CN115696190A - Method for optimizing positioning of wireless sensor network node - Google Patents
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Abstract
The invention discloses a method for optimizing the positioning of a wireless sensor network node, which specifically comprises the following steps: s1: estimating the Hop count and the Hop distance between nodes by adopting a DV-Hop algorithm; s2: obtaining a positioning error according to the hop count and the hop distance between the nodes estimated in the step S1; s3: correcting the hop count between nodes; s4: and correcting the average hop distance between the nodes so as to improve the precision of the position coordinates of the nodes. The DV-Hop algorithm is wide in application, easy to expand and less in constrained conditions, can meet the positioning effect required by a relevant application scene, optimizes Hop count and Hop distance information, and improves the positioning effect of the DV-Hop.
Description
Technical Field
The invention belongs to the technical field of wireless sensor networks, and particularly relates to a method for optimizing positioning of a wireless sensor network node.
Background
A Wireless Sensor Network (WSN) is composed of a plurality of micro Sensor nodes having data collection, analysis, and processing capabilities, as well as information transceiving capabilities. The deployment position of the sensor nodes in the WSN can be changed at any time, the network setting is very flexible, a multi-hop network which is randomly distributed is self-organized through a wireless communication mode, and the multi-hop network can be deployed in certain specific areas which need to be monitored, so that the obtained information is cooperatively sensed, collected and processed in the areas covered by the sensors, and then the information collected by the nodes is transmitted to the sink nodes and is sent to collection personnel through the base station. Because a large number of nodes are usually placed in an area with rare or dangerous human smoke, the nodes have the characteristics of no need of accurate deployment, good viability, lower cost and smaller volume, and provide powerful help for human exploration and various artificial activities.
The WSN technology has many problems to be solved in various applications. The general positioning of the sensor nodes is usually in a GPS mode. However, if a GPS receiver is deployed for each sensor node to locate the node, the deployment cost and power consumption of the sensor network will be greatly increased. In view of this problem, the existing positioning technology usually calculates the location of an unknown node by combining an anchor node with a network topology, so that the energy of the sensor node can be saved.
Therefore, a positioning technology capable of accurately obtaining the position coordinates of the sensor nodes becomes an important part in the research of the sensor technology. Among many positioning algorithms, the DV-Hop positioning algorithm is an algorithm widely used at present due to simple and convenient implementation, but is limited by various factors, positioning accuracy of the algorithm is influenced to a certain extent, and optimization is required.
Disclosure of Invention
The invention aims to solve the problem of providing a method for optimizing the positioning of a wireless sensor network node on the basis of a DV-Hop positioning algorithm.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: the method for optimizing the positioning of the wireless sensor network node specifically comprises the following steps:
s1: estimating the Hop count and the Hop distance between nodes by adopting a DV-Hop algorithm;
s2: obtaining a positioning error according to the hop count and the hop distance between the nodes estimated in the step S1;
s3: correcting the hop count between nodes;
s4: and correcting the average hop distance between the nodes so as to improve the precision of the position coordinates of the nodes.
According to the characteristics of the DV-Hop algorithm, nodes which can be in a communication area are all regarded as single-Hop nodes, when a large amount of single-Hop data participates in distance estimation, the average Hop distance cannot truly reflect the distance between the nodes in the wireless sensor network WSN, so that the estimated distance and the actual distance have a certain difference, and the positioning precision can be reduced by substituting calculation.
In the step S2 of the above technical solution, whether the DV-Hop algorithm is effective or not is accurately determined from the estimated value of the average Hop distance, the average Hop distance estimated by a single anchor node cannot completely express the Hop distance of the whole WSN, and in the case of having to adopt multiple hops, the estimated distance cannot be calculated according to a straight line, the fold line rate of a region with low density will be increased, the distance error will be further increased, and a negative effect will be brought to positioning; WSN nodes randomly scattered in a network are often irregular in topological structure, the density degree of the nodes in an area is different, hop count information and average hop distance estimated by different densities are slightly different, and the hop count information and the average hop distance are further accumulated in subsequent calculation.
