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

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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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