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AIRBORNE KINEMATIC GPS POSITIONING FOR PHOTOGRAMMETRY THE DETERMINATION OF THE CAMERA EXPOSURE ... - page 8 / 11

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Errors introduced by the observed quantities and interpolation model can be propagated through the above system of interpolation equations if the variances for the unknown

parameters

and

time

can

be

estimated.

The

variance-covariance

for

the

parameters

is

obtained

from

the

inverse

of

the

normal

equation matrix scaled by the a

weight. The as follows:

estimate

for

timing

posteriori variance of unit error is obtained empirically

1.

Knowledge of the

precision

for

the

GPS

time

tags

which

are

receiver

dependent.

2. Knowledge the camera and GPS dependent.

of the uncertainty in timing delay between which is GPS receiver and camera system

3.

Knowledge about the uncertainty of shutter timing

offset measurement at the midpoint is camera dependent (Taylor 1964).

of

shutter

opening

which

The first two error sources are insignificant considering the velocity of the aircraft and the stability of the receiver

and timing therefore,

clocks.

The largest contributing factor is,

the

shutter

timing

offset.

This

error

is

currently

estimated

to

be

0.0005

sec

(Lucas

1989).

This

estimate

will

decrease

in

magnitude

as

camera

manufacturers

refine

internal

timing

techniques

associated

with

forward

motion

compensation

requirements (Coker 1989). position is given as 2 cm in

The error estimate for planimetry and 4 cm in

the GPS elevation

(Mader 1992)

.

These values have been accepted as true.

Assuming that there is no correlation between the position,

timing matrix

and can

unknown parameters, a combined variance-covariance

be

derived.

The

derivation

can

be

found

in

the

author's dissertation at this time.

(Lapine

1991)

and

will

not

be

developed

Several assumptions are made about the camera and aircraft attitudes and the resultant contribution to the error in the exposure station position:

a.The exposure station will be defined as the entrance node to the lens system of the camera.

b.Vertical photography is assumed a priori and refined during

the aerotriangulation.

estimated

by

the

azimuth

The initial

between

two

swing angle consecutive

is antenna

positions and obtained from

can be refined as improved aerotriangulation.

knowledge

is

c.The pitch and drift angles are measured between the aircraft

and the

the camera.

The

spatial

offsets

pitch and drift were measured.

angles

were

zero

when

d.The variance-covariance matrix for the exposure station can be propagated through the various models using a priori estimates of the precision for the observations.

The antenna and camera coordinate systems are right-handed

as

are

the

three

rotations

about

the

camera

axes.

Three

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