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.