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

Chapter 5 / Missile State Observer
_ _
Relative bearing:
∂ Ψ
∂ P
ϕ
1
S
B
A
t
: =
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
: =
1 − T
T
T
S
A
S
A
∂ Ψ
ϕ ⋅ sec
1
S
A
P
Relative elevation:
m,
t
2
o,
t
S
B
Θ
S
B
∂ X : = ∂
TL
⎛
⎜
⎜
⎜
⋅
⎜
sin
⎜
⎜
⎝
2
5-18
Ψ
S A T
( ∂ Ψ P , 0 )
S
B
⋅
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
B
T
T
T
B
A
B
A
B
A
( 1 )
( 4 )
( 7 )
t
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
− cos
6
2
Ψ
Equation 5.8-28
S
B
⋅
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
T
T
T
B
A
B
A
B
A
( 2 )
( 5 )
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⎞
( ) ⎟ ⎟⎟⎟⎟⎟⎟
8
⎠
Equation 5.8-29
S
S S
S S
( 1 ) ⋅ T ( 1 ) , T ( 1 ) ⋅ T ( 2 ) , T ( 1 ) ⋅ T ( 3 )
S
S S
S S
( 1 ) ⋅ T ( 2 ) , 1 − T ( 2 ) ⋅ T ( 2 ) , T ( 2 ) ⋅ T ( 3 )
A
( ) ( ) ( ) ( ) ( ) ( ) ⎟⎟⎟⎟⎟⎟
S
S S
S S
1 ⋅ T 3 , T 2 ⋅ T 3 , 1 − T 3 ⋅ T 3
S
B
A
∂ Ψ
S
B
A
S
B
TL
A
A
∂ X : = ∂
A
t
P ⋅ cosΘ
⋅ ∂ Ψ ∂ P : = ϕ ⋅
1
A
A
A
A
S A T
( ∂ Ψ P , 0 )
B
t
6
A
A
A
A
A
A
⎞
⎠
Equation 5.8-30
Equation 5.8-31
( ( ) ( ) ( ) ) T
B
B
B
T 3 , T 6 , T 9
A
A
A
Equation 5.8-32
Apportioning the range, range-rate, bearing and elevation innovations to the
missile linear states,
H ≡ ∂ Z ∂ X : = − ∂ Z ∂ X
ML
SK
ML
SK
TL
Equation 5.8-33
Apportioning the target range, range-rate, bearing and elevation innovations
to the missile angular states,
MA
SK
MA
( ) T
S
S
0 , ∂ Ψ ∂ X , ∂Θ
X
H ≡ ∂ Z ∂ X : =
∂
10x2
B
ML
B
ML
Equation 5.8-34