Autonomous Star Tracker Development

Copyright © IFAC Automatic Control in Aerospace. Onobrunn. Gennany, 1992

AUTONOMOUS STAR TRACKER DEVELOPMENT R.W.H. ,an 8ezooijen Lockheed f'a lo Alto Research lLlhoratory . 3251 Hanover Street. Palo Alto. CA 94304. USA

~.

The aUitude control. pointing control. and navi gation systems of future advanced spacec raft will be characterized by a high degree of autonomy. very hi gh accuracy. efficient commandability, and fast fault recovery. These characteristics are incompatible with the constraints of conventional star trackers which mandate a-priori definition and careful pre parati on of each on-board auitude tix. and only work if auitude uncertai nties are small. With the availability of a highly-e fficient, non-iterative star pattern recognition algorithm. accurate CCD star trackers. fast microprocessors. and high density me mory chips. it is now feasible to build an Autonomous Star Tracker (AST ) capable of determining its auitude rapidly and reliably without having any a-priori auitude knowledge. The Lockheed Pal o Alto Researc h Laboratory is developing an AST prototype that will use the true sky to de monstrate its capabilities. In addition to being capable of aUitude acquisition. the AST is designed to also perform autonomous attitude updating and to provide attitude information continuously. The paper describes a number of functions that are enabled or e nhanced by the AST, including: gyroless/cheap-gyro aUitude control. attitude safing , fast fault rec overy. autonomous acquisition of celestial targets by space-borne astronomy telescopes, autonomous optical navigation. precisi on pointing to terrestrial targets. and unc al ibrated attitude acquisition. In addition. an overview of the star paue rn recognition algorithm is provided, a thorough. computer simulation program using a 248.516 s ta r catalog is described. and simulation results are presented. These simulations show that an anti-blooming capable AST with an 11.3 degree FOY diame ter. a 4148 guide star database, and a MC68030 class microprocessor performs an attitude acquisition in 0.6 seconds with a success rate of99.25%. Rai sing this number to IOO% should be achieved easily by selecting the guide stars more carefully.

KEYWORDS . Intelligent sensors. star trackers. pattern recognition , attitude determination, autonomous systems, space vehicles, optical navigation. inertial navigation, fault recovery, position determination.

UNCERTAJNTY AREA

INTRODUCTION +

The attitude control, pointing control, and navigation systems of future advanced spacecraft will be characterized by a high degree of autonomy, very high acc uracy, efficient commandability, and fast fault recovery. These characteristics are incompatible with the constraints of conventional star trackers which mandate apriori defmition and careful preparation of each on-board attitude fix. onl y work when attitude unce rtainties are small , and , for some applications, require a human operator for closing the loop. In additi o n to being incapable of fulfilling the needs of future s pacecraft systems. conventional s tar trackers are c urre ntl y costl y to use due to their lack of intelli gence, which necess itates the ex penditure of significant human , ground so ftware . uplink. on-board storage. and telemetry resources.

GUIOESTAR

o

OBSERVED STAR

•

OBSERVED GUIDE STAR

Xo

EXPECTEO LOCAT1ON OF STAR

mACKER FIELD OF VlEW TRUE LOCAnOH Of STAR

TRACKER FIELD OF VSEW

Fig. 1. Attitude De termination Problem. computer simulati on program needed for predicting the AST performan ce. This paper describes a number of AST applications. outlines th e development approac h. gives an overview of th e sta r identification algorithm, descrihes the si mul ation program. and presents computer si mul ation results.

With the availability of a robust. highly efficient star pattern recog niti on algorithm (van Bezoo ijen. 1989a and 1989b ). accurate CCD cameras. fas t mi croprocessors. and high density memory c hips. it is now feasihle to build an Autonomous Star Tracker (AST) capab le of de termining its attitude rapid ly and reliahly wit hout having any a-priori auitude kn owledge. In the past. analys is was used to show that an AST with a field of view mea suring Il.~ degrees in diameter. a 10 arcsec (I s igma ) s patial accu racy. an all-sky datahase of some 4,100 guide stars. an d a n MC6ROOO class mi c ro processo r. is capable o f determining its attitude in approximately I seco nd with a success rate very close to lOO'fto (van Be zoo ije n. 1986 and 1989a).

The computer simulations arc performed for an AST with an 11.3 degree FOY diameter (FOY area of 100 square degrees ). Thi s FOY is sufficiently large to ensure fast and reliable star ide ntificati on at the cost of a moderate amount of memory , and it is small enough for achieving a high AST accuracy. While reducing the amount of me mory required, ASTs with a larger FOY have many disadvantages, including: (I) higher probability of inte rfere nce fr om th e Sun. the Earth. and the Moon. (2) more complex optical design. (3) increased optical distorti on, (4) more difficult to accomm odate o n the spacecraft, and (5) lower accuracy. In addition, a preliminary analysis shows tha t. for a co nstant focal ratio, the integration time does not decrease with an increase in the FOY. Going from a circular to a more practical square FOY is expected to have a negligible effect on the performance. In the following, the AST with the 11.3 degree FOY diameter is called the "Reference AST" .

