A WANs positioning method based on three-anchor centroid and quantum adaptive grey wolf optimization algorithm

Abstract

The present invention relates to the technical field of wireless sensor network node positioning, and discloses a WANs positioning method based on three anchor centroids and quantum adaptive gray wolf optimization algorithm, which includes the following steps: first, a distance estimation model based on the centroids of three anchor points and the expected jump progress is established, and the geometric position relationship of the three anchor points and the expected jump weighting method are introduced; second, a node positioning model based on the quantum adaptive gray wolf optimization algorithm is established, and the iterative update of the individual wolf position is optimized on the basis of the gray wolf algorithm in combination with the quantum behavior mechanism. The method of the present invention can improve the accuracy of the distance between the unknown nodes of the anchor node, and optimize the calculation process of the final position, and has good node positioning accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless sensor network node positioning, and in particular to a WANs positioning method based on three-anchor centroids and a quantum adaptive grey wolf optimization algorithm. Background Art

[0002] Wireless sensor networks are becoming a transformative force in various fields. These networks consist of spatially distributed autonomous sensors that seamlessly transmit environmental data to enable intelligent automation and decision-making in numerous applications, playing a vital role in information communication in smart home systems, surveillance, and entertainment industries. Node localization in wireless sensors is a fundamental problem involving multiple key technologies such as data fusion and network topology, and tracking the location information of these nodes has become a research focus.

[0003] In the field of wireless sensor node positioning, traditional positioning technologies are divided into ranging-based methods and non-ranging methods. Ranging-based wireless sensor positioning determines its position by receiving signals from other nodes. These signals include signal strength, arrival time difference, and arrival angle. They require specialized hardware to send, receive, and process signals, which increases the cost of equipment and limits their widespread use. Non-ranging methods do not require additional hardware for distance measurement, such as ultrasonic sensors or radars, which greatly reduces the cost of sensor nodes. Such algorithms are usually simple, easy to implement and deploy, and are particularly suitable for resource-constrained sensor nodes. However, the positioning accuracy of this method is usually low because it relies on relative information rather than precise ranging data. Its main shortcomings are: in the distance estimation stage, the accuracy of distance estimation depends largely on the network node density, the number of anchor points, or the network model, and an undesirable network structure will lead to excessive deviation in distance estimation; in the position estimation stage, the positioning algorithm still faces problems such as slow convergence speed, low convergence accuracy, and easy to fall into local optimality. Summary of the invention

[0004] The present invention is to solve the problems of large distance estimation deviation, slow convergence speed and low convergence accuracy in the prior art, and proposes a WANs positioning method based on three-anchor centroid and quantum adaptive gray wolf optimization algorithm. The content includes the following steps:

[0005] Step 1: Deploy network nodes in the target area. All anchor nodes will send messages containing location coordinates and hop count information. The unknown node calculates the hop count based on the received message and broadcasts the information in the network to obtain the hop count from the anchor node to the unknown node.

[0006] Step 2: Determine whether the geometric relationship between the anchor point and the unknown node satisfies the geometric relationship of the centroid of the three anchor points. If so, the distance between the anchor node and the unknown node is obtained by a weighted algorithm of the centroid of the three anchor points and the expected hop distance according to the number of hops from the anchor node to the unknown node in step 1; if not, the distance between the anchor node and the unknown node is calculated according to the expected hop.

[0007] Step 3: Introduce adaptive strategies and quantum behavior mechanisms into the Grey Wolf Optimization Algorithm to obtain the quantum adaptive Grey Wolf Optimization Algorithm, which optimizes the dynamics and convergence of the entire process.

[0008] Step 4: According to the estimated distance between the anchor node and the unknown node obtained in step 2, the unknown node is located by the quantum adaptive gray wolf optimization algorithm described in step 3 to obtain the estimated coordinates of the unknown node.

