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

Appendix H / Steady State Tracking Filters
_ _
Where,
2
∆ ⋅ E &
2
2
2
( X ) : = ( 2 ⋅ γ ⋅ ( 2 − α ) + 4 ⋅ β ⋅ ( β − γ ) ) ⋅ 3
t χ
3
2
2
( X&
, X&
& ) : = ( 4 ⋅ β ⋅ γ − 2 ⋅ β ⋅ γ ) ⋅ 3
∆t
⋅ E
χ
4
2
2
( X&
& ) : = 4 ⋅ β ⋅ γ ⋅ 3
∆t
⋅ E
χ
χ : = 2 ⋅
1
χ : = 2 ⋅ 2
2
χ
3
21-6
( α ⋅ β − γ ) + α ⋅ γ
: =
( − α ) − β
( X )
E I
χ ⋅ χ
1
2
Equation 21.3-10
Equation 21.3-11
Equation 21.3-12
Equation 21.3-13
Equation 21.3-14
Equation 21.3-15
Steady-state filters are a balance between tracking accuracy and noise
suppression hence the choice of (α) is application dependent, and
something of an art-form. The following emprical relationship is often
used to set the filter gains instead of Equation 21.3-5,
α
: =
⎛
⎜
⎝
b ⎞
b 1
⎟
+ ⎠
1
3
where
b
: =
&P
&
o,
t
2 ⋅ P
o
, t
∆t
2
⋅ σ
M
Equation 21.3-16
Errington [E.1] suggests that (α) should be tuned to the maximum lateral
acceleration capability of the target (AMAX),
⎛
⎜
⎜
⎝
2 ⋅ σ
AMAX
⋅ ∆t
+ A ⋅ ∆t
M
( α , β , γ )
MAX
2
2
,
: =
⎛ α β
⎜ +
⎝ 4 8
⎞
⎟
⎠
2
,
2 ⎞
β ⎟
2 ⋅ α ⎟
⎠
Equation 21.3-17
Now consider the constant acceleration filter in the frequency domain,