The Lockhced Palo Alto Researc h Lah oratory is currently de ve lop ing an AST pro to t y pe that incorporates the aforementioned sta r id en tifi cati on alg o rithm . This AST is designed to operate in three different modes. In the "acquisition mode." the tracker is requi red to determine its altitude without having any a-priori attitude knowledge. In the "update mode," it is prov ided with its expec ted anitude and its atti tude e rror and is requested to re turn its meas ured anitude. The AST will output its altitude co ntinu ousl y a t frequencies up to 10 Hz when operating in the "continuous mode ".

The attitude determination proble m requiring star identification is illustrated in Fig. 1. Due to attitude errors, the coordinate system assoc iated with the star tracker (Xo • Y o • Zo) deviates from its expected inertial orientation (Xi. Y i . Z;). Employing

In additi o n to huilding and testing the AST prototype. the research program also invo lves the evaluation of different guide star selection algorithms and the development of a reliable

513

geometric and brightness criteria. the star identification algorithm determines which of the stars observed by the tracker (the "observed stars") correspond to which of the a-priori selected "guide stars". If at least two of the observed stars are guide stars. and these stars are correctly identified . the attitude about all three axes (angles Cl, ~, and y) can be computed. The area in which the guide stars are selected, referred to as the "uncertainty area." needs to be sufficiently large to ensure that it will include the field of view of the star tracker. In the case of the AST acquisition mode. the uncertainty area covers the entire sky. As is illustrated by Fig. 1. some of the guide stars within the FOV of the STR may not be observable. while some of the observed stars may be non-guide stars. The recognition algorithm needs to be sufficiently robust to cope with this situation.

a collision avoidance maneuver. The AST would enable the ACRV to achieve this attitude within the limited time available. Combined with a GPS receiver. the AST enables autonomous, high-precision pointing to terrestrial targets as is required for laser communication and efficient ground observation. Assuming a I arcsec accuracy for the newest generation CCD trackers, it should be feasible to point to terrestrial targets with a better than 20 m accuracy from an altitude of 500 km . An AST. integrated with a device for measuring the direction of the local vertical (e.g .. a three-axis accelerometer) enables planetary rovers to determine their position autonomously. To achieve this. the AST is used to determine the inertial direction of the local vertical. Given the time of the star field observation and the inertial direction of the local vertical, the position of a vehicle on Mars can be computed to an accuracy of a few hundred meters.

APPLICA nONS Applied to high-precision space-borne astronomy telescopes, the AST (coboresighted with the telescope) allows automation of target acquisition. Following a slew to a new target, the AST. operating in the update mode. provides its. and hence the telescope's attitude. down to an error that is small relative to the field of view of the Fine Guidance Sensor (FGS). This allows the FGS to acquire its tracking stares) used for pointing control. following a correction of the post-slew pointing error. Relative to other automated acquisition methods (van Bezooijen, Lorell. and Powell, 1985), the AST eliminates the need for ground selection and on-board storage of guide stars around each target (in addition to the tracking stars).

DEVELOPMENT APPROACH The AST research program depicted in Fig. 2 involves three main activities : guide star database generation. creation of a computer simulation program for predicting the AST performance, and demonstration of the AST performance using a prototype and the true sky. The simulation program is described in a separate section. GUDESTAR DATABASE GEHERATlON

Used for updating the attitude of gyro-based attitude control systems. the AST eliminates the need to perform ground selection and on-board storage of guide stars for each planned update. Operating in the update mode. the AST performs an attitude fix upon request from the attitude control system. Since there is no penalty for performing frequent updates, the AST can be used either to improve accuracy. or to reduce cost by allowing the use of cheaper. less accurate gyros. Because the AST can provide its attitude continuously. it would be possible to eliminate gyros in a number of cases.

COIIPlITU YlULAnON OF AST PEf\. FORMANCE

TRUE·SKY

ASTPER· FOAIIANCE DEMON-

STRAnoNS

The AST is also ideally suited for updating the attitude of strapdown inertial navigation systems. Due to the absence of an inertial platform, these systems need more frequent attitude updates to maintain navigational accuracy. In addition to being able to perform updates at the desired frequency, the all-sky capability of the AST eliminates the need to reorient the vehicle for updates.

WITH AST PROTOTYPE

Fig. 2. AST Development Approach. Guide Star Database Generatjon. The guide star database needed for performing star identification consists of: (1) The position and predicted AST brightness of the selected guide stars, and (2) All pairs of guide stars having a mutual angular distance less than a certain value. typically chosen to be equal to the greatest FOV dimension. The guide stars are obtained from the SKYMAP version 3.3 star catalog (McLaughlin. 1989) which has been compiled primarily for the purpose of satellite attitude determination and provides 622 bytes of information for each of its 248.563 stars.

Operating in its acquisition mode, the AST will allow fast recovery from faults that cause a loss of attitude knowledge. This is important for systems where outages are very costly. or where a loss of attitude could lead to catastrophe if not remedied quickly. The Space Infrared Telescope Facility (SIRTF) and the Cassini planetary spacecraft are examples of spacecraft where an AST could be used to avert catastrophe.

