CN113939015A - Non-ranging WSN node positioning method based on Jaccard similarity - Google Patents

Non-ranging WSN node positioning method based on Jaccard similarity Download PDF

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CN113939015A
CN113939015A CN202111181450.1A CN202111181450A CN113939015A CN 113939015 A CN113939015 A CN 113939015A CN 202111181450 A CN202111181450 A CN 202111181450A CN 113939015 A CN113939015 A CN 113939015A
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CN113939015B (en
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章光
张可
胡少华
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Wuhan University of Technology WUT
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Abstract

A non-ranging WSN node positioning method based on Jaccard similarity comprises the steps of determining the estimated distance between each adjacent sensor node according to the network connectivity of the sensor nodes and the information of the adjacent sensor nodes, then obtaining the shortest estimated distance, the shortest path and the shortest path neighbor node set between all the sensor nodes and the anchor sensor nodes in the network through flooding of the anchor sensor nodes, determining the correction coefficient of the shortest path between any two anchor sensor nodes, then calculating the Jaccard similarity of the shortest path neighbor node set between the sensor node to be positioned and the anchor sensor node and the shortest path neighbor node set between the anchor sensor nodes, and correcting the shortest estimated distance between the sensor node to be positioned and the anchor sensor node by using the correction coefficient of the path with the highest similarity, and finally determining the estimated position of the sensor node to be positioned according to the corrected distance. The positioning accuracy of the WSN node is improved by the design.

Description

Non-ranging WSN node positioning method based on Jaccard similarity
Technical Field
The invention belongs to the field of wireless sensor network node positioning, and particularly relates to a non-ranging WSN node positioning method based on Jaccard similarity.
Background
Node position information of a Wireless Sensor Network (WSN) plays an important role in WSN applications. In the WSN monitoring, the monitoring data without position information cannot help a user to obtain the real condition of a monitored object, so that an effective decision cannot be made, and the practical application significance of the system is weakened.
Currently, positioning algorithms are classified into two categories, ranging-based positioning algorithms and non-ranging positioning algorithms according to whether ranging is required or not. The ranging and positioning algorithm is to estimate the distance between nodes by using some hardware tools, such as the commonly used Received Signal Strength (RSSI), Arrival Time (AOV), and ultrasonic ranging, which mostly require additional hardware facilities, and the ranging accuracy is easily affected by the network environment. The non-ranging algorithm mainly estimates the node Distance or position according to the communication information of the network, and typical non-ranging algorithms include an interior Point test Algorithm (APIT), a Centroid algorithm (Centroid Localization algorithm), a Distance Vector algorithm (DV-Hop), and the like. Compared with a ranging positioning algorithm, the non-ranging algorithm has the advantages of stronger environmental adaptability and higher robustness, and does not need additional ranging hardware, so the algorithm is lower in implementation cost and has a wide application prospect, but the existing non-ranging algorithm has the defects of larger estimation error of distance and larger positioning error.
Disclosure of Invention
The invention aims to solve the problem of large positioning error in the prior art and provides a non-ranging WSN node positioning method based on Jaccard similarity, which can effectively improve positioning accuracy.
In order to achieve the above purpose, the invention provides the following technical scheme:
a non-ranging WSN node positioning method based on Jaccard similarity sequentially comprises the following steps:
firstly, uniformly arranging a plurality of sensor nodes to be positioned and anchor sensor nodes with known positions at random in a monitoring area, and then determining the estimated distance between each adjacent sensor node according to the network connectivity of the sensor nodes and the information of the adjacent sensor nodes;
step two, flooding through anchor sensor nodes to obtain the shortest estimated distances, shortest paths and shortest path neighbor node sets between all sensor nodes and the anchor sensor nodes in the network, then determining a correction coefficient of the shortest path between two anchor sensor nodes by the anchor sensor nodes based on the shortest estimated distances between the anchor sensor nodes and one other anchor sensor node, and flooding the correction coefficient and corresponding path neighbor node set information into the whole network;
calculating Jaccard similarity of a shortest path neighbor node set between a sensor node to be positioned and an anchor sensor node and each anchor sensor node, and correcting the shortest estimated distance between the sensor node to be positioned and the anchor sensor node by using a correction coefficient of the shortest path with the highest Jaccard similarity to obtain the final estimated distance between the sensor node to be positioned and the anchor sensor node;
and step four, determining the estimated position of each sensor node to be positioned according to the final estimated distance between each sensor node to be positioned and all the anchor sensor nodes, thereby completing the positioning of the sensor node to be positioned.
