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Chapter 3 / Inertial Navigation
_ _
B
A
Q
DC
B
Q B G E
( T ) ≡ ϕ ( T ⋅ T T )
Q : = ϕ
⋅
A
3.3-6
DC
G
E
A
Equation 3.3-14
Both frames (E) and (A) are Earth fixed, hence the angular rate and
acceleration of frame (B) with respect to frame (A) is,
B
A,
B
ω
ω& a ω&
B
A,
B
B
A,
B
B
G
G
E,
G
: = T ⋅ ω + ω
R
B
G,
B
B B ( ω − ω ( t − ) )
: = ∆ ⋅
∆
A,
B
A,
B
The position of point (u) with respect to the Alignment frame is,
A
u
A
E
Equation 3.3-15
R
Equation 3.3-16
( ) ( ) T
E E G E
G
ZG
P + T ⋅ P − P ; P 0 , 0 , P
P : = T ⋅
≡
d
G
u
o
u
Equation 3.3-17
Equating the inertial velocity expressed in the Geodetic and Alignment
frames,
A
u
A
E
E
G
G G G E G
A A E A
( P&
u + ωC,
G ⋅ ( TE
⋅ Pd
+ Pu
) ) + ωC,
E ⋅ ( TE
⋅ Po
Pu
)
P & : = T ⋅ T ⋅
+
And similarly for the inertial acceleration of point (u),
A
u
A
E
E
G
G
u
A
C,
E
A
u
A
C,
E
A
C,
E
Equation 3.3-18
A E A
( T ⋅ P P )
P &
: = T ⋅ T ⋅ A − 2 ⋅ ω × P&
− ω × ω × +
G
u
G
u
G
C,
G
G
u
G
C,
G
G
C,
G
E
o
Equation 3.3-19
G E G
( T ⋅ P P )
A = P&
& + 2 ⋅ ω × P&
+ ω × ω × +
3.3.1.2 IMU Reference Data Derived from the State Vector
E
d
u
Equation 3.3-20
The average inertial angular rate over the 800 Hz sub-frame, expressed in
terms of the state vector components,
800
ω
B
C,
B
B
A
A
E
E
C,
E
AR
B
B
( T ( t − ∆ ) , T , )
: = T ⋅ T ⋅ ω + ϕ
∆
A
R
A
R
Equation 3.3-21
u
u