194 
- 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 + <D U *X/(4*ji)+D ic (3) 
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.