Scatterer Characterisation Using Polarimetric SAR Tomography

Let define �a ′ d = �ad/��ad� = [B ′ d ] � f ′ d as the normalised
steering vector of �ad with {[B ′ d ]=[�b ′ 1(zd) �b ′ 2(zd)]} D d=1 .It
can be shown that the ratio between the two elements of � f ′ d
corresponds to the polarisation ratio ρEd � . The estimation of
�f ′ d is given by calculating the eigenvector of the Hermitian
matrix [B ′ d ]† [EN ][EN ] † [B ′ d ], corresponding the the smallest
eigenvalue.
Finally, the two polarimetric angles {γd} D d=1 and {δd} D d=1
can be determined uniquely from:
γd = tan −1
� �
�
� 1
�
�
� �
�ρEd
� � with δd = − arg ρEd � (11)
From the spheric angle, it is possible to estimate the
orientation φ and the ellipticity τ angles characterising the
polarisation ellipse. The relations between all different angles
are:
tan 2φ = tan 2γ cos δ
sin 2τ = sin2γsin δ (12)
height (m)
height (m)
655
645
635
625
655
645
635
625
forest
MUSIC (5) - PHI
street
building
corner
reflector
ground
0 100 200 300 400 500
azimuth position (pixels)
MUSIC (5) - TAU
forest
street
building
corner
reflector
ground
0 100 200 300 400 500
azimuth position (pixels)
+15 ◦
angles (deg) −15◦
+15 ◦
angles (deg) −15◦
Fig. 5. Angles characterising the polarisation ellipse. Top Orientation angle
φ. Bottom Ellipticity angle τ
Fig. 5 presents results of this polarimetric approach of
the SAR tomography, using HH and VH polarisation data.
It represents the orientation φ and the ellipticity τ angles
retrieved using the polarimetric MUSIC approach, assuming 5
scatterers. These results show that the retrieved polarisations
are media depending. The polarisation state responses of the
forest ground and the grass field are not the same. The
response of the ground over the forest is a linear polarisation
(τ =0◦ ) with an orientation about 15◦ , whereas the polarisation
over the grass field is horizontal linear polarisation,
characteristic of a surface reflection by a wave emitted in
a horizontal polarisation. Over the building, the polarisation
state is similar with that the ground under the forest. Over the
forest canopy, polarimetric responses are random, as it can be
expected from the random behaviour of this kind of media.
This polarimetric approach of the SAR tomography shows
that the polarimetric behaviour is depending with the media
observed and make it possible to characterise partially targets
in terms of height position but also by their physical properties.
IV. CONCLUSION
This paper presents the first step into polarimetric SAR
tomography. In a first part, hight resolution methods were used
to generate high quality tomograms. The results obtained show
an improvement compared to the initial results, and different
scatterers have been detected. Nevertheless, unless having
the ground-truth of the area under study, the mono-channel
approach of the SAR tomography does not make it possible
to identify the nature of the scattering mechanism detected.
For stage with this disadvantage, a polarimetric approach of
the SAR tomography approach is proposed. Like the Caponbased
result data are not coherent and it is not possible to apply
to the obtained data a simple polarimetric decomposition like,
for instance, the Pauli decomposition, which is related to some
basic scattering mechanisms, a polarisation state estimation
based on a extension of the MUSIC algorithm has been
proposed. This method takes into account partially polarised
data. It is shown that the polarimetric behaviour is depending
with the observed media and the partial characterisation of the
target is possible. In the future, a use of fully polarimetric data
will be necessary to completely characterize the objects.
ACKNOWLEDGMENT
This work was supported by the German Science Foundation
DFG, under project No. RE 1698/1.
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