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different types of lands.
1
0.8 -
0.6 -
0.4 -
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Anisotropy
15 25 35 45 55 65 75
Surface scattering fraction
Figure.5. Anisotropy-Surface fraction scatter plot of different
types of lands.
4. PHASE ANALYSIS
Multi-mode-XSAR system provides us the possibility of Multi-
baseline polarimetric interferometry research. In the case, dual
baseline configuration can be achieved via mixed work mode of
airborne SAR system.
A dual-baseline polarimetric interferometry method of
combined characteristics of polarimetry and interferometry is
proposed as follows.
4.1 Coherence Optimization
Fully polarimetric monostatic data can be represented inthe
Pauli basis, assuming reciprocity, for one track, by the
scattering vector k, i.e.,
1 1
ke Se Sr Sm = Sw 2$, t Spy. ( )
T
Using the outer product formed from the scattering vectors and
for images 1 and 2, we can define a 6 X 6 Hermitian,
a
Where <> represents the multi-looking operator, and T the
Hermitian transformation. [T;1] and [T,,] represent the standard
Hermitian coherency matrices that contain the full polarimetric
information for each separate image. [M2] is a new 3x3
complex matrix that containsnot only polarimetric information,
but also the interferometric phase relations of the different
polarimetric channels between both images.
According to the configuration Multi-mode-XSAR system, the
temporal separations of acquisition time of different mode
datasets are relative small and assume that scatter mechanisms
(SMs) are similar at different mode of datasets. In (E.Colin,
2006) an Equal Scattering Mechanisms (ESM) optimization
method is presented for single-baselines, which constrains the
optimized SMs to be equal at the baseline end. It is based on the
numerical range, properties of the modified polarimetric
interferometric coherency matrix I1;,,
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
IT, = 719,7" where 7, — (7, € 75,)/2 (3)
The numerical range of matrix II;?, W(II;;), can be seen as the
the coherence 7 of Il.
Le n
o! JT. o
W={x",x:xeC,x'x=1] (5)
For the ESM case, complex unitary vectors wi, Ww»
corresponding to the SMs vectors are referred to the same SMs:
wj—w3- w. The maximal coherence modulus of II;? corresponds
to the numerical radius y (11).
r(II, ,) = max {ra XC Cx'x = 1} (6)
In (E.Colin, 2006) an iterative method is used to compute /
(I1,,) for the single-baseline case.
ÿ = WT, w where w =
Mixed work mode can afford three baselines interferometric
pairs, three interferograms with the optimized coherence are
respectively formed according to the ESM method.
4.2 ML Phase Estimation
MLE (Maximum Likelihood Estimation) for Multi-baseline
InSAR height estimation is thought as a good tool (S. Sauer,
2007). In the configuration of Multi-mode-XSAR system,
mixed work mode provides two kinds of baseline pairs: one
long baseline pair and two short baseline pairs, and length of
long baseline pair is exactly two times as short baseline pair.
The MLE method for three baseline pairs can be outlined as
follows.
The received signal vector from the same point on the ground
by three acquisitions can be expressed as
yo? = [E^ po 7 po Y (7)
w is the number of multi-looking.
Conditional probability density function f corresponds to the
interferometric phase
Ny = +
f 9,9, FI 1o) - TÍ — exp P Tipo (8)
wzl 7T Ir]
I represents is Hermitian covariance matrices, diagonal
elements are unitary, the off-diagonal elements are defined by
E = exp lix, , d Prise ato voit (9)
P;; is the correlation coefficient between the two acquired SAR
images and it can be calculated via formula(6), x;; is the ratio
between baseline length of image i and image j and baseline
length of imageland image 3, (1,j) = (1,3),(1,2),(2,3), x;= 1,1-p,
p.
Maximum log-likelihood function can be derived via logarithm
operation of (8)
N;
max | (los Pas los) Re ow(-je( - p)) 2 ee
pe] -2z,.2- w=l
(10)
N,
Pas |) Re [on (-je) > pepe |
wzl
N;
a e| ote) m ]
w=]
* (lel - lo:
+(
The phase Q can be calculated in terms of expression (10), one
key point is emphasized that the phase is extended from [-m, TT]
to [-2m, 2m] since the ratio of short and long baseline is exactly
two.
P5 -le:
