Geometry Handbook.pdf

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SPOT SATELLITE

GEOMETRY HANDBOOK

S-NT-73-12-SI

Edition 1 – Revision 0

2002-01-15

5 rue des Satellites

31030 Toulouse Cedex 4,France

http://www.spotimage.fr

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This document was prepared by Serge RIAZANOFF (GAEL Consultant).

The document was subjected to the technical approval of a working revision group established

by experts of Spot Image, CNES and IGN.

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Contents

T ABLE OF FIGURES ................................................................................................................................................. 5

1 I NTRODUCTION ............................................................................................................................................... 1

1.1 P URPOSE OF THIS DOCUMENT ................................................................................................................... 1

1.2 D OCUMENT O VERVIEW ............................................................................................................................ 1

1.3 R EFERENCE DOCUMENTS .......................................................................................................................... 1

1.4 A BBREVIATIONS AND A CRONYMS ............................................................................................................ 3

1.5 D EFINITIONS ............................................................................................................................................ 4

1.6 TABLE OF SYMBOLS .................................................................................................................................. 4

2 SPOT MISSIONS .......................................................................................................................................... 7

2.1 H ISTORICAL BACKGROUND ...................................................................................................................... 7

2.2 O RBIT ....................................................................................................................................................... 8

SPOT orbit characteristics .............................................................................................................................. 8

SPOT constellation.......................................................................................................................................... 8

Orbit control - DORIS ..................................................................................................................................... 9

Attitude control.............................................................................................................................................. 10

Yaw steering mode......................................................................................................................................... 14

2.3 P AYLOAD ............................................................................................................................................... 16

Instruments .................................................................................................................................................... 16

Payload modes of operations ........................................................................................................................ 16

Channel superimposition – SPOT123 ........................................................................................................... 17

Channel superimposition – SPOT4 ............................................................................................................... 18

SPOT5 –HRG instrument overview............................................................................................................... 19

SPOT5 – HRG instrument – HMA / HMB superimposition .......................................................................... 20

SPOT5 – Supermode ..................................................................................................................................... 21

SPOT5 –HRS instrument ............................................................................................................................... 22

3 SPOT PRODUCTS...................................................................................................................................... 23

3.1 P ROCESSING LEVELS .............................................................................................................................. 23

Level 1A – Raw product ................................................................................................................................ 23

Level 1B – System corrected product ............................................................................................................ 23

Level 2A – Projected product without ground reference points .................................................................... 24

Level 2B – Projected product with ground reference points ......................................................................... 24

Level 3 – Orthorectified products.................................................................................................................. 24

3.2 D ATA FORMAT ....................................................................................................................................... 24

SISA format ................................................................................................................................................... 25

CAP format.................................................................................................................................................... 25

DIMAP format............................................................................................................................................... 25

4 VIEWING GEOMETRY MODEL – THE DIRECT MODEL ................................................................ 26

4.1 P RINCIPLE .............................................................................................................................................. 26

4.2 L INE DATING .......................................................................................................................................... 27

4.3 E PHEMERIS INTERPOLATION ................................................................................................................... 27

4.4 L OOK DIRECTION IN N AVIGATION R EFERENCE C OORDINATE S YSTEM ................................................... 28

The Navigation Reference Coordinate System .............................................................................................. 28

Look direction of pixel p................................................................................................................................ 29

Look direction and mirror step value (informative) ...................................................................................... 31

4.5 L OOK DIRECTION IN O RBITAL C OORDINATE S YSTEM ............................................................................. 32

The Orbital Coordinate System ..................................................................................................................... 32

SPOT123 and SPOT4 - Integration of attitude variations ............................................................................ 34

Initial attitude values..................................................................................................................................... 35

SPOT5 – Absolute attitudes........................................................................................................................... 35

Sign of attitude data ...................................................................................................................................... 36

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Attitude interpolation .................................................................................................................................... 36

Computing look direction .............................................................................................................................. 37