In the Range-Free positioning algorithm of the wireless sensor network, DV-Hop is taken as one of the representative algorithms, the application is wide, the expansion is easy, the constrained conditions are less, the positioning effect required by relevant application scenes can be met, the Hop count and Hop distance information can be optimized, and the positioning effect of DV-Hop is improved.
Preferably, in step S4, an average hop distance error is obtained by using the hop distance between nodes estimated in step S1 and combining the actual distance between nodes and the estimated distance, so as to obtain a corrected average hop distance.
Preferably, in the step S1, the DV-Hop algorithm includes the steps of:
s1-1: estimating hop count among nodes, sending position and hop count data to a communicable node by all anchor nodes, after collecting the hop count data by a receiving node, reserving the hop count data and adding 1 to the hop count, and continuously forwarding to a target which does not obtain node data until the position and hop count data of the opposite side which can be obtained by the anchor node with the closest relative distance in the whole network;
s1-2: estimating hop distance between nodes, obtaining the minimum hop count and node data of the nearest anchor node by all anchor nodes in the WSN, and using the obtained data to carry out Hopsize on the nodes by a formula (1) i And (4) estimating:
wherein (x) i ，y j ) And (x) j ，y j ) Is the actual position coordinates of anchor nodes i, j, h ij For the minimum estimated hop count between i, j, hopsize i Average per hop distance for i;
calculating the estimated distance d of i and j by formula (2) ij ：
d ij ＝Hopsize i ×h ij (2)。
Preferably, in step S3, the correcting the inter-node hop count includes:
s3-1: limiting the value of single hop in the coverage area of the node, and determining the real distance d of i and j ij Defining the ratio of the communication radius R to obtain the relative optimal hop count H ij ：
H ij ＝d ij /R (3)；
Comparing the estimated hop count h ij And relative optimum hop count H ij The difference between the two is that in the present invention, all the estimated hops are calculated as the minimum estimated hop, and for simplicity,h ij collectively referred to as estimated hop count; the deviation coefficient σ is defined by equation (4) ij ：
σ ij ＝(h ij -H ij )/h ij (4)；
Coefficient of deviation sigma ij Inter-anchor node estimation hop count h capable of embodying mutual communication ij And relative optimum hop count H ij The difference condition that exists; sigma ij The larger the difference, the greater the deviation between the two is marked;
under the condition of constant communication radius, estimating hop count h ij Will be greater than or equal to the relative optimum hop count H ij For such a case, the difference correction coefficient ω is defined using the formula (5) ij To optimize hop count information to reduce accumulation of errors:
wherein n is an index value manually set to reduce error accumulation;
s3-2: the hop count data is also influenced by anchor node occupation ratio, broadcast area and communication radius parameters, and path selection in the communication process is influenced, so that the hop count data is changed; the number of anchor nodes in a local area is increased, a certain influence is generated on the positioning effect, for the area, the proportion of the anchor nodes is increased, the network communication condition is better, local single-hop nodes in a certain communication radius are increased, the hop count estimated by the node is applied to the whole network, the error between the relative optimal hop counts is further increased, and then a hop count correction coefficient theta is defined ij ：
Wherein L is the side length of a square sowing area, rho is the anchor node ratio, and theta ij Will decrease as the connectivity of the whole network increases, when the anchor node percentage is below 5%, theta is used ij Optimizing hop count and reducing single-hop rectificationInfluence of body hop distance calculation; when the network connectivity is good and the anchor node ratio is high, theta ij The value will be reduced, the influence on the hop count will also be reduced, and the error accumulation under the condition of multi-hop is avoided;
s3-3: correcting the coefficient omega by a difference ij And a hop count correction coefficient theta ij And (3) correcting the hop count:
using omega ij In the case of participating in the correction, when n in the formula (5) takes a value of 2, ω is ij h ij -H ij Can be unfolded into H ij (h ij -H ij )/h ij Due to H ij ＜h ij And h is ij Must be greater than 1, H can be obtained ij /h ij < 1, i.e. h' ij -H ij ＜h ij -H ij Indicating that the corrected hop count is closer to the defined relative optimum hop count H ij The hop count is used for participating in the calculation of the average hop distance, so that a more accurate hop distance value can be obtained;