We can either assume the AST magnitude of the guide stars to be the same as the visual magnitude given in the catalog, or we can translate the visual magnitude of the stars to the AST magnitude using the spectral response of the AST and the spectral star information provided by the catalog. In the former case we can either accept a large error in the predicted AST magnitude of the guide stars, or we have the option to minimize this error by adding an optical filter to the AST to bring its spectral response closer to that of the V filter.

Following a fall-back to the safe mode operated from ROM, SIRTF (Eisenhardt and Fazio. 1988) must be kept in a safe attitude relative to Sun and Earth in order to avoid damage to the cryogenically cooled telescope. This can be accomplished by bringing the telescope axis perpendicular to the sun line with the aid of the Sun Sensor. next use the AST (co-boresighted with the telescope) to determine the attitude about the sun line. and then point the telescope to either the ecliptic North or South Pole following a roll about the sun line. The 100.000 km orbit selected for SIRTF makes it impractical to use an Earth sensor for performing the safing function . Being able to acquire targets efficiently is an added benefit of using the AST on SIRTF.

Having larger magnitude errors makes star identification more difficult and necessitates a higher guide star density. Addition of a filter makes guide star selection and identification easier at the cost of a reduced AST sensitivity. Currently. translation of the visual to AST magnitude is not implemented. However. further research should be performed to determine the accuracy of V to AST magnitude translation, given the spectral information available in the SKYMAP star catalog.

In the case of Cassini (Draper. 1988). the quick fault recovery enabled by an AST would reduce the length of the critical time intervals associated with Saturn orbit insertion, Titan Probe release, and the Titan fly-by targeting bums needed for gravity assist. This reduction in critical time translates directly into a reduced probability of catastrophic failure.

Guide star database generation is performed using the following steps: (I) Conversion of the single-file SKYMAP catalog on 9 track tape to 100 files on Macintosh readable Teac (150) tape. (2) Extraction of the necessary star data. (3) Organization of the stars into a tiled-sky catalog. (4) Creation of a candidate guide star catalog, (5) Guide star selection. and (6) Formation and sorting of guide star pairs. The data currently extracted for each star at step (2) consists of its SKYMAP record number, epoch 2000.0 right ascension and declination. position error. proper motion and visual magnitude.

Used on planetary spacecraft (e.g .• Cassini) the AST could perform autonomous optical navigation. Being performed on the ground. optical navigation is currently hampered by long delay times. Following separation from the Space Station. the Assured Crew Return Vehicle (ACRV) must be placed in the correct attitude for

514

time to 0.4 s with the Y filter in place. A Macintosh IIci computer will be used to control the camera, store the video data, and perform the star identification.

The sky has been partitioned into 110 slightly overlapping tiles to allow efficient generation of the candidate guide star catalog. the guide star database. the observable sky database. and the observed stars. Within each tile. the stars of the tiled-sky catalog are sorted in sequence of increasing visual magnitude. The tiles overlap each other by at least 0.7 degrees. which permits a tile by tile generation of the candidate guide star catalog. In this catalog. each candidate is accompanied by a list of its close neighbors out to a distance of 0.35 degrees. This structure facilitates rapid guide star selection using one of the selection algorithms.

The CCD camera will be mounted in a piggyback fashion to a computer controlled 8", f/6.3 Meade LX200 telescope enabling efficient mapping of the sky.

STAR IDENTIFICATION Star identification is achieved using a star pattern recognition algorithm. The objective of this algorithm is to find the largest group of stars within the the star field observed by the AST that matches a group of guide stars. The brightest observed stars are picked for the identification process. Although the simulations allow the use of up to 12 stars, 8 is a more typical number. The anti-blooming capability of the CCD camera is exploited to ensure that the desired number of stars can be obtained. even if a very bright star is present. The recognition algorithm assumes that a group of observed stars matches a group of guide stars if all of the following criteria are met:

The tiles are sized such that an AST can never extend into more than 4 tiles. provided its largest FOY dimension is less than 16 degrees. This is achieved by arranging the tiles into 5 declination bands per hemisphere and partitioning each band in an appropriate number of tiles. The core area (i.e .• area minus overlap border zone) of the first band. extends to 16.2 degrees from the pole and comprises one tile. the "polar cap" . The core width of the second. third. fourth and fifth bands is 16.4.20.7 . 18.4. and 18.3 degrees. respectively . These bands are partitioned into 6. 12. 18. and 18 tiles along constant right ascension lines.

I. The measured angular distance of each pair of observed stars matches the predicted angular distance of the corresponding pair of guide stars to within the distance tolerance (tdis) . 2. The measured magnitude of each of the observed stars matches the predicted magnitude of the corresponding guide stars to within the magnitude tolerance (tmag) . 3. The geometry of the group of observed stars is not the mirror image of that of the group of guide stars.

In the tiled-sky catalog. the number of stars in the core area of the tiles ranges from a low of 1024 to a high of 5033. while the number of stars in the border area of the tiles ranges from 78 to 407. It was found that a total of 797 stars (0.32%) lack visual magnitude information. Using the core stars with defined visual magnitude. an integrated star density model is generated for each tile. This density model assumes that the log of the integrated star density is a linear function of the magnitude. and a least squares fit is employed to establish the two model parameters. Using the model. a "model magnitude limit" is established per tile. At this limit the number of stars according to the model equals the number of stars in the tile. It ranges from 9.28 to 9.80 magnitude.