4.6 L OOK DIRECTION IN T ERRESTRIAL C OORDINATE S YSTEM ..................................................................... 37

International Terrestrial Reference Frame (ITRF) ....................................................................................... 37

From Orbital Coordinate System to Terrestrial Coordinate System............................................................. 38

4.7 L OCATION ON E ARTH MODEL ................................................................................................................. 39

Intersection of look direction with the Earth ellipsoid .................................................................................. 39

Using a DEM - Algorithm ............................................................................................................................. 41

Using a DEM – Altitude pre-processing ....................................................................................................... 42

5 GENERATION OF LEVEL 2 PRODUCTS – THE INVERSE MODEL ............................................... 44

5.1 P RINCIPLE .............................................................................................................................................. 44

5.2 T HE GEODETIC TO IMAGE PREDICTOR ..................................................................................................... 44

Sampled data (p i ,q i ) ....................................................................................................................................... 44

Computing the polynomial predictor............................................................................................................. 44

Use of the predictor....................................................................................................................................... 45

5.3 A LGORITHM ........................................................................................................................................... 45

5.4 U SING LEVEL 1B PRODUCTS IN INPUT ..................................................................................................... 47

Rationale ....................................................................................................................................................... 47

Retrieving the pixel location in level 1B image ............................................................................................. 48

6 PROCESSING OF 1B PRODUCTS........................................................................................................... 49

6.1 H ISTORICAL BACKGROUND .................................................................................................................... 49

SISA model .................................................................................................................................................... 49

CAP model..................................................................................................................................................... 49

6.2 G ENERATION OF 1B PRODUCTS .............................................................................................................. 50

6.3 M ETHOD 1 – S CENE - BASED TRANSFORM (SISA).................................................................................... 50

Direct transform ............................................................................................................................................ 50

Reverse transform ......................................................................................................................................... 51

6.4 M ETHOD 2 – S EGMENT - BASED TRANSFORM (CAP)................................................................................ 52

1A scene to / from 1A segment ...................................................................................................................... 53

1A segment centered and normalized coordinates ........................................................................................ 53

Direct transform (1A → 1B).......................................................................................................................... 54

Reverse transform (1B → 1A) ....................................................................................................................... 54

1B segment centered and normalized coordinates ........................................................................................ 55

1B scene to / from 1B segment ...................................................................................................................... 55

APPENDIX A - CARTESIAN GEOCENTRIC AND GEODETIC REFERENCE SYSTEMS .................... 56

General equations ......................................................................................................................................... 56

Programs – Rights to use .............................................................................................................................. 56

A.1 F ROM C ARTESIAN G EOCENTRIC TO G EODETIC R EFERENCE S YSTEM ..................................................... 58

Algorithm....................................................................................................................................................... 58

Program example .......................................................................................................................................... 59

A.2 F ROM G EODETIC TO C ARTESIAN G EOCENTRIC R EFERENCE S YSTEM ..................................................... 61

Algorithm....................................................................................................................................................... 61

Program example .......................................................................................................................................... 62

APPENDIX B - COMPUTATION OF INCIDENCE ANGLE ........................................................................ 64

APPENDIX C - LOCATION OF VALUES IN SPOT PRODUCTS................................................................ 65

C.1 I NTRODUCTION ....................................................................................................................................... 65

Location in CAP format ................................................................................................................................ 65

Location in DIMAP format............................................................................................................................ 65

C.2 L OCATION OF VALUES ............................................................................................................................ 65

APPENDIX D - E XAMPLE OF SPOT AUXILIARY DATA ...................................................................................... 71

D.1 SPOT4 – 126-265/2 – 29/09/1998 – A NCILLARY DATA ......................................................................... 71

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D.2 SPOT4 – 126-265/2 – 29/09/1998 – E PHEMERIS .................................................................................... 72

D.3 SPOT4 – 126-265/2 – 29/09/1998 – A TTITUDES .................................................................................... 74

Average rotation speeds ................................................................................................................................ 74

Absolute rotation angles................................................................................................................................ 74

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