will omega ij And theta ij Hop count estimation applied to nodes of the whole network together:
wherein Ns is the number of anchor nodes, h xi Is an estimated hop count, h, between the unknown node x and the nearest anchor node i xj Is an estimated hop number h 'between an unknown node x and a non-nearest anchor node j' xi And h' xj Respectively the hop counts of the nearest anchor node and the non-nearest anchor node after cooperative correction through the hop count coefficient and the deviation coefficient;
Preferably, in step S4, the average distance per hop correction includes the following steps:
calculating average jump distance by using a minimum mean square error criterion under an optimal index and correcting the average jump distance together with a single-jump average error obtained according to an actual distance so as to further reduce the error of the average jump distance and improve the positioning effect;
for the anchor node, the formula (1) can estimate the estimated value of the average distance per hop, and on the premise of acquiring the position information of the anchor node, the difference between the real distance between i and s and the estimated distance can be calculated by using the following numerical values:
wherein (x) i ，y i ) And (x) s ，y s ) Actual position coordinates, hossize, representing anchor nodes i, s i Expressed as the estimated distance, h, of node j is Expressing the minimum estimated hop number between i and s, and dividing the total difference value obtained by the formula (9) by the total hop number; the average distance per hop error epsilon can be obtained i ：
And (3) adding the average distance error of each hop by using the estimated distance to obtain the corrected average hop distance Dhop epsilon:
Dhop ε ＝hopsize i +ε i (11)；
the adaptive minimum mean square error criterion is adopted, the aim is to make the total error globally minimum, the calculation applied to the hop distance is more reasonable compared with the deviation and the variance, but the cost function f needs to be satisfied:
solving a hosize for a cost function f i The value of (a) is 0 to obtain the average hop distance D 2 op f ：
The average jump distance estimated by the formula (13) has a small difference between the estimated distance and the actual distance, in addition, a changed index value mu is introduced into the formula (13), according to the influence of different mu values on positioning errors, under a certain communication radius, an optimal value is selected by experiments to be applied to the correction of the average jump distance, and the formula (13) is rewritten as follows:
in order to avoid the situation that the single hop distance mean value cannot well reflect the hop distances in the whole network and reduce the risk of error accumulation caused by inaccurate data, the corrected Dhop is used ε Carrying out secondary average on the average jump distance calculated by using the minimum mean square error under the optimal mu value to obtain the corrected average jump Dhop ave ：
The corrected average Hop distance is obtained through the formula (14), the average Hop distance can be closer to the actual average Hop distance in the whole network, and the precision loss caused by the accumulated Hop distance errors is reduced again, so that the precision of obtaining the node position coordinates by adopting a DV-Hop algorithm is improved.
Drawings
FIG. 1 is a diagram of an error in the distance between nodes in a wireless sensor network WSN;
FIG. 2 is a graph of unknown node errors using the method of the present invention for optimizing wireless sensor network node positioning;
FIG. 3 is a diagram of unknown node error for the DV-Hop algorithm;
FIG. 4 is a graph of error versus communication radius;
fig. 5 is a graph of error versus anchor node ratio.
Detailed Description
The following embodiments of the present invention are described in detail with reference to the accompanying drawings, and the following embodiments are only used to more clearly illustrate the technical solutions of the present invention, but not to limit the scope of the present invention.
The method for optimizing the positioning of the wireless sensor network node specifically comprises the following steps:
s1: estimating the Hop count and the Hop distance between nodes by adopting a DV-Hop algorithm;
s2: obtaining a positioning error according to the hop count and the hop distance between the nodes estimated in the step S1;
s3: correcting the hop count between nodes;
s4: and correcting the average hop distance between the nodes so as to improve the precision of the position coordinates of the nodes.
In step S4, the average hop distance error per hop is obtained by using the hop distance between nodes estimated in step S1 and combining the actual distance between nodes and the estimated distance, so as to obtain the corrected average hop distance.