In step three, the Jaccard similarity is calculated by adopting the following formula:
Figure BDA0003297404090000021
in the above formula, P1For the shortest path between the sensor node to be positioned and the anchor sensor node, P2For shortest path between anchor sensor nodes, Similarity<P1，P2>Is P1Neighbor node set PN of1And P2Neighbor node set PN of2Jaccard similarity of (a).
In step three, the final estimated distance between the sensor node to be positioned and the anchor sensor node
Figure BDA0003297404090000024
The formula is adopted to calculate the following formula:
Figure BDA0003297404090000022
in the above formula, the first and second carbon atoms are,
Figure BDA0003297404090000023
for the shortest estimated distance, C, between the sensor node to be positioned and the anchor sensor nodeoptAnd the correction coefficient is the shortest path with the highest Jaccard similarity.
In the second step, the correction coefficient of the shortest path between the two anchor sensor nodes is calculated by adopting the following formula:
Figure BDA0003297404090000031
in the above formula, CmnCorrection coefficient (x) for shortest path between m and n anchor sensor nodesm，ym)、(xn，yn) The real coordinates of anchor sensor nodes m, n respectively,
Figure BDA0003297404090000032
the shortest estimated distance of m to n.
In the second step, the flooding mode of the anchor sensor node is as follows:
when a sensor node receives a flooding message broadcast by an adjacent sensor node, the ID of the forwarding sensor node is inquired to obtain the estimated distance between the sensor node and the forwarding sensor node, the accumulated distance is updated, the ID of the anchor sensor node of the message is inquired, if the internal memory contains the ID information of the anchor sensor node, the accumulated distance is compared, the message with smaller accumulated distance is stored, if the node is updated, the message is forwarded, and if the node is not updated, the message is discarded; if the anchor sensor node ID information does not exist in the memory, the information is stored and forwarded, wherein the initial value of the accumulated distance is 0.
In the first step, the estimated distance between the adjacent sensor nodes is calculated by adopting the following formula:
Figure BDA0003297404090000033
Figure BDA0003297404090000034
in the above formula, duiFor the estimated distance between adjacent sensor nodes u, I, IuiIs the intersection of the sensor nodes u, i, Mu、MiNumber of adjacent sensor nodes, m, of sensor nodes u, i, respectivelyuiThe number of the common adjacent sensor nodes of the sensor nodes u and i, and R is the communication radius of the sensor nodes.
All sensor node signals are simulated by adopting a DOI signal model, and the network connectivity of the sensor nodes and the information of the adjacent sensor nodes are obtained through the receiving signal threshold of the sensor nodes.
The receiving signal threshold value of the sensor node is obtained through the following signal propagation model:
Figure BDA0003297404090000035
Figure BDA0003297404090000036
in the above formula, RSS is the signal strength received by the sensor node, PtFor transmitting node signal strength, P (d)0) Is a reference distance d0Eta is the environmental attenuation coefficient, diIs the true distance, K, between the signal receiving node and the signal transmitting nodeiAnd the loss coefficient in the ith direction is doi, a random number related to environmental noise is doi, and N is a non-zero natural number.
In the fourth step, the estimated position X of the sensor node to be positioned is calculated according to a least square method to obtain:
X＝(ATA)-1ATB
Figure BDA0003297404090000041
Figure BDA0003297404090000042
Figure BDA0003297404090000043
in the above formula, A, B are position and distance constraint matrixes respectively, (x)u，yu) For the estimated position of the sensor node u to be positioned, (x)1，y1)，...，(xm，ym) For the coordinates of each anchor sensor node,
Figure BDA0003297404090000044
and m is the number of the anchor sensor nodes.
Compared with the prior art, the invention has the beneficial effects that:
the invention relates to a non-ranging WSN node positioning method based on Jaccard similarity, which comprises the steps of firstly determining the estimated distance between each adjacent sensor node according to the network connectivity of the sensor node and the information of the adjacent sensor nodes, then flooding through the anchor sensor node to obtain the shortest estimated distance, the shortest path and the shortest path neighbor node set between all the sensor nodes and the anchor sensor node in the network, determining the correction coefficient of the shortest path between any two anchor sensor nodes, then calculating the Jaccard similarity of the shortest path neighbor node set between the sensor node to be positioned and the anchor sensor node and the shortest path neighbor node set between the anchor sensor nodes, correcting the shortest estimated distance between the sensor node to be positioned and the anchor sensor node by the correction coefficient of the shortest path with the highest similarity, and finally determining the estimated position of the sensor node to be positioned according to the corrected estimated distance, according to the method, the distance correction coefficient between the sensor node to be positioned and the anchor sensor node is determined through the similarity of the Jaccard similarity calculation path, so that the distance estimation precision of the sensor node to be positioned is improved, and the positioning error is reduced. Therefore, the invention improves the positioning precision of the sensor node.
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FIG. 1 is a schematic diagram of distance estimation based on neighboring sensor nodes.
FIG. 2 is a comparison graph of node location accuracy of the method of the present invention and DV-Hop and DV-RND algorithms under different node densities.
FIG. 3 is a comparison graph of node positioning accuracy of the method of the present invention and DV-Hop and DV-RND algorithms under different numbers of anchor sensor nodes.
Detailed Description
The present invention will be further described with reference to the following detailed description and accompanying drawings.
Referring to fig. 1, the non-ranging WSN node positioning method based on the Jaccard similarity sequentially includes the following steps:
firstly, uniformly arranging a plurality of sensor nodes to be positioned and anchor sensor nodes with known positions at random in a monitoring area, and then determining the estimated distance between each adjacent sensor node according to the network connectivity of the sensor nodes and the information of the adjacent sensor nodes;
step two, flooding through anchor sensor nodes to obtain the shortest estimated distances, shortest paths and shortest path neighbor node sets between all sensor nodes and the anchor sensor nodes in the network, then determining a correction coefficient of the shortest path between two anchor sensor nodes by the anchor sensor nodes based on the shortest estimated distances between the anchor sensor nodes and one other anchor sensor node, and flooding the correction coefficient and corresponding path neighbor node set information into the whole network;
calculating Jaccard similarity of a shortest path neighbor node set between a sensor node to be positioned and an anchor sensor node and each anchor sensor node, and correcting the shortest estimated distance between the sensor node to be positioned and the anchor sensor node by using a correction coefficient of the shortest path with the highest Jaccard similarity to obtain the final estimated distance between the sensor node to be positioned and the anchor sensor node;
and step four, determining the estimated position of each sensor node to be positioned according to the final estimated distance between each sensor node to be positioned and all the anchor sensor nodes, thereby completing the positioning of the sensor node to be positioned.
In step three, the Jaccard similarity is calculated by adopting the following formula:
Figure BDA0003297404090000051
in the above formula, P1For the shortest path between the sensor node to be positioned and the anchor sensor node, P2For shortest path between anchor sensor nodes, Similarity<P1，P2>Is P1Neighbor node set PN of1And P2Neighbor node set PN of2Jaccard similarity of (a).
In step three, the final estimated distance between the sensor node to be positioned and the anchor sensor node
Figure BDA0003297404090000066
The formula is adopted to calculate the following formula:
Figure BDA0003297404090000061
in the above formula, the first and second carbon atoms are,
Figure BDA0003297404090000062
for the shortest estimated distance, C, between the sensor node to be positioned and the anchor sensor nodeoptAnd the correction coefficient is the shortest path with the highest Jaccard similarity.
In the second step, the correction coefficient of the shortest path between the two anchor sensor nodes is calculated by adopting the following formula:
Figure BDA0003297404090000063
in the above formula, CmnCorrection coefficient (x) for shortest path between m and n anchor sensor nodesm，ym)、(xn，yn) The real coordinates of anchor sensor nodes m, n respectively,
Figure BDA0003297404090000067
the shortest estimated distance of m to n.
In the second step, the flooding mode of the anchor sensor node is as follows:
when a sensor node receives a flooding message broadcast by an adjacent sensor node, the ID of the forwarding sensor node is inquired to obtain the estimated distance between the sensor node and the forwarding sensor node, the accumulated distance is updated, the ID of the anchor sensor node of the message is inquired, if the internal memory contains the ID information of the anchor sensor node, the accumulated distance is compared, the message with smaller accumulated distance is stored, if the node is updated, the message is forwarded, and if the node is not updated, the message is discarded; if the anchor sensor node ID information does not exist in the memory, the information is stored and forwarded, wherein the initial value of the accumulated distance is 0.
In the first step, the estimated distance between the adjacent sensor nodes is calculated by adopting the following formula:
Figure BDA0003297404090000064
Figure BDA0003297404090000065
in the above formula, duiFor the estimated distance between adjacent sensor nodes u, I, IuiIs the intersection of the sensor nodes u, i，Mu、MiNumber of adjacent sensor nodes, m, of sensor nodes u, i, respectivelyuiThe number of the common adjacent sensor nodes of the sensor nodes u and i, and R is the communication radius of the sensor nodes.
All sensor node signals are simulated by adopting a DOI signal model, and the network connectivity of the sensor nodes and the information of the adjacent sensor nodes are obtained through the receiving signal threshold of the sensor nodes.
The receiving signal threshold value of the sensor node is obtained through the following signal propagation model:
Figure BDA0003297404090000071
Figure BDA0003297404090000072
in the above formula, RSS is the signal strength received by the sensor node, PtFor transmitting node signal strength, P (d)0) Is a reference distance d0Eta is the environmental attenuation coefficient, diIs the true distance, K, between the signal receiving node and the signal transmitting nodeiAnd the loss coefficient in the ith direction is doi, a random number related to environmental noise is doi, and N is a non-zero natural number.
In the fourth step, the estimated position X of the sensor node to be positioned is calculated according to a least square method to obtain:
X＝(ATA)-1ATB
Figure BDA0003297404090000073
Figure BDA0003297404090000074
Figure BDA0003297404090000075
in the above formula, A, B are position and distance constraint matrixes respectively, (x)u，yu) For the estimated position of the sensor node u to be positioned, (x)1，y1)，...，(xm，ym) For the coordinates of each anchor sensor node,
Figure BDA0003297404090000076
and m is the number of the anchor sensor nodes.
The principle of the invention is illustrated as follows:
in the non-ranging positioning process, the estimated distance of the nodes is closely related to the distribution of the nodes, so the invention provides a non-ranging WSN node positioning method for determining the estimated distance correction coefficient according to the path similarity between the nodes in the network. The invention mainly considers the problem of node positioning in a rectangular arrangement scene, needs distributed cooperation among nodes in the positioning process, and can meet the distributed deployment of a positioning algorithm.
