CN110944383B - Wireless sensor network safety positioning method for clone attack - Google Patents
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Abstract
The invention relates to a wireless sensor network safety positioning method aiming at clone attack, which considers the defects of large energy consumption, poor detection resistance and the like of clone nodes from the angle of an attacker, detects the clone nodes in a wireless sensor network by a mean square error consistency method based on the safety positioning process of RSSI ranging, eliminates the clone nodes in the wireless sensor network by adopting a minimum mean square error method, finally positions unknown nodes in a safe environment, performs positioning calculation again by the unknown nodes through the rest beacon nodes, and obtains a positioning result by a positioning method based on RSSI ranging. The method can well remove the clone node, reduce the influence of the clone node on the positioning of the unknown node, and improve the positioning precision of the unknown node.
Description
Technical Field
The invention belongs to the technical field of Internet of things, relates to a wireless sensor network technology, and particularly relates to a wireless sensor network security positioning method for clone attack.
Background
The ranging and positioning process based on the Received Signal Strength Indicator (RSSI) mainly has two stages. In the first stage, the distance from the unknown node to the beacon node is calculated. The beacon node periodically transmits information such as ID and position coordinates to surrounding nodes, and the unknown node receives the information through a wireless signal. In free space, nodes transmit radio signals, and a theoretical model is usually a fading model RSSI (d)0)-10αlog(d/d0)+PnWherein RSSI represents the signal strength value of the beacon node received by the unknown node, d represents the distance between the unknown node and the beacon node, d0For reference distances, α denotes the path loss exponent, PnRepresenting a gaussian random variable with a mean value of 0. The attenuation model is a classical calculation method for measuring the distance from an unknown node to a beacon node. Alpha and PnAccording to the specific environment setting, when the signal strength value sent from the unknown node to the beacon node is known, the distance between the unknown node and the beacon node can be calculated. And a second stage of calculating the position of the unknown node. The distance from the beacon node to the unknown node is calculated in the first stage, and then the unknown node obtains the position information of the unknown node by using a maximum likelihood estimation method in combination with the position coordinates of the beacon node.
The beacon nodes deployed in the wireless sensor network can provide positioning service for unknown nodes. The distance calculation from the unknown node to the beacon node is affected by the interference of noise, obstacles and the like in the RSSI ranging process, so that the positioning position estimated by the unknown node is deviated from the real position. The wireless sensor network is usually deployed in an unattended hostile environment and is easily damaged by clone attack, the clone attack captures nodes in the network, extracts information such as keys, positions and identity identifications of the nodes, and manufactures clone nodes through the information. When a clone node exists in the network, the position estimated by the unknown node is seriously deviated from the real position. Since the clone nodes are deployed at different positions in the network, unknown node positioning is misled, and positioning accuracy is seriously influenced.
Disclosure of Invention
Aiming at the defects of low positioning precision and the like in the prior art, the invention provides a wireless sensor network safety positioning method aiming at clone attack, which can effectively eliminate clone nodes and improve the positioning precision of unknown nodes.
In order to achieve the above object, the present invention provides a method for securely positioning a wireless sensor network against a clone attack, comprising the following steps:
firstly, a beacon node periodically sends self ID and position coordinates to nodes around the beacon node, and when a known unknown node receives a signal intensity value sent by the beacon node, the distance from the beacon node to the unknown node is calculated by using an attenuation model of the signal intensity value; and obtaining the estimated position of the unknown node by combining the position coordinates of the beacon nodes according to the calculated distance between the beacon nodes and the unknown node.
Secondly, detecting whether clone attack exists in the wireless sensor network according to the mean square error of the estimated position of the unknown node by using the mean square error consistency, and if the clone attack does not exist, determining the estimated position of the unknown node obtained in the step one as the safe positioning position of the unknown node; and (4) if clone attack exists, removing clone nodes until the minimum mean square error of the unknown node is smaller than a set mean square error threshold value gamma, and repeating the step (I) to obtain the estimated position of the unknown node, namely the safe positioning position of the unknown node.
Preferably, the wireless sensor network comprises m, m is more than or equal to 3 beacon nodes, a plurality of unknown nodes and n, n is more than or equal to 0 and less than m clone nodes, each beacon node has a unique ID, the position coordinate of each beacon node is known, the communication radiuses of the beacon nodes, the unknown nodes and the clone nodes are all R, and no communication data is lost among the nodes.
Preferably, the model of the decay of the signal strength values is expressed as: RSSI (d) ═ RSSI (d)0)-10αlog(d/d0)+PnWherein RSSI represents the signal strength value of the beacon node received by the unknown node, d represents the distance between the unknown node and the beacon node, d0For reference distances, α denotes the path loss exponent, PnRepresenting a gaussian random variable with a mean value of 0; in the wireless sensor network, the position coordinates of the m beacon nodes are respectively (x)1,y1),(x2,y2),...,(xm,ym) The distances from the unknown nodes to the beacon nodes are respectively d1,d2,...,dmAssuming that the position coordinates of the unknown node are (x, y), the formula for calculating the position coordinates of the unknown node is expressed as:
subtracting the mth equation from the first equation to the mth-1 equation of the formula (1) in sequence to obtain a linear equation, wherein:
in the formula, A, b represents a coefficient matrix, and X represents the actual position coordinates of an unknown node;
calculating the estimated position coordinates of the unknown nodes by using a maximum likelihood estimation method as follows:
wherein,
representing the estimated location coordinates of the unknown node.
Preferably, in the step (two), a specific method for detecting whether a clone attack exists in the wireless sensor network according to the mean square error of the estimated position of the unknown node by using the mean square error consistency is as follows:
the position coordinates of the estimated positions obtained by the unknown nodes are mapped on a two-dimensional plane and are relatively concentrated, the mean square error of the obtained unknown nodes is uniform in a dense area with the real positions of the unknown nodes as the center, and if the cloned nodes exist in the wireless sensor network, the calculated mean square error values of the unknown nodes are not uniform and are larger than the mean square error value of the unknown nodes in a safe state; the mean square error of the unknown node is calculated by formula (5), and formula (5) is expressed as:
in the formula,
mean square error, x, representing unknown nodejAbscissa, y, representing position coordinate of jth beacon nodejAn ordinate indicating the position coordinate of the jth beacon node,
an abscissa representing the position coordinates of the unknown node,
and a ordinate indicating the position coordinates of the unknown node.
Preferably, in the step (two), the method for removing the clone nodes comprises:
(1) assuming that p, m + n nodes exist in the communication range of the unknown node, p-1 nodes are selected from the p nodes as a group for calculating the position of the unknown node, the mean square error of the position of the unknown node is calculated again for the position of the unknown node obtained from each group, and p mean square errors are recorded as p total mean square errors
(2) Select the smallest set of mean square errors in Y, denoted
Comparing M with gamma if M<Gamma, no cloning node exists in the wireless sensor network; if M is>Gamma, then there is a clone node in the wireless sensor network, randomly removing a node from a group of nodes with minimum mean square error;
(3) and (3) selecting p-2 nodes from the p-1 nodes as a group for calculating the positions of the unknown nodes, continuing to execute the steps (1) and (2) until the minimum group of mean square errors M is less than gamma, stopping the algorithm, and finishing the elimination of the clone nodes.
Compared with the prior art, the invention has the beneficial effects that:
according to the positioning method, from the perspective of an attacker, the situation that unknown nodes, beacon nodes and clone nodes are randomly deployed in the wireless sensor network is considered, positioning is carried out by the positioning method based on RSSI ranging, and the positioning method is simple to implement, low in cost and universal. In the safe positioning process based on RSSI ranging, clone nodes existing in the wireless sensor network are detected through a mean square error consistency method, the clone nodes in the wireless sensor network are removed through a minimum mean square error method, finally, the unknown nodes are positioned in a safe environment, the unknown nodes are subjected to positioning calculation again through the remaining beacon nodes, and positioning results are obtained through a positioning method based on RSSI ranging. The method can well remove the clone node, reduce the influence of the clone node on the positioning of the unknown node, and improve the positioning precision of the unknown node.
