Abstract
A decision fusion rule using the total number of detections reported by the local sensors for hypothesis testing and the total number of detections that report “1” to the fusion center (FC) is studied for a wireless sensor network (WSN) with distributed sensors. A logistic regression fusion rule (LRFR) is formulated. We propose the logistic regression fusion algorithm (LRFA), in which we train the coefficients of the LRFR, and then use the LRFR to make a global decision about the presence/absence of the target. Both the fixed and variable numbers of decisions received by the FC are examined. The fusion rule of K out of N and the counting rule are compared with the LRFR. The LRFA does not depend on the signal model and the priori knowledge of the local sensors’ detection probabilities and false alarm rate. The numerical simulations are conducted, and the results show that the LRFR improves the performance of the system with low computational complexity.
Highlights
A wireless sensor network (WSN) has attracted considerable attention, because of its great potential in various applications such as battlefield surveillance, traffic, security, weather forecasts [1,2,3], health care, and home automation
From Eq (15), it is clear that T is a function of the global false alarm rate, the local sensors’ false alarm rate, and the total number of the sensors which send data to the fusion center (FC)
To show the influences of the variable total number of the local sensors which send data to the FC at that moment, in Fig. 5, we assume that the FC makes decisions when the number of detections sent to the FC at that moment is equal to or more than half of the initially total number of sensors deployed in region of interest (ROI)
Summary
A wireless sensor network (WSN) has attracted considerable attention, because of its great potential in various applications such as battlefield surveillance, traffic, security, weather forecasts [1,2,3], health care, and home automation. The counting rule makes a global decision by first counting the number of detections made by the local sensors and comparing it with a threshold T. From Eq (15), it is clear that T is a function of the global false alarm rate, the local sensors’ false alarm rate, and the total number of the sensors which send data to the FC. When N is known to the FC and m = N, the parameters of the logistic regression can be set as follows: Fig. 2 The FC selects data from the local sensors. In Eq (24), as an optimization problem, binary classification L2 penalized logistic regression minimizes the following cost function (
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