[0009] Furthermore, the specific contents of step 2 are as follows:

[0010] Step 2.1: The proposed three-anchor centroid algorithm estimates the distance between ordinary nodes and anchor nodes under geometric constraints. The geometric relationship is as follows: Figure 3 If a common node is located in the intersection of the circles formed by its three adjacent anchor nodes, the estimated distance between the common node and the anchor node is determined by the distance from the Euclidean centroid of the intersection area to the anchor node. The selection of the centroid is based on the Euclidean intersection of the circles formed by the centers of the three adjacent anchor nodes. Figure 4 An example of a geometric relationship that does not satisfy the centroid relationship of the three anchor points is shown. The communication range of node i is represented by the shaded area. From the intersection point C to point A along the arrow direction, although the communication ranges of the three nodes intersect, they do not overlap. None of the active anchor nodes in this process satisfy the proposed geometric relationship.

[0011] exist Figure 3 In , k is a common node, and i, j, and m are three anchor nodes within the communication range of k. The shaded area where the communication ranges of the anchor nodes intersect is crucial for calculating the geometric centroid k″ of triangles A, B, and C in the graph. This point is used as the estimated position of the common node k. We use the distance k″ to estimate the distance from the common node k to the anchor node i, expressed as

[0012]

[0013] Among them, (x a ,y a ),(x b ,y b ),(x c ,y c ) are the coordinates of points A, B, and C, (x, y) are the coordinates of the center of mass, (x i,y i ) are the coordinates of the anchor node.

[0014] Step 2.2: In the three-anchor centroid algorithm we proposed, anchor nodes and common nodes must satisfy the following conditions: Figure 3 Some geometric relationships shown in . When the geometric relationship of the centroid of the three anchors is not satisfied, we estimate the distance of the node by the expected hop. Distance estimation based on expected hops has been described in . It proposes a WSN positioning method that can achieve node positioning without using distance measurement tools. This method uses the expected distance of each jump in the random walk process to estimate the distance between nodes by calculating the number of communication hops between them. Then, the distance information of these nodes is converted into position estimation results through a polygon covering algorithm. Although the accuracy of this scheme is slightly lower than that of the ranging-based measurement method, it performs well in WSNs with high node density and has a wide range of application scenarios.

[0015] like Figure 3 As shown in Figure 2, the unknown node k is located at the maximum transmission distance of the anchor node i, while the target node d is outside the maximum transmission range. We will use θ∈(-θ k ,θ k ) as the angle range of the potential forwarding area of ​​the anchor node. The probability that there are n target points in the forwarding area is as follows:

[0016]

[0017] Where λ = M / (L×L) is the node density. o is the distance between anchor node i and the next sensor, and r o is a random variable, so i needs to be forwarded to the destination d through an intermediate node in the potential area. In the case where there is no node between R and r, r o The cumulative distribution function and probability density function less than or equal to r are as follows:

[0018]

[0019] Then, the expected transition progress can be expressed as:

[0020]

[0021] Where ω is the angle between the line between the anchor node and the next node leading to the target and the line between the anchor node and the target point. The value of θ is based on the maximum potential area, θ = li → m R arccos(R / 2x)=arccos(1 / 2)=π / 3. Then, an analytical expression for the expected jump is as follows:

[0022]

[0023] The expected hops only depend on the communication radius and node density, so it is applicable to solve non-centroid situations regardless of the geometric relationship between nodes. o The distance between the non-centroid node and the anchor node is estimated as follows:

[0024]

[0025] Experimental results show that this method can achieve accurate node positioning in sensor networks of different sizes and types, and has achieved good results in practical applications.

