Autonomous On-orbit Calibration Approaches for Star Trackers. D. Todd Griffith

Transcription

1 Autonomous On-orbt Calbraton Approaches for Star racers D. odd Grffth Colleagues Dr. John L. Junns (Graduate Adsor) Mala Samaan Puneet Sngla eas A&M Unerst Department of Aerospace Engneerng AMU College Staton, X 778 grffth@tamu.edu

2 Oerew of Star racer for E0- GIFS he StarNa II camera smultaneousl mages star felds from two parts of the s, automatcall dentfes the star patterns, and determnes the pontng drecton of the camera. Atttude accurac requrement 5 µ radans (σ). Wll requre a well-calbrated camera n order to achee ths leel of accurac.

3 Oerew of Star racer Software/Processes Centrodng of star ntenst dstrbuton Seeral dfferent approaches Image Acquston Image Processng Star ID (5,5) or (0,0) CCD Arra Measured dstance between star centrods match wth star table alues to ID star. Can then compute star ectors n nertal frame. Estmaton of anthng that dstorts locaton of mage centrods Atttude Determnaton Calbraton

4 he Bascs of a Star racer Camera Unprocessed star mage Focal length Optcs Y Image plane: CCD arra AM X Star tracer S/C Scence nstrument Image processng results n the mage plane coordnates (X,Y) and the stars n the feld of ew are dentfed. Imaged ectors ( X 0 ) ( Y ) 0 ( X 0) ( Y 0 ) f f

5 Oerew of Star racer Calbraton ) Boresght Calbraton: Estmaton of prncpal pont offsets and best effecte focal length ) Hgher order effects Estmaton of all other effects as a functon of star centrod poston optcs f o hese effects nclude optcal dstorton, nstrument agng, etc. o

6 wo approaches for estmaton of hgher order effects () Atttude Dependent Approach ) Project nertal ectors nto bod frame: ) Compare wth measured ector: ) Estmate calbraton coeffcents: C n ] ˆ ˆ [ ˆ Φ Φ Φ Φ b a a b z z z ]... [ Φ Ideall, the calbraton coeffcents a and b are estmated recursel n order to aod storng large amounts of star data and to aod ecesse computaton. LS soluton of these equatons for a and b

7 wo approaches for estmaton of hgher order effects () Atttude Independent Approach ) Form star pars ) Compare cosne of nterstar angles: ) Estmate calbraton coeffcents: j j n n [ ]( ) j j Θ Θ Φ Φ Θ 0 0 b a θ θ Φ Φ Θ d c j j j θ θ It should be noted here that for local pece-wse contnuous appromaton, we estmate sets of coeffcents. Howeer, f we see global appromaton, then we assume that we onl hae sets coeffcents to estmate such that a c and b d. ]... [ Φ

8 Atttude Dependent Calbraton Studes () Smulated S/C maneuer at GEO 5000 mages used (500 seconds at 0 Hz) Polnomal of two arable bass functons of second order Recurse LS estmaton of global calbraton coeffcents Atttude estmates usng Etended Kalman Flter EXKF and Calbraton codes feedbac approach wth correcton of measured ectors to mproe atttude estmate whch feeds the calbraton process 8

9 Atttude Dependent Calbraton Studes () -drecton Error n Y-drecton Note that post calbraton resduals hae been reduced to less than µ-radans for each component of the error. We started wth errors of magntude roughl equal to 70-0 µ-radans. 9

10 Atttude Dependent Calbraton Studes () Error n X-drecton Error n Y-drecton 00 seconds Std. de. Mean (fnal µ-radans) 00 seconds Std. de. Mean (fnal 0. µ-radans) Wh? Great! 0

11 Atttude Dependent Calbraton Studes () Gro bas Atttude errors and σ bound Note the bas that remans n the estmated ptch and aw. hs results n the µ- radan errors n the X-component of the resduals. It s also nterestng to note that, dependng on the nose propertes of the measurements, that the atttude bas s remoed for some cases.

12 Faml of Local Fts Calbraton Approach () Grdded focal plane Calbraton functons are determned locall n order to model rregular sstematc focal plane dstortons, from whateer causes. Prelmnar seast square appromatons are determned for b cell regons n a recurse fashon. Weghtng functons are appled to the prelmnar fts that oerlap the center element n order to achee a contnuous model n alue and slope for adjonng cells Weght Functon W (, ) W (, ) ( - ) ( - )

13 Faml of Local Fts Calbraton Approach () Correcton functon ald for the th cell P (, ) ald oer ß Prelmnar Appromatons ( regons): F (, ) P (, ) w(, ) F, ) P (, ) w (, ) ( (, ) P (, ) w (, (, ) P (, ) w (, F F ) ) P (, ) aldoer ß Ý P (, ) aldoer Judcous weght functons are the e: w ( ) (- ), w( ) ( ) w(, ) ( w( ))( w( )) w (, ) w( )( w( )) w (, ) w( ) w( ) w(, ) ( w( )) w( ) Ý P (, ) ald oer Fnal Appromatons ald oer central regon where the Prelm. Appromatons are aeraged (th regon): F (, ) F (, ) P (, ) w (, ), ald oer

14 Smulated pure ptch maneuer at GEO 0.00 deg/sec about ptch as Zero angular rate of boresght as Onl recorded one mage per mnute Magntude threshold of 5.7 ges appromatel 9 stars per mage Focal plane/ sensor Bod/camera aes hours hours hours For slow maneuers, hgh frame rates offer no adantage to calbraton algorthm n terms of a quc focal plane coerage. In ths case, the man queston s total acquston tme.

15 5 Autonom Health Montorng, etc. Health montorng s an essental feature of the autonomous focal plane calbraton algorthm. hs noles establshng rules n order to determne f the focal plane dstorton estmaton algorthm s behang well, that s, f t conergng on the truth. he basc feature of health montorng nclude checng the statstcs of the resdual ectors (we can also chec these statstcs n a local fashon). Mean ( ) Varance ( ) [ ] σ σ σ Correlaton ρ σ σ ρ ρ

16 Are the hgher focal plane dstortons tme narant? Or slowl tme arng? Or wll the change rapdl? For a beta angle of Swng s 70 C Results b I. Carron, A. Hensle, U. Abbas. December 00 GIFS Desgn Reew 6