The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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rate difference of each arc caused by a constant surface 
deformation rate can be deduced (Malvern, 1969) 
Minimal DEM error 
-24.9752m 
Uniform dilation strain rate 
5.0E-5/year 
Phase noise level 
20 degrees 
1 
0 
sin 0 
(10) 
Table 1 The relevant values in simulation interferometric data 
where e is strain rate tensor, L xv is the arc geometric vector, 
0 is radar side looking angle. Then the variance matrix for the 
quaternary arc phase differences in SOL can be deduced based 
on error propagation law using equation (10), it can be written 
approximately as 
D 
= (sin 9a ■ Ÿ 
(11) 
where <j 2 . is variance of components of strain rate which are 
assumed to be equal accuracy and independent, and 
dy = L^jCOsicC'-Uj) (12) 
where L,, Lj are length of the i‘ h and the j th arc respectively; 
a. is azimuth angle of the i' h arc vector with respect to the 
range axis positive direction. This variance matrix D integrated 
a priori information of constant strain rate and will take place 
the sub matrix [ ] in equation (9) during the ambiguity 
determination in the following simulation example. 3 
3. SIMULATION EXAMPLE 
The simulation scenario is same as that in Kampes (2006), 
except that the LOS deformation rate is simulated by a constant 
strain rate model, see equation (10). ERS satellite parameters 
are used in the simulation. Input data is simulated at 1000 
points, for an area of approximately IOxIOAtw 2 , of 31 SAR 
images. The 31 SLC SAR images are ordered in their 
acquisition times and the middle acquisition time image are 
used as the master image of interferometry. Totally 30 
interferograms are obtained. We randomly choose a set of 
quaternary arcs, see Fig.2, to get the four arc time series. Table 
1 lists the relevant values in simulation data set. The ILS 
method are used to solve for the ambiguity and model 
parameters. The covariance matrix of pseudo observations are 
formulated by (9) and (11). The true and estimated parameters 
are listed in Table 2, and the histogram of data residuals are 
drawn in Fig.3. 
Parameter 
Value 
Span of perpendicular baseline 
1636.2m 
Span of temporal baseline 
7.96year 
Maximal DEM error 
24.9685m 
Figure.2 Quaternary arcs chosen 
Arc one 
Arc two 
Arc three 
Arc four 
A h xy 
Ah xy 
Av,, 
A h xy 
Av xy 
Ah xy 
Av *.y 
(m) 
(mm/y) 
(m) 
(mm/y) 
(m) 
(mm/y) 
(m) 
(mm/y) 
Tru 
e 
25.989 
-24.5 
13.647 
9.1 
5.990 
-0.3 
4.718 
-10.4 
Est. 
25.860 
-24.6 
13.353 
8.9 
5.984 
-0.3 
5.019 
-10.5 
Table 2 True and estimated parameters 
Figure. 3 Histogram of data residuals 
From Table 2, we can see that the estimated SOL rate 
differences are almost same as the true values. However, the 
estimated DEM error differences are large in somewhat, the 
maximum estimated DEM error is about 0.3m, which is about 5 
cycles of phase ambiguity. Fig.3 shows the histogram of the 
120 data residuals. Most of them are located between -0.5rad 
and 0.5rad, this is comparable with phase noise level added 
(noise standard deviation is set to be 20 degrees) in the 
simulation data.