[0026] Step 2.3, when the node meets the geometric centroid condition, it is not applicable to estimate the distance using only the three-anchor centroid method. This paper estimates the distance by weighted calculation of the three-anchor centroid algorithm and the expected hop algorithm. The three-anchor centroid algorithm has higher positioning accuracy and lower energy consumption, but requires at least three anchor points, which may lead to inaccuracy if the anchor node ratio is low. The expected hop algorithm estimates the distance by the number of communication hops, and the error increases when the number of hops increases. However, it is highly scalable and suitable for various network types, and can provide reliable results even when the anchor node density is low. The estimation accuracy can be improved by combining these two algorithms through weighted calculation. The distance estimation formula based on weighted three-anchor centroid and expected hop is as follows:

[0027]

[0028] in, Represents the estimated distance from common node k to anchor node i. Represents the distance from common node k to anchor node i estimated based on the three-anchor centroid algorithm. It represents the distance from common node k to anchor node i estimated based on expected hops. u represents the optimal weight ratio. When the value of u is 0.8, the positioning accuracy is the best.

[0029] Furthermore, the specific contents of step 3 are as follows:

[0030] Step 3.1, GWO algorithm is a heuristic optimization method inspired by the hunting and social behavior of gray wolves. It simulates the hunting behavior of wolves to find the optimal solution. In the wolf pack, there is a very strict hierarchy. The levels of α, β, and δ wolves decrease in turn. The hunting behavior of gray wolves can be expressed by the following formula:

[0031]

[0032] in, represents the next position of the current gray wolf, and the position vector of the prey is expressed as represents the current position vector of the gray wolf. The coefficient vectors A and C are determined as follows:

[0033]

[0034] The parameters r1 and r2 are random values ​​in the range [0,1], and the parameter A gradually decreases from 2 to 0 during the iteration process, which determines the size of A to emphasize exploration and exploitation respectively. After the prey is surrounded, the hunting behavior is usually guided by α, β, and δ wolves, and the other wolves change their positions according to the positions of these three wolves. The mathematical model of the hunting process is as follows:

[0035]

[0036] in, They are the positions of α, β, and δ wolves, calculated according to the following formula:

[0037]

[0038] In the GWO algorithm, individuals are regarded as gray wolves, and the position of each gray wolf represents a candidate solution. The search process of this algorithm relies on collective behavior rather than individual search, so it may fall into a local optimal solution and fail to find the global optimal solution. In order to effectively solve this problem, we introduce the step size R t To guide the position update of ω wolf. In this algorithm, α wolf, β wolf and δ wolf already have good search capabilities. By updating the step size of ω wolf based on this, a good convergence effect can be achieved. Its expression is as follows:

[0039]

[0040] Where T and t are the maximum and current iteration times respectively. t In the range [0, pi / 2], R t Controls the degree of dispersion during the ω wolf search process. At the beginning, due to the small number of iterations and large step size, global exploration is prioritized. As the number of iterations increases, the gray wolf gradually approaches the optimal solution, at which point the step size will shrink, helping to develop only around the global optimal solution.

[0041] Based on quantum mechanics theory and trajectory analysis, quantum behavior uses the uncertainty principle of quantum mechanics to update each individual in a distribution probability model. Linking the behavior of individual wolves to the principles of quantum mechanics means that individual movements, position updates, and other behaviors are similar to the evolution of quantum particles under wave functions, which may lead to phenomena such as quantum superposition and interference. This association creates a more complex and dynamic optimization algorithm that may have advantages in specific problem areas.

[0042] The gray wolf group searches for the optimal solution in the virtual quantum space. The behavior of the individual gray wolf is affected by the principles of quantum mechanics. Each gray wolf is regarded as a spinless particle in the quantum space, and its behavior is described by the wave function. The evolution and measurement follow the Schrödinger equation and the rules of quantum mechanics. f is the wave normalized wave function and probability density function of the t+1th iteration:

[0043]

[0044] At the tth iteration, the particle flies in the two-dimensional quantum space with The Delta potential well is centered at . L is the characteristic length of the wave function, evaluated by the distance between the particle's current position and the position, in is the control coefficient. According to the Monte Carlo method, we can get the position of the Omega wolf with weaker search ability as follows:

[0045]

[0046] Where u is a random number between [0,1].