In the step S1, the DV-Hop algorithm includes the steps of:
s1-1: estimating hop count among nodes, sending position and hop count data to a communicable node by all anchor nodes, after collecting the hop count data by a receiving node, reserving the hop count data and adding 1 to the hop count, and continuously forwarding to a target which does not obtain node data until the anchor node closest to the anchor node in the relative distance in the whole network can obtain the position and hop count data of the opposite side;
s1-2: the jump distance between nodes is estimated, and all anchor nodes in the WSN obtain the nearest anchorThe minimum hop count of the node and the node data are used, and the obtained data is used for carrying out Hopsize on the node through a formula (1) i And (4) estimating:
wherein (x) i ，y j ) And (x) j ，y j ) Is the actual position coordinates of anchor nodes i, j, h ij For the minimum estimated hop count between i, j, hopsize i Average per hop distance for i;
calculating the estimated distance d of i and j by formula (2) ij ：
d ij ＝Hopsize i ×h ij (2)。
In step S3, the correcting the inter-node hop count includes the following steps:
s3-1: limiting the value of single hop in the coverage area of the node, and determining the real distance d of i and j ij Defining the ratio of the communication radius R to obtain the relative optimal hop count H ij ：
H ij ＝d ij /R (3)；
Comparing the estimated hop count h ij And relative optimum hop count H ij The difference between the two is defined by the formula (4) to define the deviation coefficient sigma ij ；
σ ij ＝(h ij -H ij )/h ij (4)；
Coefficient of deviation sigma ij Inter-anchor node estimation hop count h capable of embodying mutual communication ij And relative optimum hop count H ij The existence of a discrepancy condition; sigma ij The larger the difference, the greater the deviation between the two is marked;
under the condition of constant communication radius, estimating hop count h ij Will be greater than or equal to the relative optimum hop count H ij For such a case, the difference correction coefficient ω is defined using the formula (5) ij To optimize hop count information to reduce accumulation of errors:
wherein n is an index value manually set to reduce error accumulation;
s3-2: the hop count data is also influenced by anchor node occupation ratio, broadcast area and communication radius parameters, and the path selection in the communication process is influenced, so that the hop count data is changed; the number of anchor nodes in a local area is increased, a certain influence is generated on the positioning effect, for the area, the proportion of the anchor nodes is increased, the network communication condition is better, local single-hop nodes in a certain communication radius are increased, the hop count estimated by the node is applied to the whole network, the error between the relative optimal hop counts is further increased, and then a hop count correction coefficient theta is defined ij ：
Wherein L is the side length of a square sowing area, rho is the anchor node ratio, and theta ij Will decrease as the connectivity of the whole network increases, when the anchor node percentage is below 5%, theta is used ij Optimizing hop count and reducing the influence of single hop on the calculation of the whole hop distance; when the network connectivity is good and the anchor node ratio is high, theta ij The value will become small, the influence on the hop count will also be reduced, avoid the error accumulation under the condition of multi-hop;
s3-3: correcting the coefficient omega by a difference ij And a hop count correction coefficient theta ij And (3) correcting the hop count:
using omega ij In the case of participating in the correction, when n in the formula (5) takes a value of 2, ω is ij h ij -H ij Can be unfolded into H ij (h ij -H ij )/h ij Due to H ij ＜h ij And h is ij Must be greater than 1, H can be obtained ij /h ij < 1, i.e. h' ij -H ij ＜h ij -H ij Indicating that the corrected hop count is closer to the defined relative optimum hop count H ij The hop count is used for participating in the calculation of the average hop distance, so that a more accurate hop distance value can be obtained;
will omega ij And theta ij Hop count estimation applied to nodes of the whole network together:
wherein Ns is the number of anchor nodes, h xi Is an estimated hop count, h, between the unknown node x and the nearest anchor node i xj Is an estimated hop number h 'between an unknown node x and a non-nearest anchor node j' xi And h' xj Respectively the hop counts of the nearest anchor node and the non-nearest anchor node after cooperative correction through the hop count coefficient and the deviation coefficient;
In step S4, the average distance per hop correction includes the following steps:
the average hop distance in the DV-hop algorithm is very important for estimating the distance between the nodes; as shown in fig. 1, 3 hops are needed for data to be sent to B through a, and the DV-Hop algorithm uses the polyline distance as an estimated distance, obviously, a large error exists between the estimated distance and the real distance shown by the dotted line;
