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' Strips
Case A: Simultaneous determination of the 3 orientation an-
gles dp, (pitch), dw, (roll), dk, (yaw), the displace-
ments Ax, Ay and the rotation Ak of the two stereo
CCD-arrays ST6/ST7 as well as all three focal lengths
FL. (Ax, Ay and Ax of HR-channel fixed)
Case B: Simultaneous determination of dy,, dw,, dk, AX,
Ay, Ak and FL of ST6/ST7 only.
(FL, Ax, Ay and Ax of HR-channel fixed)
Case C: Determination of doo, dos, dk, only.
(All camera parameter fixed)
Results: The Tables 7 - 11 contain the theoretical standard
deviations & of the above mentioned unknown parameters,
which are deduced from the inverted normal equation matrix
and the à posteriori estimate of the reference variance 42.
Since the simulations are performed with generated error-free
observations, the à priori o2 is used instead of 82; i.e. the
resulting theoretical standard deviations & are valid for the à
priori assumed precision of the observations. The a priori c
is chosen as equal to the standard deviations of the image
coordinates, which is 0.3 pixel in all computation runs.
In the Tables the following abbreviations were used:
Version aaaa/bb: aaaa — number of GCP
bb — absolute accuracy of the camera
positions [m]
FL-HR: & of focal length of the HR5 lens
FL-ST: & of focal length of the ST6/ST7 lenses
AX Ny: & of the sensor displacements in the
image plane
AK: & of the sensor rotation in the image
plane
doo, dwo, d&o: | 6 of the 3 orientation angles
[pe1]: [pixel]
The results for case A are shown in the Tables 7 (single strip)
and 8 (two crossing strips): The dependency of the theo-
retical standard deviations on the different versions can be
distinguished in 3 groups: The first group consists of FL and
Ak, which are dependent on both, the number of GCP and
the absolute accuracy of the camera positions. Ax, dg, and
dw, solely depend on the camera position accuracy, while Ay
and Ak only depends on the number of GCP. The simulta-
Version [FL-HR]FE-ST| Ax | Ay [A«][ des | doo | d&c
[um] | [um] [pet]! [pel] ['] L L1 1 D] 1 P]
100/201 14.2 14.7 [04|0.4 |8.0]12.4|124/|11.5
100/10|| 10.7 115.102 [0.4 7.4//9.1 l'9.1 |11.5
100/5 9.4 102 | 0.17.04 |71] 7.41 74 111.5
500/20|| 11.8 12:0 | 0.4 02 15.:2]H2.4112.:3| 8.0
500/10 7:2 1.6 02102]14.21 9:0| 9:11] 8.0
500/5|| 5.0 55:.[9011]0.2|3.8]| 7.3. | 7.47|:8.0
1000/20 || 11.4 | 11.6 | 0.4 | 0.1 |4.8 |12.4|12.3] 7.4
1000/10 6.6 6.9 0.2 | 6.1 |3-54:9.0 | 9.1 | 7.4
1000/5 4.2 4.5 01 01/30] 77:3|73 434
Table 7: Case A: Standard deviations for single strip
neous adjustment of two crossing strips improves the results
significantly, especially in case of poor control information. It
is evident, that even with 10 m absolute camera position ac-
curacy better results are achieved compared to the 5 m single
97
strip versions. This fact might become important, since 5 m
orbit accuracy can only be obtained for long data takes of at
least 4 minutes time of data recording. If the expected 1000
GCP and 5 m absolute camera position accuracy are available
sufficiently precise results are obtained. The focal lengths of
all three lenses can be determined with up to 3 um, the sensor
displacement with up to 0.1 pixel, the sensor rotation with
up to 2.4" and the rotation angles with up to 7" accuracy.
In case B the focal lengths of the ST6/ST7 lenses are deter-
Version|FL-HR[FL-ST| Ax | Ay [A«][ deo | doo |d&o
[um] | [em] |[pel] [el 10 P1 DT IE]
100/20 8.3 85 [03 {01 4 53/10. 1}1L 3119
100/10| 4.9 5.1 01/0114 3/|| 79/85 7,5
100/5 3.6 3.8 01/01 (4217.2 (7417.9
500/20 8.2 8.3 0310.]3.8//10.0|10.9] 7.3
500/10|| 4.6 44. [0410.1 |[34]|. 28.1.8.4 [| 7.3
500/5 3.1 34,1,0.1:1,0.1./2 8] 7-1 1,7.3 1 £.3
1000/20 8.1 22.102]0.1[35]100/107/7 1
1000/10 4.5 4.6 01 |01127]|7.98 8371
1000/5 2.9 3:2 07 l'o11241 7173171
Table 8: Case A: Standard deviations for two crossing strips
mined relative to the focal length of the HR5 lens, which is
assumed to be precisely known and fixed. Tables 9 (single
strip) and 10 (two crossing strips) show that FL-ST is deter-
mined essentially better compared to case A. Concerning the
other parameters, there is no significant difference to case A.
The 500 GCP versions therefore were omitted. As in case
ersion | FL-ST | Ax |J Ay | A& || deo | deo | d&o
[pm] [pet] t feet] i PES PETTT ITI
100/20 4.8 03 104 l'90]124111247]115
100/10 3.6 0.2 0.4 | 7.4 9.1 9d 15
100/5 2.9 0.1 0:4. 107.3 7:4] 4| 115
1000/20 4.6 0.2 0.1:4:4.8: }1:12.4 i123: 7.4
1000/10 3:2 0.1 0.11.3.5 9.0 9.1 1.4
1000/5 24 9 1.4. 0.1 4.3.0 1 43:3, 4-3. 125.4
Table 9: Case B: Standard deviations for single strip
A, two crossing strips lead to essentially improved results.
Here even poor control information suffices to determine the
sensor displacements with 0.1 pixel accuracy. Dependent on
the camera position accuracy FL-ST is determined with stan-
dard deviations up to 2 um. In case C all camera parameters
ersion || FL-ST | Ax | Ay ] Ar || dpo | dwo | dko
[um] | [ret] | [pel | C] E T1 1 D1 11]
100/20 3.3 0.1 0.1 |49 |10.1 11.3. | 8.0
100/10 2.2 0-1 0:1--|-4-3-1|-7:3-—|-8.5--4-8-0
100/5 19 61.101 |42'| 7:271 74 | 8.0
1000/20 3.3 0.1 01 |.3.5 | 10.0) 10.7 | 7.1
1000/10 22 0.1 01127 791837 71
1000/5 1.8 0.1 01 "254-171 Y 324
Table 10: Case B: Standard deviations for two crossing strips
are fixed, assuming perfect à priori knowledge of the camera
geometry. Here the control information contributes to the
determination of the orientation angles only. Table 11 shows
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996
