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Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

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Appendix I / Utilities / Earth, Atmosphere and Gravity<br />

_ _<br />

Endif . Whereupon,<br />

ξ<br />

11<br />

22.6-3<br />

: = 1 − ξ<br />

2<br />

12<br />

( ξ , ξ , ξ , ξ )<br />

Equation 22.6-13<br />

2<br />

hE<br />

( 1 − e ⋅ ξ , R ξ , ξ ⋅ ξ , P − ξ ⋅ ξ )<br />

11<br />

13<br />

a<br />

14<br />

13<br />

15<br />

6<br />

14<br />

16<br />

: =<br />

p<br />

14<br />

12<br />

Equation 22.6-14<br />

ZE<br />

( ξ , ξ ) : = ( P − ξ ⋅ ξ , ξ ⋅ ξ + ξ ⋅ ξ )<br />

17<br />

18<br />

⎛<br />

⎜<br />

⎝<br />

p<br />

15<br />

11<br />

12<br />

16<br />

11<br />

17<br />

Equation 22.6-15<br />

( ) ⎟ ⎜<br />

19<br />

, ξ : = ξ ⋅ ξ − ξ ⋅ ξ ,<br />

ξ19 20<br />

12 17 11 16<br />

−1<br />

ξ15<br />

⋅ ξ13<br />

The geodetic co-ordinates are given by,<br />

ZG<br />

( µ , λ , P )<br />

ξ<br />

+ ξ<br />

18<br />

⎞<br />

⎠<br />

Equation 22.6-16<br />

−1<br />

YE XE<br />

'<br />

ZE<br />

−1<br />

( tan ( P P ) , ( λ + ξ ) ⋅ sign ( 1,<br />

P ) , ξ + 2 ⋅ ξ ⋅ ξ )<br />

p<br />

p<br />

22.6.5 Conversion from WGS84 to ECEF Co-ordinates<br />

p<br />

p<br />

20<br />

p<br />

d,<br />

p<br />

: =<br />

p<br />

18<br />

19<br />

20<br />

Equation 22.6-17<br />

WGS84_TO_ECEF takes the co-ordinates of point (p) on the geodetic<br />

vertical intersecting the Earth’s geoid at (d), returning its ECEF position.<br />

WGS84_TO_E CEF<br />

P<br />

E<br />

p<br />

: =<br />

⎛<br />

⎜<br />

⎜<br />

⎜<br />

⎜<br />

⎜<br />

⎜<br />

⎝<br />

ZG ( R + P )<br />

r,<br />

d<br />

ZG ( R + P )<br />

r,<br />

d<br />

d,<br />

p<br />

d,<br />

p<br />

ZG E<br />

( µ , λ , P , P )<br />

d<br />

d<br />

⋅ cosµ<br />

⋅ sin µ<br />

d,<br />

p<br />

⋅ cosλ<br />

⋅ cosλ<br />

( ( )<br />

) ⎟ ⎟⎟⎟⎟⎟⎟<br />

2<br />

ZG<br />

1 − e ⋅ R + P ⋅ sin λ<br />

r,<br />

d<br />

p<br />

p<br />

d,<br />

p<br />

p<br />

p<br />

p<br />

p<br />

Equation 22.6-18<br />

⎞<br />

⎠<br />

Equation 22.6-19

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