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Secure localization has become very important in wireless sensor networks. However, the conventional secure localization algorithms used in wireless sensor networks cannot deal with internal attacks and cannot identify malicious nodes. In this paper, a localization based on trust valuation, which can overcome a various attack types, such as spoofing attacks and Sybil attacks, is presented. The trust valuation is obtained via selection of the property set, which includes estimated distance, localization performance, position information of beacon nodes, and transmission time, and discussion of the threshold in the property set. In addition, the robustness of the proposed model is verified by analysis of attack intensity, localization error, and trust relationship for three typical scenes. The experimental results have shown that the proposed model is superior to the traditional secure localization models in terms of malicious nodes identification and performance improvement.

WSNs (wireless sensor networks) are composed of a large number of static or mobile sensors. Positioning technologies based on WSN [

Due to random deployment and network topology dynamicity, the locating in the WSN is more vulnerable to various attacks [

The remainder of the paper is organized as follows. Section

According to the usage of distance in the positioning, the positioning technologies can be divided into two main categories: distance-based (range-based) positioning technologies and distance-independent (range-free) positioning technologies. In the distance-based positioning algorithms, the absolute distance, or angle, between anchor node and unknown node is required. On the other hand, in distance-independent localization algorithms, there is no need to obtain the exact distance between anchor and unknown nodes. The distance-based localization algorithms usually consist of two steps: firstly, the distance (or angle) is measured, and, secondly, the measured distance is used to calculate the coordinates of unknown node. The distance measurement methods can be divided into following categories: methods based on time, methods based on signal arrival angle, and methods based on received signal strength.

The principle of distance-independent localization is simple and easy to implement, and it has advantages in terms of cost and power consumption. Besides, its performance is not affected by environmental factors. These algorithms can be divided into four categories: APTI algorithm, DV-Hop algorithm [

In the WSN, the localization algorithm can be attacked in many ways. The attacks can be divided into two categories: internal attacks and external attacks. Four types of external attacks are concerned: Sybil attack [

Due to limitation on sensor nodes, it is impossible to have a well-integrated defense system in the traditional WSN. The secure localization algorithms intended for WSN need to balance availability and integrity. According to that, the security localization algorithms can be divided into three categories: secure localization algorithms based on robust observation, secure localization algorithms based on isolation of malicious beacon node, and secure localization algorithms based on localization verification.

The gradual application of WSN localization caused the appearance of various attack methods [

In 1994, Marsh proposed a model of trust and cooperation for the first time, which has been regarded for a long time as a scope of sociology and psychology. In addition, Marsh introduced the concept of trust relationship formalization. In 1996, Blaze et al. proposed the concept of trust model in order to solve the complex security problems in the Internet [

The trust management models can be roughly divided into two categories: objective trust management models and subjective trust management models. The objective trust management models abstract the trust value into Boolean value; thus, there are only two possibilities for trust value. Due to the aforementioned, the commonly used trust management models are subjective trust management models. The most popular subjective trust management models are presented in the following.

The disadvantage of this model is that the arithmetic mean is used to calculate the indirect trust degree. In addition, this method processes data roughly and cannot accurately reflect the characteristics of the fuzzy trust value.

The disadvantage of this model is that it is not resistant to the collusion attacks. Namely, malicious nodes can give each other a high trust value.

The convergence rate of Sun’s model is limited by the length of trust chain, and it is difficult to get the trust value when the trust chain length increases.

The concepts in trust valuation and roles of nodes are listed as follows.

Comprehensive trust value is based on the localization error and time consumption of the beacon nodes, and it refers to the adoption level of the information provided by the beacon nodes.

Direct trust value refers to the confidence of unknown node in the anchor node, which is directly involved in the localization process.

Indirect trust value refers to the confidence of unknown node in the anchor node based on recommendation from other nodes.

Recommended trust value refers to the confidence of unknown node in the recommended nodes.

Source node represents an unknown node in the localization process.

Target node represents an anchor node needed for the localization.

Recommended nodes represent all nodes used in the localization except source node and target node.

In the WSN localization, the unknown node

Frame diagram of trust validation.

According to the multidimensional decision theory [

Each attribute value has different influence on calculation of direct trust value; thus, the weight vector is defined as

Based on the above function, the

All previous direct trust values are combined in order to obtain the final result:

The trust model is composed of three types of nodes, the source node, the target node, and the recommended node, which form the trust chain as shown in Figure

Trust chain.

