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AIRBORNE KINEMATIC GPS POSITIONING FOR PHOTOGRAMMETRY THE DETERMINATION OF THE CAMERA EXPOSURE ... - page 4 / 11

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2 Sec

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5 sec

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5 sec

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0.000/0.031 0.000/0.063

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0.000/0.032 0.001/0.084 0.000/0.063

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Aircraft

Sample

Sample

% of

Mean/Std Dev

Type

Size

Rate

sample

of Sample (m)

> 20 cm

X,Y, and Z

Table 1 Evaluation of 2- and 5-Second Sample Rates for GPS Phase Information During a Photo Mission

____________________________________________________________ 0.000/0.055

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INTERPOLATION ALGORITHM

The objective of the interpolation is to compute, using a limited portion of the navigation file, a position for the antenna phase center at the time of exposure which is within a half epoch of the central time of the limited data set i.e., less than 0.5 second for a 1-Hertz sample.

The interpolation algorithm uses a second-order polynomial whose three coefficients are solved for by least squares method.

The polynomial represents a curve which fits the aircraft

trajectory over a 5-epoch to each coordinate axis.

period.

A different curve is fit

The

coefficients

of

this

polynomial

can and

be used to compute the aircraft position offset, acceleration in each coordinate direction.

velocity

The following models are used for interpolating the antenna

phase center coordinates:

.

.

.

.

.

.

.

.

(1)

X1

where ti

(2)

(3)

=

= timei

Xi = ax + bxti + cxti - time3; when i = 1,2,...5; 2

2

a X x 2

+ b x t =a 1 x + c x t + bxt 1 2 2 + cxt2

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