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 [1–3]. WSNs which are deployed in a real environment may easily fail due to many reasons, such as software malfunctions, hardware failures, radio interference, battery depletion, malicious damage and so on [4–6]. As mentioned in [5], about 40% to 60% of data measured by sensor nodes can be faulty in a real environment deployment. Therefore, fault-tolerance is a particular important issue in WSN applications.

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 [7–9]. In a distributed approach, nodes exchange sensors observation information with the surrounding neighbors and determine who is the cluster node [10–12]. The cluster nodes run a localization algorithm and determine the location of the sources. Centralized approaches can collect more information and accurately determine the location of the events, but they always consume more energy. Distributed approaches, on the other hand, have less computation overhead, but are not accurate enough for determining the location of the events. This paper mainly focuses on the fault-tolerance issue for multiple event detection and localization in wireless sensor networks, and devises a simple, fault-tolerant multiple event localization algorithm with higher estimation accuracy.

Maximum likelihood estimation is an important approach used for event localization [13–16]. Michaelides [17] proposed a distributed multiple event source localization algorithm based on maximum likelihood estimation. In the algorithm, each node exchanges information with the surrounding neighbors and some nodes are elected as cluster nodes. Then, the cluster nodes construct the likelihood matrix by analyzing the information of its neighbor nodes. Finally, the cluster nodes determine the location of all the events through maximum likelihood estimation. However, when constructing the likelihood matrix, faulty nodes may have a great effect on the value of the maximum likelihood matrix elements and result in a great deviation of positioning.

In this paper, we introduce the trust index for each sensor node, which used to evaluate the trust degree of a node according to its previous alarm reporting and determine the weight of the node’s reporting data in the event localization process, to reduce the impact of faulty nodes in event localization. We 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 has three main phases: determine the number of events, localization and updating of the trust index: (1) 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. First, the alarmed nodes send binary data to the sink and other nodes remain silent. Next, the sink computes all the likelihood functions F_n according to the collected data. Each alarmed node n has a corresponding likelihood function F_n. If F_n > 0, we think that there is an event around the alarmed node n. Then the alarmed node whose corresponding likelihood function value is the maximal value in a certain area is selected as a cluster node; (2) the sink 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; (3) the sink updates the trust index of all nodes according to the behavior in the previous reporting. According to the location of all nodes and their reported data, the sink judges whether or not the data reported by them is true. If it is judged true, the sink increases the trust index of the node. Otherwise, the sink reduces its trust index. The trust index of nodes ranges from 0 to 1. By introducing the trust index model, the algorithm enhances the influence of normal nodes and reduces the influence of faulty nodes, and it has higher localization accuracy and better performance of fault tolerance.

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 [13,14]. The localization techniques can be classified into four main categories: (1) Angle of Arrival (AOA) [18]; (2) Time of Arrival (TOA) [19,20]; (3) Time Difference of Arrival (TDOA) [21,22]; (4) Energy-based [9,11,23,24]. The energy-based approach uses event signal strength of sensor measurements to estimate event location [13–17]. It does not need precise synchronization among the sensor nodes. Hence, it is more suitable for event localization in large scale wireless sensor networks.

Ding proposed the Centroid Estimator (CE) algorithm [9]. It first gets the middle value of the sampling, filtering the incorrect data caused by occasional faults. Then it simply takes the centroid of the positions of all alarmed sensor nodes as the estimated event location. Let (x_n, y_n), n = 1, 2, …, P (p ≤ N) denote the position of all alarmed sensor nodes. Then, the event location estimated by CE is the centroid of these positions: (1) θ ^ C E = [ x ^ s , y ^ s ] = [ 1 P ∑ n = 1 P x n , 1 P ∑ n = 1 P y 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 [15] proposed an algorithm called Maximum Likelihood (ML) that uses only binary readings which are communicated to the base station to estimate the event position. The likelihood function is given by: (2) log ( p | θ ) = ∑ n = 1 N ∑ m = 1 M I n , t × log [ Q ( T − S n ( θ ) σ ω ) ] + ( 1 − I n , t ) × log [ 1 − Q ( T − S n ( θ ) σ ω ) ]where I_n,t is the binary reading. S_n(θ) is the measured signal by sensor without any noise. ML is sensitive to false negatives (nodes detected the event but not alarmed). These faults can result in large errors, especially for the faulty nodes close to the event that do not become alarmed.