In the invention, the derivation process of the estimated distance calculation formula between adjacent sensor nodes is as follows:
the distance between two adjacent sensor nodes is inversely proportional to the area covered by the sensor nodes, i.e. the farther the distance is, the smaller the area covered by the sensor nodes is. Because the sensor nodes are randomly and uniformly arranged, the larger the number of common neighbor nodes between the sensor nodes is, the smaller the distance between two adjacent sensor nodes is, and the smaller the distance d between two adjacent sensor nodes u and i isuiArea A (d) covered with nodeui) The geometrical relationship between them is as follows:
Figure BDA0003297404090000081
because the sensor nodes in the network are all randomly and uniformly arranged, and the number of the nodes is in direct proportion to the area, the estimation can be carried out by the number of the common adjacent sensor nodes of the two sensor nodesCommon coverage area of two adjacent nodes
Figure BDA0003297404090000082
As shown in formula (2):
Figure BDA0003297404090000083
in order to estimate the area of the coverage area more accurately, the estimated average value of the number of the neighbor nodes of u, i two nodes is used as the final neighbor node number value, the number of the common neighbor nodes of the two nodes and the common coverage area of the two neighbor nodes
Figure BDA0003297404090000084
The functional relationship between them can be calculated by equation (3):
Figure BDA0003297404090000085
definition IuiAs shown in formula (4):
Figure BDA0003297404090000086
this gives the formula (5):
Figure BDA0003297404090000087
for equation (5), equation (6) is obtained from a taylor expansion where x is 0:
Figure BDA0003297404090000091
since u, i are adjacent sensor nodes, the distance d between two nodesuiR is ≦ R, depending on x ═ duiX is more than or equal to 0 and less than or equal to 0.5 according to the/2R, and the value of the higher-order term of more than 3-order terms in the formula (6) is smaller according to the value range of x, compared with the value of the higher-order termThe influence of the value of π -4x is negligible, resulting in formula (7):
Figure BDA0003297404090000092
changing x to duiThe 2R is taken into formula (7) and combined with formula (3), formula (4) to give duiExpression (c):
Figure BDA0003297404090000093
in the invention, the estimated position X of the sensor node to be positioned is calculated according to a least square method. According to the coordinates of the anchor sensor nodes and the final estimated distance between the sensor node to be positioned and each anchor sensor node, the following can be obtained:
Figure BDA0003297404090000094
subtracting the last term from all terms in the above equation yields:
Figure BDA0003297404090000095
writing the above formula as AX ═ B gives:
Figure BDA0003297404090000096
Figure BDA0003297404090000101
Figure BDA0003297404090000102
X＝(ATA)-1ATB
example 1:
referring to fig. 1, the non-ranging WSN node positioning method based on the Jaccard similarity is sequentially performed according to the following steps:
1. the method comprises the steps that a plurality of sensor nodes to be positioned and anchor sensor nodes with known positions are randomly and uniformly arranged in a monitoring area, a system is initialized after the arrangement, all the sensor nodes broadcast messages containing self IDs according to communication radiuses, and meanwhile broadcast messages from neighbor nodes are received, and a neighbor node set of the nodes is determined. Under actual deployment conditions, the communication radius of a node is usually affected by the surrounding environment, which results in a circle with a non-standard actual communication radius of the node, in order to simulate the influence of the environment on signals, the present embodiment adopts a DOI signal model to simulate the propagation of node signals in space, where DOI parameters are defined as path losses in different directions, when DOI is 0, the communication range of the node is a complete circle, and the DOI-based signal propagation model is as follows:
Figure BDA0003297404090000103
Figure BDA0003297404090000104
in the above formula, RSS is the signal strength received by the sensor node, PtFor transmitting node signal strength, P (d)0) Is a reference distance d0Eta is the environmental attenuation coefficient, diIs the true distance, K, between the signal receiving node and the signal transmitting nodeiIs the loss coefficient in the ith direction, DOI is a random number related to the environmental noise, DOI is equal to [ -DOI, DOI]DOI is a threshold value of DOI, and N is a non-zero natural number;
the network connectivity of the sensor node and the information of the adjacent sensor nodes can be obtained through the receiving signal threshold of the sensor node;
