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- Find S so that:
MS-V M =-X*MS*f D /2 (l)
- Find P(X, Y, Z) with the following
three equations:
MP = R 0 + AR * (col -1) (2)
SP = MP +
MP-V M =-X*MP*f D /2 (4)
where:
V M master velocity vector,
X radar wavelength,
f D Doppler centroid frequency,
R 0 near range,
AR pixel spacing in range,
O u unwrapped phase,
D IC interferometric constant.
Figure 1: InSAR geometry and point wise generation of the 3D irregular grid.
3. ANALYSIS OF THE InSAR PARAMETERS
The model employed to generate the InSAR grid of 3D
points includes several parameters that describe the
satellite orbits, the acquisition geometry and the SAR
processing. The parameter accuracy directly affects the
quality of the generated grid. To avoid geometric
distortions in the grid, the parameters known with
inadequate accuracy must be refined through least
squares (LS) adjustment using ground control points
(GCPs).
The parameters of the InSAR geometric model are briefly
described in the following.
3.1 Sensor and SAR Processing Parameters
For the sensor and SAR processing parameters we adopt
the parametric model proposed by Tannous and Pikeroen
(1994).
One of the two model parameters that appear in the slant
range equation is the near slant range Ro. Instabilities in
oscillators and other electrical components of the radar
along with inhomogeneities in atmosphere cause phase
error in the signal in both range and azimuth directions.
This phase error engenders an error in the near slant
range Ro. Furthermore, a timing error in the sampling
window introduces additional error in R 0 . Setting Ro as
parameter (i.e. as unknown) in the LS adjustment allows
compensating for both errors.
The second parameter that appears in the slant range
equation is the pixel size in range AR. Instabilities in
oscillators and other electrical components cause an error
in the slant range sampling. Assuming the error constant
for the whole scene, it can be compensated for by setting
AR as parameter in the adjustment.
A timing error in the first line acquisition time To of the
master image engenders a positioning error in the along
track direction. Such an error adds to the along track
component of the master orbital errors. The along track
positioning error of the master satellite can be removed by
setting To as a parameter in the LS adjustment. In our
procedure the timing error of the slave image is ignored
because the position of the slave satellite is calculated
with respect to the master satellite position (by projection
on the Doppler plane, see equation (1) in Figure 1).
An error in the pulse repetition frequency of the SAR
system results in an error in the pixel size in azimuth AT.
Assuming a constant error for the whole scene, AT can be
treated as a parameter in the adjustment.
The ERS SAR images are usually focused at zero
Doppler (i.e. the Doppler frequency fo that appears in
equation (4) is supposed to equal zero). However, the
errors associated to the SAR focusing make the zero
Doppler assumption not correct. The recorded phase
history differs from the actual phase history because of
small changes in the radar carrier frequency and because
of instabilities in the receiver system. Furthermore, the
Doppler centroid determination, based on the use of
preliminary orbits, is not accurate enough. A refinement of
the Doppler frequency is required. A bilinear variation of
the frequency over the SAR image is considered:
f D = f D0 + fD1 • co1 + fD2 • lin + f D3 • co1 • lin ( 5 )
where foo, foi, fD2 and fD3 have to be estimated in the
adjustment.