[0047] For the characteristic length L, only the tth iteration position is used To evaluate, it is easy to cause the local optimum to fall into a cycle. The gray wolf optimization classifies individual positions and introduces the mean value F of the best position in the front half of the wolf pack. avg As a global point, avoid local loops. Therefore, combined with the above description, a quantum grey wolf optimization algorithm combining quantum behavior and global optimization is introduced. It updates the ω wolf, retains the original position advantage, and increases its dynamics, as shown in the formula:

[0048]

[0049] Where λ and u represent random numbers in the range [0,1]. The algorithm extracts the global search capability of GWO and the exploration characteristics of quantum individuals respectively. Quantum search is designed as a local search to prevent premature convergence to the local optimum. This optimizes the dynamics and convergence of the whole process.

[0050] Step 3.2: When dealing with the objective function of the optimization algorithm, an effective objective function is very important. It is not only used to evaluate the quality of the model prediction results, but also helps to find the optimal solution. Usually, the least squares method and maximum likelihood estimation are selected to perform the location information estimation of the optimization problem. These estimation methods are based on statistical inference and require a large amount of independent and identically distributed data for accurate estimation. However, in practical applications, it is usually not possible to obtain a large enough sample size to support high-quality model training. In order to estimate the location information more accurately and effectively, we use the distance difference as the objective function:

[0051]

[0052] Among them, (x, y) represents the coordinates of the jth anchor node, and (x k ,y k ) represents the coordinates of a common node.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] 1. Improved distance estimation accuracy. This invention proposes a distance estimation scheme based on the geometric centroid of triple anchor points. Different from the traditional algorithm, we use the communication range of the anchor points to form the geometric centroid of the triangle, thereby greatly improving the accuracy of distance estimation.

[0055] 2. Classification of node processing. This paper proposes a new algorithm that divides regular nodes into two categories: one is the nodes that satisfy the triple anchor point geometric centroid relationship, and the other is the nodes that do not satisfy this geometric relationship. For the former, we estimate the node distance by weighting the triple anchor point centroid and the expected jump, while for the latter, the distance is calculated by the expected jump. This weighted strategy fuses the estimated distances obtained by the two algorithms in a certain proportion, making the distance estimation more accurate.

[0056] 3. Enhanced optimization strategy. This paper introduces an enhanced gray wolf optimization strategy, which combines quantum parallelism and adaptive step size, significantly improving the efficiency of the original algorithm. Especially for the ω wolf with weaker search ability, we add adaptive step size and quantum behavior mechanism, thereby optimizing its search process and improving the overall optimization performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a schematic diagram of the algorithm flow framework;

[0058] Figure 2 It is the distribution diagram of O-type and S-type network nodes;

[0059] Figure 3 It is a schematic diagram of the geometric relationship of three anchor points;

[0060] Figure 4It is a schematic diagram of the geometric relationship of the three anchor points;

[0061] Figure 5 This is the result diagram of the influence of the proportion of anchor nodes on positioning accuracy in the O-type network structure under the condition of R = 20m;

[0062] Figure 6 This is the result diagram of the influence of node density change on positioning accuracy in O-type network under the condition of anchor point ratio of 40% and R = 20m;

[0063] Figure 7 This is the result diagram of the influence of the proportion of anchor nodes in the S-type network structure on the positioning accuracy under the conditions of R = 20m and λ = 0.01. DETAILED DESCRIPTION

[0064] In order for professionals in the field to have a deeper understanding of the technical content of the present application, detailed explanation and description are provided through the drawings of the embodiments of the present application. Please note that the embodiments shown only represent part of the present application and do not cover all possible implementation methods. Based on these embodiments, all other embodiments obtained by ordinary technicians in the field without the need for creative work should be included in the protection scope of the present application.

[0065] The present invention will be further described below in conjunction with the accompanying drawings and specific implementation methods.

