Nomenclature
System matrix
Compensated VSPND signal
Identity matrix
Expectation operator
State transition matrix
Prompt fraction of output signal of VSPND
Delayed fraction of output signal of VSPND
Transfer function of VSPND
Measurement matrix
Null hypothesis
Total output current of VSPND
Steady–state output current of VSPND at time zero
Gain matrix for Kalman filter at time
Number of sample data points
Number of ion chambers, 3
Number of Co SPNDs, 42
Number of steady state sample points
Number of VSPNDs, 102
Dimension of measurement, 1
Power from th Co SPND, % Full Power (FP)
Bulk power from Co SPNDs, % FP
Bulk power from ion chambers, % FP
a–priori error covariance matrix at discrete time
a–posteriori error covariance matrix at discrete time
Uncompensated power from th VSPND, % FP
Uncompensated bulk power from VSPNDs, % FP
Probability that a reaction leads to an electron contributing to the detector current
Probability that a reaction leads to an electron contributing to the detector current
Process noise covariance matrix
Measurement noise covariance
Reference signal (Cobalt SPND/Ion Chamber)
Complex frequency in Laplace transformation
Steady state calibration factor
Sampling time
Scalar measurement noise at time
Process noise vector at time ,
State vector in Kalman filter,
a–priori state estimate vector,
a–posteriori state estimate vector,
Intermediate state variable in DI compensator
Scalar measurement output
Complex number in Z–transform
Chi-square distribution with n degrees of freedom
Kronecker delta function
Decay constant of
Zero mean white noise
Thermal neutron flux sensed by SPND
Thermal neutron flux reconstructed by compensator
Steady–state neutron flux at time zero
Covariance of innovation sequence
Absorption cross - section of , 4.5 barns
Time constant of , 325.47 seconds
Innovation at th time step
State variable in Kalman filter