Drawings
FIG. 1 is a schematic diagram illustrating an influence of a cloning attack on unknown node positioning in an existing wireless sensor network;
fig. 2 is a schematic view illustrating a cloned node participating in positioning of an unknown node in a wireless sensor network security positioning method for cloning attack according to an embodiment of the present invention;
FIG. 3 is a schematic diagram illustrating a comparison of influences of the number of cloned nodes on a mean square error of an estimated position of an unknown node in a wireless sensor network security positioning method for cloning attack according to an embodiment of the present invention;
FIG. 4 is a schematic diagram illustrating the impact of the number of cloned nodes on the positioning of unknown nodes in the method for safely positioning a wireless sensor network for clone attack according to the embodiment of the present invention;
fig. 5 is a schematic diagram illustrating a comparison of influences of distances from cloned beacon nodes to unknown nodes on mean square errors of estimated positions of the unknown nodes in the wireless sensor network security positioning method for clone attack according to the embodiment of the present invention;
fig. 6 is a schematic diagram illustrating an influence of a distance from a cloned beacon node to an unknown node on positioning of the unknown node in the wireless sensor network security positioning method for clone attack according to the embodiment of the present invention;
fig. 7 is a performance comparison diagram of the wireless sensor network security positioning method for clone attack according to the present invention and different positioning methods in the prior art.
Detailed Description
The invention is described in detail below by way of exemplary embodiments. It should be understood, however, that elements, structures and features of one embodiment may be beneficially incorporated in other embodiments without further recitation.
The distance calculation from the unknown node to the beacon node is affected by the interference of noise, obstacles and the like in the RSSI ranging process, so that the positioning position estimated by the unknown node is deviated from the real position. Referring to fig. 1, when a cloned node exists in a wireless sensor network, an estimated position of an unknown node is seriously deviated from a real position, and in fig. 1, a triangle represents a beacon node, a square represents the cloned node, and a circle represents the unknown node.
The mean square error can well reflect the offset degree between the estimator and the estimated quantity, and when only a beacon node exists in the wireless sensor network, the mean square error of an unknown node fluctuates within a certain range. When the cloned nodes exist in the wireless sensor network, the mean square error of the estimated positions of the unknown nodes increases along with the increase of the number of the cloned nodes. The mean square error value of the unknown node is inconsistent according to the existence of the clone node. The invention provides a wireless sensor network safety positioning method aiming at clone attack, which is based on the safety positioning process of RSSI ranging, adopts a mean square error consistency method to detect clone nodes, eliminates the clone nodes, ensures that unknown nodes are positioned in a safety environment and has high positioning precision.
Specifically, the wireless sensor network comprises m, m is more than or equal to 3 beacon nodes, a plurality of unknown nodes and n, n is more than or equal to 0 and less than m clone nodes, each beacon node has a unique ID, the position coordinate of each beacon node is known, the communication radiuses of the beacon nodes, the unknown nodes and the clone nodes are all R, and no communication data are lost among the nodes. The clone node participates in the positioning process of the unknown node by acquiring the ID and the unknown coordinate information of the beacon node, and the positioning accuracy of the unknown node can be influenced. The performance and the function of the nodes are the same, and the nodes have a data fusion function.
The invention provides a wireless sensor network safety positioning method aiming at clone attack, which specifically comprises the following steps:
firstly, a beacon node periodically sends self ID and position coordinates to nodes around the beacon node, and when a known unknown node receives a signal intensity value sent by the beacon node, the distance from the beacon node to the unknown node is calculated by using an attenuation model of the signal intensity value; and obtaining the estimated position of the unknown node by combining the position coordinates of the beacon nodes according to the calculated distance between the beacon nodes and the unknown node.
