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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This paper investigates the use of wireless sensor networks for multiple event source localization using binary information from the sensor nodes. The events could continually emit signals whose strength is attenuated inversely proportional to the distance from the source. In this context, faults occur due to various reasons and are manifested when a node reports a wrong decision. In order to reduce the impact of node faults on the accuracy of multiple event localization, we introduce a trust index model to evaluate the fidelity of information which the nodes report and use in the event detection process, and propose the Trust Index based Subtract on Negative Add on Positive (TISNAP) localization algorithm, which reduces the impact of faulty nodes on the event localization by decreasing their trust index, to improve the accuracy of event localization and performance of fault tolerance for multiple event source localization. The algorithm includes three phases: first, the sink identifies the cluster nodes to determine the number of events occurred in the entire region by analyzing the binary data reported by all nodes; then, it constructs the likelihood matrix related to the cluster nodes and estimates the location of all events according to the alarmed status and trust index of the nodes around the cluster nodes. Finally, the sink updates the trust index of all nodes according to the fidelity of their information in the previous reporting cycle. The algorithm improves the accuracy of localization and performance of fault tolerance in multiple event source localization. The experiment results show that when the probability of node fault is close to 50%, the algorithm can still accurately determine the number of the events and have better accuracy of localization compared with other algorithms.

Wireless Sensor Networks (WSNs) consist of many sensor nodes capable of computation and communication which are distributed in a specified area. The sensor nodes can collaborate to deal with many kinds of complicated tasks including monitoring ecological environments, protecting infrastructures, tracking targets and so on [

WSNs are often used to detect the occurrence of an event in a region and determine its location, such as monitoring of pollution sources, detection of fire occurrence and so on. In these applications, all events are continually emitting signals whose strength is attenuated inversely proportional to the distance from the source. The sensor nodes report the strength of the signal to the sink regularly, and then the sink estimates the location of the source according to the information of the alarmed nodes reporting. The event localization algorithms can be divided into centralized approaches and distributed approaches. In a centralized approach, all sensor measurements are sent to the sink, and the location estimation is performed at the sink [

Maximum likelihood estimation is an important approach used for event localization [

In this paper, we introduce the _{n}_{n}_{n}

The paper is organized as follows: first, in Section 2, we present the related work in event localization in sensor networks. Next, in Section 3, we introduce the model we have adopted and the underlying assumptions. In Section 4, we provide the details of the TISNAP algorithm for multiple event source localization. In Section 5, we theoretically compare the TISNAP algorithm with the DSNAP algorithm. Section 6 presents the simulation results and comparison of the performance with other algorithm. Finally, in Section 7, we present the conclusions of our research.

Event localization is an important research issue in WSNs [

Ding proposed the Centroid Estimator (CE) algorithm [_{n}_{n}

However, this algorithm is sensitive to the presence of false positives (sensor nodes not in the region of the source but alarmed). These faults can result in large errors, especially if the faulty node is far away from the event location.

Niu [_{n,t}_{n}

Michealidis proposed Subtract on Negative Add on Positive (SNAP) [

Sheng [

In the DSNAP [

Trust and reputation models have been used in the realm of network security [

In this paper, we use the trust index model to evaluate the fidelity of information that sensors nodes have reported in the context of multiple event source localization. As the sensor network system runs over a period of time, a number of trust index states are built up as the indicator of the fidelity of data nodes reporting. Then, we reduce the weight of the faulty nodes according to the nodes’ trust index in the process of multiple event location estimation to achieve better fault tolerance performance.

For the sensor network that estimates the position of multiple events, we make the following assumptions:

A set of sensor nodes, denoted as _{n}_{n}

A set of event sources, denoted as

The event sources emit continuous signals that propagate evenly in all directions.

We assume that the signal strength of the event source _{k}_{n,k}^{+}_{n,k}_{n,k}_{n,k}

As a result, the _{n}_{n}_{max} reflects the maximum extent of sensor measurement, _{n}

We assume that the sensor nodes have been preset with a common threshold

_{n,t}

_{n,t}

Next, we explain some definitions [

As referred in

If the two event sources are identical, _{1} = _{2} =

We assume that the distance between any two events is greater than

From the sensor node perspective, we define two more regions for the single source case.

For a single event source, it can be obtained by the expression of _{n}

Since energy efficiency is the major issue in sensor networks and communication is the most expensive operation in terms of energy. We assume _{n}_{n}

We consider two types of node alarm fault in the paper:

This fault model is reflecting two fault types in event localization using binary data which is proposed in SNAP [

We are introducing a

Each node in the field is assigned a _{t}_{k,t}_{k,t}_{t}

As mentioned above, each node’s

In this section, we introduce the Trust Index based Subtract on Negative Add on Positive (TISNAP) localization algorithm, which reduces the impact of faulty nodes on the event localization by decreasing their trust index, to improve the accuracy of event localization and performance of fault tolerance for multiple event sources localization. It has three phases:

In multiple events localization, the first step is to identify the number of events in an area, and this is the precondition for estimating the location of the event sources. During the phase, the alarmed nodes send ‘1’ (alarm packet) to the sink, other nodes remain silent. In the sampling period, if the sink did not receive the alarm packet from a node, the sink regards it as a non-alarmed node. After the sink collected all alarm data in a sampling period, it computes the following likelihood function _{n}_{n}

This process is equivalent to the majority voting rule. By introducing the trust index of nodes, the algorithm enhances the influence of normal nodes and reduces the influence of faulty nodes in the likelihood function. Then the sink selects the alarmed nodes, whose corresponding likelihood function values are the maximal value in their surrounding area respectively, as the cluster nodes. Generally, the number of cluster nodes is equal to the number of event sources which we can find in the whole area. The algorithm of selecting cluster nodes is shown in

Finding the cluster nodes.

