Appendix A - Prediction and Classification of Respiratory Motion - page 137

G(k) s 9 p matrix denoting the Kalman gain that is an integral part of

the EKF algorithm

C ðÞ p 9 p matrix denoting the global conversion factor for the entire

network

P(k|k-1) s 9 s prediction-error covariance matrix

P(k|k) s 9 s filtering-error covariance matrix

G Designated number of mutually exclusive disjoint weight groups

ˆ i (k|k) Filtered weight vector for the group i, where i = 1, 2,…,g

P i (k|k) Subset of the filtering-error covariance matrix for the group i,

where i = 1, 2,…,g

Gi(k) Kalman gain matrix for the group i, where i = 1, 2,…,g

c Designated number of mutually exclusive channel

ðÞ Filtered weight vector
G i CP (k)

w CP
i

kk

Kalman gain matrix for the channel i

P i CP (k|k-1)

Prediction-error covariance matrix for the channel i

P i CP (k|k) Filtering-error covariance matrix for the channel i

C CP

Global conversion factor for the coupled entire network

ðÞ

d i (k) Desired response for the linearized system

l ij Coupling degree to which component (i) depend on one another (j)

P Coupling matrix

a CP
i

ðÞ Difference between di(k) and coupled estimations for the channel

number i

P(k) Adaptive coupling matrix

H(k) Error-gain matrix

D(k) Difference of the consecutive global error gain values

m i d-dimensional sample mean for group i

n i Component number of group i

S W Within-class scatter value in the given samples

S B Between-class scatter value in the given samples

J(•) Objective function to get the optimized group number (g)

h Set of neural network true weights and biases

h Least square estimation of h

c Marginal value to judge prediction overshoot

r Standard deviation estimator

I Candidate feature combination vector

Î Estimated feature combination vector

c Class number

ˆ Estimated class number to get the minimum of the objective

function value (J(c))

l m Mean vector of the mth component

R m Covariance matrix of the mth component

N Neuron number of the input layer

H Neuron number of the hidden layer

x Feature combination vector