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This paper is concerned with the problem of multitarget coverage based on probabilistic detection model. Coverage configuration is an effective method to alleviate the energy-limitation problem of sensors. Firstly, considering the attenuation of node’s sensing ability, the target probabilistic coverage problem is defined and formalized, which is based on Neyman-Peason probabilistic detection model. Secondly, in order to turn off redundant sensors, a simplified judging rule is derived, which makes the probabilistic coverage judgment execute on each node locally. Thirdly, a distributed node schedule scheme is proposed for implementing the distributed algorithm. Simulation results show that this algorithm is robust to the change of network size, and when compared with the physical coverage algorithm, it can effectively minimize the number of active sensors, which guarantees all the targets

Wireless sensor networks (WSNs) have attracted a great deal of attention. They are widely used in the fields of military affairs, intelligent family, environment surveillance and commercial management, and so on [

Recently, many literatures focus on the coverage problems in WSNs. They are generally classified into three types [

In this paper we address the multitarget coverage problem based on probabilistic detection model; our contributions are as follows: based on Neyman-Peason probabilistic detection model,

The rest of this paper is organized into the following sections. In Section

In this paper, we deal with the multitarget coverage problem based on Neyman-Peason probabilistic detection model. The goal is to minimize the number of active sensors while guaranteeing that each target can be covered with the required coverage probability.

We consider a WSN consisting of large number of sensors and a set of targets deployed in the WSN region randomly. To reduce the energy consumption of network, we want to find the minimum number of active sensors with the property that each target is monitored by sensors around it with the required network coverage probability.

We assume that

For sensor

Assume that all the sensors use the same detection threshold

The detection probability to

In WSN, many sensors are deployed in the monitoring region to detect the targets. Usually, a target in the monitoring region can be sensed by more than one sensor. The detection probability of

The relationship of total detection probability

Relationship of single detection probabilities and total detection probability with different number of sensing nodes.

From Figure

From Definition

Probabilistic Cover Set. If a target

Basic Cover Set. If

In this section, we first propose a simplified judging rule which can make the sensor judge whether the target can be

The PCJ-Rule is proposed based on Neyman-Peason probabilistic detection model. In this paper, we assume that each sensor can obtain the distances between itself and the targets in its sensing range.

Suppose a target

Given the requested total detection probability is

Due to the mean value theorem, then

Considering the fact that

It is assumed in Theorem

Form Theorem

The method of quantification is presented as follows.

Assuming that

Quantification Coefficient. If a sensing distance

Figure

Example of quantification with a target

Quantification Cover Set. If a sensor set

From Definition

Suppose

Given

As the assumption in Theorem

Suppose there is a target

Given the distance between sensor,

When

From the proof of Corollary

In our paper, through the information interaction between nodes, a sensor can receive quantification coefficients of the targets in its sensing range. Using Corollary

In this section, we design a distributed node schedule scheme, which make the sensor decide the self-working state by local judgment.

The flow chart of the node schedule scheme executed by a sensor locally is shown in Figure

Flow chart of the node schedule scheme executed by sensor locally.

Working state transfer diagram on each sensor.

From Figure

After the initialization, if the sensor does not receive any message from the others during the backoff time, it will switch to the ACTIVE state and broadcast the ACTIVE-Msg messages to its neighbor sensors.

The data format of ACTIVE-Msg contains three fields: the local ID, targets’ ID in the sensing range of the sensor, and the coverage coefficients

Before the step of “execute the PCJ-Rule” in Figure

None of the targets can be

Some but not all of the targets can be

All of the targets are

At last of the node schedule scheme, the sensor will work in ACTIVE state or SLEEP state. However, the node schedule scheme can be executed when the topology of network changes. The sensor will return to the IDLE state when the network coverage needs to be reconfigured.

In this section, we evaluate the performance of our distributed node schedule scheme. We simulate a stationary network with sensors and targets randomly deployed in a

signal strength from the target

standard deviation of noise in the channel

signal decay exponent

false alarm rate of Neyman-Peason detection rule

number of sensors

number of targets

maximum node number of sensing together

requirement probabilistic coverage probability

backoff weighted coefficient

In Figure

Comparison between the physical coverage configuration and the probabilistic coverage configuration with different

In Figure

Number of active sensors required with different number of targets, which make the network satisfy the

In Figure

Number of active sensors needed which make the network satisfy different requirement detection probabilities.

The simulation result can be summarized as follows.

In this paper, based on probabilistic detection model, we propose a distributed probabilistic coverage algorithm for the WSN with multiple static targets. The goal of our work is to find a simplified judging method, which can turn off the redundant sensors and guarantee all the targets covered by active sensors. In this paper, we define and formalize the target probabilistic coverage problems based on Neyman-Peason probabilistic detection model and propose a distributed node schedule scheme using the simplified judging rule. Simulation results show that our algorithm is robust to the change of network size. When compared with the physical coverage algorithm, the number of active sensors based on probabilistic detection model is smaller than that based on a physical one; at the same time, all the targets can be monitored at the requirement of network coverage probability.

In our future work, we will try to design a distributed and localized protocol that organizes the sensor nodes in disjoint set covers. By this way, the disjoint covers will work in turns, which can avoid sensors judging the local state frequently. Furthermore, we will integrate the sensor network connectivity requirement. The network connectivity is another important requirement of the network quantity of service (Qos), which makes the exchange of information between sensors easy.

The authors declare that there is no conflict of interests regarding the publication of this paper.