Fig. 3. Configuration of control and check points.
recordings in the order of 1.6 s. Further adjustment runs using all GCP led to the rejection of 4 GCP due
to large planimetric residuals. From the remaining 64 Ž
. GCP root-mean-square rms residuals of 9 m in X,
8 m in Y and 0.1 m in Z were obtained. The Z component is quite small due to the high weighting
Ž .
of the GCP Z coordinates s s 1 m compared to the weighting of the corresponding image coordinates
Ž .
s s 0.4 pixel . The planimetric residuals of nearly 10 m reflect the identification uncertainty mentioned
above. In a series of adjustment runs using subsets of 4,
10 and 20 GCP, empirical accuracies were derived from the remaining 44 points, which served as inde-
Ž .
pendent check points see Fig. 3 . The Tables 2 and 3 contain the empirical accura-
Ž .
cies rms values computed for the different GCP configurations and sets of tie points using all naviga-
Ž .
Ž .
tion data Table 2 and orbit data only Table 3 . The comparison between Tables 2 and 3 shows no
significant differences in the results, indicating that attitude information is not required. From Tables 2
and 3 it can be seen that the results are only slightly improved if 1000 instead of 100 tie points are used.
Despite of the given uncertainties, a height accuracy of up to 4.1 m is obtained, corresponding to 0.3 of
the ground pixel size of the oblique looking channels
Table 2 Ž
. Empirical accuracies rms values ´ using all navigation data
1000 tie points 100 tie points
4 GCP 10 GCP 20 GCP 4 GCP 10 GCP 20 GCP w x
´ m
11.6 10.8
10.3 11.6
11.0 10.1
X
w x ´
m 12.8
9.3 8.9
12.8 9.7
9.4
Y
w x ´
m 4.1
4.6 4.3
5.3 4.9
4.7
Z
Table 3 Ž
. Empirical accuracies rms values ´ using orbit data only
1000 tie points 100 tie points
4 GCP 10 GCP 20 GCP 4 GCP 10 GCP 20 GCP w x
´ m
10.8 10.5
10.0 11.4
10.6 9.5
X
w x ´
m 12.6
9.8 9.3
13.9 10.0
9.4
Y
w x ´
m 4.1
4.5 4.3
5.2 4.6
4.6
Z
Ž .
13.5 m . The planimetric accuracy potential of MOMS-02rD2 is not verified, since the GCP and
check points could not be identified in the imagery with the required accuracy.
5. Computer
simulations on
MOMS-2P r r
r r
r
PRIRODA image orientation
A series of computer simulations have been car- ried out to analyze the effect of certain parameters
on the accuracy of MOMS-2P image orientation, especially the effect of block configuration and con-
trol information.
5.1. Input parameters 5.1.1. Block configurations
The computer simulations were performed for three different block configurations:
Ø Single strip
Ø Block of six strips with q s 20 side overlap q
two crossing strips Ø
Block of 13 strips with q s 60 q two crossing Ž
. strips Fig. 4
Fig. 4. Block consisting of 13 strips with four baselengths each and 60 side overlapqtwo crossing strips. The region of interest
is within the dotted lines. The GCP locations are marked with a triangle.
The strip length was chosen to four baselengths Ž
. 640 km . This results in the fact that points at the
beginning and the end of the single strip are pro- jected into two images only, whereas each point in
the central part of the strip is projected into three images. The strip width amounts to 50 km. The
2
Ž entire block covers 320 = 250 km
without two-ray .
Ž area , corresponding to the area of Catalonia 270 =
2
. 250 km , which was thought to be the most impor-
tant test site of the MOMS-2P experiment. 5.1.2. Interior orientation parameters
All parameters of the interior orientation were introduced as error-free values.
5.1.3. Conjugate points The object coordinate system is defined as
topocentric Cartesian system XYZ with the positive direction of the X-axis parallel to the direction of
flight. The object points are arranged in two different grids:
Case 1: D X s 40.0 km, DY s 20.0 km, Z s 0.0 km. Case 2: D X s 2.0 km, DY s 10.0 km, Z s 0.0 km.
Consequently the single strip consists of 27 and the blocks contain 117 object points in the first case,
whereas the single strip consists of 805 and the blocks contain 4025 object points in the second case.
For each block configuration, the image coordinates of the object points were computed assuming a flight
path with a constant altitude of 400 km and attitude values equal to zero.
In case 1 only a few conjugate points are included Ž
. which can be measured high precisely s s 0.1 pixel
using a digital stereo comparator, whereas in case 2 additional tie points derived from digital image
Ž .
matching s s 0.3 pixel are introduced. Thus, we have the following two cases for the image coordi-
nates, which were treated as being uncorrelated:
Case 1: s s 0.1 pixel for all image coordinates. Case 2: s s 0.3 pixel for all image coordinates,
Ž .
Ž .
except for the 27 points strip and 117 points block of Case 1, respectively, having s s 0.1 pixel.
5.1.4. Ground control information The simulations have been carried out for two
different configurations of ground control informa- tion:
Case a: no ground control. Case b: 16 GCP with s s s s s s 1.0 m.
X Y
Z
The 16 GCP are arranged in four groups of four points each, located at the corners of the at least
three-ray area of the strip or the block. The standard deviations of the GCP’s image coordinates are as-
sumed to 0.3 pixel.