In the above. the angular distance of a star pair is defined as the angle between the two stars of the pair. In practice. the "vector distance" between two stars is used as a measure of the angular distance. The vector distance is defined as the linear distance between the stars, assuming that the stars are located on a celestial sphere with unit radius.

Generation of the candidate guide star catalog requires definition of a close neighbor radius value and an upper magnitude limit. defined as a delta relative to to the aforementioned model magnitude limit. Using 2.5 for the magnitude delta and 0.35 degrees for the close neighbor radius. a candidate guide star catalog comprising a total of 16.603 candidates is generated. The density of the candidates varies roughly from 0.23 per square degree to 0.82 per square degree. The selection of guide stars and the generation of the guide star pairs is covered in the simulation section.

IllATQI

H

®

~~~';>~~------------------~

11T .... U8H THAlIHOlD 1'"0lIl: MATCH

Q~

*Zl (TWA1HlD)

The need for a catalog with the depth of SKYMAP is illustrated by the fact that even if there were no error in the predicted AST magnitude and the SKYMAP catalog were lOO % complete down to the model magnitude limit. the faintest guide star candidates could have unknown close neighbors with a brightness up to 10% (2.5 magnitude) of that of the candidate. AST Prototype. Since the simulations can only approximate the truth. suffer from some statistical uncertainties, and cannot possibly account for all parameters involved, it is absolutely necessary to validate the AST performance using a proof-ofconcept or prototype model. Using this prototype, a large area of the sky will be mapped and the raw video data will be stored on disk or tape. In the lab. each of the frames thus obtained can be further processed and used to test the star identification capability of the AST. Following verification of its star identification capabilities using true sky images in the lab, its capabilities will be demonstrated in real time at an observatory. Fig. 3. Recognition Algorithm Flow Diagram.

The AST prototype and its Support Equipment will be assembled from the following commercially available components: (1) A thermoelectrically cooled CCD camera head with a NuBus interface board for a Macintosh II computer. associated software. and a camera lens adapter. (2) A 35 mm fll.4 and a 50 mm f/1.2 camera lens, and (3) A computer controlled telescope with equatorial wedge and tripod.

A high level flow chart of the star pattern recognition algorithm is depicted in Fig. 3. First it is checked if a sufficient number of stars is available to enable successful identification. For the acquisition mode this number needs to be at least 3. If a sufficient number of observed stars is available for identification, match groups are generated (see first box). This match group generation process is clarified using the example shown in Fig. 4. In this example, 8 observed stars (01 through 08) are available for identification. Four of the 8 stars are guide stars. namely observed stars 01 . 02, 04, and 07 which are equal to guide stars G14, G26, G51, and G3 respectively. We will assume that the observed brightness of the 4 observed guide stars deviates less than tmag from their predicted values, while the measured 6 distances between the observed guide stars deviates less than tdis from their predicted values.

The anti-blooming capable CCD camera will be equipped with a 1024x1024 pixel CCD that is used in a Frame Transfer mode, implying a sensitive area of 512x 1024 pixels. Equipped with the 35 mm lens, the FOY can be selected within the range from IOxlO to lOx20 degrees. The integration time will be approximately l.l s using a Y filter and the smallest FOY, and will be much shorter without this optical filter. With the 50 mm lens, the FOY can be selected within the range from 7x7 to 7xl4 deg. The larger aperture allows a reduction of the integration

515

Following generation of all observed star pairs (28 for the example shown in Fig. 4), it is checked which pairs of guide stars match each of the observed star pairs. To make this checking efficient, all guide star pairs are stored in the AST guide star database in sequence of increasing angular distance. We start with checking if the pair consisting of 01 and 02 matches any guide star pairs, and find that guide star pair G 14G26 is among its matching guide star pairs. This latter match results in the formation of two "match groups," j and k, where match group j consists of a "kernel star match" made up of 01 and G 14 and one member, being the kernel of match group k.

TABLE 1 List of Initial Match Groups

+ 55

06

+ 91

08

01

04 07

+41

+

+51

We now have a means to find the observed and guide stars that correspond to member 1 of match group j; these are given by OMAT(MAT(j ,I)) = 2 and GMAT(MAT(j,I)) = 26. Th~ array values as obtained are shown in Table I, assuming that J and k are match groups 10 and II respectively. The two match groups are also depicted in Fig. 5.

-

L

14

MEMBER. 1 (KERNEL OF MATCH GROUP 11

- - KERNEL (1 .14)

MATCH GROUP 10

/

L

10

14

11

11

26

JO

41 41

41

51

10

11

57

JO

11

41

57 57

-

-

• VALIDATED DISTANCES

.... MEMBER

,, oE-----i-,-/- ......

If '

(GAP 1' )

\

\

KERNEL OF MATCH GROUP 10 ~

MEMBER If 2 (GAP 41 )

/

.... MEMBER If 3 (GAP 57)

26

1

Member

