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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
R-Cp model may not be suitable for.
Range Coplanrity
equation: equation:
Ball ; xiv Coplanrity
=. equation:
Col/Range 4 ground en
> e/Arc
Se imag Range
ee 3 equation:
image points circularity
Range M
equation: Denier
Bali equation: ter
Cone equation:
hyperbola
> zit
Fig 2 R-D model and R-Cp model positioning principle
2.3 Orbit attitude model of spaceborne SAR
In SAR imaging process, the motion compensation and
focusing were occurred, so the satellite orbit and attitude data
were compensated to an ideal state. Therefore, no matter what
rigorous model, SAR remote sensing image geometry
processing should use the data that motion compensation
referenced. As the stability of the satellite in orbit, under normal
circumstances, when imaging the reference orbit, the speed and
the actual track, speed is approximately the same. Reference
attitude is generally constant or uniform changes, in the absence
of a reference value then the middle or mean value of original
data could be taken as the initial value, and could get according
to the Doppler parameter value.
TerraSAR-X image adopt the O0 value Doppler imaging
parameters for focus, this means that the beam center planarity
is perpendicular to the velocity direction in imaging. in this
paper, according to this conditions to calculate the sensor
initialization attitude value after SAR imaging motion
compensation. When the three attitude angles are all zero, the
beam center plane is perpendicular to the axis Xo vector, when
the Doppler parameter is 0, the beam center plane is
perpendicular to the velocity vector. Xo axis and speed
direction can achieve the coincidence by rotating around the
Yo-axis of ¢ angle, therefore, when the Doppler parameter is 0,
equivalent to the three original attitude value is (0,¢,0) . Asa
result, unit speed vector in geocentric rectangular coordinate
could also be calculated by a unit vector Xo axis and associated
rotation matrix , that is:
[s v x28 Rt o d (en
[vs v, v.]" is unit speed vector. Based on the formula (6),
Xo,Yo,Zo,Vx,Vy,Vz is the satellite position and speed state
vector in ECR coordinate system, the pitch angle ¢, could be
calculated:
A --asin (2), VHD), - » HZ), »] d
As the satellite's orbit and attitude in a certain time with very
good stability, errors of initial value of orbit and attitude in a
certain time expressed as systemic, and its orbit error and
attitude error with low-level polynomial fitting could meet the
positioning accuracy. For one scene the TerraSAR-X imaging
track is short, linear polynomial is used as refined model for
orbit attitude model, namely:
X, =X ta tat
Y, =Y,, +b, + bt (8)
Ze = Zug Cop t6
9-9 *f,t*ft
K-Kytgy t gil
In the formula (8) (X50. Yso. 750: PoKo) are the ephemeris attitude
initial value, a,b;,c.f;,gi(i=0,1...) are ephemeris and attitude
refined model parameters.
2.4 Stereo positioning model of spaceborne SAR
In order to achieve the high accuracy of the remote sensing
image positioning the orbital and attitude parameters must be
refined. Substituted the linear model (8) into formula (4). the
refined orbit attitude model parameters aj, bacfig: (1,2) and
the ground point coordinates increment (AX, AY, AZ) as the
unknowns, coordinates measurement error equation of the
image point are got through linearized R-Cp equations:
V. m fug Pus fa infa figno
+f 8 ful hl a FSF, (0)
V, m fat foh fo opo og
+o + habt an Ef +1 FX NY,
Where, f. are coefficient of error equation about refined orbit
and attitude model parameters and unknown ground point
coordinates increment. Ix. [y for the constant term. Based on
R-Cp geometric imaging model error equations of pixel
coordinates, ground coordinate, refined model coefficient of
ephemeris and attitude are got for adjustment model of satellite
SAR images positioning:
