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

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Appendix I / Utilities / Covariance<br />

_ _<br />

ξ<br />

ξ<br />

1<br />

2<br />

: =<br />

: =<br />

P&<br />

XA<br />

b<br />

P&<br />

YA<br />

b<br />

⋅ P<br />

⋅ P<br />

ZA<br />

b<br />

ZA<br />

b<br />

− P<br />

− P<br />

XA<br />

b<br />

YA<br />

b<br />

22.13-9<br />

⋅ P&<br />

⋅ P&<br />

ZA<br />

b<br />

ZA<br />

b<br />

− ϕ ⋅ P<br />

1<br />

− ϕ ⋅ P<br />

The target and missile pitch rate uncertainties.<br />

1<br />

XA<br />

b<br />

YA<br />

b<br />

⋅ P<br />

⋅ P<br />

ZA<br />

b<br />

ZA<br />

b<br />

⋅<br />

( ) 2 hA −<br />

P<br />

b<br />

Equation 22.13-40<br />

⋅<br />

( ) 2 hA −<br />

P<br />

b<br />

Equation 22.13-41<br />

T ( δΘ ) : = CV_DTHT_AB ( X , C , 9 )<br />

&<br />

E A<br />

SO TL SO TLL<br />

Equation 22.13-42<br />

M ( δΘ ) : = CV_DTHT_AB ( X , C , 9 )<br />

&<br />

E A<br />

SO ML SO MLL<br />

22.13.11 Differential Angle Uncertainty<br />

Equation 22.13-43<br />

The elevation and azimuth errors are combined to determine the expected<br />

pointing error whose generic form is,<br />

E<br />

( ) ( ) ⎟ ⎛ B ⎞<br />

⎛ B ⎞<br />

B 2<br />

⎜<br />

∂ ξ ⎛<br />

T<br />

A ⎟<br />

A A ⎞ ⎜<br />

∂ ξA<br />

ξ : =<br />

⋅ E ⎜ δP<br />

⋅ δP<br />

⎟ ⋅<br />

δ A<br />

A<br />

b b<br />

A<br />

∂ P ⎝<br />

⎠<br />

b<br />

∂ Pb<br />

⎜<br />

⎝<br />

⎟<br />

⎠<br />

T<br />

⎜<br />

⎝<br />

Equation 22.13-44<br />

When using the individual Euler angles the cross-correlation terms must be<br />

taken into account whose expected value is determined from,<br />

⎛<br />

⎜<br />

⎜<br />

⎝<br />

⎛<br />

⎜<br />

⎝<br />

∂ Θ<br />

∂ P<br />

B<br />

A<br />

A<br />

b<br />

⎞<br />

⎟<br />

⎠<br />

T<br />

⋅<br />

E<br />

⎛<br />

⎜<br />

⎝<br />

E<br />

δP<br />

B B<br />

( δΘ<br />

, δ Ψ )<br />

A<br />

b<br />

⋅<br />

A<br />

B<br />

A T ⎛ ⎞<br />

A<br />

B<br />

( P ) ⎜<br />

∂ Ψ<br />

⎟ ⎟<br />

δ<br />

⎞<br />

⎟ ⋅<br />

⋅ cosΘ<br />

b<br />

A<br />

⎠<br />

: =<br />

⎜<br />

⎝<br />

∂ P<br />

A<br />

b<br />

⎟<br />

⎠<br />

⎞<br />

⎟<br />

⎠<br />

A<br />

Equation 22.13-45<br />

The estimated pointing error is then determined from the quadratic form,<br />

A<br />

≡<br />

⎡<br />

⎢<br />

⎢<br />

⎢<br />

⎣<br />

σ<br />

σ<br />

2<br />

Θ<br />

L<br />

ΨΘ<br />

M<br />

M<br />

M<br />

σ<br />

σ<br />

ΘΨ<br />

L<br />

2<br />

Ψ<br />

⎤<br />

⎥<br />

⎥<br />

⎥<br />

⎦<br />

⎡ E<br />

⎢<br />

: = ⎢<br />

⎢<br />

⎢<br />

E<br />

⎣<br />

B 2<br />

B B<br />

( δΘ<br />

) M E ( δΘ<br />

, δ Ψ )<br />

L<br />

( ) ( ) ⎥ ⎥⎥⎥<br />

B B<br />

B 2<br />

δ Ψ , δΘ<br />

M E δ Ψ<br />

A<br />

A<br />

A<br />

M<br />

A<br />

L<br />

A<br />

⎠<br />

A<br />

Equation 22.13-46<br />

⎤<br />

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