14.02.2013 Views

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

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

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

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

Chapter 3 / Sensors / NAVSTAR GPS<br />

_ _<br />

σ<br />

UERE<br />

⋅ VDOP : = E ∆<br />

The Time Dilution of Precision (TDOP),<br />

σ<br />

UERE<br />

⋅ TDOP : = E ∆<br />

3.11.7.2 Satellite Selection using Geometrical Methods<br />

3.11-18<br />

ZE ( P )<br />

g<br />

( R )<br />

CK<br />

Equation 3.11-65<br />

Equation 3.11-66<br />

Whilst receivers now track all visible satellites, earlier systems with limited<br />

CPU capacity selected 4 satellites using geometrical techniques. The GDOP<br />

is simply the rss value of the diagonal elements of [G] -1 . The 4 satellites can<br />

be chosen simply on the basis of which combination has the smallest<br />

GDOP. Alternatively, the combination is chosen that minimises the<br />

tetrahedron formed with the receiver using the Gram-Schmidt<br />

orthogonalisation proposed by Kihara [K.8] and Higgins [H.13] . This volume is<br />

equivalent to the smallest GDOP with a theoretical lower bound of 1.581.<br />

The 1 st satellite selected is the one closest to the zenith through the receiver.<br />

The first row in [G], the vector (G1), is then calculated and normalised,<br />

U1 : = G1<br />

2<br />

Equation 3.11-67<br />

The 2 nd satellite is the one closest to 90° from the first. This is determined<br />

by taking the satellite with the smallest dot product between vector (G1) and<br />

(Gi) for the remaining visible satellites. The Gram-Schmidt procedure is<br />

then used to produce a normalised vector orthogonal to (U1),<br />

U<br />

2<br />

: =<br />

G1<br />

−<br />

G −<br />

1<br />

( U1<br />

• G 2 ) ⋅ U1<br />

( U1<br />

• G 2 ) ⋅ U1<br />

Equation 3.11-68<br />

The 3 rd satellite is chosen such that its (Gi) minimises the following<br />

parameter for the remaining visible satellites,<br />

ϕ<br />

1<br />

( U1<br />

• G i ) ⋅ U1<br />

− ( U 2 • Gi<br />

) U 2<br />

: =<br />

⋅<br />

Equation 3.11-69<br />

The Gram-Schmidt procedure gives a normalised vector orthogonal to (U1),<br />

U<br />

3<br />

=<br />

G3<br />

−<br />

G −<br />

3<br />

( U1<br />

• G3<br />

) ⋅ U1<br />

− ( U2<br />

• G3<br />

) ⋅ U<br />

( U1<br />

• G3<br />

) ⋅ U1<br />

− ( U2<br />

• G3<br />

) ⋅ U2<br />

2<br />

Equation 3.11-70

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!