Department of the Air Force Report, 1996

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F = 0.8, only the most recent 25 or so data points contribute to the final result, since all
older data points are essentially weighted out of the solution.
1.0
0.9
0.8
0.7
... ­
i:!:
0.6
u..-
.c -
0.5
........
. ...........
i ..........................J ...........................+········-­
F = ~ (equally weighted)
!
F=0.J9
I
!
I
--.:
···········;···························
....
--········-----···--
····
-•-1-
+-
=0.9! 5
!
C)
·a5
i
I
~
' ............................~............................
ca
0.4
Cl
0.3
0.2
0.1
0.0
ca
i -­
0.99
.....
...........................:.......
.
.....
1
/.-····---;
-----i··········
-1..................
+o.s
.......... ,
I
0
50
100
150
200
250
300
Data Index (older->)
Figure 35. Exponential Weights for Fading-Memory Filters
For the exponentially-weighted fading-memory filter, it can be shown that the
recursive filter factor used in Eq. (12) is
1-F
a=--
(20)
n
1-Fn
Since OS F S 1, an in Eq. (20) does not approach zero as n approaches infinity (as the
other two filters do), but instead approaches the value (1 - F). If F = 0, then an= 1 for all
n, the filter has no memory at all, and the filtered value always equals the last
measurement. In the limit as F approaches one, L'Hospital' s rule can be applied to
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