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Mapping without the sun
Zhang, Jixian

X s — X s» X $ (t 1 0 )
B = B 0 + t(t - t 0 )
\ a x a i
L = BX = I rol lift, b 2
U C 2
Linearized equation (2) will get the measurement error equation.
Showed in equation (5).
V x =A x X-L x
Vx =
A =
V .V
. V
L x y 7 Z
a X2
a il7
a 2\
a 22
a 217
_ a 3i
X — [AX S0 ,AY S0 ,AZ S0 ,A(p 0 ,A(O 0 ,AK 0 ,AÀ X) ,
AX° s ,AYs,AZ° s ,A

where Z, = coordinates matrix of GPS
B = coordinates matrix of image
X= conversion coefficient matrix
For determining the conversion coefficient, there shall be at
least 3 light points made by the comer reflectors in the SAR
When more comer reflectors are available, the least square
estimation algorithm could be used to obtain the conversion
coefficient. The observation equation and the least square
estimation are shown in equation (7) and equation (8).
L = BX + A
There are 17 unknown parameters in equation (5), so 6 GPS
ground control points needed at least to compute the orbital
2.2.3 Geometric correction
Geometric correction of InSAR data could be realized by using
accurate orbital parameters, but this method cannot meet the
demand of monitoring the surface subsidence in mining area
accurately. Generally, it can only used to monitor the surface
subsidence as a qualitative tool , and cannot achieve
quantitative degree entirely (Ge, L., et al., 2003).
Another approach is to deal with InSAR data geometric
correction with GPS measurements. This work also needs
comer reflectors or ground permanent scatterers (PSs). Using
the geodetic coordinates of PSs (which can be obtained by GPS)
and InSAR imageries’ pixel coordinates, precise InSAR
geographic coding products could be created.
The permanent scatterer InSAR (PS-InSAR) technique is an
advanced InSAR technology (Bürgmann, R., et al., 2006). By
selecting isolated ground points which exhibit extremely stable
interferometric phase behavior in a certain period, the new
approach overcomes most problems such as the resolution,
temporal and spatial baseline limitations that hindered
conventional InSAR processing. It has greatly improved the
accuracy of InSAR to ground deformation monitoring,
especially in the cities or the places where the rocks are well
exposed. Sometimes the ground deformation can be measured
to millimetre level accuracy under certain conditions (Zhang, J.,
et al., 2007). But PS-InSAR technique needs large amount of
InSAR images, and it can only used to small areas for slow
surface deformation of mining area generally.
If the image coordinates of a reflector are assumed to be
(Irowdcol)j and the corresponding geodetic coordinates is to be
(G, at>G[ on ), the conversion between them with the same
projection could be expressed in equation (6).
where A = observation error vector
X = (b t PbYb t PL (8)
where p = £)“'
Z) A = variance of vector A
After conversion parameters are obtained, image coordinates
can be converted one by one. The geometric corrected InSAR
imagery then could be overlapped with other graphics to make
detail analysis on the mining-induced surface subsidence.
2.3 InSAR and GPS data’s interpolation
Compared with cities, the mining area has a higher speed in
surface subsidence. The repeated monitoring period (about a
month) could meet the demand approximately. However, for
determining the subsidence parameters, the repeat monitoring
period must be shortened during the active stages of mining
surface subsidence. In the case, the InSAR data must be
interpolated with other data.
As mentioned above, during monitoring mining subsidence,
InSAR and GPS technology are very strong complementary in
temporal and spatial domain. Therefore, it is very necessary to
interpolate the InSAR data with GPS measurements by
effective means.
To interpolate InSAR and GPS data (Diao, J., 2005), the
following steps could be applied.
Firstly, select the InSAR image that was corrected with GPS
data as the spatial distribution model, and the GPS data can be
interpolated in the spatial domain at grid points. Least-square
adjusted can be used here to get distribution model of
subsidence deformation from the InSAR and GPS results. Then
the GPS subsidence original results with the spatial
interpolation could be obtained.