Respiratory Motion Estimation with Hybrid Implementation - Prediction and Classification of Respiratory Motion - page 79

(2) Discriminant Criterion to Compare HEKF and DEKF

Using Fisher Linear Discriminant on the discriminant analysis in Sect. 4.3.3 ,we
can expect that HEKF or DEKF could be more optimized by comparison with the
objective function values J( ). Figure 4.6 shows the objective function values J( )
defined in Eq. ( 4.16 ). HEKF has fewer values themselves than DEKF has, thus
HEKF has more discriminated or further discriminant degree with comparison to
DEKF across any group numbers selected, which means HEKF has less error than
DEKF.

4.4.3 Prediction Overshoot Analysis

To evaluate the performance of overshoot for the prediction values, we derived the
marginal value (c) using Eq. ( 4.20 )in Sect. 4.3.4 . In this Chapter, we would like to
use this marginal value to judge whether the predicted outcomes exceed or not, and
how many overshoots occur. With the marginal value (c), we can define the upper
bound and the lower bound by adding the marginal value to the measurement
value and subtracting the marginal value from the measurement value,

respectively.
Figure 4.6 shows the comparison of prediction overshoots between HEKF and
DEKF. As can be seen in Fig. 4.7 , most of the estimation values of HEKF align
between the upper bound and the lower bound. After the transient state, we can
notice that the average percentage of prediction overshoot for HEKF is 3.72 %,
whereas the average percentage of prediction overshoot for DEKF is 18.61 %. As

0.48

HEKF
DEKF
Measurement
Upper Bound
Lower Bound

0.46

0.44

0.42

0.4

0.38

0.36

0.34

2935 2940 2945 2950

Data Time Index (Second)

Fig. 4.7 Comparison of prediction overshoot between HEKF and DEKF. With this figure, we
can notice that most of the estimation values of HEKF align between the upper bound and the
lower bound, whereas the values of DEKF do not. After the transient state, we can evaluate that
the average percentage of prediction overshoot for HEKF is 3.72 %, whereas the average
percentage of prediction overshoot for DEKF is 18.61 %, thus HEKF has less prediction
overshoot value than DEKF has