therefore, the average jump distance is calculated by utilizing the minimum mean square error criterion under the optimal index and is corrected together with the single-jump average error obtained according to the actual distance so as to further reduce the error of the average jump distance and improve the positioning effect;
for the anchor node, the formula (1) can estimate the estimated value of the average distance per hop, and on the premise of acquiring the position information of the anchor node, the difference between the real distance between i and s and the estimated distance can be calculated by using the following numerical values:
wherein (x) i ，y i ) And (x) s ，y s ) Indicating the actual location coordinates of the anchor nodes i, s, hossize i Expressed as the estimated distance, h, of node j is Expressing the minimum estimated hop number between i and s, and dividing the total difference value obtained by the formula (9) by the total hop number; the average distance per hop error epsilon can be obtained i ：
The average jump distance Dhop after correction is obtained by adding the average distance error of each jump to the estimated distance ε ：
Dhop ε ＝hopsize i +ε i (11)；
The adaptive minimum mean square error criterion is adopted, the aim is to make the total error globally minimum, the calculation applied to the hop distance is more reasonable compared with the deviation and the variance, but the cost function f needs to be satisfied:
hossize is solved for cost function f i The partial derivative value of (A) is 0 to obtain the average hop distance D 2 op f ：
The average jump distance estimated by the formula (13) has a small difference between the estimated distance and the actual distance, in addition, a changed index value mu is introduced into the formula (13), according to the influence of different mu values on positioning errors, under a certain communication radius, an optimal value is selected by experiments to be applied to the correction of the average jump distance, and the formula (13) is rewritten as follows:
in order to avoid the situation that the single hop length mean value cannot well reflect the hop length in the whole network and reduce the risk of error accumulation caused by inaccurate data, the corrected Dhop epsilon and the average hop length calculated by using the minimum mean square error under the optimal mu value are subjected to secondary averaging to obtain the corrected average hop Dhop ave ：
The corrected average Hop distance is obtained through the formula (14), the average Hop distance can be closer to the actual average Hop distance in the whole network, the precision loss caused by the accumulated Hop distance errors is reduced again, and therefore the precision of obtaining the node position coordinates by adopting a DV-Hop algorithm is improved
In order to test the performance of the method for optimizing the positioning of the wireless sensor network node in the embodiment, an MATLABR2016b simulation platform is adopted to carry out simulation experiments on the algorithm and the DV-Hop algorithm from different mu values of the minimum mean square error, different n values of difference correction coefficients, the total number of nodes in the network, communication radius and changes of the anchor node in comparison with the positioning effect. Simulation experiment environment: in a simulation area of 100m × 100m, 150 nodes are irregularly arranged, wherein the anchor node proportion is 10%, and the communication radius of all nodes participating in the experiment is R =30m.
Taking the mean positioning Error ave As a standard for checking the positioning effect.
Wherein Ns is the number of anchor nodes, k is the number of unknown nodes, R is the communication radius, (x) k ，y k ) And
for the true and estimated coordinates of the unknown node, N a The total number of nodes in the experimental area is shown. Firstly, the influence of the change of the index value under the least mean square criterion on the correction of the average hop distance is verified, 150 nodes are arranged in a simulation area of 100m, the percentage of the anchor nodes is 10%, and R =30m.
Under the same experimental environment, the change situation of the average positioning error of the method and the DV-Hop algorithm is verified under the condition that the communication radius is set to be increased from 20m to 40m in a single increment mode.
And (3) verifying the positioning effect of the method and the comparison algorithm under the condition that the anchor node occupation ratio is sequentially increased by 2-20% from the initial 8%.
When the total node number is set to be sequentially increased from 20 to 200 from initial 100, the DV-Hop algorithm and the method of the invention perform Error under the condition of node number change ave A trend of change.
