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

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Chapter 3 / Sensors / NAVSTAR GPS<br />

_ _<br />

σ<br />

The least squares solution to this problem is,<br />

⎛<br />

⎜<br />

∆P<br />

⎜ L<br />

⎜<br />

∆R<br />

⎝<br />

E<br />

g<br />

CK<br />

⎞<br />

⎟<br />

⎟<br />

⎟<br />

⎠<br />

: =<br />

⎛<br />

⎜<br />

⎝<br />

3.11-17<br />

T [ G ]<br />

T [ G ] ⋅ [ G ]<br />

⎞<br />

⎟ ⋅ ∆P<br />

⎟<br />

⎠<br />

L<br />

s<br />

Equation 3.11-58<br />

The measured geodetic position is given by the conversion in §22.5.4,<br />

G T G E E<br />

( P ) : ( P P )<br />

~ ~<br />

µ ~ λ<br />

= ϕ + ∆<br />

g<br />

g<br />

d,<br />

g<br />

The expected pseudo-range measurement errors,<br />

⎛ E E<br />

P P ⎞<br />

⎜<br />

∆ g ⊗ ∆ g ⎟ ⎛<br />

E ⎜ L ⎟ : = E ⎜<br />

⎜<br />

T<br />

⎜ 2<br />

R ⎟<br />

∆<br />

⎝<br />

⎠<br />

⎝ CK ⎠<br />

The GDOP is the geometric scaling factor UERE,<br />

2<br />

UERE<br />

2<br />

GDOP<br />

2<br />

: =<br />

E<br />

g<br />

g<br />

Equation 3.11-59<br />

T L [ G ] ⋅ ∆P<br />

⎞<br />

2<br />

g,<br />

s ⎟ σUERE<br />

: =<br />

T [ G ] ⋅ [ G ] ⎟ [ G ] ⋅ [ G ]<br />

trace<br />

( [ ] [ ] ) 1<br />

T<br />

−<br />

G ⋅ G<br />

Equation 3.11-60<br />

Equation 3.11-61<br />

( ) ( ) ( ) ( ) 2<br />

XE 2<br />

YE 2<br />

ZE 2<br />

∆P<br />

+ E ∆P<br />

+ E ∆P<br />

+ E R<br />

⋅ GDOP : = E<br />

∆<br />

The Position Dilution of Precision (PDOP),<br />

σ<br />

2<br />

UERE<br />

2<br />

g<br />

g<br />

g<br />

CK<br />

Equation 3.11-62<br />

( ) ( ) ( ) 2<br />

XE 2<br />

YE 2<br />

ZE<br />

∆P<br />

+ E ∆P<br />

+ E P<br />

⋅ PDOP : = E<br />

∆<br />

The Horizontal Dilution of Precision (HDOP),<br />

σ<br />

2<br />

UERE<br />

2<br />

g<br />

g<br />

( ) ( ) 2<br />

XE 2<br />

YE<br />

∆P<br />

+ E P<br />

⋅ HDOP : = E<br />

∆<br />

The Vertical Dilution of Precision (VDOP),<br />

g<br />

g<br />

g<br />

Equation 3.11-63<br />

Equation 3.11-64

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