Michealidis proposed Subtract on Negative Add on Positive (SNAP) [16] for event location only using binary data from the sensor nodes. The main idea is that the base station uses the binary observations to construct a matrix by adding ±1. The size of the matrix is fixed and the sensor is at the center of the area. Specifically speaking, the alarmed sensors add 1 to the region of their coverage, while the silent sensors subtract 1. By summing the contribution of each sensor, the maximum of the matrix points to the estimated event location. The Add on Positive (AP) algorithm is a variant of the SNAP algorithm. It only uses positive contributions from the alarmed sensors to construct the likelihood matrix. It may be used to obtain a low-complexity implementation and can be robust to false negatives, but it has low accuracy.

Sheng [8] presented a maximum likelihood (ML) acoustic source localization method which use the intensity attenuation function of acoustic signal. Analog measurements from sensors are required to estimate the source location. This incurs high communication and computation overhead. Therefore, it is desirable that only binary or multi-bit data are transmitted from local sensors to the processing node in the context of resource limited WSNs.

In the DSNAP [17] algorithm and SNAP [16] algorithm, binary data from local sensors is transmitted to the sink to estimate the location of events. According to the alarmed status, each node sends a data packet including binary data 0 or 1 to the sink. Using the binary data, the sink constructs the likelihood matrix and estimates all the event location. Since binary data is transmitted from local sensors to the processing node, the method needs lower communication energy and less calculation. However, node faults, e.g., false negative, false positive, have a great impact on accuracy of event localization.

Trust and reputation models have been used in the realm of network security [25–28] to detect misbehaving nodes and exclude them from the network. The concept of trust is interpreted as a relation among entities that participate in collaborative protocol in the sensor network system. Trust relations are based on evidence created by the previous interactions of entities within a protocol. Srinivasan [25] proposed a reputation based scheme for excluding malicious beacon node that provide false location information. Probst [27] presents a distributed approach that establishes reputation-based trust among sensor nodes in order to identify malfunctioning and malicious sensor nodes and minimize their impact on applications. In [28], trust is used to indicate the fidelity of event nodes reported in the context of sensor data gathering. It proposes a fault tolerant method to diagnose and mask arbitrary node failures in an event-driven wireless sensor network.

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.

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 this section, we theoretically compare the TISNAP algorithm with the DSNAP one. The DSNAP algorithm is similar to the SNAP algorithm in [16], and in essence, they are all methods of maximum likelihood estimation which use the information of sensor nodes located in the area of event source’s ROI. DSNAP is used for multiple event sources localization, while SNAP is used for single event source localization. According to the description of the literature [16], we assume that a set of sensor nodes, K, located in an event source’s ROI area. For node k, k ∈ K, we define the indicator function I_k for k = 1, …, K and t = 1, …, M: (16) I k , t = { 0 , Z k , t < T 1 , Z k , t ≥ T

Thus, the sensor data can be represented as I = {I_k,t: k = 1, …, K, t = 1, …, M}. The goal is to estimate the source location θ = [x_k, y_k] using the collected data I. The joint likelihood function is given by: (17) lg p ( I k | θ ) = ∑ k = 1 K ∑ t = 1 M I k , t × lg [ Q ( T − S k ( θ ) σ ω ) ] + ( 1 − I k , t ) × lg [ 1 − Q ( T − S k ( θ ) σ ω ) ]where Q ( x ) = 1 2 π ∫ x ∞ e − t 2 2 d t and S_k(θ) is the signal that would have been measured by sensor k if the source was at location θ and there was no noise (given by Equation (5)). In [16], they propose the following arbitrary probability assignment for their indicator function I_k,t: Pr { I k , t = 1 | θ } = Q ( T − s k ( θ ) σ ω ) = 0.99 , Pr { I k , t = 0 | θ } = 1 − Q ( T − s k ( θ ) σ ω ) = 0.01

Next, consider the modified likelihood function p′(I_k | θ) = 10^2KM p(I_k | θ). Taking the logarithm of the modified likelihood function, they get: (18) log p ′ ( I k | θ ) = ∑ k = 1 K ∑ t = 1 M I k , t × log ( 9.9 ) + ( 1 − I k , t ) × log ( 0.1 ) ≈ ∑ k = 1 K ∑ t = 1 M I k , t × ( + 1 ) + ( 1 − I k , t ) × ( − 1 )

The SNAP estimator is given as the following: (19) θ ^ S N A P = max θ log p ′ ( I k | θ )

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 Equation (18), the joint likelihood function we define is given by: (20) log p ″ ( I k | θ ) = ∑ k = 1 K ∑ t = 1 M T I k , t [ I k , t × ( + 1 ) + ( 1 − I k , t ) × ( − 1 ) ]where: (21) T I k , t = e − λ ν tand TI_k,t denotes the trust index of node k in the t-th sampling period. v_t is obtained by Equation (8).

Based on the Equation (18), F_k,t denotes the impact on the likelihood function by node k in the t-th sampling period. It is given by: (22) F k , t = I k , t × ( + 1 ) + ( 1 − I k , t ) × ( − 1 )

If the node is alarmed, I_k,t = 1 is obtained by Equation (16). Then F_k,t = 1. Otherwise, I_k,t = 0 and F_k,t = −1. However, when the node is faulty, the alarm status of the node is the opposite. A node should have been alarmed under normal conditions, but it is non-alarmed due to a fault, so I ′ k , t = 0 is obtained by Equation (16) and F ′ k , t = − 1. Similarly, a node should have been non-alarmed under normal conditions, but it is alarmed due to a fault, so I ′ k , t = 1 and F ′ k , t = 1. In the DSNAP algorithm, the difference caused by a single faulty node is 2. Therefore, with the increasing of faulty nodes, the likelihood function will be greatly affected.

However, in this paper, the sink assigns a trust index to every node and the impact of faulty nodes is reduced. Based on the Equation (20), FI_k,t denotes the impact on the likelihood function by node k in the t-th sampling period. It is given by: (23) F I k , t = T I k , t [ I k , t × ( + 1 ) + ( 1 − I k , t ) × ( − 1 ) ]

According to the Equation (9), if the node is normal, its trust index is 1, so FI_k,t = F_k,t. However, when the node is faulty, the alarm status of the node is the opposite and the difference caused by a single faulty node is 2TI_k,t. According to the Equations (8) and (9), after several rounds of event localization operations, the TI_k,t of the faulty node k is greatly reduced after t-th sampling period and it plays a minimal role in the process of event localization. Therefore, in the TISNAP algorithm, the value of the likelihood function is mainly determined by the normal nodes. The algorithm reduces or even ignores the impact of the faulty nodes. It is the reason that the TISNAP algorithm has better fault-tolerant performance and higher accuracy of localization after several rounds of event source locating operations.

All experiments in this paper are performed in a simulation environment. In the experiments, we use a square 200 × 200 sensor field with N = 1,000 randomly deployed nodes. We assume that the nodes in the sensor network gradually become faulty nodes over time. In the beginning, all nodes are normal. As time goes through, the number of faulty nodes increases at the rate of 5%. Two event sources are randomly deployed in the area and their distance is not less than 2 2 R O C. The signal strength at the location of the sources is identical. For the parameters used in the experiments, we use the default values shown in Table 1. According to Equation (5), the sensor readings are given by: (24) Z n ( t ) = min { 3000 , ∑ k = 1 K c k r n , k 2 ( t ) + ω n ( t ) }

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 ( x s , b 1 , y s , b 1 ) ∈ A and ( x s , b 2 , y s , b 2 ) ∈ A. The location of the two event sources estimated by TISNAP algorithm is ( x ^ s , b 1, y ^ s , b 2) and ( x ^ s , b 1, y ^ s , b 2), where b = 1, …, B. The RMS Error is given by: (25) R M S   E r r o r = 1 2 B ∑ k = 1 B ( ( x s , k 1 − x ^ s , b 1 ) 2 + ( y s , k 1 − y ^ s , b 1 ) 2 + ( x s , k 2 − x ^ s , b 2 ) 2 + ( y s , k 2 − y ^ s , b 2 ) 2 )

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.

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.