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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: