Premalatha Balan 
  
1.1 Phase trend due to flat earth 
The fringe pattern of a hypothetically perfect flat terrain should be uniform with a fringe rate depending only on the 
baseline separation between the satellite positions at which the master and slave images were acquired. A shorter . 
baseline produces a low fringe rate, i.e. widely spaced fringes, whereas a longer baseline produces an interferogram 
with a high fringe rate, i.e. closely spaced fringes. This uniform fringe pattern gives an impression of uniform slope for 
this hypothetically flat terrain. This phase variation is called phase trend due to flat earth. To arrive at phase variation 
due to terrain height variations only, we need to remove the phase trend due to flat earth very accurately, as any 
inaccuracy in this process would lead to the introduction of a residual slope in the final DEM. To remove the flat earth 
phase trend, an accurate baseline estimate is required. 
The baseline can be estimated from orbital information for the master and slave images. The co-ordinates of the orbital 
position are given in the leader file in the form of state vectors. Baseline estimation using state vectors would be the 
appropriate method if these vectors truly represented the satellite positions. The European Space Agency (ESA) 
provides four types of state vectors with different accuracy levels, details of which and of the accuracy associated with 
them can be found at ESA's website (http://earthent.esrin.esa.it). A brief description is provided here. 
The types of state vectors provided by ESA are predicted orbits, restituted (or operational) orbits, preliminary orbits and 
precise orbits. Predicted orbit is calculated using fast delivery altimeter data from the last three days to predict the orbit 
for the next nine days. These estimates are updated daily to improve accuracy. The error of prediction is about 400m for 
a 6-day prediction, around 125 m for 3-day prediction and 25 m for 1-day prediction. The restituted orbit information is 
calculated using the predicted orbits and the orbital information of the central day of a three-day moving window. As a 
result, this information is available with a one-day delay after the satellite pass. The accuracy estimated is 2 — 4 m along 
track, and 1 — 2 m across track. Preliminary orbits are calculated on the basis of fast delivery tracking data for every 
120 seconds with a spatial resolution of 900 km. Precise orbit results from a computation all available satellite tracking 
data and is corrected using dynamic models. The radial accuracy is in the order of 8-10 cm. This is the most accurate 
state vector available from ESA. Closa (1998) has studied the error introduced by inaccurate baseline estimations using 
different state vectors mentioned above, and suggests that very precise orbital information is needed to remove the 
residual phase due to flat earth. He also noted that additional altimeter data would improve the precision of the position 
of the orbit, even when precise state vectors are provided. 
1.2 Methods of estimating baseline 
When a user obtains data from a data provider, information about the type of state vectors provided in the leader file 
may not be available. If the state vectors are not of “precision” type, then an alternative method is needed to estimate 
the baseline. The Gamma software used in this study provides the user an opportunity to estimate baseline length using 
one of the following methods: 
(a) Orbital information . 
(b) Image offset polynomial developed during co-registration of the SLC images 
(c) Fringe rate method, and 
(d) Combinations of the above methods. 
It is reported in the Gamma documentation that baselines estimated using orbital information could be used as an initial 
estimate to input to other methods of baseline estimation, if the orbital information provided in the form of state vectors 
is not accurate. The methods using image-offset parameters use the image offset polynomial developed for the co- 
registration of the slave image to the master image, to estimate baseline separation. This method estimates the parallel 
baseline component more accurately than other methods. The fringe rate method uses the fringe rate in the 
interferogram over a flat terrain to estimate the baseline. The assumption in the second method is that the terrain 
covered by the estimation window is completely flat and that any fringe rate within this window is considered as the 
phase trend due to flat earth. This method estimates the perpendicular baseline component more accurately if the 
estimation window is positioned over a flat terrain of negligible slope (or negligible height variation) and if the window 
size is carefully specified in such a way that it is small enough to cover the area of flat terrain and large enough to allow 
the calculation of a stable estimate. Iterative estimations over different flat terrain windows positions and different flat 
terrain window sizes and combining all the estimates to produce a final baseline estimate would improve the results. 
However, this method estimates the parallel component very poorly. Combining different baseline estimation 
techniques is suggested as a method to improve the final baseline estimate. Using offset information to estimate the 
parallel component and using the fringe rate method to estimate the perpendicular component is believed to be the best 
combination for accurate baseline estimation. 
  
30 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000. 
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