In Figure

Received Signal Strength Indicator (RSSI) represents the strength of the received signal [

Due to the influence of environmental noise, there may be errors when measuring RSSI. Thus, (

Some experiments were carried out in article [

Relationship between distance and error.

As can be seen from Figure

The error, that is, the difference between measured and actual distance values, increases with the increase of distance between nodes [

According to Theorem

Finally, the indirect trust value is obtained by

Based on direct and indirect trust values, the comprehensive trust value of the source node for the target node is obtained, namely,

In the calculation of comprehensive trust value, the information entropy of direct trust value is defined by

Similarly, the information entropy of indirect trust value is defined by

Through the calculation of direct and indirect trust values of information entropy, the certain information can be acquired. The weight distribution is obtained as

The unknown node’s location reference set is defined as

The residual represents the deviation of observed distance value and real distance value, and the total localization residual is defined as

In (

The residuals are used to indicate the degree of each node’s deviation from its true location. The mean residual error is defined as

The concept of Sybil attack in the WSN indicates that a single node has a multiple identity.

The RSSI signal attenuation model in WSN environment is defined by (

According to the attenuation model, the distance ratio can be deduced as

Based on the above analyses, we know that if the distance between receiver and transmitter is constant, the RSSI difference is stable. The positioning in the case of Sybil attack is presented in Figure

Localization in the case of Sybil attack.

In Figure

The coordinates of

(

(

The discriminant of circle defined as

When

According to the above conclusions, the difference of RSSI is stable only when the faked nodes are distributed strictly in standard circle or straight line. Therefore the difference between

At time moment

Thus, the definition of attribute value

Communication process between nodes.

Node

Based on the experimental results, the definition of attribute value

In Section

In the environment without obstacles, according to Definition

The second parameter of normal distribution is determined in the literature [

According to the above analysis, when distance between unknown node and anchor node is

Localization in the presence of obstacles.

In Figure

In the case of localization failure, the RSSI values of the nodes are

If

At the same time, (

According to the values of

In an environment with obstacles,

In (

In the WSN positioning, the reference node set is

According to Definition

In (

According to the central limit theorem [

Based on the above conclusions, (

According to (

According to the trust valuation model, the trust value of each anchor node can be obtained in the communication range of the unknown node. Three anchor nodes with the largest value of trust are used for computing.

Trilateral-centroid localization [

Trilateral-centroid localization.

The coordinates of three anchor nodes are (

According to (

In addition, due to the presence of measurement errors, in some cases, the equations may not be solvable (as shown in Figure

There are six intersections among three circles in Figure

Trilateral-centroid localization.

Matlab7.0 experimental platform is used as the simulation environment. In this simulation environment, 100 nodes are randomly deployed in the range of 100 m

In the simulation experiment, three types of nodes are listed as follows: attack node, anchor node, or unknown node. First of all, three groups of experiments are carried out under different environments. The experimental conditions are listed as follows: nonexisting attack nodes, attack nodes existing, and attack nodes existing under trust valuation model.

According to Figures

Normal localization.

Localization under attack node.

Localization under trust valuation model.

In addition, the robustness of the model is also investigated. One is attack power and the other is the number of attack nodes.

As can be seen from Figure

Localization algorithms comparison.

As can be seen from Figure

Localization algorithms comparison.

In addition, this algorithm is compared with other secure localization algorithm in localization error.

As can be seen from Figure

Localization algorithms comparison.

As can be seen from Figure

Trust relationship.

The problem of secure localization is closely related to the structure characteristics and application background in WSN. Traditional security algorithms in WSN are constrained by the limited resources of sensor nodes. Trust management can improve the security and reliability of the localization system with low system overhead. In this paper, a number of attributes related to the localization are adopted and the threshold of the attribute value is discussed to ensure that the method can deal with the internal attacks and a certain degree of collusion attack. This model is superior to the traditional secure localization algorithm based on WSN in the success rate of identifying malicious nodes and performance overhead.

The authors declare that they have no competing interests.

The subject is sponsored by the National Natural Science Foundation of China (no. 61373017, no. 61572260, no. 61572261, no. 61672296, and no. 61602261), the Natural Science Foundation of Jiangsu Province (no. BK20140886 and no. BK20140888), Scientific & Technological Support Project of Jiangsu Province (no. BE2015702 and no. BE2016777, BE2016185), China Postdoctoral Science Foundation (no. 2014M551636 and no. 2014M561696), Jiangsu Planned Projects for Postdoctoral Research Funds (no. 1302090B and no. 1401005B), Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks Foundation (no. WSNLBZY201508).