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

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Chapter 3 / Sensors / Seeker<br />

_ _<br />

3.9.8.3 Bearing and Elevation<br />

The target angles with respect to the Missile Body frame are the sum of the<br />

measured gimbal angles and the measured position of the target with respect<br />

to the detector boresight,<br />

~ S ~ S ~ H ~ S ~ H ~ S<br />

( Ψ , Θ ) : = ( Ψ + Ψ , Θ + Θ )<br />

B<br />

B<br />

3.9-14<br />

B<br />

H<br />

B<br />

H<br />

Equation 3.9-24<br />

The target angles with respect to the detector are corrupted by signal-tonoise<br />

dependent random noise, zero-mean Gaussian noise with a deviation<br />

of 2 mrad, residual radome aberration, and glint.<br />

Θ<br />

Ψ<br />

S<br />

H<br />

S<br />

H<br />

⎛<br />

+ N ⎜<br />

⎝<br />

⎛<br />

+ N ⎜<br />

⎝<br />

0 ,<br />

0 ,<br />

SK<br />

2 ⋅<br />

SK<br />

2 ⋅<br />

ξ<br />

ξ<br />

BW<br />

SK<br />

BW<br />

SK<br />

SN<br />

SN<br />

⎞<br />

⎟ + N<br />

⎟<br />

⎠<br />

⎞<br />

⎟ + N<br />

⎟<br />

⎠<br />

~<br />

Θ<br />

S<br />

H<br />

: =<br />

( 0 , SKσΘRN<br />

) + N ( 0 , SKσΘRA<br />

) + SKΘG<br />

~<br />

Ψ<br />

S<br />

H<br />

: =<br />

Equation 3.9-25<br />

( 0 , SKσ<br />

ΨRN<br />

) + N ( 0 , SKσ<br />

ΨRA<br />

) + SKΨG<br />

Equation 3.9-26<br />

Missile radomes are calibrated to reduce optical aberration effects leaving<br />

residual errors whose generic form is given by Garnel [G.1] . From Burks [B.12] ,<br />

π<br />

6<br />

H<br />

ΘB < ⇒ SKσ<br />

Θ RA<br />

π<br />

6<br />

3.9.8.4 Signal to Noise Ratio<br />

H<br />

ΨB < ⇒ SKσ<br />

Ψ RA<br />

: =<br />

: =<br />

0.<br />

005<br />

0.<br />

0025<br />

⋅ sin<br />

⋅ sin<br />

H ( 6 ⋅ Θ )<br />

B<br />

Equation 3.9-27<br />

H ( 12 ⋅ Ψ )<br />

B<br />

Equation 3.9-28<br />

From the Radar Equation in §3.8.6 the SNR for mono-pulse extraction,<br />

SK<br />

SN<br />

: =<br />

SK<br />

P ⋅<br />

SK<br />

G<br />

2<br />

⋅<br />

SK<br />

3<br />

4<br />

( 4 ⋅ π ) ⋅ k ⋅ T ⋅ L ⋅ P<br />

B<br />

t<br />

P<br />

⋅<br />

SK<br />

SK<br />

λ<br />

2<br />

T<br />

SK<br />

⋅<br />

SK<br />

σ<br />

m,<br />

t<br />

RCS<br />

Equation 3.9-29

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