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# AIRBORNE KINEMATIC GPS POSITIONING FOR PHOTOGRAMMETRY THE DETERMINATION OF THE CAMERA EXPOSURE ... - page 7 / 11

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0

0

1 cm2

0

0

0

0

0

0

or

0

4 cm2 0

• 0

0

• 0

22*0.01 m2

0

0

0

• 0

(24)

0

4 cm2

0

2 cm2

0

0 0

0

2 cm2 0

The time separation from the central observation is

inversely proportional to the weight.

considered

between

observations.

The

No correlation was P (weight) matrix is

a

diagonal matrix with the following elements when a 1 Hertz sample

rate is used:

= 1/(2

2

= 1/(2

1

= 1/(2

0

= 1/(2

1

= 1/(2

2

Sigma

2

1

Sigma

2

2

Sigma

2

3

Sigma

2

4

Sigma

2

5

P

11

P

22

P

33

P

44

P

55

= 1.0 /

2 * 0.01 m )

(25)

= 1.0 /

2 * 0.01 m )

(26)

= 1.0 /

2 * 0.01 m )

(27)

= 1.0 /

2 * 0.01 m )

(28)

= 1.0 /

2 * 0.01 m )

(29)

The a priori variance of unit weight is 1.0.

The validity

of of

this the a

weight system can be proven using a Chi Square test posteriori variance of unit weight against the a priori

variance of in 43 of 45 be tempered

unit weight. The test selected interpolation

by

the

knowledge

that

indicated equal variances

tests.

# The

validity

must

the

degrees

of

freedom

for

the 5-

test is only 3 = 2).

2

(number

of

observations

• -

number

of

unknowns,

The interpolated values for the antenna phase center at the time of the exposure are expressed as follows:

Xexp

= Kx(1) + K Kx(3)*(time

x exp

(2)*(time - time3)

exp 2

Yexp

= Ky(1) + K Ky(3)*(time

y exp

(2)*(time - time3)

exp 2

Zexp

= Kz(1) + K Kz(3)*(time

z exp

(2)*(time - time3)

exp 2

• -

time3) +

(30)

• -

time3) +

(31)

• -

time3) +

(32)

# As a final note, the model used in this paper only

approximates mathematical

the actual trajectory of the aircraft.

The

modeling

process

acts

as

a

filter,

smoothing

the

aircraft

trajectory

using

a

second

order

polynomial.

It

would

be interesting to examine the extent of smoothing which actually

takes place.

The model

is

validated

by

the

results

illustrated

in Table 1. This same model James Lucas (Lucas 1989) and National Geodetic Survey.

was independently is currently used

developed by within the

# ANTENNA PHASE CENTER TRANSFORMATION TO EXPOSURE STATION

The interpolated geocentric position of the antenna phase center at the exposure time can now be transformed through the previously determined system of spatial offsets to the position of the exposure station.

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