Specifically, the attenuation model of the signal strength values is expressed as: RSSI (d) ═ RSSI (d)0)-10αlog(d/d0)+PnWherein RSSI represents the signal strength value of the beacon node received by the unknown node, d represents the distance between the unknown node and the beacon node, d0For reference distances, α denotes the path loss exponent, PnRepresenting a gaussian random variable with a mean value of 0. Wherein, alpha and PnIt needs to be set up in a false manner according to specific environments. In free space, the nodes transmit wireless signals, and when the unknown node is known to receive the signal strength value sent by the beacon node, the distance between the unknown node and the beacon node can be calculated.
Specifically, in the wireless sensor network, the position coordinates of m beacon nodes are (x) respectively1,y1),(x2,y2),...,(xm,ym) The distances from the unknown nodes to the beacon nodes are respectively d1,d2,...,dmAssuming that the position coordinates of the unknown node are (x, y), the formula for calculating the position coordinates of the unknown node is expressed as:
subtracting the mth equation from the first equation to the mth-1 equation of the formula (1) in sequence to obtain a linear equation, wherein:
in the formula, A, b represents a coefficient matrix, and X represents the actual position coordinates of an unknown node;
calculating the estimated position coordinates of the unknown nodes by using a maximum likelihood estimation method as follows:
wherein,
representing the estimated location coordinates of the unknown node. Here, when calculating the estimated position coordinates of the unknown node, a least square method may also be employed.
Secondly, detecting whether clone attack exists in the wireless sensor network according to the mean square error of the estimated position of the unknown node by utilizing the mean square error consistency, if no clone attack exists, positioning the unknown node in a safe environment, and determining the estimated position of the unknown node obtained in the step one as the safe positioning position of the unknown node; and (3) if clone attack exists, removing clone nodes until the minimum mean square error of the unknown node is smaller than a set mean square error threshold value gamma, determining that the unknown node is positioned in a safe environment, repeating the step (I), and obtaining the estimated position of the unknown node, namely the safe positioning position of the unknown node. The mean square error threshold γ is an upper limit of error that is calculated experimentally in a safe state.
Specifically, the specific method for detecting whether the clone attack exists in the wireless sensor network according to the mean square error of the estimated position of the unknown node by using the mean square error consistency comprises the following steps:
the position coordinates of the estimated positions obtained by the unknown nodes are mapped on a two-dimensional plane and are relatively concentrated, the mean square error of the obtained unknown nodes is uniform in a dense area with the real positions of the unknown nodes as the center, and if the cloned nodes exist in the wireless sensor network, the calculated mean square error values of the unknown nodes are not uniform and are larger than the mean square error value of the unknown nodes in a safe state; the mean square error of the unknown node is calculated by formula (5), and formula (5) is expressed as:
in the formula,
mean square error, x, representing unknown nodejAbscissa, y, representing position coordinate of jth beacon nodejAn ordinate indicating the position coordinate of the jth beacon node,
an abscissa representing the position coordinates of the unknown node,
and a ordinate indicating the position coordinates of the unknown node.
Specifically, the method for eliminating the clone nodes comprises the following steps:
(1) assuming that p, m + n nodes exist in the communication range of the unknown node, p-1 nodes are selected from the p nodes as a group for calculating the position of the unknown node, the mean square error of the position of the unknown node is calculated again for the position of the unknown node obtained from each group, and p mean square errors are recorded as p total mean square errors
(2) Selecting the minimum group of mean square errors in Y through bubbling algorithm, and recording the minimum group of mean square errors as
Comparing M with gamma if M<Gamma, if no clone node exists in the wireless sensor network, stopping the algorithm; if M is>Gamma, then there is a clone node in the wireless sensor network, randomly removing a node from a group of nodes with minimum mean square error;
(3) and (3) selecting p-2 nodes from the p-1 nodes as a group for calculating the positions of the unknown nodes, continuing to execute the steps (1) and (2) until the minimum group of mean square errors M is less than gamma, stopping the algorithm, and finishing the elimination of the clone nodes.
