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Appendix I / Utilities / Digital Filters
_ _
1
χ− 1 : = χ−2
: =
⎜
⋅
3 ⋅ ξ ⎟
1 − ξ2
− ξ3
22.8-6
⎛
⎜
⎝
ξ
−1
⎞
⎟
⎠
X
I
Equation 22.8-41
If (I := 1), and on first use, the filter is re-initialised without integration
using input (XI). Each filter is identified by a unique number (N).
22.8.7 Digital α−β−γ Filters
D_ABG propagates 50 α−β−γ filters with time varying gains (α,β,γ). The
input (XI) is returned filtered (F_X) together with its 1 st and 2 nd derivatives
(F_DX and F_D2X) using the equations given in §21.2.
D_ABG
( , X , DX , D2X
, α , β , γ , F _ X , F _ DX , F _ D2X
, N , I )
t I I I
Equation 22.8-42
The provision of current time (t) allows for variable update rates, the time
interval for filter propagation being determined for each channel (N),
∆
t : = t − t k −1
Equation 22.8-43
If argument (I) is set to 1, and on first use, the filter is re-initialised using the
input (XI) and its 1 st and 2 nd derivatives. Each filter is identified by a unique
number (N).
22.8.8 Tuned Digital α−β−γ Filters
T_ABG propagates 50 weave frequency (ωW) tuned α−β−γ filters using 1 st
order integration with time varying gains based on the filter bandwidth (ωE).
The input (XI) is returned filtered (F_X) together with its 1 st and 2 nd
derivatives (F_DX and F_D2X) using the equations given in §21.4.
T_ABG
( t , X , DX , D2X
, ω , ω , F _ X , F _ DX , F _ D2X
, N , I )
I
I
WT
ϕ
I
αβγ
E
≡
( X , ω , ω )
Equation 22.8-44
If (I := 1), and on first use, the filter is initialised using input (XI) and its 1 st
and 2 nd derivatives. Each filter is identified by a unique number (N).
22.8.9 Digital α−β−γ Filter Covariances
I
ABG_COVARS takes a set of α−β−γ filter gains at time (t), and the input
variance (E(XI)), and returns a [3,3] covariance matrix [P] using the
equations given in §20.2.
W
E
W