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rectified using few GCPs and a second order

polynomial fit between image and map coordinates.

In order to retain the parallax effect in these

pseudo-rectified (intermediate level) products,

GCP locations must be specified in elevation above

an arbitrary datum plane as well as

projected position.

The correction to intermediate level imagery

also requires knowledge of incidence angle 0^

for each GCP. An orbit model derived from the

initial ephemeris data for each path was

established in order to provide the incidence

angle estimates for any point (see Figure 1).

Consistency between relative positions as measured

from the orbital model and GCP coordinates and

those from ground/slant range values obtained from

the imagery were also used to refine the

positioning of the orbital flight. Those new

ephemeris values were subsequently used for the

three-dimensional terrain modeling.

2.1 Orbit model

The shuttle position in a Cartesian coordinate

system can be specified completely either by a set

of six orbit elements (p,Q,I,W,e x ,ey) (see

Figure 2) or by six vector componpnts - a position

vector It plus a velocity vector £. As these

parameters evolve with time, variation resulting

from non-spherical and non-homogeneous earth make

it easier to handle these parameters in their

orbit element form.

X-Y: the equatorial plane;

S: the shuttle position;

0: the center of the earth;

p: the Euclidean distance between S and 0;

N: the ascending node;

P: the perigee of the orbit;

I: the inclination of the orbit relative tc

ascending node N;

Q: right ascension of the ascending node;

oj: the argument of the perigee;

W: the argument of the shuttle (ui + true

anomaly);

Figure 2. Geometry of the elliptic orbit

movement.

Path and position of the shuttle can be

extrapolated using linear development of orbit

equations, for any time t^=t + At, providing we

know at least one set of parameters. Considering

that ephemeris data were available approximately

every ten seconds, it has been sufficiently

accurate to keep only the linear variation part of

the orbital parameters. Assuming also that e x

and ey (which are the components of eccentricity

vector and are expressed as follows: e x =e cosw;

ey=e sinw, for a quasi-circular but

non-equatorial orbit) are relatively constant over

a short period of time, the development of the

osculatory parameters as a function of time reduces

to the following:

p = p 0 + 6p t

Q = Qq + 6Q t

I = I 0 + 61 t

W = W Q + 6W t

where linear variations 6p,6I3,6l,6W are known by

celestial mechanic laws.

Taking the image centre as a reference point,

linearization of the osculatory parameters for any

time tj**t allows for an accurate position S of

the shuttle for each corresponding image point

M^. Considering that parameter linearization and

shuttle position make it possible to know the time

at which any ground point was imaged and that

shuttle apparent heading (taking into account for

earth rotation effect) is orthogonal to the line of

sight, (Figure 3), one can write the line of sight

equation developed as a function of time which

makes the scalar product of the two following

vectors equal to zero:

[X( ti ) - t ± t e - XiJ.foti) -7 e ]=0

where • is the scalar product operator;

X( ti ) is the shuttle position vector at time

Jrl*

X(t^) is the shuttle velocity vector at time

" e is the earth velocity vector;

Hfj. is the geocentric coordinates of point M^.

Figure 3. Line of sight representation in

non-inertial (terrestrial) reference system.

Developing this equation, we obtain this

non-linear expression for the time t-^:

t = 1

i [arcsin(C) - y - W ]

6W o

where C and y are a function of V e , and of

the osculatory parameters also a function of t^.

If an approximate value of the viewing time

t^ 0 (obtained from image measurement) is known

for each point M^, one can use an iterative

computation process to refine the value of t^ at

each step: