The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part BI. Beijing 2008
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Compute the distance /^between the image center and
the earth’s center with the data of incidence angle (j and
length of slant range r N/2 at the image central point.
Compute Q by use of r according to Equ.9
r] +H 2 - R.
ß / = arccos(-
2 Hr.
-)
(9)
5. Compute the flat ground phase difference between column
j and the central column N/2 in Equ.10
■ _ 2xBcos(6 N!2 -a) 2nB 2 Ar j AkB{H 2 -R h 2 )cos(<9 v/2 - or)
AH sin 0 NI1 1 Arf 2 2AHrf 2 sin0 NI2
(10)
6. After some practical revision of Equ. 10, flat ground phase
of every point at the coordinate of (i, j) can be presented
in Equ. 11
,/./ 2nBcos(0 NI2 -a) 2 kB 2 4kB(H 2 -R h 2 )cos(d Nn -a) +KxAr)
R AH sin0 NI2 Arf 2 2AHrf 2 s\n0 N/2
(11)
However, it can not be directly applied to compute elevation
because the phase recorded on intergerogram is only a part of
its real value called major value with a range of(-^,^]. The
real value of a phase is equal to its major value plus integral
multiple of2;r, in a process call phase unwrapping [3]. After
establishing the relation between the real phase difference
A^and the elevation Az as shown in Equ. 11, interferogram can
be used to produce DEM by elevation computation.
4*3cos(11)
Ar 0 H sin 9 0
2.3.2 Algorithm for Elevation Computation
Based on the geometric information in Fig.2 and algebraic
relation in Equ.ll, we proposed an algorithm for elevation
computation shown in Fig.4. This algorithm grounded on Price
Geometry Model (PGM) brings improved ambiguity of height
in Equ. 12 compared to those of Approximate Geometry Model
(AGM) in Equ. 13. While two equations have the same value
only at image central point, the ambiguity of height rooting in
PGM which involves curvature of the earth has better precision
at other points.
7. To a point P(i,j), the result of flattening phase can be
attained by phase recorded in a SAR image minus the
flat ground phase A(f>f , namely ¡f, = 0 iJ - Aff
8. Observe the output of this step: if unsatisfactory result is
gained, we should adjust some basic parameters and go
back to reprocess it; otherwise, we need only store it for
next steps
2.3 Algorithm for Elevation Computation
^ ArH sin 9
2Bcos(9-a)R h
(12)
. Ar sin 9 n
=— ~
2 B L
(13)
2.3.1 Principle of Elevation Computation
With the assumption of no noises, the left information of
interferogram after flattening phase merely reflects elevation.
Baseline
Incidence angle ¡3 at
image center
DistanceHbetween satellites
and the earth’s center
Slant range r „ n at
image center
Distance R 4 between image
center and earth’s center
Relative height h, at the point P(i,j) compared to image center
Relative height jj at the point P(i,j) compared to the earth’s
I
Store output
Slant range at column
j and its resolution
estimation
Length 2? of baseline and
Angle 9 Mn of slant range
V
Angle of si
'
ant range
angle a.
at image center
at colu
inn J
Fig.2 flow chart of algorithm for elevation computation
2.4 Algorithm for Baseline Estimation
As shown in Fig. 4, there are five vector points on the master
track including P mX P m2 P m} P m4 P m5 which are separately
corresponding to its UTM timef mi t m2 t mi t mA t m5 ■ Similarly,