Appendix A - Prediction and Classification of Respiratory Motion - page 135

A.2 Symbol Definitions

x(k) n-dimensional state vector (data vector)
z(k) Measurement vector
u(k) n-dimensional known vector
v(k) Process noise with the property of the zero-mean white
Gaussian noise with covariance Q(k)
w(k) Measurement noise with the property of the zero-mean
white Gaussian noise with covariance R(k)
Q(k) Covariance value of process noise v(k)
R(k) Covariance value of measurement noise w(k)
F(k) State transition model matrix which is applied to the
previous state x(k-1)
G(k) Control-input model matrix which is applied to the control
vector u(k)
H(k) Observation model matrix which maps the true state space
into the observed space
^x ðÞ Predicted state vector
t(k) Recording time at time k
P(k) State prediction covariance vector
W(k) Filter gain value
S(k) Measurement prediction covariance value
l Weighting coefficients
F CV System matrix for CV filter
C CV Process noise gain matrix for CV filter
F CA System matrix for CA filter
C CA Process noise gain matrix for CA filter
l ij Mixing probability given that the target is in state j that
the transition occurred from state i
x 0j Mixed initial condition matrix
P 0j Mixed initial Kalman filter covariance matrix
K r Likelihood function corresponding to filter r
l j Mode probability update value for filter r,(j =1,…, r)
^xk jðÞ Combination of the model-conditioned estimate
Pk jðÞ Combination of the model-conditioned estimates and covariance
L Observations or measurement number that is corresponding

to the number of sensor

G Group number to partition L measurements into G sets

a y Prior probability value for the group y (y [ G)

m y Mean value of group y to be the centroid of the observations in the

cluster (y [ G)

R y Covariance value of group y that describes the configurations of

clusters (y [ G)

/ ðÞ General multivariate Gaussian density function