The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part BL Beijing 2008 
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<Kt,) = v(t, -t 0 ) + ^a-0,-t„f + ^A a ■(/,-( 0 ) 3 (7) 
1 o 
Where V , a and A a are the unknown mean velocity, mean 
acceleration, and mean acceleration variation respectively, the 
unknown model vector p in (6)is 
vector and the phase velocity vector, then use the least 
square (LS) method to solve the equation(lO). 
4. The undesired atmosphere phase signal is detected as the 
result of the cascade of a low-pass filtering step, performed 
in the two-dimensional (2-D) spatial domain (i.e., azimuth 
and range), and a high-pass filtering operation with respect 
to the time variable. 
p T = [v,a, Aaf 
(8) 
and the model matrix M is 
M = 
t\ t 0 
^2 i /j 2t 0 
(A *o) 
(¿2-Q 3 -(ii-Q 3 
6(¿2 _ h ) 
¿N "*■ ¿N-1 ^0 (?N A)) (¿N-1 ^0) 
¿N-1) 
(9) 
By including this model, the equation system in (6) is generally 
simplified, for such a smooth temporal model, the product 
BM is nonsingular, the estimate of p can then be obtained by 
solving the following equation in an optimal LS way. 
BMp + c-Ah+ (f) A = 8(f) 
(10) 
where C • Ah accounts for possible topographic artifacts due to 
error in the Digital Elevation Model (DEM) used for removal 
of the topographic phase , Az is the DEM error, 
c T = [(4n / 2){B n / r sin v), ■ • •, (4/r / 2)(B XM / r sin y)] 
, B L is perpendicular baseline, Y is sensor target distance, V 
is look angle). 
The key steps involved in the displacement time series retrieval 
implemented via the SBAS-DInSAR algorithm can be 
summarized as the follows:* 
1. Properly chosen the data pairs to generate the multilook 
DInSAR interferograms, the key objective of this step is to 
mitigate the decorrelation phenomena by introducing 
constraints on spatial baseline and temporal separation 
between the orbits relevant to interferometric SAR image 
couples. 
2. Phase unwrapping of the original phase 8(f) t (x, Y) , then 
calibrating them to a reference pixel as mentioned 
previously. 
3. Assuming a relationship between the model parameter 
4. RESULTS 
A test site in the city Nanjing P. R. China has been chosen, see 
Fig. 1. Nanjing is the capital of Jiangsu Province, in an area 
surrounded to the west by the Yangtze River, to the east by 
Purple Mountain. New Qinhuai River in the south and the 
branches of Qinhuai River in the middle flow across the city 
from west to east, the west area of Qinhuai River is a new 
developed residential area which located in the stratum of the 
Yangtze River valley flat, where it is easily suffered from 
ground deformation. 
Fig. 1: City Nanjing in SAR amplitude image, the investigated 
area is highlighted 
In order to validate the presented method, an ERS2 SAR data 
set composed by 8 acquisitions acquired from August 19,1996 
until April 10,2000, on descending orbit, was first coregistered 
to the August 19,1996 scene, then we selected the combinations 
that exhibited a mutual perpendicular baseline less than 100m, 
and temporal baseline less than 4 years, this resulted in 2 
different subsets, the 13 interferograms were generated by Doris 
software (Bert Kampes, 1999), characterize by a perpendicular 
baseline from 21.9m to 98.2m, temporal baseline from 35 days 
to 1158 days, in order to reduce the phase noise, a complex 
multi-look operation with 4 and 20 looks in range and azimuth, 
respectively, is carried out, the ground range pixel dimension of 
all products is therefore about 80><80m in the range and azimuth 
directions, respectively , see Table l.The topographic 
component has been removed using a SRTM3 DEM, which has 
the height accuracy of about 16m (Bamler,1999), the ERS2 
precise orbit state vector computed by the Technical University 
of Delft was used for flat earth reduction. 
In order to exclude decorrelated areas from the study, we 
selected only the pixels that exhibited an estimated coherence 
value larger than 0.3, in at least 30%of the interferograms, 
based on the selected pixels, a Delauney triangulation was 
generated to connect these pixes, and interpolation was done for 
all the images in order to ease the phase unwrapping of the 
selected interferograms, see Fig. 2.