[0066] Combination Figure 1 , the present invention comprises the following steps:

[0067] Step 1: Deploy wireless sensors in a 100m*100m square monitoring area, including 100 nodes. The node density is 0.01. In the monitoring area, the number of anchor nodes is M. a , the number of unknown nodes is M b Therefore, there is M a +M b =M. Each node has a communication radius R, and each node can communicate with any other node within its communication radius. In addition, in order to simulate various anisotropic networks, such as Figure 2 As shown in the figure, a hybrid network structure is adopted, which combines an O-type network with one hole and an S-type network with two holes for node distribution. All anchor nodes will send messages containing location coordinates and hop count information. The unknown node calculates the hop count based on the received message and broadcasts the information in the network to obtain the hop count from the anchor node to the unknown node.

[0068] Step 2: Determine whether the geometric relationship between the anchor point and the unknown node satisfies the centroid geometric relationship of the three anchor points.

[0069] If not satisfied, Figure 4As shown, the distance between the anchor node and the unknown node is calculated based on the expected jump:

[0070]

[0071] Among them, E(r o ) represents the expected hop distance, λ represents the node density, h ik represents the number of hops from anchor node i to unknown node k. Represents the distance between anchor node i and unknown node k.

[0072] If satisfied, such as Figure 3 As shown, according to the number of hops from the anchor node to the unknown node in step 1, the distance between the anchor node and the unknown node is obtained by a weighted algorithm of the centroid of three anchor points and the expected hop distance;

[0073] The geometric relationship between the centroids of the three anchor points is as follows: Figure 3 As shown in Figure 1, k is a common node, and i, j, and m are three anchor nodes within the communication range of k. The shaded area where the communication ranges of the anchor nodes intersect is crucial for calculating the geometric centroid k″ of triangles A, B, and C in the graph. This point is used as the estimated position of the common node k. We use the distance k″ to estimate the distance from the common node k to the anchor node i, expressed as

[0074]

[0075] Among them, (xa,ya), (xb,yb), (xc,yc) are the coordinates of points A, B and C respectively, (x,y) are the coordinates of the center of mass, and (xi,yi) are the coordinates of the anchor node.

[0076] The distance between the anchor node and the unknown node is obtained by the weighted algorithm of the centroid of three anchor points and the expected hop distance, as follows:

[0077]

[0078] in, Represents the estimated distance from common node k to anchor node i. Represents the distance from common node k to anchor node i estimated based on the three-anchor centroid algorithm. It represents the distance from common node k to anchor node i estimated based on expected hops. u represents the optimal weight ratio. When the value of u is 0.8, the positioning accuracy is the best.

[0079] Step 3, initialize the gray wolf population with the number of iterations Tmax = 500, the population size N = Mb, and the population dimension D = 2. Calculate the individual fitness to determine the α wolf, β wolf, δ wolf, and ω wolf. In the continuous iteration process, through the quantum adaptive gray wolf optimization algorithm, the α wolf, β wolf, and δ wolf update their positions according to formula (22), and the ω wolf updates its position according to formula (26).

[0080] Step 4: If α wolf has reached the maximum number of iterations or meets the iterative loop end condition, the loop is stopped and the α wolf coordinate information is output as the final estimated coordinates of the unknown node.

[0081] The following is an experimental demonstration of the method of the present invention with specific examples, and the specific contents are as follows:

[0082] 1. Experimental environment:

[0083] In order to verify the positioning accuracy of the algorithm, MATLABR2019a was used for simulation. The performance comparison of the algorithm and other algorithms under the same environment was discussed. The range-free positioning of anisotropic wireless sensor networks based on reliable anchor pair selection and quantum behavior Salp group algorithm (marked as LRAQS), a new range-free positioning scheme based on anchor pair conditional decision in wireless sensor networks (marked as LAPCD), and range-free positioning using expected jump progress in wireless sensor networks (marked as LAEP) were respectively used. The experiment distributed 100 network nodes in an O-type and S-type network structure in a 100m*100m square network monitoring area, with anchor nodes ranging from 10% to 70%, a communication radius of 20m, node density varying from 0.006 to 0.02 azimuths, and the irregularity of the network varying from 0 to 0.3.

