The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi XXXVII. Part Bl. Beijing 2008
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(step=5pxXS =>f< 250). So we have to filter aliasing
secondary frequencies.
:
u-
Di f
T [20 ft 4 4 ms ; f c = 70 Hz
t—f
¡1: m =7.2ms; f = 140 Hz
T| 21 j=21.6 ms ; f¿= 46 Hz
*
Figure 7: PHR focal Plane
The delays between the various couples aren’t independent so
there is some blind frequencies. We have the good luck that no
harmonics are on this blind frequency and that the excitatory
frequencies are variables over time.
3.3 Processing
3.3.1 Colocalisation and correlation
On each retina couples, the processing computes
colocalisation map (with an average altitude or with a DTM),
and the effect of slight differences in roll and pitch to calculate
the partial derivatives. Secondly it chooses the most relevant
points for the correlation to avoid erroneous interpretations (sea
and clouds) and to reduce the computing time, using a a-priori
criterion built on HF radiometric local gradient (.Delon,
B.Rouge 2007). The need of the core process is 20 points for
each line correlation of a couple. Then it computes the
subpixel level image matching by similarity. For PHR we chose
a correlation window of 3 pixels in line and 31 in column.
For further processing correlation grids of different couples will
be synchronous.
3.3.2 Instant synthesis
First, displacements residues (filtered at 3 sigma) are computed
with the best knowledge of attitude (eventually obtained by
iteration with local integration). Second, on each correlation
line and each couple , attitude errors differentials in the two
directions (roll and pitch in the viewing referential) are fitted on
residues by a weighted least-squares. These synthesis are
performed in assumption that the two retina of couple are
almost parallel and distant of rj
3.3.3 Local integration
The goal is to calculate the correction attitude signal from
several or one differentials. For PHR it implements the
innovative approach (patent pending) of local integration by
combining linear p x k differential measurements (p couples
shifts of the k samples around this time ti) for each moment ti.
So the inputs must be various differentials at the same instant
of quasi harmonic signals and almost stationary .
Then the retrieved signal is interpolated and supplemented on
areas where p couples lack information on the interval k. On the
edges of holes we use the retrieved signal above and
differential measures to avoid irrelevant extrapolation .
3.3.4 Complementary Processing
This data processing is specific to PHR. The TDI PAN pixel
date is the time of the last stage of integration and not of the
middle. So the correction Pan signal must be out of phase with
the correction XS signal.
In another hand, the PAN TDI retina is rather distant of the XS
retina used by the correction calculation. A landscape hole
viewed on XS retina at one time and an interesting landscape
viewed on PAN retina can be simultaneous. And for this time
no correction signal is available and the almost stationary
disruptive signal does not allow extrapolation.
So the second step of this complementary process uses
correlation between Pan and B2 retina (colocated on DTM) and
the XS correction signal. It calculates by least square (like
“Instant synthesis“) the correction signal of the line image PAN,
depending on the residue and correlation signal correction XS.
This step is being developed.
4. RESULTS
A great number of simulation cases are checked, even on 2
different landscape and with various pilot conditions. The
results are very accurate.
So taking the case of a disruptive signal with magnitudes of
almost one pixel in each direction (roll & pitch) and the overlay
of 8 disruptive signals which are composed of two main
frequencies in the range of 50 to 80Hz, with a frequency drift of
0.2 to 1.1 %., a little frequency noise, a strong measurement
noise associated to the correlation of images 0.17 pixels XS
( o ), using three retina couples measurements and six local time
samples, with one iteration and a phase correction we get errors
less than 0.16 prad=0.04 pixel XS on 99.7% of the time
(0.013pixel XS rms) on the worse direction (r©/)
This processing does not allow not only to find the principal
harmonics but also a part of the secondary as we can see in
Figure 6.
dc{pt _à_t) = ^(pt_à_ t)AR(t, Tj ) +~ (pt _ à _ t)AT (t, zv )
dl(pt _à _t) = -^-(pt _à _t)AR[t,Tj) + ^-(pt _à _t)AT(t,r.)
OK ol
An optional algorithm removes the TBF frequencies (less than
16 Hz) from this synthesis.
5. CONCLUSION
The development of this process line for improving the
geometric model attitude HF on the image required an
important work. The processing gave results of unexpected
accuracy and enabled a great improvement over our previous
work. This treatment will be used operationally during Pleiades
in-flight commissioning because of its robust behaviour on
slightly random signals disturbances and lack of correlation.
