Detection Fusion of Weak Signal under Chaotic Noise Based on Distributed System

Table 1

Mathematical notations and descriptions.

Mathematical notations	Description
	The null hypothesis
	The alternative hypothesis
	The prior probability, which represents the probability without signal
	The prior probability, which represents the probability with signal
	The observation of the th local sensor at time
	The target signal to be detected at time
	The background signal of chaotic noise at time
	The observed white noise of the th local sensor at time
	The variance of white noise
	The decision result of the th local sensor
	Decision vectors for all local sensors
	The decision result of the fusion center
	The decision rule of the th sensor
	The fusion rule of fusion center
	A continued vector mapping
	The fitting errors
	The threshold value for testing the model
	The time delays
	The embedding dimensions
	The Bayes risk of the detection fusion system
	The decision threshold of the th local sensor
	The detection probability of the th sensor
	The false alarm probability of the th sensor
	The detection probability of fusion center
	The false alarm probability of fusion center
	The cost of the global decision being when is present
	The vector with the resulting decision of all local sensors except the th sensor