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Chapter 3 / Sensors / NAVSTAR GPS
_ _
C
g
C
E
E E A A B
( P + T ⋅ ( P + T P ) )
P : = T ⋅
⋅
The reference LOS range to each satellite is therefore,
C
g,
s
C
O
O
s
C
E
o
3.11-8
A
m
E E A A B
( P + T ⋅ ( P + T P ) )
P : = T ⋅ P − T ⋅
⋅
o
A
B
m
g
B
Equation 3.11-16
g
Equation 3.11-17
The velocity of each satellite with respect to the missile GPS receiver is,
C
g,
s
C
s
V : = V − V
Expressed with respect to the "natural" co-ordinate systems,
C
g,
s
C
O
O
s
C
E
C
g
Equation 3.11-18
E E A A B
( V + T ⋅ ( V + T V ) )
V : = T ⋅ V − T ⋅
⋅
o
A
m
B
g
Equation 3.11-19
The inertial velocity of each satellite expressed in the Orbital frame is,
O
s
r,
s
OS
( ) T
−sin
κ cos 0
V : = P ⋅ ω ⋅
κ
The inertial velocity components of the receiver are,
E A B
( V , V , V )
o
m
E E A A A B B
( ωC,
E × Po
, P&
m + ωC,
E × Pm
, ωA,
B × Pg
)
Combining these velocity terms,
C
E
L − T
V
⋅
C
g,
s
: =
P
r,
s
⋅ ω
OS
⋅
g
: =
( − sin κ , cos κ , 0 )
Equation 3.11-20
Equation 3.11-21
E E E A A A A B B
( ωC,
E × Po
+ TA
⋅ ( P&
m + ωC,
E × Pm
+ TB
⋅ ( ωA,
B × Pg
) ) )
From §17.6 the reference LOS rates are,
T
−
L
Equation 3.11-22