[0084] 2. Evaluation criteria

[0085] We use the normalized root mean square error (NRMSE) and mean distance error (MDE) to represent the positioning error and distance error, respectively, to judge the accuracy and effectiveness of a WANs positioning method based on the three-anchor centroid and quantum adaptive gray wolf optimization algorithm. The expression is as follows:

[0086]

[0087] Among them, (x,y), They represent the actual coordinate position and estimated coordinate position of the rule node k respectively, Mb represents the number of location nodes, and R represents the communication radius.

[0088]

[0089] Among them, dik, They represent the actual distance and estimated distance between anchor point i and unknown node k respectively, and Ma represents the number of anchor nodes.

[0090] 3. Experimental results

[0091] 1) Discussion on the impact of anchor node ratio on algorithm accuracy,We experimentally study the impact of anchor node ratio on positioning accuracy and distance estimation in S-type networks.,The ratio of anchor nodes starts from 10% and increases by 5% each time until 70%, the irregularity of the network is 0.05, and the communication range is set to 20 meters. Figure 5 The distance error and positioning error of LAEP, LRAQS, LAPCD, and our proposed triple anchor centroid and quantum adaptive gray wolf optimization algorithms are shown under different anchor node ratios. The simulation experimental results show that the positioning accuracy of these algorithms is improved with the increase of anchor node ratio. However, among all these algorithms, the triple anchor centroid and quantum adaptive gray wolf optimization algorithms perform the best, with the optimal normalized root mean square error NRMSE reaching 0.2168, which is 30.04% better than the LAPCD algorithm and 19.64% better than the LRAQS algorithm. Although the reliable anchor pair scheme proposed by LRAQS does improve the positioning accuracy, its anchor node coverage is insufficient. At the same time, in the LAPCD algorithm, there are nodes whose distance cannot be estimated, which leads to ranging errors. The reason why our proposed algorithm has higher accuracy is that it performs positioning through triple anchor points, thus avoiding the impact caused by node jumping.

[0092] 2) To discuss the effect of node density on the accuracy of the algorithm, we adjusted the node density in the O-type network, starting with a density of 0.006 and increasing it by 0.002 each time until the density reached 0.02. Meanwhile, the proportion of anchor nodes was fixed at 40%. Figure 6The positioning distance error and positioning error under different node densities are shown. The observation results show that although the node density has little effect on the performance of the algorithm, our proposed algorithm still shows the best positioning efficiency and the lowest error. The proportion of anchor nodes has a significant impact on the effectiveness of the algorithm, and the use of the quantum adaptive gray wolf algorithm further improves the ability to quickly and accurately locate nodes with limited node information. Therefore, the accuracy of the algorithm will be maintained at a certain level when the proportion of anchor nodes remains unchanged. At the same time, the inter-node distance estimated by the expected hop is least affected by the network density, which is also reflected in algorithms including LRAQS. Although LRAQS uses QSSA to determine the node position to reduce the positioning error, it still produces some errors compared with QAGWO due to the influence of the number of hops. By comparison, our algorithm significantly improves the positioning accuracy. The results show that when λ is 0.008, the NRMSE achieves the optimal value, which is 1.45% better than LAPCD, 19.49% better than LRAQS and 16.08% better than LAEP, respectively.

[0093] 3) Discuss the impact of network structure on algorithm accuracy. The above experiments were conducted in an O-type network, which has only one network hole, a relatively regular shape, and relatively uniform distances between nodes. High-precision node positioning can be easily achieved using methods such as triangulation. However, the S-type network has two holes, a curved shape, lacks regularity, and other factors. The distances between nodes vary greatly, the signal propagation path is complex, and has nonlinear characteristics. Therefore, we focus on studying and comparing the impact of increasing the proportion of anchor nodes on positioning error and distance error in anisotropic networks to explore whether the algorithm proposed in this article is applicable. Figure 7 It shows how the anchor node ratio and node density affect the localization algorithm in an S-shaped network. When the anchor node ratio increases and the node density increases, the algorithm still has the highest localization accuracy due to the use of geometric constraints. Other algorithms are also applicable to anisotropic networks, but the performance is worse.

