Biomedical Engineering Reference
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Table 4.1
Prediction overshoot analysis (HEKF vs. DEKF)
Datasets
# Total
frames
HEKF (# overshoot frame /#
total frame: %)
DEKF (# overshoot frame /#
total frame: %)
Improvement
(%)
DB00
79078
17.09
31.10
45.06
DB01
145336
3.23
7.72
58.13
DB02
140704
8.65
39.03
77.84
DB03
175896
5.24
6.35
17.52
DB04
93653
4.44
27.78
84.03
DB05
100739
4.14
26.55
84.41
DB06
159855
1.66
32.51
94.89
DB07
110417
0.12
41.50
99.70
DB08
225785
1.49
32.67
95.44
DB09
144149
0.27
0.40
31.75
DB10
185697
4.29
15.31
71.98
DB11
108327
0.95
12.01
92.11
DB12
129503
0.03
2.16
98.46
DB13
146145
0.53
0.51
-4.15
DB14
134683
3.59
3.49
-2.94
can be seen in Table
4.1
, most of the prediction overshoot of HEKF are within 5 %
except the datasets DB00, DB02, and DB03. We have also noticed that DEKF is
slightly better than HEKF in the case of datasets DB13 and DB14, which include
some discontinuities as well as the system noise because of the irregular patient
breathing and the system latency during the breathing record [
40
]. We think these
lacks of continuity could decrease the Kalman filter gain during the target pre-
diction. In spite of these defect, however, the proposed HEKF can improve the
average prediction overshoot by 62.95 % with comparison to DEKF.
4.4.4 Comparison on Estimation Performance
We evaluate the target estimation by comparing the proposed HEKF described in
Sect. 4.3.2
, with the alternative DEKF described in
Sect. 4.3.1
.
(1) Tracking Position Estimation
Figure
4.8
shows the average target position estimation of the 3D Euclidian
distance between the predicted value and the measurement values with respect to
the data time index given by the original Cyberknife dataset. The unit of vertical
axis in Figs.
4.8
and
4.9
is dimensionless for the amplitude, i.e. the target esti-
mation corresponds to the 3D position has the range of [-1, +1], corresponding to
the real measurement dataset range [-1.4735 9 10
3
, -1.5130 9 10
3
]. As you can
see, the position estimation values of HEKF align closer to the measurement
values than DEKF values.
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