig. 3, four of the five candidate stars are closely grouped in right ascension along the incoming intersection. Altair is by itself at the other end and provides a spread in star right ascension which will tend to reduce the engenvalues of WW T and, hence, the uncertainty of the estimate 8x. It is this effect that makes Altair so important in the star scan process and distinguishes it from the other star candidates. The t S i n c e the tilt angle ~x c a u s e s a skewing of the downlinked weather pictures, it is referred to here as the skew c o m p o n e n t of tilt.

A star scan/attitude determination on the Geostationary Meteorological Satellite

153

data in Tables 9 and 10 indicate that in the absence of Altair it is difficult to separate the 7/y tilt c o m p o n e n t from the ex attitude angle. When Altair is present, the most difficult state c o m p o n e n t to estimate is the skew tilt component. The reason is that VISSR operation is limited to the - 10° declination band, and r/x is the state c o m p o n e n t most affected by this limitation. For example, if tilt were the only unknown in the state vector, a single star sighting would fix the r/y tilt c o m p o n e n t to within the measurement accuracy (i.e. 35/zrad, 3tr). The skew tilt uncertainty on the other hand would be 7 times as large (i.e. 7.16 × 35 g r a d , 3tr) for a star declination of 8 °, and would go to infinity as the declination went to zero. For zero declination, the skew tilt c o m p o n e n t constitutes a rotation about the vehicle-star line and the star itself provides no information on the size of this rotation. A similar situation holds for several stars. The skew uncertainty decreases as the declination spread of the various stars increases. The fact that star scanning does not provide an accurate update for the tilt c o m p o n e n t r/x is not particularly serious. The reason for this is that skew is the one state variable that is accurately measured with VISSR Earth horizon data and on the basis of a single picture. The accuracy stems from the fact that horizon information on 1000 or more data lines enters i~to the measurement process, a situation akin to using 1000 stars in the star detection process. Thus, a combination of VISSR Earth horizon data and star data should provide excellent state estimation accuracy and in a reasonably short time interval. Conclusions The star scan test shows star scanning to be a practical and attractive attitude determination method. The camera easily sees five stars: Betelgeuse, Rigel, P r o c y o n , Altair and a Hydrae. Camera star detection is unlikely for stars within 15° of the Sun. Since none of the above five stars fall within this envelope at any time of year, Sun interference with their detection is not expected. Sun image and Moon interference will occur but the time periods are so short and the intervals so infrequent that no problems are anticipated. The Earth will block out each star for some part of each day but never for longer than 1 hr 20 min. At least three stars are required to update the state vector. The time required to scan out a small region about each of three stars should take less than 15 rain on an operational basis. The key star for accuracy is Altair. Any 4-star group and many 3-star groups containing this star will provide accuracy very nearly equal to that resulting from the use of all 5 stars. The 3tr uncertainty in the state vector amplitude is on the order of three to four visible channel fields of view. The average 3~ uncertainty in any one component of the state is less than two fields of view. When Altair is one of the detected stars, four of the state vector components are determined very accurately and the fifth to much lower accuracy. The inaccurate c o m p o n e n t is that part of the spin axis tilt vector which produces a skewing of the camera weather picture. To place star scan (SS) in perspective, a brief qualitative comparison with the two other attitude determination methods, VISSR Earth horizon (VEH) and

154

J . E . McIntyre, S. C. Jennings and R. C. Cox, Jr.

landmark tracking (LT) is in order. For the VEH and LT methods, data must be collected over a long data arc (approaching 24 hr) to achieve good estimation accuracy, while the SS method takes about 20 rain. This collection time is important after an abrupt attitude change following a maneuver, since the long data arc requirement prevents accurate state estimation until after several pictures. For VEH and LT, the attitude information is contained in the picture data stream as a useful by-product. For SS, the picture schedule must be interrupted to collect attitude data. In addition, there are not a lot of stars that the camera sees so that measurement errors go unsmoothed and can substantially affect the state estimate. However, the data handling and processing algorithms of SS are simpler with less computer time and capacity required. In short, the methods tend to complement each other, with best results most likely achieved through some combination of the three. Acknowledgements--The test described in this paper could not have been performed without the cooperation and encouragement of the National Space Development Agency of Japan (NASDA) and the Japanese Meteorological Agency (JMA). The authors gratefully acknowledge the assistance of the following individuals who directly participated in the star scan test: Mr. Y. Suzuki of NASDA, Messrs S. Ueda and T. Fukui of JMA, Mr. K. Tano of NEC, and Messrs H. Ausfresser and C. Boykin of Westinghouse.

References Doolittle R., Ellickson J. and DeMeo J. (1975) Attitude determination support for the SMS/GOES satellites. In Central Processing and Analysis of Geostationary Satellite Data (Edited by C. Bristor) Chap. 3. NOAA Tech. Memorandum NESS-64. Ellickson J. (1975) Earth locator grids for VISSR images. In Central Processing and Analysis of Geostationary Satellite Data (Edited by C. Bristor) Chap. 5. NOAA Tech. Memorandum NESS-64. Fuchs A., Velez C. and Goad C. (1975) Orbit and attitude state recoveries from landmark data. Paper No. AAS 75-508 presented at the AAS/AIAA Astrodynamics Specialist Conf., Nassau, Bahamas. Hirai M., Watanabe K., Tsuru H., Miyagi M. I. and Kimura M. (1975) Development of Geostationary Meteorological Satellite (GMS) of Japan. Paper presented at the l lth Int. Syrup. on Space Technology and Science, Tokyo, Japan. Hussey W. J. (1974) The geostationary environmental satellite system. Paper presented at the EASCON-74 Conf. Washington, D.C. lmbert R. and Gault P. (1975) Le satellite meteosat. Paper presented at the 14th European Space Syrup. Toulouse, France. Leese J. and Novak C. (1971) An automated technique for obtaining cloud motion from geosynchronous satellite data using cross correlation. J. Appl. Meteorol. 10, 118-132. Mackison D. and Gutshall R. (1973) Star scanner attitude determination for the OSO-7 Spacecraft. J. Spacecraft and Rockets 10, 262-267. Sierer W. and Del Riego J. (1969) TACSAT attitude determination. Proceedings of the Symposium on Spacecraft Attitude Determination. The Aerospace Corporation Report TR-0066(5306)-12, Vol. 1. Smith E. and Phillips D. (1972) Automated cloud tracking using precisely aligned digital ATS pictures. IEEE Transactions on Computers C-21,715-729. Whitney L. (1972) Effect of orbital inclination and spin axis attitude on wind estimates from photographs by geosynchronous satellites. NOAA Tech. Memorandum NESS-41. World Weather Watch (1975) Satellite subsystem, information on meteorological satellite programs operated by members and organizations. World Meteorological Organization Rep. No. 41 I, Geneva, Switzerland.