[0094] According to the above experiments, the influence of anchor node ratio, node density and network structure on the positioning accuracy of the algorithm is discussed. Thanks to the stability of the triple anchor weighting technology and the high precision of the quantum adaptive gray wolf optimization algorithm, the algorithm has achieved significant advantages in positioning accuracy and almost achieved perfect positioning effect. This scene not only demonstrated the technical superiority of the algorithm, but also highlighted its competitiveness in the market. However, due to the geometric constraint relationship of the sensor nodes used in the distance estimation stage, the algorithm performs better when applied to the positioning of large building equipment than in small positioning scenarios. For example, it can be used for navigation services in large buildings such as shopping malls and airports. In subsequent work, we will continue to improve the geometric constraints to make them more applicable and accurate.

[0095] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any technician familiar with the profession, without departing from the scope of the technical solution of the present invention, makes any simple modifications, equivalent changes and modifications to the above embodiments based on the technical essence of the present invention, which still fall within the scope of the technical solution of the present invention.

Claims

1. A WANs positioning method based on three-anchor centroid and quantum adaptive grey wolf optimization algorithm, characterized by: The following steps are involved: Step 1: Deploy network nodes in the target area. All anchor nodes will send messages containing location coordinates and hop count information. The unknown node calculates the hop count based on the received message and broadcasts the information in the network. The distance between the anchor node and the unknown node is obtained through the weighted algorithm of the centroid of the three anchor points and the expected hop distance. Step 1.1: The three-anchor centroid algorithm estimates the distance between the unknown node and the anchor node under geometric constraints. If an unknown node is located in the intersection of the circles formed by its three adjacent anchor nodes, the estimated distance between the common node and the anchor node is determined by the distance from the Euclidean geometric centroid of the intersection area to the anchor node. The selection of the centroid is based on the Euclidean geometric intersection of the circles formed by the centers of the three adjacent anchor nodes. The distance is expressed as: (x,y)=((x a +x b +x c ) / 3,(and a +y b +y c ) / 3), Among them, k is a common node, i, j, and m are three anchor nodes within the communication range of k, and the coordinates of the intersection of the communication ranges of the anchor nodes are (x a ,y a ),(x b ,y b ),(x c ,y c ), the coordinates of the centroid are (x,y), and the coordinates of the anchor node are (x i ,y i ), we use the distance Estimate the distance from common node k to anchor node i; Step 1.2: Estimating distance based on expected hops. In the three-anchor centroid algorithm proposed in step 1.1, anchor nodes and common nodes must satisfy the geometric relationship of the three anchor points. When the geometric relationship of the three anchor centroids is not satisfied, we estimate the distance of the nodes by expected hops. Distance estimation based on expected hops is a method for achieving node positioning without using distance measurement tools. This method uses the expected distance of each hop in the random walk process and estimates the distance between nodes by calculating the number of communication hops between them. Then, the distance information of these nodes is converted into position estimation results through the polygon cover algorithm, which is expressed as: Among them, E(r o ) represents the expected hop, λ is the node density, R is the communication radius, h ik Indicates the number of hops, r o is the distance between the anchor node and the next sensor; Step 1.3: Estimate the distance by weighted calculation of the three-anchor centroid algorithm and the expected hop algorithm. The three-anchor centroid algorithm requires at least three anchor points. If the proportion of anchor nodes is low, it will lead to inaccuracy. The expected hop algorithm estimates the distance by the number of communication hops. When the number of hops increases, the error will also increase. The estimation accuracy is improved by combining these two algorithms through weighted calculation. The distance estimation formula based on the weighted three-anchor centroid and expected hop is as follows: in, represents the estimated distance from ordinary node k to anchor node i, represents the distance from common node k to anchor node i estimated based on the three-anchor centroid algorithm, represents the distance from common node k to anchor node i estimated based on the expected hopping algorithm, and u represents the optimal weight ratio; Step 2: Based on the gray wolf optimization algorithm, an adaptive strategy and the uncertainty principle of quantum mechanics are introduced to update the position of the ω wolf, adjust the dynamics and convergence of the global search process, and obtain a quantum adaptive gray wolf optimization algorithm; Step 3: Based on the distance between the anchor node and the unknown node obtained in step 1, the quantum adaptive gray wolf optimization algorithm proposed in step 2 is used to locate the unknown node to obtain the estimated coordinates of the unknown node.

