A New Star Pattern Recognition Method: Star Pair Axis And Image Template Matrix Method. Texas A&M University H. Kim, J.L. Junkins, and D.

Transcription

1 A New Star Pattern Recognition Method: Star Pair Ais And Image Template Matri Method Teas A&M Universit H. Kim, J.L. Junkins, and D. Mortari

2 Wh Star Tracker? Provide three-aes attitude information. No need of additional attitude sensors Accurate and reliale reference information Astronom data is etremel accurate Accurate Measurements due to improvement of CCD Technolog and Image Centroiding Technique High precision (su-tens arcsec) and fast update rate (3-Hz) Not restricted to earth orit S/Cs

3 Star Pattern Recognition (SPR) Matching process of the measurementderived unit vectors toward measured stars in the spacecraft od frame (W) and the corresponding reference unit vector in the known inertial frame (V). Based on the invariant properties of the vector geometr under general coordinate transformation W = CV where C is the direction cosine matri. V i W i

4 SPR Modes Normal mode Stailized or slowl rotating S/Cs A-priori attitude information availale Su-catalog ma e utilized relativel eas and reliale Lost-in-space mode Initializing sensors or recovering them from sudden failure Increase searching time and amiguit

5 Polgon Matching Method c a d Θ a c d a Θa Θac Θad - Θc Θd c - - Θcd Measured Stars N k c = In general N m ( N ) N ( N ) m 4 k g k g Nm : Measured Stars Ng k : Guide Stars c a θ a d e a c d c d θa θac θad - θc θd - - θcd Guide Stars e θae θe θce θde Nc k : Numer of Comparisons Cominatorial Comparisons

6 Ojective of Star Pair Ais And Image Template Matri Method Solve the lost-in-space prolem without a-priori attitude information. Reduce the numer of comparisons and searching time. Avoid cominatorial comparisons. Satisf various storage requirements.

7 Star Image Regulation Using Star Pair Ais () Regulate star images sstematicall proper rotation and translation so that the new -ais is aligned with the line connecting a pair of stars. a a

8 Star Image Regulation Using Star Pair Ais (2) The new location (, ) of a star on the regulated image plane is given WC = W C W W W a a =, 3 =, W Wa Wa + W 3 C where f is the focal length of the star tracker. + W = [ Cij ] = [ 2 3 ] + W + W C C W C z + W C z 3 33 f, = T, W C W C 2 3 i j 2 = 3 3 =, K,3 =, K,3 + W + W C C W C z + W C z f

9 Image Template Matri Regulated Measured Star Image Regulated Reference Star Image Numer of Comparisons Nc k =Ng k Stars are found in the same locations of cells in oth regulated image planes if the two images match each other ecept difference in noise level and the size of the cell (g) is large enough.

10 Mission Catalog () Mission Catalog Generation Create a set of guide stars and reference guide star pairs using 2 nd order thinning method. Find a curve-fit model etween lookup inde and interstar angles of star pairs. Find adjacent stars for each star pair, which depends on the size of Field of View (FOV). Calculate the locations of adjacent stars on the regulated image plane (optional). Note Pre-generate and store information aout the regulated reference images.

11 Mission Catalog (2) nd Order Thinning Method 2 nd Generate the near minimum numer of reference star pairs so that at least one of these pairs can e measured inside the FOV in ever possile oresight direction. Generate a guide star set satisfing the requirement of the minimum numer of guide stars (MNGM) that should e measured inside a given FOV in ever possile oresight direction. A B

12 Mission Catalog (3) Candidate Star Pairs Utilize piecewise curve-fit method for the eas access to candidate star pairs k=g(θ) Access rule for an aritrar interstar angle (θ a ) k [k start, k end ] k start =G d(s),d(s+) (θ a ) ε d(s),d(s+) ε m k end =G d(s),d(s+) (θ a )+ε d(s),d(s+) +ε m

13 Mission Catalog (4) Information Pre-generated and Stored Direction cosines of guide stars (V) Inde of reference star pairs (Star A and Star B) Coefficients of curve-fits (G) Maimum estimate inde errors in the interval [d(s), d(s+)] (ε d(s),d(s+) ) Inde error due to measurement noise (ε m ) Inde of Adjacent guide stars for each star pair Locations of adjacent guide stars on the regulated image plane (X,Y) AB (optional)

14 SPR Star Pair Ais Template Method Algorithm (). Otain the rightest two measured stars 2. Appl the star pair ais method to otain a regulated image plane. 3. Find candidate reference star pairs using the curve-fit model. 4. Introduce a K K zero ITM. 5. The addresses of measured stars on the ITM are given ( p, p ) i = round i g + K 2, round i g + K 2

15 SPR Star Pair Ais Template Method Algorithm (2) 6. Assign value on the (p,p)i elements of ITM 7. Addresses of adjacent guide stars of a candidate reference star pair are given ( P AB, P AB ) j = round X AB j g Y,round g Otain the numer of matching stars (NMS) AB AB checking whether ( P, P ) j elements of ITM have value. + K 2 AB j + K 2

16 SPR Star Pair Ais Template Method Algorithm (3) 8. If NMS NMPCS, Successful SPR. Go to step 9. If NMS<MNPCS, repeat the process for the net candidate reference star pair (step 7). If no more candidate reference star pair is availale, otain the net rightest two measured stars and repeat steps Reset used addresses of ITM to zeros. NMPCS The numer of matching pairs of measured stars and guide stars to confirm the successful SPR

17 Simulation Result For the 8 8 squared FOV Measurement Uncertaint (σ) Visual Magnitude Uncertaint (φ) NMPCS The Size of Image Template Matri Success SPR (%) Mismatch (%).5-5 ± ± Minimum Numer of Matches 5 5 Maimum Numer of Matches 8 8 Mean Numer of Matches Mean ( θ t, θ e, ) (arcsec) Mean ( θ t,2 θ e,2 ) (arcsec) Mean ( θ t,3 θ e,3 ) (arcsec) Mean Process Time (sec).24.76