_{n}, Y_{n}, F_{n}]for sensor nodes n = 1,2, …, N which F_{n}> 0_{m}, Y_{m}] for sensor nodes m = 1,2,…, M which M < N_{i}_{j}> F_{i}_{i} is larger than all F_{j} which j = 1,2,…, K_{i}, Y_{i}] // cluster nodes |

This phase is mainly used to estimate the location of all event sources. We divide the phase into three steps:

The area is divided into a grid with _{n}_{n}_{n}_{n}

Since the events are highly likely to occur in the _{k}_{k}_{k}

The cluster node _{k}_{k} × G_{k} cells, centered around its location (_{k}_{k}_{k}_{k}

The sink defines a _{k}_{k}_{k}_{k}_{k}_{k}_{k}_{k}_{k}_{m}

Likelihood Matrix Construction.

_{n}_{n}_{n}_{k}_{k}_{k}^{−1}(i_{k}^{−1}(i, j)_{n}_{k}(i, j)_{k}(i, j)_{n} |

Let (_{k}_{k}_{k}_{k}

We provide a simple example to illustrate the TISNAP algorithm. In the example, the

_{k}

According to the estimated location of the events, the sink decides whether all the information reported by nodes is true or false after a round of event localization operation. Then, the sink updates the

The node is in the

The node is in the

The node is out of the

The node is out of the

In this section, we theoretically compare the TISNAP algorithm with the DSNAP one. The DSNAP algorithm is similar to the SNAP algorithm in [_{k}

Thus, the sensor data can be represented as _{k,t}_{k}_{k}_{k}_{k,t}

Next, consider the modified likelihood function _{k}^{2KM} _{k}

The SNAP estimator is given as the following:

When constructing the likelihood function, the TISNAP algorithm has taken into account the impact of faulty nodes. The sink assigns a trust index to every node, and the impact of faulty nodes is reduced. Therefore the algorithm has better performance of fault tolerance. Based on _{k,t}_{t}

Based on the _{k,t}

If the node is alarmed, _{k,t}_{k,t}_{k,t}_{k,t}

However, in this paper, the sink assigns a trust index to every node and the impact of faulty nodes is reduced. Based on the _{k,t}

According to the _{k,t}_{k,t}_{k,t}_{k,t}

All experiments in this paper are performed in a simulation environment. In the experiments, we use a square 200 × 200 sensor field with

We use the root mean square error (RMS Error) as a method of performance evaluation. We assume that the actual location of the two event sources is

In this paper, we assume that B = 100. In every experiment, the location of the sensor nodes is fixed and the event sources are randomly deployed in the area.

In this section, we evaluate the performance of fault tolerance of the TISNAP algorithm and the DSNAP algorithm under conditions of different fault probability and different numbers of alarmed sensor nodes. Also, we observe how many times all the event sources can be detected in 100 tries and how much the location deviation is. We assume that there are two fault types in the area: one is a

As shown in

In this section, we investigate the performance of the two algorithms if packets are dropped by the network. As mentioned in Section 4.1, in the first phase of TISNAP, each alarmed node sends a data packet to the sink and other nodes remain silent. Therefore, in the sampling period, if the sink does not receive the packet from a node, it will regard it as a non-alarmed node and assumes that the node does not detect the events. To investigate the effect of dropped packets, we assume that there is only one kind of fault which is dropping packets. And each node has the same probability of dropping packets.

As shown in

In sensor networks, due to working long hours, the boards of sensor nodes may be overheating and this may cause the sensor nodes to report false events, as the node is always alarmed. We assume that each node has the same probability of the fault of board overheating.

As shown in

TISNAP is a simple, efficient, fault-tolerant localization algorithm for multiple event source localization in sensor networks. It only uses the binary data reporting from the sensor nodes in the localization process. The trust index model is introduced to measure the fidelity of data reported by sensor node and to reduce the impact of faulty nodes on the multiple event localization by decreasing their trust index value. Compared to the DSNAP, TISNAP has the same computational overhead but can achieve higher accuracy in multiple event localization when a large percentage of the sensor nodes report erroneous observations. Experimental results show that when 50% nodes are in failure mode, the algorithm can still identify all events correctly and accurately estimate their location. For our future work, we plan to study the performance of TISNAP with respect to energy, bandwidth, and QoS. Furthermore, we will investigate real propagation models, such as in problems of environmental pollution, where an actual substance is released in the environment. Finally, we try to combine this algorithm with Kalman Filtering to achieve tracking of multiple event sources.

This work is supported by National Science Foundation of China (Grant No. 60873023, 60973029), and Science and Technology Research and Development Program of Zhejiang Province, China (Grant No. 2008C11100, 2009C03015-1).

The scenario of various regions used in this paper.

The family curves of

Likelihood matrix

the

The state of nodes located in different regions.

Fault tolerance performance for different signal strength of event sources. (

The Fault tolerance performance under different probability of dropped packets.

Estimator performance

Default Parameter Values.

The area | A | 200 m × 200 m |

Number of sensor nodes | 1,000 | |

Saturation voltage | _{max} |
3,000 |

Source amplitude | 3,000 | |

Noise variance | _{n,t} |
_{n,t} |

Threshold | 14 | |

Grid resolution | 1 | |

Scaling factor | 2 | |

Sensor gain | 1 |