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Chapter 3 / Sensors / NAVSTAR GPS
_ _
The universal navigation constant (G), and the Earth mass (M) define the
WGS 84 gravitational constant (µG),
µ
G
: = G ⋅ M : =
3.11-7
3.
986005 x
10
14
Equation 3.11-11
Transmission quantisation errors and the use of 2 nd order satellite clock
corrections, introduces a pseudorange error of < 0.1 m in the first 1.5 hrs
after a navigation message up-link. Thereafter, the degradation reaches
90 m after 3.5 hrs, Dierendonck (D.17) .
3.11.4 Reference Pseudo-Data
From Kepler’s laws, the satellite period (TS) is related to its orbital rate (ωS),
T
S
: =
2 ⋅ π
ω
S
: =
2 ⋅ π
P
µ
3
r,
s
G
Equation 3.11-12
The satellite period is revised using the correction for the computed orbital
rate (∆ωS) in the Ephemeris data. For simplicity, 24 satellites are modelled
travelling in circular orbits about the Earth centre at a radius (Pr,s) of
20_183 km with an orbital speed (ωS) of 0.00833333 rad/s. The position of
the j’th satellite in the i’th orbital plane is defined by the Mean Anomaly
with respect to the rising node (κij),
∀
( i , j ) : i = [ 1 ( 1 ) 6 ] ; j = [ 1 ( 1 ) 4 ]
κ
ij
: =
ω
S
⋅ t
m
π
+ ⋅
6
( 2 ⋅ i + 3 ⋅ j − 5 )
⇒
Equation 3.11-13
(tm) is the time after midnight General Mean Time (GMT). The position of
a particular satellite in the Orbital frame,
O
r,
s
r,
s
( ) T
cos κ , sin , 0
P : = P ⋅
κ
Equation 3.11-14
A satellite's position with respect to the Celestial frame is therefore,
C
s
C
O
P : = T ⋅ P
The position of the receiver with respect to the Celestial frame is,
O
s
Equation 3.11-15