2. calculating the estimated distance between adjacent sensor nodes by adopting the following formula:
Figure BDA0003297404090000111
Figure BDA0003297404090000112
in the above formula, duiFor the estimated distance between adjacent sensor nodes u, I, IuiIs the intersection of the sensor nodes u, i, Mu、MiNumber of adjacent sensor nodes, m, of sensor nodes u, i, respectivelyuiThe number of the sensor nodes which are adjacent to the sensor nodes u and i together is R, and the R is the communication radius of the sensor nodes;
3. firstly, obtaining shortest estimated distances, shortest paths and shortest path neighbor node sets between all sensor nodes and anchor sensor nodes in a network through anchor sensor node flooding, then determining a correction coefficient of the shortest path between two anchor sensor nodes by the anchor sensor nodes based on the shortest estimated distances between the anchor sensor nodes and other anchor sensor nodes, and flooding the correction coefficient and corresponding path neighbor node set information to the whole network, wherein the anchor sensor node flooding mode is as follows:
the method comprises the steps that an anchor sensor node floods a self ID, a forwarding sensor node ID, an anchor sensor node position, a path and an accumulated distance (an initial value is 0) in a network, after a certain sensor node receives a flooding message broadcasted by an adjacent sensor node, the estimated distance between the sensor node and the forwarding sensor node is obtained by inquiring the ID of the forwarding sensor node, the accumulated distance is updated, the anchor sensor node ID of the message is inquired, if the internal memory contains the anchor sensor node ID information, the accumulated distance is compared, the message with the smaller accumulated distance is stored, if the node is updated, the message is forwarded, and if the node is not updated, the message is discarded; if the anchor sensor node ID information does not exist in the memory, the information is stored and forwarded;
the correction coefficient of the shortest path between the two anchor sensor nodes is calculated by adopting the following formula:
Figure BDA0003297404090000113
in the above formula, CmnCorrection coefficient (x) for shortest path between m and n anchor sensor nodesm，ym)、(xn，yn) The real coordinates of anchor sensor nodes m, n respectively,
Figure BDA0003297404090000114
the shortest estimated distance of m and n;
4. calculating the Jaccard similarity of the shortest path neighbor node set between the sensor node to be positioned and the anchor sensor node and the shortest path neighbor node set between the anchor sensor nodes by adopting the following formula:
Figure BDA0003297404090000115
in the above formula, P1For the shortest path between the sensor node to be positioned and the anchor sensor node, P2For shortest path between anchor sensor nodes, Similarity<P1，P2>Is P1Neighbor node set PN of1And P2Neighbor node set PN of2Jaccard similarity of (a);
5. correcting the shortest estimated distance between the sensor node to be positioned and the anchor sensor node by using the correction coefficient of the shortest path with the highest Jaccard similarity to obtain the final estimated distance between the sensor node to be positioned and the anchor sensor node
Figure BDA0003297404090000121
Figure BDA0003297404090000122
In the above formula, the first and second carbon atoms are,
Figure BDA0003297404090000123
for the shortest estimated distance, C, between the sensor node to be positioned and the anchor sensor nodeoptThe correction coefficient is the shortest path with the highest Jaccard similarity;
6. and determining the estimated position X of each sensor node to be positioned according to the final estimated distance between each sensor node to be positioned and all anchor sensor nodes by adopting a least square method:
X＝(ATA)-1ATB
Figure BDA0003297404090000124
Figure BDA0003297404090000125
Figure BDA0003297404090000126
in the above formula, A, B are position and distance constraint matrixes respectively, (x)u，yu) For the estimated position of the sensor node u to be positioned, (x)1，y1)，...，(xm，ym) For the coordinates of each anchor sensor node,
Figure BDA0003297404090000127
and m is the number of the anchor sensor nodes.
To examine the positioning accuracy of the method of the present invention, the following tests were performed:
1. setting the communication radius of the sensor nodes to be 20, setting the number of anchor sensor nodes to be 20, setting DOI to be 0.01, namely DOI belongs to [ -0.01, 0.01], respectively and randomly deploying 100 to 400 sensor nodes in a monitoring area, comparing the node average positioning accuracy adopting the method with the average positioning accuracy of two non-ranging positioning algorithms DV-Hop and DV-RND, and obtaining a result shown in figure 2.