As shown in FIGS. 1-5, under the simulation experiment environment, the positioning effect of the invention and the comparison algorithm is achieved under the condition that the anchor node occupation ratio is sequentially increased from initial 8% to 20%. Because the anchor node occupation ratio in the simulation environment is increased in sequence, the positioning effect is improved in different degrees. Under the condition that the occupation ratio of DV-Hop anchor nodes is increased from 8% to 10%, the precision is obviously improved, and then the number is increased, so that the change range of the positioning effect is not obviously helped, and the DV-Hop anchor nodes are gradually in a stable state. The method can optimize the influence effect of the DV-Hop due to the fact that nodes are distributed unevenly randomly when the anchor node proportion is low, and precision is improved remarkably. Under the condition that the fixed value of the control anchor node ratio is 12%, the error of the DV-Hop is 32.8%, the rate of the invention is 22.04%, and the overall effect is better than that of the DV-Hop algorithm; as shown in fig. 2 and 3, the deviation between the actual position and the estimated position of the node to be measured can be clearly seen through the connection of line segments, and the longer the line segment is, the greater the deviation degree between the actual position and the estimated position is. In contrast, the distance of most of the line segments in fig. 2 is short, which indicates that the difference between the estimated position and the actual position of the algorithm is not large, and the actual position of the node to be measured and the estimated position have large position deviation, which indicates that the effect is not ideal at this time, as shown in fig. 3, the positioning accuracy of the invention and the DV-Hop algorithm is improved along with the increase of R, and in addition, the two algorithms have stable effect in the process of increasing R without the occurrence of the situation of large data fluctuation amplitude, which also indicates that the characteristics of the DV-Hop algorithm are retained on the premise of improving the performance of the algorithm and the invention. Overall, the invention is approximately reduced by 6.58% -9.56% and 13.1% -14.5% compared to DV-Hop, and overall performance is better when R is at a higher value than DV-Hop, resulting in reduced node routing.
The specific embodiments of the present invention described are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or scope of the invention as defined in the appended claims.
Claims (5)
1. A method for optimizing the positioning of a wireless sensor network node is characterized by comprising the following steps:
s1: estimating the Hop count and the Hop distance between nodes by adopting a DV-Hop algorithm;
s2: obtaining a positioning error according to the number of hops between nodes and the estimation of the hop distance between the nodes in the step S1;
s3: correcting the hop count between nodes;
s4: and correcting the average hop distance between the nodes so as to improve the precision of the position coordinates of the nodes.
2. The method of claim 1, wherein in step S4, an average hop-per-hop distance error is obtained by using the hop-per-hop distance estimated in step S1 and combining the actual distance between the nodes and the estimated distance to obtain a corrected average hop-per-hop distance.
3. The method for optimizing the location of a wireless sensor network node according to claim 2, wherein in the step S1, the DV-Hop algorithm comprises the steps of:
s1-1: estimating hop count among nodes, sending position and hop count data to a communicable node by all anchor nodes, after collecting the hop count data by a receiving node, reserving the hop count data and adding 1 to the hop count, and continuously forwarding to a target which does not obtain node data until the anchor node closest to the anchor node in the relative distance in the whole network can obtain the position and hop count data of the opposite side;
s1-2: estimating hop distance between nodes, obtaining the minimum hop count and node data of the nearest anchor node by all anchor nodes in the wireless sensor network WSN, and using the obtained data to carry out Hopsize on the nodes by a formula (1) i And (4) estimating:
wherein (x) i ，y j ) And (x) j ，y j ) Is the actual position coordinates of anchor nodes i, j, h ij For the minimum estimated hop count between i, j, hopsize i Average per hop distance for i;
calculating the estimated distance d of i and j by formula (2) ij ：
d ij ＝Hopsize i ×h ij (2)。
4. The method of claim 3, wherein in step S3, the inter-node hop count modification comprises the steps of:
s3-1: numerical advance of single hop in coverage area of nodeLine limitation, the real distance d of i and j ij Defining the ratio of the communication radius R to obtain the relative optimal hop count H ij ：
H ij ＝d ij /R (3)；
Comparing the estimated hop count h ij And relative optimum hop count H ij The difference between the two is defined by the formula (4) to define the deviation coefficient sigma ij ：
σ ij ＝(h ij -H ij )/h ij (4)；