For example: randomly removing a node from a node information set L to generate a new set having q groups in total, wherein the new set is as follows:
substituting q groups of data of the set into the mean square error calculation of an unknown node to obtain a group of mean square errors
The group with the smallest mean square error is selected and compared with gamma. And if the mean square error is less than gamma, stopping rejecting the nodes. If the mean square error is greater than γ, then one node is again randomly reduced from the set where the mean square error is the smallest. The previous operation is continued until the mean square error is less than γ.
And (3) eliminating clone nodes by adopting a minimum mean square error method, randomly eliminating one node from a group of node information sets, and then calculating the mean square error of an unknown node. When the removed node is a clone node, the mean square error of the obtained unknown node is reduced. Then randomly removing a node from a group of nodes with the minimum mean square error, and calculating the mean square error of an unknown node until the minimum mean square error is less than gamma, so that the unknown node is positioned in a safe environment, the unknown node is positioned in the safe environment, and the positioning precision of the unknown node is effectively improved.
To further illustrate the advantages and effectiveness of the above-described method of the present invention, the present invention is further described below with reference to the accompanying drawings and examples.
Example (b): a batch of beacon nodes and unknown nodes are randomly deployed in the wireless sensor network, U is the unknown node, and B1, B2, B3, B4 and B5 are the beacon nodes. The beacon nodes acquire position coordinate information of the beacon nodes in advance and provide positioning service for unknown nodes. The unknown node needs to acquire the position coordinates of the unknown node through a positioning technology. B2 'and B4' capture cloned nodes copied by B2 and B4 for the clone attack respectively, and the cloned nodes can influence the positioning accuracy of unknown nodes in the positioning process of the unknown nodes by acquiring the ID and the position coordinate information of beacon nodes. The nodes can communicate information with each other. Each beacon node has a unique ID, and the cloned node can participate in the positioning process of the unknown node as well as the ID of the beacon node. Communication radiuses of the unknown nodes, the beacon nodes and the clone nodes are all R, and d2', d2, d4' and d4 are distances from U to B2', B2, B4' and B4 respectively. The problem of communication data loss between nodes is not considered.
When the unknown node U sends a positioning request, the beacon node and the clone node both send position coordinate information after receiving the broadcast. The theoretical model adopted by the nodes for wireless signal transmission is an attenuation model RSSI (d) ═ RSSI (d)0)-10αlog(d/d0)+PnWherein RSSI represents the signal strength value of the beacon node received by the unknown node, d represents the distance between the unknown node and the beacon node, d0For reference distances, α denotes the path loss exponent, PnRepresenting a gaussian random variable with a mean value of 0. Therefore, the distances d1, d2', d3, d4' and d5 from the beacon nodes to the unknown nodes U are calculated. And the unknown node obtains estimated position information of the unknown node by using a maximum likelihood estimation method through the calculated distance between the beacon node and the unknown node and combining the position coordinates of the beacon node. When the wireless sensor network is in a safe state, the position coordinates of the unknown nodes obtained by using a maximum likelihood estimation method are mapped on a two-dimensional plane to be relatively concentrated, and the mean square error values of the obtained unknown nodes are consistent in a dense area with the real positions of the unknown nodes as centers. And if the clone nodes exist in the wireless sensor network, calculating to obtain the mean square error value of the unknown nodes, wherein the mean square error value of the unknown nodes is inconsistent and is greater than the mean square error value of the unknown nodes in a safe state. Referring to fig. 2, the position coordinates of B1, B2', B3, B4', B5 and the distance to the unknown node are substituted into formula (1), the position coordinates of the unknown node are calculated, the calculated result is substituted into formula (5), the mean square error of the unknown node is obtained, and whether a clone node exists in the wireless sensor network is judged by comparing with γ. In this example, the position coordinate information sent by B2 'and B4' is the position coordinate information of B2 and B4, so the mean square error of the unknown node U is obtained to be larger than the upper limit of the experimental statistics, namely the mean square errorAnd a threshold value gamma is set, so that the cloned nodes in the beacon node set are judged to be contained, and the cloned nodes are further removed by using a minimum mean square error method.
