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Surface scattering fraction 
Figure.4. Scattering diversity—Surface fraction scatter plot of 
different types of lands. 
1 
  
0.8 - 
0.6 - 
0.4 - 
0.2 - 
0 
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. 
  
  
  
  
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