163
At =
i
1
[arc sin C - y - W - 6Wt ]
6W o i
Next with the exact value of viewing time t^
for the point M^, it is possible to calculate
the osculatory parameters (p,R,I,W,e x ,e y ) and
the shuttle coordinates X and S'.
Referring again to Figure 1, we can then write
the following vector equation in a non-inertial
(terrestrial) reference system:
SMi = OMi - OS
which is equivalent to the vector slant range that
one can rewrite in terms of elements of Figure 3
as follows:
r= xi - fx(t ± ) - tiVe]
Normalizing the vector s’, one obtains
s = IIsit *u which gives the direction cosine of the
line SM^. One can obtain a more accurate value
of the scalar slant range directly from the image
data, so that only the orientation u of the vector
slant range need be kept from 3. By combining
these two parts, image scalar(s) and vector(H), a
refined value is obtained for Is:
Snew = s TT
Referring to Figure 1, note that the local
incidence angle 0^ is the angle between the two
lines M^S and OM-^. The coordinates for the
three points S, Mj[ and 0 (intersection of the
first normal and the Z axis) are known and allow
one to compute the direction cosine (l,m,n) of
each line. Thus, the local incidence angle 0 L
is given by:
cos©l = 1}I2 + m^n^ + n i n 2
The advantage to use the image slant range module
in the calculation of the new shuttle position at
time t^ has been shown when comparing both slant
range values as obtained from image and from orbit
calculations. In fact, such a comparison has
shown an average difference of 613 metres (based
on a twenty point dataset). A second calculation
on the same dataset but with a second initial
shuttle position (modified with only one
checkpoint for image slant range value), has shown
the average difference reduced to approximately 50
metres. This second approach has been finally
preferred due to the consistency of both measures
of slant range.
2.2 Image resampling and filtering
The rectification of raw SIR-B images into the
intermediate level was achieved by using a
polynomial fit between GCP locations obtained from
raw image (but with a modified pixel location
which excludes terrain parallax effect from the
model) and those extracted from topographic maps.
Using respectively 14 and 13 GCPs for the 29 and
53 degree SIR-B dataset, a quadratic polynomial
regression was found to best fit the
transformation with few independent check points
(see Table 1). The residuals obtained for each
image and for both sets of GCPs (test and model
points) were always less than 37.5 metres (1.5
pixel) in either line or pixel direction. These
results are in agreement with those published by
Welch and Ehlers in 1985.
Table 1. Quadratic polynomial fit residuals for
SIR-B image rectification at the intermediate
level.
Incidence Residuals On Test On All Points
Angle RMS (Pixel Points (Model & Test)
Unit): (Total) (Total)
29°
Pixel
1.49(5)
1.44(19)
Line
1.28
1.22
53°
Pixel
1.30(3)
1.28(16)
Line
1.44
1.43
The SIR-B images were then resampled into a
rotated UTM intermediate grid defined also at 25
metre pixel size. A 50 degree UTM rotation was
applied in order to minimize the differences in
geometry between the raw and the intermediate
level products. Figure 4 shows both resampled
images which cover an area 56.75 km long by
15.125 km. These images have also been
radiometrically corrected by applying a 3 by 3
pixel window filter (Lee, 1981) in order to reduce
the speckle effect (which was found to be
necessary at the digital stereo matching level).
Figure 4. SIR-B images (29° left, 53° right)
processed at intermediate level.