Wireless Sensor and Actuator Networks for Lighting Energy ...

Figure 5-5 Prediction performance of adaptive Wiener filtering.
Double exponential smoothing
Since the change of daylight over a day usually presents a linear trend of
increasing or decreasing over time, double exponential smoothing method is the most
reasonable choice of predictive models in the exponential smoother family. The model
is shown in (5.11), where b 1 and b 2 are constants and k is random noise with zero mean
and variance
2
.
y k
= b 1
+ b 2
k + k
(5.11)
The first order and second order smoothed statistics at time k can be calculated in (5.12)
and (5.13), where is the smoothing constant.
S k
= y k
+ (1 )S k 1
(5.12)
S [2] [2]
k
= S k
+ (1 )S k 1
(5.13)
The one-step prediction equation can then be derived as in (5.14).
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