Randomly removing a node from a group of node information sets, and then calculating the mean square error of an unknown node. When the removed node is a clone node, the mean square error of the obtained unknown node is reduced. Then randomly removing one node from a group of nodes with the minimum mean square error, and carrying out the same operation until the minimum mean square error is less than gamma. In this example, a node is randomly removed from a beacon node set L { B1, B2', B3, B4', B5}, a new set-up total 5 groups are generated, which are L1 ═ { B2', B3, B4', B5} L2 { (B1, B3, B4', B5}, L3 ═ B1, B2', B4', B5}, L4 ═ B1, B2', B3, B5}, L5 { (B1, B2', B3, B4' }, data of the 5 groups of sets are brought into the mean square error calculation of an unknown node, and the mean square error is obtained as the mean square error
The group with the smallest mean square error is selected and compared with gamma. And if the mean square error is less than gamma, stopping rejecting the nodes. If the mean square error is larger than gamma, randomly reducing one node again from the set with the minimum mean square error, and repeating the previous operation steps until the mean square error is smaller than gamma.
The clone attack is detected through the consistency of the mean square error, then the clone nodes are removed by using a minimum mean square error method, the unknown node is positioned in a safe environment, and finally the safe positioning of the nodes is realized by a positioning method based on RSSI ranging.
Referring to fig. 3 and 4, the more cloned nodes contained in the wireless sensor network, the greater the positioning influence on unknown nodes and the lower the positioning accuracy. Specifically, with reference to fig. 3, the larger the number of cloned nodes is, the larger the mean square error influence on the estimated position of the unknown node is, and in the case of the same number of beacon nodes, the larger the number of cloned nodes is, the larger the mean square error of the estimated position of the unknown node is. With reference to fig. 4, the larger the number of the cloned nodes is, the larger the influence on the positioning error of the unknown node is, and in the case of the same number of beacon nodes, the larger the number of the cloned nodes is, the larger the positioning error of the unknown node is, and the lower the positioning accuracy is.
Referring to fig. 5 and 6, as the distance from the cloned node to the unknown node in the wireless sensor network increases, the mean square error of the estimated position of the unknown node is larger, and the positioning error of the unknown node is larger.
Referring to fig. 7, the unknown nodes of the wireless sensor network are positioned by using the above-mentioned security positioning method, the positioning method with the clone attack and the positioning method without the clone attack, and with the increase of the number of the beacon nodes, the positioning error of the unknown nodes is basically kept unchanged by using the positioning method with the clone attack and the positioning method without the clone attack, and the positioning error of the unknown nodes without the clone attack is obviously smaller than the positioning error of the unknown nodes with the clone attack. With the adoption of the safe positioning method, along with the increase of the number of the beacon nodes, the positioning error of the unknown node is obviously reduced, and compared with a positioning method with cloning attack and a positioning method without cloning attack, the positioning error of the unknown node is obviously smaller than that of the two methods. It should be noted that, although the positioning error of the unknown node using the above-mentioned safety positioning method of the present invention is greater than the positioning error of the unknown node using the positioning method without clone attack when the number of beacon nodes is less than 20, the difference is not obvious, however, when the number of beacon nodes is greater than 20, the positioning error of the unknown node using the above-mentioned safety positioning method of the present invention is significantly less than the positioning error of the unknown node using the positioning method without clone attack as the number of beacon nodes increases.
Therefore, the method for safely positioning the wireless sensor network aiming at the clone attack can effectively detect the clone nodes and remove the clone nodes, ensures that the unknown nodes are positioned in a safe environment, can greatly reduce the influence of the clone nodes on the positioning of the unknown nodes, improves the positioning accuracy, and is more effective compared with the existing method.
The above-mentioned embodiments are merely provided for the convenience of illustration of the present invention, and do not limit the scope of the present invention, and various simple modifications and modifications made by those skilled in the art within the technical scope of the present invention should be included in the above-mentioned claims.
