Design and Implementation of Acoustic Sensing System for Online Early Fault Detection in Industrial Fans

Table 1

Summary of the adaptive Kalman-filtering variables.

Variable	Definition	Dimension
	State vector at time	M-by-1
	Observation vector at time	N-by-1
	State transition matrix from time to	M-by-M
	Measurement matrix at time	N-by-M
	Correlation matrix of process noise vector	M-by-M
	Correlation matrix of measurement noise vector	N-by-N
	Predicted estimate of the state vector at time , given the observation vectors	M-by-1
	Filtered estimate of the state vector at time , given the observation vectors	M-by-1
	Kalman gain at time	M-by-N
	Innovation vector at time	N-by-1
	Correlation matrix of the innovation vector	N-by-N
	Correlation matrix of the error in	M-by-M
	Correlation matrix of the error in	M-by-M