5.1.5. Orbit and attitude obserÕations For the orbit and attitude observations two differ-
ent cases were investigated: Ž
.
Case A: error-free observations s s 0 . Case B: realistic orbit and attitude observations.
Ž .
Table 4 Case A defines the accuracy limit, whereas case B
is the realistic one. In Table 4 the standard deviations describing the relative accuracy of the position pa-
rameters are nearly zero, since all camera positions are constrained to lie on the orbit trajectory. The
standard deviations describing the absolute accuracy are 5 m for the position and 2 cmrs for the velocity
components of the epoch state vector. For each orientation point attitude observations were intro-
duced with a relative accuracy of 10
Y
. Due to the poor alignment precision of the MOMS-2P camera
with respect to the Astro 1 star sensor, no observa-
Table 4 Standard deviations of the observed position and attitude parame-
Ž .
ters –: no observation Position
Attitude
Y
Relative 0.1 m
10 Absolute
position 5.0 m
– velocity
2 cmrs –
Absolute bias
– –
Y
drift –
0.16 rs
tions for the attitude bias are assumed. The drift of the IMU gyros should not exceed 0.16
Y
rs during one MOMS-2P imaging sequence.
Based on experiences with MOMS-02rD2 data, the distance between the orientation points was cho-
Ž .
sen to 4940 rows ca. 90 km leading to nine orienta- tion points per strip.
5.2. Results Ž
. For analysis, the rms values m
planimetry
ˆ ˆ
X Y
Ž .
and m height of the theoretical standard deviations
ˆ
Z
s , s and s
of all points within the dotted lines
ˆ ˆ
ˆ
X Y
Z
in Fig. 4 were calculated. Moreover, the rms values m
of the theoretical standard deviations of the
ˆ ˆ
zhu
ˆ
ˆ ˆ
estimated exterior orientation parameters z , h, u at
ˆ
the orientation points were computed. All accuracy figures were derived from the inverted normal equa-
tion matrix. In case of a free adjustment the seven data parameters are determined by minimizing the
trace of the covariance matrix of the estimated object point coordinates. So the free adjustment represents
the interior accuracy of point determination. In Figs. 5–8 the rms values m
and m are shown graphi-
ˆ ˆ ˆ
X Y Z
cally. First the results of the single strip and block
Ž .
adjustments with GCP are discussed Figs. 5 and 6 . Ž .
Assuming error-free position and attitude data A ,
the accuracy of point determination only depends on
Fig. 5. Rms values m for different block configurations with
ˆ ˆ
X Y
Ž .
Ž GCP case b , observed position and attitude parameters cases A
. Ž
. and B and different number of object points cases 1 and 2 .
Fig. 6. Rms values m for different block configurations with
ˆ
Z
Ž .
Ž GCP case b , observed position and attitude parameters cases A
. Ž
. and B and different number of object points cases 1 and 2 .
the standard deviations of the image coordinates, the number of tie points and the geometric constellation
of the ray intersections. The rms values are 1.1 m in planimetry and 3.5 m in height for the single strip.
The planimetric and height accuracies decrease only moderatly, if the position and attitude data are intro-
Ž .
duced with realistic standard deviations case B , Ž
. even with a small number of tie points case 2 .
Using the equal number of GCP the accuracies improve by factor 1.4 for the q s 20 blocks and by
Fig. 7. Rms values m for different block configurations without
ˆ ˆ
X Y
Ž .
ground control case a , observed position and attitude parameters Ž
. Ž
cases A and B and different number of object points cases 1 .
and 2 .
Fig. 8. Rms values m for different block configurations without
ˆ
Z
Ž .
ground control case a , observed position and attitude parameters Ž
. Ž
cases A and B and different number of object points cases 1 .
and 2 .
factor 1.8 for the q s 60 blocks compared to the single strip, due to the increasing block strength. The
blocks with q s 60 and two additional crossing strips provide excellent rms values of about m
s
ˆ ˆ
X Y
0.9 m, m s 2.5 m and m s 1.6
Y
, respectively, in
ˆ ˆ ˆ
Z zhu
ˆ
case 2. From Figs. 5 and 6 it can be also seen that the
number of tie points has only little influence on the rms values for the blocks. Even a small number of
117 points provides high accuracies in planimetry and in height.
In the following the adjustment results without Ž
. GCP are analyzed Figs. 7 and 8 . The single strip
leads to an undetermined configuration because no observations are available for attitude bias, and other
observations are not able to compensate for that. If a block with q s 20 and two crossing strips is ad-
justed, all angles are determined due to the absolute position data, which were introduced for each strip
of the block. A comparison of Figs. 7 and 8 with Figs. 5 and 6 shows that the object points are less
accurate, if no GCP are introduced at all. A high
Ž .
number of conjugate points case 2 , however, leads to improvements of factor 1.3 for m
and m
ˆ ˆ ˆ
X Y Z
Ž .
compared to a small number of points case 1 . The best accuracies without ground control are achieved
using observed position and attitude parameters for blocks with 13 q 2 strips and 4025 tie points, where
the rms values amount to m s 3.5 m, m s 4.6 m
ˆ ˆ ˆ
X Y Z
and m s 2.3
Y
, respectively.
ˆ ˆ
zhu
ˆ
6. Summary and outlook