The remaining match groups are then validated, an operation where it is checked if each of the angular distances between the members of the match groups satisfies the distance tolerance. For the example of match group 10, these distances are indicated by dashed lines in Fig. 6. Next, redundant groups are eliminated which is followed by eliminating match groups where the pattern of guide stars is the mirror image of the pattern of observed stars. In the example shown in Fig. 4, match groups 11 , 41. and 57 are redundant. Finally, the largest remaining match group(s) are extracted.

19

GUIDE STARS IN CORRESPONDING PART OF TIlE SKY

/:r

Third

parameters of the star pattern recognItion algorithm. It is usually set at the upper hound of the match group size minus 2. All match groups that are smaller than the threshold are eliminated in the following operation (included in fourth box). In addition to the elimination of these small match groups, which are likely to be spurious, it is also necessary to eliminate each member of a remaining match group that is associated with a match group that has been eliminated.

Fig. 4. Example of Matching Star Patterns.

OBSERVED STAR PAIR

Second Member

57

+73 +3 +,04

OBSERVED STARS USED FOR PATTERN RECOGNmON

First Member

+26

+14

03

Guide Star

OMAT(i) GMAT(i ) NASS(i) MAT(i.l ) MAT(i.2) MAT(i. 3 )

ASTFOV,

02

Numb. of Match Groups associated with Members Members of Match Group i

Match

Obs. Star

As a result of the match, the arrays identifying the observed and guide stars corresponding to the kernel of match groups j and k are updated, resulting in: OMAT(j) = I, GMAT(j) = 14, and OMAT(k) = 2, GMAT(k)=26. In addition, the array that keeps track of the number of members associated with the kernel of each match group is updated, resulting in: NASS(j) = I and NASS(k) = I. Also, the array that indentifies the match group associated with each member of a match group is updated , resulting in MAT(j, I) = k, and MAT(k,l) = j.

05

Kernel

Match Group

Fig. 6. Match Group Validation. MATCHING GUIDE STAR PAIR (ONE OF MANY)

If the size of the extracted group(s) is insufficient, iterations are permitted, and it is allowed to lower the threshold, the process is repeated starting with the thresholding of the initial match groups. If only one non-redundant valid match group of sufficient size is left, the star identification is deemed to be successful. If there are multiple non-redundant match groups, there are three possibilities: all of them are correct, at least one of them is correct, or they are all faulty.

__ KERNEL (2.26 )

MEMBER # l (KERNEL OF MATCH GROUP 10)

MATCH GROUP 11

The probability of the first of these possihilities to occur is fairly high because it frequently happens that one of the angular distances does not match because of a large attitude error of one of the observed guide stars. This case can be salvaged by checking if all match groups have 2 star matches in common as is shown in the flow diagram. If there are no two common star matches, it can be attempted to find a solution by lowering the threshold, or by selecting the "best group", either immediately (select best group first time = Y), or if all else fails.

Fig. 5. Match Group Generation. When we check which guide star pairs match observed star pair 01-04, it is found that guide star pair G14-G51 is one of the matching guide star pairs. As a result, a member is added to match group 10, while a new match group (41) having 04, G51 as its kernel is created. This match results in the following array updates: NASS(10) = 2, MAT(lO,2) = 41; OMAT(41) = 4, GMAT(41) = 51, NASS(41) = I , and MA T(4J,J) = 10. Processing of observed star pair 01-07 results in the addition of a third member to match group 10.

The RSS value of the distance errors is currently used as the criterion for finding the best match group. The group with the lowest value is selected as the correct match group.

After having processed all 28 observed star pairs all initial match groups (typically 7000 for the reference AST) have been generated. The array values for the 4 match groups with kernel star matches 01, G14; 02, G26; 04, G51; and 07. G3, are shown in Table I. Because of false matches, each of these four groups typically has more members than the 3 shown.

SIMULATION PROGRAI\I An overview of the simulation is shown in Fig. 7. A simulation run consists of: (I) Generation of the guide star datahase , (2) Generation of the observable sky, (3) Evaluation of the star identification performance at the prescrihed sky locati ons, and (4) presentation of the simulation results. The param eters used to simulate the reference AST case are shown in Table 2. The numbers quoted below are for the AST reference case, while compute times are valid when using a Mac IIci.

The upper bound for the size of valid match groups is determined next (second box in flow diagram) by evaluating the NASS vector. In order to have a valid match group of i star matches (I kernel plus i-I members), we need to have at least i match groups with i-I or more members as may be seen from the example of Fig. 4 where i = 4. If the upper bound of the match group size is less than the minimum value required (3 or 4 for the acquisition mode), star ID failure is reported.

Guide star database. The guide stars are selected from the candidate guide star catalog using the specified guide star density, the close neighbor acceptance criteria, and the specified selection mode as inputs. Stars with close neighbors will be accepted as guide stars only if the integrated magnitude of

In the next step, the threshold for the match group size is established (third box). This threshold is one of the control

516

