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

Chapter 9 / Performance
_ _
LAUNCH
≥
4
LAUNCH ≤ 3 ⇒ PIE
: =
⇒
PI
E
: =
9-6
1
4000
⋅
∑
0
Equation 9.2-1
2 ( & YB
ZB
P&
) ( &P
& )
⎜
⎛
o,
m +
⎝
o,
m
2
⎟
⎞
⎠
Equation 9.2-2
This metric is applied when the missile is fully controlled. The summation
is performed at the simulation integration rate. For each target tracking
filter, and the combined IMM output, a normalised distance metric is
provided. For example, the position error along X A for the i’th filter,
i
PX
XA
t
XA
t
i XA i XA
( P P )
ˆ
i i
P P ˆ
PI : = −
−
t
t
Equation 9.2-3
The metrics associated with each individual axis are referred to graphically
as TMPX_AOT, the “P” being replaced by “V” and “A”, and “X” by “Y”
and “Z” as appropriate. Spherical errors, denoted by (PIP), (PIV) and (PIA),
are referred to as TG_P_MET , TG_P_SIG etc. For the i’th filter the true
and estimated spherical position errors are,
⎛
⎜
⎜
⎝
1
3
⋅
∑
i
i
( PI , E ( PI ) )
P
: =
i jA i jA 2
i iA i jA
( − ) ⋅ ( P − P ) ⎟
⎟ ˆ
1
P P ,
E
ˆ
∑
t t
3
j:
= X,
Y,
Z
j:
= X,
Y,
Z
P
t
t
⎞
⎠
Equation 9.2-4
Normalised spherical errors are referred to graphically as TG_PNMET, the
“P” being replaced by “V” and “A” as appropriate. The i’th filter the
normalised spherical position error,
i
PI
P
: =
∏
i : = X,
Y,
Z
iA iA
iA iA
( − ( P − P ) ) ˆ
P P E
ˆ
t
t
t
t
Equation 9.2-5
The Eigen observability metric (PIC) is the Condition Number (CN) defined
in §5.10.9. This is identified by F1_E_MET on the graphs, the number
identifying the IMM filter.