Review: Prediction of Respiratory Motion - Prediction and Classification of Respiratory Motion - page 28

Recurrent network activities v ( t )

Input
vector
u ( t )

Network nonlinearity
b (

Recurrent neural
networks (RNN)

( t|t −1), v ( t ), u ( t ))

Weight state vector
( t −1| t −1)=

( t | t −1)

Weight state update & Delay
( t|t ) =

Bank of unit-time
delays

( t|t −1)+ G ( t )α( t )

Desired
response
d ( t )

Extended Kalman
filter (EKF)

Innovation process
α( t )= d ( t )− b ( ( t|t −1), v ( t ), u ( t ))

Fig. 2.16 Closed-loop feedback system incorporating EKF for RNN. RNN performs a role of
the predictor with network nonlinear function, whereas EKF performs a role of the corrector with
innovation process in a recursive manner in this system

prediction, so that independent parallel filters should be implemented for 3D
motions [ 83 ]. Furthermore, IMM method was investigated to compare with a pre-
diction method based on the first-order extended Kalman filter by Hong et al. [ 72 ].
Breathing variation, such as deep or fast breathing, results in a relatively low
accuracy of breathing motion prediction. King et al. showed that a multiple sub-
model method based on breathing amplitude can provide an adaptive motion model
with adjusting basic sub-models [ 100 ]. They validated that the combined models
with multiple sub-models can show the prediction errors of 1.0-2.8 mm.

2.3.3.4 Hybrid Extended Kalman Filter

Kalman filters are widely used for training nonlinear function of the state esti-
mation and prediction for desired input-output mappings [ 72 , 81 , 83 ]. Kalman
filter can also be used for supervised training framework of recurrent neural net-
works using nonlinear sequential state estimators. The prediction and correction
property is an intrinsic property of Kalman filter. In Hybrid extended Kalman filter
(HEKF), recurrent neural network (RNN) performs a role of the predictor with
network nonlinear function including input vector (u), recurrent network activities
(v), and adaptive weight state vectors (w), whereas EKF performs a role of the
corrector with innovation process in a recursive manner, as shown in Fig. 2.16
[ 101 , 102 ].