AST sensitivity limit is brighter than the threshold, the threshold is replaced by the sensitivity limit. Magnitude errors Will be generated for all stars down to the AST threshold magnitude plus a sufficiently conservative margin. In the case of the reference AST, this margin is set at 0.77 magnitude, implYing that all stars having at least a I % probability of exceeding the AST threshold are considered.

(SI

MLlCTALLGUIOlIT,US

(100.)

QlHUIA TI ......, SOfIT All. OUIDE It All "AlAI

(52 .)

OVOE Sf AA CAT ABASE GEN

UtUUSH 8"IGHTNl"lMT FOR EACH IK' flU

(170 " OBSERVASlE SKY GEN

SlUCT ST AAS TO 8E USf.D FOR IDf.NTIFlCA nOH

The guide stars are are processed first. A fraction of the guide stars is made non-observable at random to account for a nonperfect catalog reliability. For the reference AST case, 198 of the 4148 guide stars were ehmtnated because of thiS reason. Because of the incom pleteness and hmlled depth of the star catalog, additional "unknown ". close stars are genera~ed randomly within the close dlsturbmg star area of the remal.mng guide stars. The magnitude limll for the se stars IS speCified relative to the faintest guide star tn the !lie, while their density can be biased using a "clumping faclOr" different from I 10 reflect the fact that most stars are members of rnulliple systems. Seven hundred and fifty unknown close disturbing stars were generated for the reference AST case and added 10 the 350 known ones.

(0.6. per k>op)

PERFORM STAA 1000NT1F1CAnoN

NOTES

(1) FAO'" CANDIDATE GUIDE STAR CATA.lOG (2) FAOM TIL.£O SKY ST AR CATALOG (3) COIolPUTE nMeS FOR 45T REF. CAse (T. , . 2) & "'-c: IIeI

The guide star position errors include the effect of the star position error in the catalog, the contribution of the AST, the effect of uncompensated proper motion, and the effect of any close disturbing stars. The laller effect is incorporated by computing the combined centroid location. The guide star magnitude errors are generated randomly using the combined 1 cr value of the catalog and AST contributions and accounting for close disturbing neighbors.

Fig. 7. Simulation Overview. neighbors closer than a specified distance (close disturbing star radius) exceeds the guide sur magnitude by the specified margin (close disturbing star magnitude ":lar~in). Currentl~, the required number of guide stars per !lIe IS obtatn.ed by simply picking the brightest q~alifyin& stars. The dl.stnbuIJon of the guide stars obtained thiS way IS not very umform and beuer methods are being developed. Given the gUide star patr distance limil, all guide star pairs are generated and soned In sequence of increasing angular distance.

Next, magnitude errors are randomly assigned to all non guide star ca!alog stars down to the aforementioned conservative limit. All stars with a "true" AST magnitude brighter than the AST magnitude threshold are retained. For the reference AST case, a total of 6,360 of these stars were collected. Additional observable stars are generated randomly to account for the imperfect catalog completeness. A total of 537 of these stars were generated for the reference AST case. The catalog completeness used for the simulation is modeled as a function of the magnitude. This model is obtained by evaluating the curve describing the logarithm of the integrated density of the stars in each tile versus magnitude and postulating that this relation should be linear.

TABLE 2 Parameter Values for Reference AST Parameter Value

Operation

Parameter Descrtpdon

Guide Star DalAbase

FOV Shape FOV Area Guide Star Density Oose Disturbing Star Radius Oose DiSl Star Magnitude Margin Guide Star Selection Mode Guide Star Pair Distance Limit

: Circular : 100 square degrees : 10 pe< AST FOV

Catalog Completeness Caulog Reliability CataJog Magnirude Error AST Sensitivity Limit AST Magnirude Error AST Spatial Accuracy per axis Star Clumping Factor

: 95% : 95 % : 0 .0 magnitude : 7.5 magnitude : 0 .3 magnitude ( I crI : IQ arcsec ( I 0 ) : 3x mean density

Gene"tion

Observable Sky Database Generation

: 240 arcsec : 2.5 magnitudes : Bri ghleSt Stars : 11.3 degrees

I! takes 170 seconds to generate the 10,847 observable stars of the reference AST case. Among them are 3,950 guide Stars.

Tune from Guide Star (GS) Epoch .• 010.4Y 2ears m,g ,bove f"n"'( -,ch. GS Magnitude Threshold for Observable Stars ..................

Star Identification Testin~ . The test sequence consists of positioning the AST FOV on the sky, collection of the observable stars within the FOV, selection of a subset of these for identification use, star identification, and evaluation of the identification result. The FOV can be positioned using the prescribed, all-sky method. the prescribed single position method, or the all-sky random method. The first method, which allows up to 10,000 evenly di stributed positions covering the entire sky is the most useful as it represents a very systematic way for detec ting problematic sky areas. Having detected these difficuI! SPOtS, the single position method can be used to diagnose the identification failures.

: 0 .77 magnitude Magnitude: Margin relative ( 0 Threshold Magnitude: Lim it for Oose Star generation : 4.0 mag above faintest G S in tLle Star Identification Testing

FOV Positioning Mode FOY Positioning Pitch AST Dynamic Range AST Saturation Range Number of Stars used for ID Limit 10 Number of Sarur.u.ed StarS Tolerance on Guide Star Pair Distance Relaxed Distance Tolerance Tolerance on G uide Star Magnitude Number of ide ntified stars needed Initial Threshold for Match Group Size Limit \0 match grp size (kernel+members) Star ID Confusion Handling Iterations permitted ?

