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AIRBORNE KINEMATIC GPS POSITIONING FOR PHOTOGRAMMETRY THE DETERMINATION OF THE CAMERA EXPOSURE ... - page 9 / 11

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rotations and three translations are used in the transformation:

a.The antenna coordinates at the time of exposure are converted

from

WGS84

rectilinear

to

ellipsoidal

latitude,

longitude

and

elevation.

The

latitude

(lat)

and

longitude

(lon)

are then used to rotate the WGS84 coordinates into an East,

North,

local

vertical

system.

b.The covariance matrix from the interpolation model error propagation is similarly transformed to obtain a covariance matrix in the local vertical system.

c.The spatial offset components between the camera and antenna

are the

then rotated into the standard gimbal form.

local coordinate system The rotation elements of

using Kappa

and drift are combined into a single rotation.

Rotational

elements of Phi and pitch are also combined. No determination of roll was made during the flight, so is treated independently.

Omega

It may be argued that the camera rotates about a set

mechanical coincident

gimbals whose rotational center may or may not

with

the

exposure

station.

If

there

is

any

of be

eccentricity

between

the

gimbal

rotational

center

and

the

exposure station, then the angles of exterior

not and

be algebraically summed with the observed

swing.

The

eccentricity

discussion

will

orientation can angles of pitch begin with the

particular situation encountered pitch and swing angles are small

in NOAA's application (less than 2o).

where

By design of the RC-10 camera mount, the optical axis, about which swing is measured also coincides with the vertical axis of the mount, therefore swing and kappa angles can be

combined without an eccentricity correction.

case

for

the

pitch

angle.

The

exposure

station

Such

has

is not the a vertical

separation of gimbal center

approximately 27 mm from the gimbal origin (the is probably at the camera's center of gravity).

The aircraft pitch relative to the camera mount was measured during actual flight conditions and is referenced to the

gimbals.

A

maximum

and

generally

constant

pitch

angle

of

1.50

was

measured

and

occurred

at

the

lower

limit

of

the

Citation's

operating speed. eccentricity into

The consequences of not account are as follows:

taking

the

Maximum pitch error = 0.027m * sin(1.50) = 0.0007 m

A displacement error of the exposure station of less than 1 mm in the direction of flight is introduced if the eccentricity

correction is neglected.

mount

consists

of

a

double

In the most

concentric

general case, a camera two orthogonal axis

gimbal.

The mechanical design of the gimbals and

of the rotation angles may dictate a more thorough

the magnitude investigation

of

the

effect

of

the

eccentricity.

The gimbal form rotation matrix (Merchant 1988) is formed by the product of the three independent rotations of pitch roll

and the the

swing.

The order of multiplication is important only in

general case mentioned above. specific case is not critical,

The order of rotation for considering, the design of

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