Coefficient of deviation sigma ij Inter-anchor node estimation hop count h capable of embodying mutual communication ij And relative optimum hop count H ij The existence of a discrepancy condition; sigma ij The larger the difference, the greater the deviation between the two is marked;
under the condition of constant communication radius, estimating hop count h ij Will be greater than or equal to the relative optimum hop count H ij For such a case, the difference correction coefficient ω is defined using the formula (5) ij To optimize hop count information to reduce accumulation of errors:
wherein n is an index value manually set to reduce error accumulation;
s3-2: the hop count data is also influenced by anchor node occupation ratio, broadcast area and communication radius parameters, and can influence path selection in the communication process, so that the hop count data is changed, and a hop count correction coefficient theta is defined ij ：
Wherein L is the side length of a square sowing area, rho is the anchor node ratio, and theta ij Will decrease as the connectivity of the whole network increases, when the anchor node percentage is below 5%, theta is used ij Optimizing hop count and reducing single hop to integral hopThe impact of the distance calculation; when the network connectivity is good and the anchor node ratio is high, theta ij The value will be reduced, the influence on the hop count will also be reduced, and the error accumulation under the condition of multi-hop is avoided;
s3-3: correcting the coefficient omega by a difference ij And a hop count correction coefficient theta ij And (3) correcting the hop count:
using omega ij In the case of participating in the correction, when n in the formula (5) takes a value of 2, ω is ij h ij -H ij Can be unfolded into H ij (h ij -H ij )/h ij Due to H ij ＜h ij And h is ij Must be greater than 1, H can be obtained ij /h ij < 1, i.e. h' ij -H ij ＜h ij -H ij Indicating that the corrected hop count is closer to the defined relative optimum hop count H ij The hop count is used for participating in the calculation of the average hop distance, so that a more accurate hop distance value can be obtained;
will omega ij And theta ij And (3) hop number estimation commonly applied to nodes of the whole network:
wherein Ns is the number of anchor nodes, h xi Is an estimated hop count, h, between the unknown node x and the nearest anchor node i xj Is an estimated hop number h 'between an unknown node x and a non-nearest anchor node j' xi And h' xj Respectively the hop counts of the nearest anchor node and the non-nearest anchor node after the cooperative correction through the hop count coefficient and the deviation coefficient;
is the mean value of deviation coefficients between x and i, which can better reflect the characteristics of the network by using the hop number value between anchor nodes when the node x is the most than the node xWhen a near anchor node i is communicated, the average deviation coefficient ratio is used for replacing the deviation coefficient between two nodes, then the hop count is corrected by using the hop count correction coefficient, and omega is used for j and x ij And correcting to make the corrected hop count closer to the relatively optimal hop count.
5. The method for optimizing the positioning of a wireless sensor network node according to claim 4, wherein in the step S4, the average distance per hop correction comprises the following steps:
for the anchor node, the formula (1) can estimate the estimated value of the average distance per hop, and on the premise of acquiring the position information of the anchor node, the difference between the real distance between i and s and the estimated distance can be calculated by using the following numerical values:
wherein (x) i ，y i ) And (x) s ，y s ) Indicating the actual location coordinates of the anchor nodes i, s, hossize i Expressed as the estimated distance, h, of node i is Expressing the minimum estimated hop number between i and s, and dividing the total difference value obtained by the formula (9) by the total hop number; the average distance per hop error epsilon can be obtained i ：
The average jump distance Dhop after correction is obtained by adding the average distance error of each jump to the estimated distance ε ：
Dhop ε ＝hopsize i +ε i (11)；
And adopting a self-adaptive minimum mean square error criterion to ensure that the cost function f meets the following requirements:
hossize is solved for cost function f i The partial derivative value of (A) is 0 to obtain the average hop distance D 2 op f ：
The average jump distance estimated by the formula (13) is smaller in the difference between the estimated distance and the actual distance, and the changed index value mu is introduced into the formula (13), and the formula (13) is rewritten as:
corrected Dhop ε Carrying out secondary average with the average jump distance calculated by using the minimum mean square error under the optimal mu value to obtain the corrected average jump Dhop ave ：
And (4) obtaining the corrected average Hop distance through a formula (14), and improving the precision of obtaining the node position coordinate by adopting a DV-Hop algorithm.
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