: Prescribed. all sky : 2.()475 deg ( for 10.000 positions) : 5 magnitudes : 5 magnitudes : 8
:J : 37 arcsec : 37 arcsec : 0.77 magnitude : al least 3 fo r success

: 2 below maximum ""a1ue : 11 : Select best group if al l else fails : yes

Following collection of the observable stars within the FOV, it is allempted to seleCt the desired number for identification use (8 for the reference ASD. The selection of these surs is influenced by the dynamic range constraint, the AST anti-blooming capability (defined in terms of a saturation range) , and the number of stars allowed to be in saturati on. In addition to the desired num ber of ID stars, the tolerance on the guide star pair distance, the rela xed distance tolerance (applicable when performing the match group validation), and the magnitude tolerance need to be provided to the star pallern rec ognition algorithm. For the reference AST case the tolerances are selected such that the probability of meeting each of these tolerances is 99%. I! is also necessary to specify how to resolve star ID confusion cases (more than one final match group) and whether or not to allow iterations.

I! takes lOO s to select the 4148 guide stars for the reference AST case. The faintest guide stars have a 6.3 visual magnitude. A highly efficient algorithm enables generation and sorting of all 82,316 guide star pairs in JUSt 52 s. This speed allows the amount of AST ROM needed for slOring the guide star database 10 be reduced from 552 Kbytes 10 42 Kbytes for applications where an allitude acquisition delay of some 60 s can be tolerated.

Observable Sky Generation. The objective of this operation is to generate the AST magnitude and "true" sky ~os ition of all st.ars brighter than the AST threshold. The magnllude and poslllOn are computed by combining the error contributions of the AST and the catalog, making it possible to compute these parameters only once per simulation run . The threshold for each tile is established by specifying it relative to the faintest reachable guide star. Guide stars within the area that covers the tile and extends up to a FOV diameter distance beyond the edge of the tile are defined as being reac hable.

The average time needed for performing one loop is 0.6 s for the AST reference case. The high speed is made possible, among other things , by storing the guide star database and the observable sky database in RAM.

For the reference AST, the threshold is set at 0.42 mag, which gives a randomly selected guide star a 99% probability of exceeding this threshold , given a magnitude error of 0.3. If the

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the false identification rate, and the compute time, as well as the required array space. Four simulation runs were performed where the number of stars used for recognition was varied from 6 to 12. The result is shown in Fig. 8, from which it may be seen that it is fairly optimal to use 8 stars for the identification. Having a larger number of stars makes it easier to falsely match a subgroup of them with a group of non corresponding guide stars. Actually, as might be expected, the observed false match probabilities of 0.09,0. 17, and 0.25% correspond very well with the number of triplets for 8, 10, and 12 stars, which are equal to 56, 120, and 220 respectively.

RESULTS The simulations show that the AST, operating in its acquisition mode, is capable of successfully identifying the stars within its FOY in 9,927 out of 10,000 cases. It performs the identification in just 0.57 seconds on the average, with a minimum of 0.23 and a maximum of 2.70 s, assuming use of Mac IIci equivalent computer. The AST was incapable of identifying the star field in 64 cases (failed ID), while there were 9 cases where the AST erroneously deemed the identification successful (false ID). The result is shown in the firs row of table 3.

':%Lill

TABLE 3 Simulation Predictions of AST Performance ID Compucc Tune' Needed Array Space Magn. Success Failed False Mean Min . Mu. Toler. (s) (s) (s) (Kbycc )

ParameCClli used for Star ID Select iteraL Match Bes, OK? Group Group Size 1st x'! Cap no yes yes yes

yes no no no

11 11 6 6

ID Results'

9.927 9.925 9.925 9.869

64

66 66 103

9 9 9 28

0.57 0.57 0.57 1.19

0.23 2.70 0.23 1.70 0.23 1.68 0.33 5.63

01

98 8

I

10

I

00

12

8'

Numbef of alii,.. uMd tor I)

520 304 214 310

0.5

0.0

STAR IDEHTlACAnoH . SUCCESS RATE

0.77 0.77 0.77 2.00

:.aLill

:~%twl I I .

10

12

8

Nl..mber of Ita,.. UMd for Il PROBABI..ITY OF FALSE STAR IDENTlFlCATlON

10

12

Number of sUi,.. UMd lOt ID

I I

TWE NEEDED FOR STAR IDENTl ACATlON

I

Fig. 8. Sensitivity to Number of Stars used for ID

CONCLUSIONS AND ACKNOWLEDGEMENTS

1) For a IOW of 10.000 evenly distributed FOV locations. covering lIle entire sky 2) Using a MC68030 class microprocessor running aI 25 Mhz

Using realistic simulations, it has been shown that an Autonomous Star Tracker with an 11 .3 deg ..ee FOY diameter, a spatial accuracy of 10 arcsec (1 sigma), a brightness accuracy of 0.3 magnitude (1 sigma), a database of 4148 guide stars, a highly efficient non-iterative star pattern recognition algorithm, and an MC68030 class microprocessor running at 25 Mhz, will be capable of determining its attitude in approximately 0 .6 s without having any a-priori attitude knowledge. It can do so with a demonstrated success probability of 99.25%, while the probability of false identification is less than 0.1 %.