As can be seen from FIG. 2, under different node densities, the average positioning accuracy of the method of the present invention is superior to DV-Hop and DV-RND. The method considers the influence of the distribution condition of the nodes in the non-ranging process on the ranging precision, and determines the optimal distance correction coefficients of different paths by comparing the similarity of the nodes, so that the better distance estimation precision is obtained, and the positioning precision of the nodes is further improved.
2. Setting the communication radius of the sensor nodes to be 20, setting the total number of the sensor nodes to be 300, setting DOI to be 0.01, namely DOI belongs to [ -0.01, 0.01], respectively arranging 20, 25, 30 and 35 anchor sensor nodes in the network, comparing the node average positioning accuracy adopting the method of the invention with the average positioning accuracy of two non-ranging positioning algorithms DV-Hop and DV-RND, and obtaining the result shown in FIG. 3.
As can be seen from FIG. 3, in the arrangement scene of 300 sensor nodes, the number of anchor sensor nodes has little influence on the positioning accuracy of the nodes, and the average positioning accuracy of the nodes of the method is the highest, the positioning error is about 4 meters, next, DV-RND, the positioning error is about 4.5 meters, the accuracy of the DV-Hop algorithm is the worst, and the error is about 10 meters.

Claims (9)

1. A non-ranging WSN node positioning method based on Jaccard similarity is characterized in that:
the positioning method sequentially comprises the following steps:
firstly, uniformly arranging a plurality of sensor nodes to be positioned and anchor sensor nodes with known positions at random in a monitoring area, and then determining the estimated distance between each adjacent sensor node according to the network connectivity of the sensor nodes and the information of the adjacent sensor nodes;
step two, flooding through anchor sensor nodes to obtain the shortest estimated distances, shortest paths and shortest path neighbor node sets between all sensor nodes and the anchor sensor nodes in the network, then determining a correction coefficient of the shortest path between two anchor sensor nodes by the anchor sensor nodes based on the shortest estimated distances between the anchor sensor nodes and one other anchor sensor node, and flooding the correction coefficient and corresponding path neighbor node set information into the whole network;
calculating Jaccard similarity of a shortest path neighbor node set between a sensor node to be positioned and an anchor sensor node and each anchor sensor node, and correcting the shortest estimated distance between the sensor node to be positioned and the anchor sensor node by using a correction coefficient of the shortest path with the highest Jaccard similarity to obtain the final estimated distance between the sensor node to be positioned and the anchor sensor node;
and step four, determining the estimated position of each sensor node to be positioned according to the final estimated distance between each sensor node to be positioned and all the anchor sensor nodes, thereby completing the positioning of the sensor node to be positioned.
2. The Jaccard similarity-based non-ranging WSN node positioning method according to claim 1, wherein:
in step three, the Jaccard similarity is calculated by adopting the following formula:
Figure FDA0003297404080000011
in the above formula, P1For the shortest path between the sensor node to be positioned and the anchor sensor node, P2For shortest path between anchor sensor nodes, Similarity<P1，P2>Is P1Neighbor node set PN of1And P2Neighbor node set PN of2Jaccard similarity of (a).
3. The Jaccard similarity-based non-ranging WSN node positioning method according to claim 1 or 2, wherein:
in step three, the final estimated distance between the sensor node to be positioned and the anchor sensor node
Figure FDA0003297404080000012
Is calculated by the following formulaCalculating to obtain:
Figure FDA0003297404080000021
in the above formula, the first and second carbon atoms are,
Figure FDA0003297404080000022
for the shortest estimated distance, C, between the sensor node to be positioned and the anchor sensor nodeoptAnd the correction coefficient is the shortest path with the highest Jaccard similarity.
