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Appendix I / Utilities / Digital Filters
_ _
t D
22.8-12
: =
m ⋅ ∆t
[ ( ) ] ( ) I X : k X m 1 1 ⇒
k =
∈
Equation 22.8-82
k ∈ m −1
2 ⇒ X k : = X
Equation 22.8-83
k −1
[ ( ) ] ( ) ( )
( ) I X : 1
X =
y : =
X ( m )
Equation 22.8-84
Equation 22.8-85
Equation 22.8-86
After initialisation the output remains constant at the input value for (tD) s.
The time increment and time delay may be different for each input
parameter. The parameter channels are identified by a unique number (N).
22.8.17 Covariance Matrix Transformation
COVARIANCE_TM takes a covariance matrix in frame (A), the transform
from (A) to frame (B), and returns the covariance matrix in (B).
22.8.18 State Transition Matrix
COVARIANCE _TM
B
B
A
A B B
( C , T , C )
A
C : = C ⋅ P ⋅ C
A
B
A
Equation 22.8-87
Equation 22.8-88
STATE_TM takes state matrix [A] of dimension (N) and returns the state
transition matrix [Φ] using series approximation of order (k) limited to the
range [1(1)3], over time interval (∆t).
STATE_TM
Φ
( [ A ] , [ Φ ] , N , ∆t
, k )
k
∆t
: = I 3 + ⋅
k!
[ ] k
A
Equation 22.8-89
Equation 22.8-90