The majority of the failures (55) are due to having less than 3 guide stars among the observed stars, clearly an indication that a more sophisticated guide star selection method is needed. Identification of 17 of the 170 cases with 3 guide stars among the observed stars was unsuccessful (4 of the 17 were false IDs). There was only one case where identification was unsuccessful with more than 3 guide stars (4) among the observed stars. An investigation of this case showed that one of the 4 guide stars had an out of tolerance magnitude, thus reducing the number of usable guide stars to 3. The value of selecting the best match group to resolve ambiguity is illustrated by the fact that this method raised the number of successes by 17. However, this method was also responsible for 4 of the 9 false identifications.

Failures are caused by an insufficient number of guide stars in certain parts of the sky due to the use of a very simple guide star selection method. This problem can be remedied easily by using a more sophisticated selection algorithm. Therefore, it is expected that an AST with an improved guide star database will achieve a 100% success rate. The potential of a perfect success rate is enabled by anti-blooming capable CCDs that make it possible to eliminate failures caused by a lack of dynamic range (van Bezooijen, 1989a and 1989b).

Of the 9936 cases that were deemed successful by the star pattern recognition algorithm, there were 8732 cases with only one final match group (5 of them were false), 1183 cases with multiple final match groups that all had 2 star matches in common, and 21 multiple final match groups where the best match had to be picked.

A very high success rate of 98.69% is retained when the star brightness is not used for star pattern recognition, implying that the AST will function, even if a sensitivity calibration is not available, as may be the case for certain applications (e.g., the ACRY). Because of the high mechanical stability of CCD trackers, geometrical re-calibrations are probably not required. The success rate for the non-calibrated AST is expected to reach 100% once an improved guide star database has been generated.

The simulations show a maximum of 8,184 initial match groups, from which it can be deduced that the recognition algorithm needs 520 Kbytes of array space. By prohibiting iterations, this array space can be reduced to 304 Kbytes, as there is no need to preserve the matrices associated with the initial match groups. A simulation showed that not allowing iterations (see Fig. 3) increased the number of failed identifications by only 2, while no additional false identifications occurred. The results of the latter simulation are shown in the second row of table 3. Avoiding iterations had the additional benefit of reducing the maximum compute time from 2.7 to 1.7 seconds

The author gratefully acknowledges the Astronomical Data Center at the NASA Goddard Space Flight Center for providing the SKYMAP star catalog. He also would like to thank Paul Reshatoff and Ted Havas for their outstanding technical support. REFERENCES

A further reduction of array space can be achieved by limiting the maximum match group size to 6, instead of 11, which allows the space needed for the MAT matrix (see Identification section) to be cut in half to 90 Kbytes, implying that the needed total array space can be reduced to 214 Kbytes. According to the simulations (third column of table 3) the reduction in the cap has no impact on the identification performance. However, limiting the number of identified stars to 6 (instead of 8) impacts the accuracy of the computed spacecraft attitude somewhat

Draper, R.F. (1988). The Mariner Mark II Program . Paper AlAA 88-0067, AlAA 26th Aerospace Sciences Meeting, Reno, Nevada, Jan 1988. Eisenhardt, P., and G.G. Fazio (1988). The SIRTIF concept and its realization. NASA Ames Research Center, Moffett Field, CA, Nov 17, 1988. McLaughlin, S.F. (1989). SKYMAP Star Catalog, version 3.5. National Space Science Data Center, Goddard Space Flight Center, Greenbelt, Maryland. van Bezooijen, R.W.H., K.R. Lorell, and J.D. Powell (1985). Automated star pattern recognition for use with the Space Infrared Telescope Facility (SIRTF). Xth IFAC symposium on automated control in space, Toulouse, France, June, 1985. van Bezooijen, R.W.H. (1986). Success potential of automated star pattern recogrtition. Paper AlAA-86-0254, AlAA 24th Aerospace Sciences Meeting, Reno, Nevada, Jan 6-9, 1986. van Bezooijen, R.W.H. (1989a). Automated Star Pattern Recognition, Ph.D. Dissertation, Stanford University, Stanford, California. van Bezooijen, R.W.H. (1989b). A Star Pattern Recognition Algorithm for Autonomous Attitude Determination, XIth IFAC Symposium on Automatic Control in Aerospace, Tsukuba, Japan, July, 1989.

In some applications (e.g., the ACRY) the AST has been dormant for a long time prior to its use. Consequently, there may be a substantial error in the AST sensitivity. To determine the performance of an AST with unknown sensitivity, the star brightness was effectively eliminated from the recognition algorithm by opening up the tolerance to 2 magnitudes. As may be seen in row 4 of table 3, this uncalibrated AST retains a very high success rate of 98.69%, which will most likely increase to 100% through use of a more sophisticated guide star selection algorithm. Elimination of the star brightness in the recognition algorithm does impact the compute time and the needed array space as may be seen from table 3. The number of observed stars used for the star pattern recognition has an impact on the star identification success rate, 518