14.02.2013 Views

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

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

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

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

Appendix I / Utilities / Covariance<br />

_ _<br />

This equation is implemented in COV_SUM. The uncertainty in commonly<br />

used tracking and guidance parameters is expressed in terms of the PVA<br />

state vectors, and associated covariances. Figure 22-15 shows two frames<br />

(B) and (C) located at point (a) rotating such that X B passes through point<br />

(b), and X C passes through the point (c). They both rotate independently<br />

with respect to the static frame (A) also located at point (a) the origin of all<br />

three frames.<br />

a<br />

Z A<br />

Z A<br />

P XB<br />

ab<br />

ξ B<br />

A<br />

22.13-2<br />

X A<br />

ξ C<br />

A<br />

Y A<br />

b<br />

P XC<br />

ac<br />

ξ C<br />

B<br />

X B<br />

c<br />

X C<br />

Figure 22-15 : Parameter Uncertainty – Frame Definitions<br />

The following terms are used when defining generic uncertainty expressions<br />

in Cartesian PVA co-ordinates,<br />

XA XA YA YA XA YA YA XA<br />

( ϕ , ϕ ) : = ( P ⋅ P&<br />

+ P ⋅ P&<br />

, P ⋅ P&<br />

− P ⋅ P&<br />

)<br />

1<br />

2<br />

b<br />

b<br />

b<br />

( ϕ&<br />

, ϕ&<br />

)<br />

1<br />

b<br />

b<br />

b<br />

b<br />

Equation 22.13-6<br />

hA 2 XA YA YA XA<br />

( P&<br />

) ⋅ − ⎟<br />

⎞<br />

b , Pb<br />

P&<br />

&<br />

b Pb<br />

P&<br />

&<br />

b<br />

⎠<br />

⎜<br />

⎛ XA XA YA YA<br />

Pb<br />

⋅ P&<br />

&<br />

b + Pb<br />

⋅ P&<br />

&<br />

b +<br />

⋅<br />

⎝<br />

2<br />

: =<br />

Equation 22.13-7<br />

COV_CONTROL controls the computation of state vector errors, errors in<br />

parameters that are a function of the state vector, and (1σ,2σ,3σ) error<br />

statistics in respect of:<br />

A<br />

1 Target position E ( δ P )<br />

A<br />

2 Target velocity E ( δ<br />

P&<br />

t )<br />

b<br />

t

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!