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

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Chapter 5 / Missile State Observer<br />

_ _<br />

SK<br />

Z ~<br />

( ) T<br />

XS XS ~ S ~ S<br />

o,<br />

m P o,<br />

m , B , B<br />

~ ~<br />

P , Ψ Θ<br />

: = &<br />

The estimated seeker measurements,<br />

⎛<br />

⎜<br />

⎜<br />

⎝<br />

P<br />

A<br />

m,<br />

t<br />

•<br />

P<br />

A<br />

m,<br />

t<br />

,<br />

P<br />

A<br />

m,<br />

t<br />

• P&<br />

P<br />

m,<br />

t<br />

A<br />

m,<br />

t<br />

,<br />

5-17<br />

SK<br />

Z<br />

tan<br />

−1<br />

: =<br />

⎛<br />

⎜<br />

⎝<br />

T<br />

S<br />

B<br />

S<br />

B<br />

T<br />

( 1 )<br />

( 4 )<br />

The linearised measurement matrix decomposes as follows,<br />

⎞<br />

⎟<br />

⎠<br />

,<br />

sin<br />

Equation 5.8-22<br />

−1<br />

S ( − T ( 7 ) )<br />

B<br />

⎞<br />

⎟<br />

⎟<br />

⎠<br />

T<br />

Equation 5.8-23<br />

T<br />

SK Z<br />

SK Z SK Z SK Z<br />

SK H :<br />

, ,<br />

X XTL<br />

XML<br />

X ⎟<br />

MA<br />

⎟<br />

∂ ⎛ ∂ ∂ ∂ ⎞<br />

≡ = ⎜<br />

∂<br />

∂ ∂ ∂<br />

⎝<br />

⎠<br />

Equation 5.8-24<br />

The range, range-rate, bearing and elevation innovations are apportioned to<br />

the target states by,<br />

SK<br />

H<br />

TL<br />

≡<br />

Relative range:<br />

∂<br />

∂<br />

SK<br />

X<br />

∂ P<br />

Z<br />

TL<br />

XS<br />

m,<br />

t<br />

Relative range-rate:<br />

∂ P&<br />

XS<br />

o,<br />

m<br />

∂ X<br />

TL<br />

: =<br />

⎛<br />

⎜<br />

⎜<br />

⎝<br />

: =<br />

∂ X<br />

TL<br />

⎛<br />

⎜<br />

⎝<br />

∂ P<br />

∂ X<br />

: =<br />

XS<br />

m,<br />

t<br />

TL<br />

⎛<br />

⎜<br />

⎝<br />

,<br />

∂ P&<br />

∂ X<br />

XS<br />

m,<br />

t<br />

TL<br />

,<br />

∂ Ψ<br />

∂ X<br />

S<br />

B<br />

TL<br />

A T<br />

T<br />

( P ) ⎞<br />

m,<br />

t Pm,<br />

t , 06<br />

⎟<br />

⎠<br />

A T<br />

XS A T<br />

( P&<br />

m,<br />

t ) P&<br />

m,<br />

t ⋅ ( Pt<br />

) A<br />

−<br />

, ( P )<br />

P<br />

m,<br />

t<br />

P<br />

2<br />

m,<br />

t<br />

t<br />

,<br />

∂ Θ<br />

∂ X<br />

S<br />

B<br />

TL<br />

⎞<br />

⎟<br />

⎠<br />

T<br />

Equation 5.8-25<br />

Equation 5.8-26<br />

T<br />

P<br />

m,<br />

t<br />

,<br />

0<br />

T<br />

3<br />

⎞<br />

⎟<br />

⎟<br />

⎠<br />

Equation 5.8-27

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