4. The Jaccard similarity-based non-ranging WSN node positioning method according to claim 1 or 2, wherein:
in the second step, the correction coefficient of the shortest path between the two anchor sensor nodes is calculated by adopting the following formula:
Figure FDA0003297404080000023
in the above formula, CmnCorrection coefficient (x) for shortest path between m and n anchor sensor nodesm，ym)、(xn，yn) The real coordinates of anchor sensor nodes m, n respectively,
Figure FDA0003297404080000024
the shortest estimated distance of m to n.
5. The Jaccard similarity-based non-ranging WSN node positioning method according to claim 1 or 2, wherein:
in the second step, the flooding mode of the anchor sensor node is as follows:
when a sensor node receives a flooding message broadcast by an adjacent sensor node, the ID of the forwarding sensor node is inquired to obtain the estimated distance between the sensor node and the forwarding sensor node, the accumulated distance is updated, the ID of the anchor sensor node of the message is inquired, if the internal memory contains the ID information of the anchor sensor node, the accumulated distance is compared, the message with smaller accumulated distance is stored, if the node is updated, the message is forwarded, and if the node is not updated, the message is discarded; if the anchor sensor node ID information does not exist in the memory, the information is stored and forwarded, wherein the initial value of the accumulated distance is 0.
6. The Jaccard similarity-based non-ranging WSN node positioning method according to claim 1 or 2, wherein:
in the first step, the estimated distance between the adjacent sensor nodes is calculated by adopting the following formula:
Figure FDA0003297404080000025
Figure FDA0003297404080000026
in the above formula, duiFor the estimated distance between adjacent sensor nodes u, I, IuiIs the intersection of the sensor nodes u, i, Mu、MiNumber of adjacent sensor nodes, m, of sensor nodes u, i, respectivelyuiThe number of the common adjacent sensor nodes of the sensor nodes u and i, and R is the communication radius of the sensor nodes.
7. The Jaccard similarity-based non-ranging WSN node positioning method according to claim 6, wherein: all sensor node signals are simulated by adopting a DOI signal model, and the network connectivity of the sensor nodes and the information of the adjacent sensor nodes are obtained through the receiving signal threshold of the sensor nodes.
8. The Jaccard similarity-based non-ranging WSN node positioning method according to claim 7, wherein:
the receiving signal threshold value of the sensor node is obtained through the following signal propagation model:
Figure FDA0003297404080000031
Figure FDA0003297404080000032
in the above formula, RSS is the signal strength received by the sensor node, PtFor transmitting node signal strength, P (d)0) Is a reference distance d0Eta is the environmental attenuation coefficient, diIs the true distance, K, between the signal receiving node and the signal transmitting nodeiAnd the loss coefficient in the ith direction is doi, a random number related to environmental noise is doi, and N is a non-zero natural number.
9. The Jaccard similarity-based non-ranging WSN node positioning method according to claim 1 or 2, wherein:
in the fourth step, the estimated position X of the sensor node to be positioned is calculated according to a least square method to obtain:
X＝(ATA)-1ATB
Figure FDA0003297404080000033
Figure FDA0003297404080000034
Figure FDA0003297404080000041
in the above formula, A, B are position and distance constraint matrixes respectively, (x)u，yu) For the estimated position of the sensor node u to be positioned, (x)1，y1)，...，(xm，ym) For the coordinates of each anchor sensor node,
Figure FDA0003297404080000042
and m is the number of the anchor sensor nodes.
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CN101873691A (en) * 2010-06-09 2010-10-27 中国人民解放军海军航空工程学院 Method for positioning wireless sensor network node without ranging based on connectedness
CN109587626A (en) * 2018-11-28 2019-04-05 郑州轻工业学院 Wireless sensor network neighbor node method for estimating distance towards concave domain

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101873691A (en) * 2010-06-09 2010-10-27 中国人民解放军海军航空工程学院 Method for positioning wireless sensor network node without ranging based on connectedness
CN109587626A (en) * 2018-11-28 2019-04-05 郑州轻工业学院 Wireless sensor network neighbor node method for estimating distance towards concave domain

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