2. A WANs positioning method based on three-anchor centroid and quantum adaptive grey wolf optimization algorithm according to claim 1, characterized in that: The gray wolf optimization algorithm in step 2 includes the following steps: Step 2.1, in the gray wolf optimization algorithm, a gray wolf population consisting of N individuals is randomly generated in the initial stage. By evaluating the fitness of each individual, α wolf, β wolf and δ wolf are determined, and the remaining individuals are classified as ω wolf. In the subsequent iteration process, α wolf, β wolf and δ wolf jointly predict the location of the prey and guide the ω wolf group to adjust their respective positions according to these predicted positions; Step 2.2: The hunting behavior of gray wolves is divided into three main stages: encircling, chasing and attacking prey. Gray wolves search by encircling prey. The mathematical model is as follows: in, represents the next position of the current gray wolf, and the position vector of the prey is expressed as Represents the current position vector of the gray wolf, and the coefficient vectors A and C are determined as follows: The parameters r1 and r2 are random values ​​in the range [0,1], and the parameter A gradually decreases from 2 to 0 during the iteration process; Step 2.3, after surrounding the prey, the hunting behavior is usually guided by α, β, and δ wolves. The other wolves change their positions according to the positions of these three wolves. The mathematical model of the prey hunting process is as follows: in, They are the positions of α, β, and δ wolves, calculated according to the following formula: in, are the position vectors of α, β, and δ in the wolf pack, Represents the position of the gray wolf.

3. The WANs positioning method based on three-anchor centroid and quantum adaptive grey wolf optimization algorithm according to claim 1, characterized in that: The adaptive strategy in step 2 is: The step size R is introduced t To guide the ω wolf's position update R t =2×(1-sin((t / T max )×(π / 2))), Among them, T max and t are the maximum and current iteration numbers respectively, R t In the range [0, pi / 2], R t Controls the degree of dispersion during the ω wolf's search.

4. According to claim 1, a WANs positioning method based on three-anchor centroid and quantum adaptive grey wolf optimization algorithm is characterized by: The uncertainty principle of quantum mechanics in step 2 is used to update the position of ω wolf, specifically: When the gray wolf group searches for the optimal solution in the virtual quantum space, its behavior is affected by the principles of quantum mechanics. Each gray wolf individual is regarded as a spinless particle in the quantum space, and its behavior is described by the wave function. The position of the ω wolf is updated: Among them, λ and u represent random numbers in the range [0,1], F avg is the mean of the best positions of the front half of the wolf pack, is the control coefficient.

5. The WANs positioning method based on three-anchor centroid and quantum adaptive grey wolf optimization algorithm according to claim 1, characterized in that: In step 3, the quantum adaptive grey wolf optimization algorithm performs the following steps to locate the unknown node: Step 5.1: Obtain the fitness values ​​of all gray wolf individuals according to the fitness function: Among them, (x j ,y j ) represents the coordinates of the jth anchor node, and (x k ,y k ) represents the coordinates of common nodes, M a is the number of unknown nodes; Step 5.2, α, β, δ wolf according to the formula Update the position, the ω wolf updates the position according to the formula in claim 4. When the number of wolf position updates reaches the maximum number of iterations, the iteration is stopped and the output α wolf position information is the final position of the unknown node.

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