Respiratory Motion Estimation with Hybrid Implementation - Prediction and Classification of Respiratory Motion - page 82

because of the unstable initialization of the original dataset. After the steady state,
the error value of HEKF aligns more close to zero point. Two significant position
errors are shown in DEKF, whereas the position error is negligible in HEKF.

4.4.5 Error Performance Over Prediction Time Horizon

Prediction Time Horizon is the term to represent the time interval window to
predict the future sensory signal. We would like to compare the error performance
among the various prediction time horizon between HEKF and DEKF in
Table 4.2 . For the comparison, we used a normalization that is the normalized root
mean squared error (NRMSE) between the predicted and actual signal over all the
samples in the test dataset, as follows [ 36 ]:

X

t

Þ 2 , X
i

2

NRMSE ¼ ð y i y i y i m y ; ð 4 : 29 Þ

i

where y i is the ith measurement, ˆ i is the estimation of the ith measurement, and m y
is the mean of all the measurements. This metric is dimensionless and allows us to
compare prediction accuracy for different signals of widely varying amplitude.
As can be seen in Table 4.2 , the error performance in the proposed HEKF has
improved for all the datasets by 26.65 % in the average of the prediction time
horizon for 38.46 ms. The prediction interval time has increased and the calculated
NRMSE has increased. Notice that the 7 datasets are shown in the bold fond since
the improvement of error performance for the proposed method maintained over
25 %, with 50 % across the prediction time horizons in datasets DB01, DB03,
DB07, and DB12. Compared to the patient of the Cyberknife dataset in the latest
research [ 47 ], the proposed HEKF showed the better NRMSE performance across
all variable prediction interval times; for example at the prediction time horizon of
500 ms, a 422 % NRMSE improvement.

4.4.6 Comparisons on Computational Complexity

We would like to evaluate how much additional computational time is required
when we implement the proposed HEKF method by comparing to DEKF method.
For HEKF, we used three RMLPs for each channel, whereas we used one RMLP
for DEKF, where the neuron number for the first and the second hidden layer is
two for HEKF and 6 for DEKF, respectively. Regarding CPU experimental time,
we have evaluated the overall performance of average CPU time, using a PC of
Pentium core 2.4 GHz with RAM 3.25 GB.