Claims (2)
1. A wireless sensor network safety positioning method aiming at clone attack is characterized in that the wireless sensor network comprises m, m is more than or equal to 3 beacon nodes, a plurality of unknown nodes and n, n is more than or equal to 0<Each beacon node has a unique ID (identity), the position coordinate of each beacon node is known, the communication radiuses of the beacon nodes, the unknown nodes and the clone nodes are all R, no communication data is lost among the nodes, and the position coordinates of the m beacon nodes are (x) respectively1,y1),(x2,y2),...,(xm,ym) The distances from the unknown nodes to the beacon nodes are respectively d1,d2,...,dm(ii) a The method comprises the following steps:
firstly, a beacon node periodically sends self ID and position coordinates to nodes around the beacon node, and when a known unknown node receives a signal intensity value sent by the beacon node, the distance from the beacon node to the unknown node is calculated by using an attenuation model of the signal intensity value; obtaining the estimated position of the unknown node by combining the position coordinates of the beacon nodes according to the calculated distance between the beacon nodes and the unknown node;
secondly, detecting whether clone attack exists in the wireless sensor network according to the mean square error of the estimated position of the unknown node by using the mean square error consistency, and if the clone attack does not exist, determining the estimated position of the unknown node obtained in the step one as the safe positioning position of the unknown node; if clone attack exists, removing clone nodes until the minimum mean square error of the unknown node is smaller than a set mean square error threshold value gamma, repeating the step (I), and obtaining the estimated position of the unknown node, namely the safe positioning position of the unknown node; the specific method for detecting whether the clone attack exists in the wireless sensor network according to the mean square error of the estimated position of the unknown node by utilizing the mean square error consistency comprises the following steps:
the position coordinates of the estimated positions obtained by the unknown nodes are mapped on a two-dimensional plane and are relatively concentrated, the mean square error of the obtained unknown nodes is uniform in a dense area with the real positions of the unknown nodes as the center, and if the cloned nodes exist in the wireless sensor network, the calculated mean square error values of the unknown nodes are not uniform and are larger than the mean square error value of the unknown nodes in a safe state; the mean square error of the unknown node is calculated by formula (5), and formula (5) is expressed as:
in the formula,
mean square error, x, representing unknown nodejAbscissa, y, representing position coordinate of jth beacon nodejAn ordinate indicating the position coordinate of the jth beacon node,
an abscissa representing the position coordinates of the unknown node,
a vertical coordinate representing a position coordinate of the unknown node;
the method for eliminating the clone nodes comprises the following steps:
(1) assuming that p, m + n nodes exist in the communication range of the unknown node, p-1 nodes are selected from the p nodes as a group for calculating the position of the unknown node, the mean square error of the position of the unknown node is calculated again for the position of the unknown node obtained from each group, and p mean square errors are recorded as p total mean square errors
(2) Select the smallest set of mean square errors in Y, denoted
Comparing M with gamma if M<Gamma, no cloning node exists in the wireless sensor network; if M is>Gamma, then there is a clone node in the wireless sensor network, randomly removing a node from a group of nodes with minimum mean square error;
(3) and (3) selecting p-2 nodes from the p-1 nodes as a group for calculating the positions of the unknown nodes, continuing to execute the steps (1) and (2) until the minimum group of mean square errors M is less than gamma, stopping the algorithm, and finishing the elimination of the clone nodes.
2. The method for securely positioning a wireless sensor network against clone attacks according to claim 1, wherein the decay model of the signal strength value is expressed as: RSSI (d) ═ RSSI (d)0)-10αlog(d/d0)+PnWherein RSSI represents the signal strength value of the beacon node received by the unknown node, d represents the distance between the unknown node and the beacon node, d0For reference distances, α denotes the path loss exponent, PnRepresenting a gaussian random variable with a mean value of 0; assuming that the position coordinates of the unknown node are (x, y), the formula for calculating the position coordinates of the unknown node is expressed as:
subtracting the mth equation from the first equation to the mth-1 equation of the formula (1) in sequence to obtain a linear equation, wherein:
in the formula, A, b represents a coefficient matrix, and X represents the actual position coordinates of an unknown node;
calculating the estimated position coordinates of the unknown nodes by using a maximum likelihood estimation method as follows:
wherein,
representing the estimated location coordinates of the unknown node.
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