Final_1.pdf

Kalman Filtering 65

Therefore, numerically speaking, it may be sufficient to use, say, the last
10 observations in the state estimation process. Table 4.1 lists the weightings
to use for the 10 observations.
With the available weights and the observations, the computation
process becomes a simple calculation of the weighted average of the ob-
served values, resulting in a unique sequence of states. This set of states is
optimal under the assumptions discussed.
Although this is all nice, note that the typical user of moving averages
probably works with them over multiple time periods. The time periods are
used to modify the coarseness of the approximation, and it may be argued
that looking at moving averages calculated over multiple time frames gives

FIGURE 4.3 Reciprocals of Fibonacci Numbers.

0 2 4 6 8 10 12 14 16 18 20

Index

0.0

0.2

0.4

0.6

0.8

1.0

Reciprocals of Fibonacci Numbers

TABLE 4.1 Reciprocals of Fibonacci Numbers.

12345678910

0.6180 0.2360 0.0901 0.0344 0.0131 0.0050 0.0019 0.0007 0.0002 0.0001