Respiratory Motion Estimation with Hybrid Implementation - Prediction and Classification of Respiratory Motion - page 76

( 4.18 ), an approximate marginal value (c) with 100(1-a) confidence can be
obtained [ 59 , 63 ]:

s

1 þ X

n

c ¼ t 1 a = 2 ; n r

ð

F i F i

Þ ; ð 4 : 20 Þ

i ¼ 1

where t 1-a/2,n is the 1-a/2 quantile of a t-distribution function with n degrees of
freedom, r is the standard deviation estimator, and F i is the Jacobian matrix of
neural network outputs with respect to weights, respectively. r and F i are calcu-
lated as follows:

s

1
n

2

X

n

y i U ð x i ; h Þ r ¼ ; ð 4 : 21 Þ

i ¼ 1

" #

;

F i ¼ o U ð x i ; h Þ
oh 1

o U ð x i ; h Þ
oh s

ð 4 : 22 Þ

In the experimental Sect. 4.4.5 , we use this marginal value to judge whether the
predicted outcomes exceed or not, and how many overshoots occur.

4.3.5 Comparisons on Computational Complexity
and Storage Requirement

The computational requirements of the DEKF are dominated by the need to store
and update the filtering-error covariance matrix P(k|k) at each time step n.Fora
recurrent neural network containing p output nodes and s weights, the computa-
tional complexity of the DEKF assumes the following orders:

!

Computational complexity : Op 2 s þ p X

g

s i

; ð 4 : 23 Þ

i ¼ 1

!
; Storage requirement : O X

g

s i ð 4 : 24 Þ

i ¼ 1

where s i is the size of the state in group i, s is the total state size, and p is the
number of output nodes [ 17 ].
The computational requirements of the HEKF are also determined by the need
to store and update the filtering-error covariance matrix P CP at each time step n.In
the HEKF, it needs to calculate the coupling matrix that contains all components of
coupling degree as well. That means we need additional p 2 computation at each
time step n. Therefore, the computational complexity of the HEKF assumes the
following orders: