A non-rangefinder node positioning method under irregular network node distribution

Abstract

This invention provides a non-ranging node localization method for irregular network node distributions. It utilizes the classic DV-hop non-ranging node localization algorithm to obtain the distance between unknown nodes and anchor nodes, thus transforming the node localization problem into an optimization problem. The method includes the following steps: First, uncertainty is used to describe the communication links between nodes. Then, by introducing the average hop distance of the anchor nodes, two anchor nodes are selected along a detour path. Their geometric relationship with the unknown node is assessed to determine three possible node pairs: optimal, suboptimal, and unavailable, and the distance between nodes is calculated. Finally, based on the minimax criterion, the original node localization optimization problem is constructed. Using auxiliary variables and continuous convex approximation, the original non-convex problem is relaxed and iteratively solved as a convex optimization problem, achieving efficient node localization. This invention ensures the accuracy of unknown node estimation even in irregular networks with detours in communication paths between nodes, while reducing the energy consumption and cost of anchor node deployment.

Description

Technical Field

[0001] This invention relates to the field of wireless sensor node localization, and in particular to a non-ranging node localization method under irregular network node distribution. Background Technology

[0002] Wireless sensor networks (WSNs) typically consist of numerous sensor nodes used for continuous monitoring, detection, and collection of data from various environments or objects. Due to their ease of deployment, self-organization, low cost, and dynamic topology, WSNs are becoming increasingly important in the Internet of Things (IoT). Because of their short transmission range, sensor nodes often cannot communicate directly with base stations, thus opting for multi-hop communication. However, if the location of the data collection node is unknown, the sensor data may become useless, making localization a critical issue in the WSN field. In practical applications, network node localization accuracy faces several challenges: Firstly, the electromagnetic radiation range, direction, and angle of the network environment are not always identical, meaning the communication radius of network nodes is no longer an ideal circle. Secondly, for irregular networks with meandering communication paths between nodes, approximating a straight-line distance using the average multi-hop distance of all anchor nodes accumulates significant errors, leading to low node localization accuracy.

[0003] Localization algorithms are used in various real-world applications, such as inventory monitoring in industry, locating and detecting sensor nodes in underwater areas, and outdoor exploration. Node localization algorithms are designed with the help of various types of natural heuristic algorithms, such as genetic algorithms and bee colony algorithms, to solve the node localization problem in isotropic WSNs. Anisotropic WSNs are also troubled by localization problems, and these networks have been utilized in practical applications. Localization algorithms designed to solve the localization problem in anisotropic WSNs generally utilize the principle of multilateral positioning to estimate node positions and distance-free measurement methods based on hop count. Unlike distance-based methods that directly measure the distance between nodes, the latter requires distance measurement equipment for the node to be located, leading to higher energy consumption and increased overall cost. Therefore, distance-free methods are often used in anisotropic WSNs.

[0004] Anisotropic networks are affected by various problems, including non-uniform sensor node distribution and uneven monitoring areas. Notably, the DV-Hop (distance vector-Hop) algorithm has attracted increasing attention in both academia and industry. In the DV-Hop algorithm, the minimum hop count between an unknown node and pre-defined anchor nodes is known. The estimated distance between them is calculated as the product of the minimum and average hop counts. Finally, triangulation or least squares is used to estimate the location of the unknown node. However, the DV-Hop algorithm still cannot meet the requirements of many applications with strict requirements for node localization accuracy. The Hyperbolic (Hyperbolic location algorithm) uses a probabilistic selective strategy to select anchor nodes. Based on these selected anchor nodes, a two-dimensional hyperbolic function is further used to predict the location of unknown nodes, but this algorithm suffers a significant drop in localization accuracy when anchor nodes are sparsely distributed. AAML (Accurate Analytical-based Multi-hop Localization) uses neighbor nodes to estimate the distance between directly connected node pairs during the network initialization phase. Then, the optimal weighting matrix and hyperbolic estimation are used to reduce the impact of accumulated errors, but this algorithm is prone to getting trapped in local optima and performs poorly in localization. LARQS (Localization algorithm based on Reliable Anchorpair selection and Quantum-behaved Salp swarm algorithm) proposes a method to estimate the distance between sensor nodes based on geometric constraints for different types of anchor pairs, but in anisotropic networks, the existence of detours easily leads to poor localization performance in some optimal solutions. The above localization methods, which can estimate the position of unknown nodes, still do not achieve optimal localization performance. Summary of the Invention

[0005] The purpose of this invention is to provide a non-range-based node localization method for irregular network node distribution, which can better improve the localization accuracy of unknown nodes in irregular anisotropic networks.

[0006] The technical solution adopted in this invention is as follows:

[0007] A non-range node localization method for irregular network node distribution includes the following specific steps:

[0008] Step 1: Parameter Settings

[0009] N sensor nodes are randomly topologically positioned within an L×L square monitoring area. m sensor nodes, equipped with GNSS signal receiving units, can achieve self-positioning or manual calibration; these are the anchor nodes. The remaining Nm sensor nodes are unknown nodes, whose positions cannot be determined through self-sensing. Furthermore, each node has a communication radius of R and can communicate directly with nodes within its coverage area. The accuracy threshold ε is used, and the uncertainty p(d) describes the communication connection between two nodes at a distance d. The specific steps include:

[0010]

[0011] Where DoI represents the percentage change in maximum path loss per unit degree along the radio propagation direction, d

[0012] R represents the distance between any two nodes, and R represents the communication radius of the node.

[0013] Step 2: Calculate the estimated distance from the unknown node to the anchor node:

[0014] By leveraging the reliability of anchor nodes and based on the anchor pair type, the distance between nodes is estimated through probabilistic geometric estimation and by multiplying the average distance per hop by the minimum number of hops from the unknown node to the anchor node. Specifically, the steps include:

[0015] Steps 2.1 and 2.2 yield the average jump distance.

[0016]

[0017] in, and These represent anchor node a respectively. i and a j Minimum hop count to unknown node u, distance between two anchor nodes as follows:

[0018]

[0019] Where ||·||2 represents the l2 norm, They represent the a-th i The anchor node and the a-th anchor node j The position of each anchor node, where m represents the number of anchor nodes.

[0020] Step 2.3 calculates the distance estimates between the unknown node and the anchor node based on the geometric relationship judgment conditions.

[0021] (1) Criteria for determining the optimal anchor node pair:

[0022] For an unknown node u, if the anchor node ai and a j Two anchor nodes can be considered an optimal anchor node pair if the following inequalities are satisfied. Intuitively, the optimal pair is constrained by two conditions: Condition 1, both anchor nodes are located outside each other's maximum potential coverage area; Condition 2, the maximum potential coverage areas of the anchor nodes must overlap, and this overlap can be determined by the law of cosines. Since the intersecting areas are relatively small, the optimal anchor node pair provides an ideal geometric relationship to obtain an accurate distance estimate. Therefore, the expected distance between the anchor node and the unknown node is considered a good choice for estimating their distance.

[0023]

[0024]

[0025]

[0026] Because the intersection area is small, the optimal anchor node pair provides an ideal geometric relationship for obtaining accurate distance estimates. Assume there is an unknown node u, and anchor node a... i and a j If the above criteria are met, then the optimal anchor node pair is determined by the estimated distance. It can be obtained through calculation. Therefore, the unknown node u and the anchor node a i Distance estimate between

[0027]

[0028] Among them, Represents line segment a i a j and a i The angle between u, Indicates the average jump distance. express The probability density.

[0029] (2) Criteria for determining suboptimal anchor node pairs:

[0030] Unknown node u attempts to estimate its relationship with anchor node a i The distance between anchor nodes is such that if the anchor node pair satisfies the following inequality, then the distance between anchor nodes is determined by anchor node a. i and a j The resulting anchor node pairs are defined as suboptimal anchor node pairs.

[0031]

[0032]

[0033]

[0034] In this case, anchor node a in the suboptimal anchor node pair i Distance estimate between the unknown node u

[0035]

[0036] in, and These represent anchor node a respectively. i To the unknown node u and the anchor node a i to a j The minimum jump value, Represents anchor node a i and a j The distance between them.

[0037] (3) Criteria for determining unusable anchor node pairs:

[0038] Anchor node pairs that are neither optimal nor suboptimal are classified as unusable anchor pairs. There are two scenarios: First, the distance between the two anchor nodes is very small, and both anchor nodes are located in overlapping areas. This situation is usually caused by large coverage gaps in the network that bypass most of the routing paths between nodes. Second, the maximum potential coverage areas of the anchor nodes do not overlap at all. Irregularity in communication range is the main cause of this situation. Since unusable anchor node pairs cannot provide reliable information, the above criteria are not met, and therefore, unusable anchor node pairs will not be used in our plan.

[0039] Step 3: Considering the impact of the unknown node's position offset error and the minimum number of hops on the estimated distance, construct the objective function for a weighted minimum-maximum residual optimization problem, specifically:

[0040] The anchor node position can be obtained from steps 2.1 and 2.2. and estimated distance Using the norm approximation method, the node localization problem can be constructed into the following weighted minimum-maximum residual optimization problem:

[0041]

[0042] Where, x u Indicates the position of the unknown node u to be optimized, Δx u This represents the position offset error of the unknown node. This represents the position of the i-th anchor node, ||·||² represents the L2 norm, |·| represents the absolute value, and m represents the number of anchor nodes. This represents the estimated distance between the i-th anchor node and the unknown node u. It is a weighting factor, which represents the influence of the i-th anchor node on the accuracy of the position estimation of the unknown node u. It is a weighting factor. The calculation is as follows:

[0043]

[0044] Step 4: Solve the unknown node coordinates using iterative convex optimization, which includes the following steps:

[0045] Step 4.1: Relax the non-convex objective function into a constrained convex objective function by introducing auxiliary variables. Specifically:

[0046] Based on the objective function of the weighted minimum-maximum residual optimization problem constructed in step 3, since the objective function is non-convex, let... To maximize the weighted residual, the original problem can be transformed into the following optimization problem:

[0047] Objective function:

[0048] Constraints:

[0049]

[0050] Where ||·||2 represents the l2 norm, x u Let represent the position of the unknown node u to be optimized, and t represent the maximum weighted residual distance from the unknown node to the anchor node. This represents the position of the i-th anchor node. Let m represent the estimated distance between the i-th anchor node and the unknown node u, and m represent the number of anchor nodes.

[0051] Step 4.2: Iterative optimization using continuous convex approximation to estimate the location of unknown nodes, specifically:

[0052] Based on step 4.1, relaxing the non-convex constraints to convex constraints yields the following convex optimization problem, given the initial optimization value of the unknown node u. Iterative solution yields And The initial value obtained from the optimization solution for the next iteration is... Iterate and optimize in this way until... Given that the precision threshold ∈ , we can obtain the following convex optimization problem:

[0053] Objective function:

[0054] Constraints:

[0055]

[0056] Where ||·||2 represents the l2 norm, (·) T Indicates transpose, x u This indicates the position of the unknown node u to be optimized. It is a weighting factor, Δx u The unknown node position offset error is represented by t, where t represents the maximum weighted residual distance from the unknown node to the anchor node. This represents the position of the i-th anchor node. This represents the initial value of the position of the unknown node u to be optimized. Let m represent the estimated distance between the i-th anchor node and the unknown node u, and m represent the number of anchor nodes.

[0057] The beneficial effects of this invention are:

[0058] By employing the above technical solution, this invention addresses the problem of low localization accuracy of unknown nodes caused by irregular networks with detours. It proposes a non-ranging node localization method for irregular network node distributions. First, uncertainty is used to describe the communication links between nodes. Then, by introducing the average hop distance of anchor nodes, two anchor nodes are selected along the detour path. Their geometric relationship with the unknown node is assessed to determine three cases: optimal, suboptimal, and unavailable node pairs, and the distance between nodes is calculated. Finally, based on the weighted minimum-maximum criterion, the original node localization optimization problem is constructed. Using auxiliary variables and continuous convex approximation, the original non-convex problem is relaxed into an iterative convex optimization problem for solution, achieving efficient network node localization. Attached Figure Description

[0059] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0060] Figure 1 This is a flowchart of the present invention;

[0061] Figure 2 Distribution diagram of unknown nodes and anchor nodes;

[0062] Figure 3 Comparison of localization errors of different methods for unknown nodes; Detailed Implementation

[0063] like Figure 1 As shown, the present invention includes the following steps:

[0064] Step 1: Parameter Settings

[0065] N sensor nodes are randomly topologically positioned within an L×L square monitoring area. m sensor nodes, equipped with GNSS signal receiving units, can achieve self-positioning or manual calibration; these are the anchor nodes. The remaining Nm sensor nodes are unknown nodes, whose positions cannot be determined through self-sensing. Furthermore, each node has a communication radius of R and can communicate directly with nodes within its coverage area. The accuracy threshold ε is used, and the uncertainty p(d) describes the communication connection between two nodes at a distance d. The specific steps include:

[0066]

[0067] Where DoI represents the percentage change in maximum path loss per unit degree along the radio propagation direction, d

[0068] R represents the distance between any two nodes, and R represents the communication radius of the node.

[0069] Step 2: Calculate the estimated distance from the unknown node to the anchor node:

[0070] By leveraging the reliability of anchor nodes and based on the anchor pair type, the distance between nodes is estimated through probabilistic geometric estimation and by multiplying the average distance per hop by the minimum number of hops from the unknown node to the anchor node. Specifically, the steps include:

[0071] Steps 2.1 and 2.2 yield the average jump distance.

[0072]

[0073] in, and These represent anchor node a respectively. i and a j Minimum hop count to unknown node u, distance between two anchor nodes as follows:

[0074]

[0075] Where ||·||2 represents the l2 norm, They represent the a-th i The anchor node and the a-th anchor node j The position of each anchor node, where m represents the number of anchor nodes.

[0076] Step 2.3 calculates the distance estimates between the unknown node and the anchor node based on the geometric relationship judgment conditions.

[0077] (1) Criteria for determining the optimal anchor node pair:

[0078] For an unknown node u, if the anchor node ai and a j Two anchor nodes can be considered an optimal anchor node pair if the following inequalities are satisfied. Intuitively, the optimal pair is constrained by two conditions: Condition 1, both anchor nodes are located outside each other's maximum potential coverage area; Condition 2, the maximum potential coverage areas of the anchor nodes must overlap, and this overlap can be determined by the law of cosines. Since the intersecting areas are relatively small, the optimal node pair provides an ideal geometric relationship for obtaining an accurate distance estimate. Therefore, the expected distance between the anchor node and the unknown node is considered a good choice for estimating their distance.

[0079]

[0080]

[0081]

[0082] Because the intersection area is small, the optimal anchor node pair provides an ideal geometric relationship for obtaining accurate distance estimates. Assume there is an unknown node u, and anchor node a... i and a j If the above criteria are met, then the optimal anchor node pair is determined by the estimated distance. It can be obtained through calculation. Therefore, the unknown node u and the anchor node a i Distance estimate between

[0083]

[0084] Among them, Represents line segment a i a j and a i The angle between u, Indicates the average jump distance. express The probability density.

[0085] (2) Criteria for determining suboptimal anchor node pairs:

[0086] Unknown node u attempts to estimate its relationship with anchor node a i The distance between anchor nodes is such that if the anchor node pair satisfies the following inequality, then the distance between anchor nodes is determined by anchor node a. i and a j The resulting anchor node pairs are defined as suboptimal anchor node pairs.

[0087]

[0088]

[0089]

[0090] In this case, anchor node a in the suboptimal anchor node pair i The distance between the unknown node u and the unknown node u can be estimated as follows:

[0091]

[0092] in, and These represent anchor node a respectively. i To the unknown node u and the anchor node a i to a j The minimum jump value, Represents anchor node a i and a j The distance between them.

[0093] (3) Criteria for determining unusable anchor node pairs:

[0094] Anchor node pairs that are neither optimal nor suboptimal are classified as unusable anchor pairs. There are two scenarios: First, the distance between the two anchor nodes is very small, and both anchor nodes are located in overlapping areas. This situation is usually caused by large coverage gaps in the network that bypass most of the routing paths between nodes. Second, the maximum potential coverage areas of the anchor nodes do not overlap at all. Irregularity in communication range is the main cause of this situation. Unusable anchor node pairs cannot provide reliable information; the above criteria are not met, and therefore, unusable anchor node pairs cannot provide reliable information. Thus, they will not be used in our plan.

[0095] Step 3: Considering the impact of the unknown node's position offset error and the minimum number of hops on the estimated distance, construct the objective function for a weighted minimum-maximum residual optimization problem, specifically:

[0096] The anchor node position can be obtained from steps 2.1 and 2.2. and estimated distance Using the norm approximation method, the node localization problem can be constructed into the following weighted minimum-maximum residual optimization problem:

[0097]

[0098] Where, x u Indicates the position of the unknown node u to be optimized, Δx u This represents the position offset error of the unknown node. This represents the position of the i-th anchor node, ||·||² represents the L2 norm, |·| represents the absolute value, and m represents the number of anchor nodes. This represents the estimated distance between the i-th anchor node and the unknown node u. It is a weighting factor, which represents the influence of the i-th anchor node on the accuracy of the position estimation of the unknown node u. It is a weighting factor. The calculation is as follows:

[0099]

[0100] Step 4: Solve the unknown node coordinates using iterative convex optimization, which includes the following steps:

[0101] Step 4.1: Relax the non-convex objective function into a constrained convex objective function by introducing auxiliary variables. Specifically:

[0102] Based on the objective function of the weighted minimum-maximum residual optimization problem constructed in step 3, since the objective function is non-convex, let... To maximize the weighted residual, the original problem can be transformed into the following optimization problem:

[0103] Objective function:

[0104] Constraints:

[0105]

[0106] Where ||·||2 represents the l2 norm, x u This indicates the position of the unknown node u to be optimized. It is a weighting factor, Δx u The unknown node position offset error is represented by t, where t represents the maximum weighted residual distance from the unknown node to the anchor node. This represents the position of the i-th anchor node. Let m represent the estimated distance between the i-th anchor node and the unknown node u, and m represent the number of anchor nodes.

[0107] Step 4.2: Iterative optimization using continuous convex approximation to estimate the location of unknown nodes, specifically:

[0108] Based on step 4.1, relaxing the non-convex constraints to convex constraints yields the following convex optimization problem, given the initial optimization value of the unknown node u. Iterative solution yields And The initial value obtained from the optimization solution for the next iteration is... Iterate and optimize in this way until... Given that the precision threshold ∈ , we can obtain the following convex optimization problem:

[0109] Objective function:

[0110] Constraints:

[0111]

[0112] Where ||·||2 represents the l2 norm, (·) T Indicates transpose, x u This indicates the position of the unknown node u to be optimized. It is a weighting factor, Δx u The unknown node position offset error is represented by t, where t represents the maximum weighted residual distance from the unknown node to the anchor node. This represents the position of the i-th anchor node. This represents the initial value of the position of the unknown node u to be optimized. Let m represent the estimated distance between the i-th anchor node and the unknown node u, and m represent the number of anchor nodes.

[0113] By employing the above technical solutions, this invention addresses the problem of low positioning accuracy for unknown nodes caused by irregular networks with detours. It proposes a non-ranging node positioning method for irregular network node distributions. First, uncertainty is used to describe the communication links between nodes. Second, by introducing the average hop distance of anchor nodes, two anchor nodes are selected along the detour path. Their geometric relationships with the unknown node are then assessed to determine three possible pairings: optimal, suboptimal, and unavailable. The distance between nodes is then calculated. Third, based on the weighted minimum-maximum criterion, a primary optimization problem for node positioning is constructed. Using auxiliary variables and continuous convex approximation, the original non-convex problem is relaxed into an iterative convex optimization problem, achieving efficient positioning of network nodes.

[0114] This example uses 150 nodes in a random topology within the monitored area (e.g., ...). Figure 2 The algorithm has 30 anchor nodes and 120 unknown nodes. The RMSE (root mean square error) performance of the proposed algorithm, DV-hop, Hyperbolic, AAML, and LARQS in locating unknown nodes is compared (e.g., ...). Figure 3 ).pass Figure 3The RMSE of each unknown node can be used to calculate the average RMSE of each algorithm. The average RMSEs of the four algorithms are 0.1429, 1.0271, 0.8057, 0.7340, and 0.3812, respectively. Compared with DV-hop, Hyperbolic, AAML, and LARQS algorithms, the proposed algorithm improves the positioning accuracy by 86.08%, 82.26%, 80.53%, and 62.51%, respectively. The proposed algorithm has the highest positioning accuracy among the four algorithms. In summary, this invention utilizes the weighted minimum-maximum criterion combined with geometric constraints to effectively solve the problem of low positioning accuracy in irregular networks. Furthermore, iteratively solving the convex problem of node positioning improves the positioning accuracy of unknown nodes.

Claims

1. A non-ranging node localization method for irregular network node distribution, characterized in that: It includes the following steps: Step 1: Parameter Settings N sensor nodes are set in a random topology. Square monitoring area Each sensor node is equipped with a GNSS signal receiving unit, enabling it to achieve self-position awareness or manual calibration; these are known as anchor nodes. The remaining... The sensor nodes are unknown nodes, and their locations cannot be determined through their own sensing; furthermore, the communication radius of the nodes is... Furthermore, it can communicate directly with nodes within its coverage area, through uncertainty. To describe the distance between two nodes as Communication connection, precision threshold ; Step 2: Calculate the estimated distance from the unknown node to the anchor node: Determine the anchor pair type using the anchor node's criteria, and calculate the estimated distance between nodes using different anchor pair types. The calculation of the estimated distance from the unknown node to the anchor node specifically includes the following steps: Step 2.1: Propagation of anchor node information in the network; Step 2.2: Calculate the average jump distance using anchor nodes: Based on the anchor positions and jump counts broadcast in Step 2.1, the anchor nodes... and Obtain any unknown node Minimum jump value and ; The actual location of the anchor node is known, and the distance between two anchor nodes is used. This indicates that, based on the minimum jump value between different anchor nodes, the average jump distance is calculated. and broadcast it to the network; Step 2.3: Calculate the distance estimates between the unknown node and the anchor node based on the geometric relationship conditions. The average jump distance of the anchor nodes obtained in step 2.2 In the detour path, select two anchor nodes and determine their geometric relationship with the unknown node to classify them into three cases: optimal, suboptimal, and unusable node pairs. Calculate the distance between the nodes. ; Step 3: Considering the impact of the unknown node's position offset error and the minimum number of hops on the estimated distance, construct the objective function of the weighted minimum-maximum residual optimization problem; the objective function of the weighted minimum-maximum residual optimization problem in Step 3 is calculated using the following method: The anchor node position can be obtained from steps 2.1 and 2.

2. and estimated distance Using the norm approximation method, the node localization problem can be constructed into the following weighted minimum-maximum residual optimization problem: ； in, Indicates unknown nodes to be optimized Location, This represents the position offset error of the unknown node. Indicates the first The location of each anchor node express Norm, Represents absolute value. Indicates the number of anchor nodes. Indicates the first Anchor nodes and unknown nodes Estimated distance between them; It is a weighting factor. The calculation is as follows: ; Step 4: Solve the unknown node coordinates by iteratively solving the convex optimization problem.

2. The non-ranging node localization method under irregular network node distribution according to claim 1, characterized in that: In step 1, uncertainty is used. Describing the communication links between nodes specifically includes the following steps: ； in, This represents the percentage change in maximum path loss per unit degree along the direction of radio propagation. ; This represents the distance between any two nodes. Indicates the communication radius of the node.

3. The non-ranging node localization method under irregular network node distribution according to claim 1, characterized in that: Step 2.1: Propagation of anchor node information in the network, specifically: Anchor Node One of the anchor nodes broadcasts data including its own identification information, ID, and location. The initial jump value of itself to an unknown node, which is 0. Information, which is called a data packet, is spread to unknown nodes in the network through a flooding strategy. Once a neighboring node receives this data packet, it increments its hop count by 1 and selects to save the hop count data packet of the nearest anchor node. Then it broadcasts this data packet to the other neighboring nodes. The flooding process ends when every node in the network has finished receiving the data packet. It is expected that the unknown node will obtain the necessary information, including the anchor's location and hop count, in order to locate itself.

4. The non-ranging node localization method under irregular network node distribution according to claim 3, characterized in that: In step 2.2, the average jump distance is calculated using the anchor nodes using the following formula. : ； in, and Representing anchor nodes and To unknown node The minimum jump value, the distance between two anchor nodes as follows: ； Where, ||·||2 represents Norm, , They represent the first The anchor node and the first The location of each anchor node Indicates the number of anchor nodes.

5. The non-ranging node localization method under irregular network node distribution according to claim 4, characterized in that: Step 2.3, which calculates the distance estimates between the unknown node and the anchor node based on the geometric relationship judgment conditions, specifically includes the following steps: (1) Criteria for determining the optimal anchor node pair: For unknown nodes If anchor node and If the following inequalities are satisfied, then these two anchor nodes can be considered as an optimal anchor node pair. Intuitively, the optimal anchor node pair is constrained by two conditions: Condition 1, both anchor nodes are located outside each other's maximum potential coverage area; Condition 2, the maximum potential coverage areas of the anchor nodes must overlap, and the overlap can be determined by the law of cosines. Since the intersecting area is relatively small, the optimal anchor node pair provides an ideal geometric relationship to obtain an accurate distance estimate. Therefore, the expected distance between the anchor node and the unknown node is considered a better choice for estimating its distance. ； Because the intersection area is small, the optimal anchor node pair provides an ideal geometric relationship for obtaining accurate distance estimation: assuming there are unknown nodes. And anchor node and If the above criteria are met, then the optimal anchor node pair is determined by the estimated distance. It can be obtained through calculation; therefore, the unknown node and anchor node Distance estimates between : ； in, Represents line segment and The angle between them Indicates the average jump distance. express The probability density; (2) Criteria for determining suboptimal anchor node pairs: Unknown node Try to estimate itself and the anchor node The distance between anchor nodes is determined by the following inequality: and The resulting anchor node pairs are defined as suboptimal anchor node pairs; ； In this case, the anchor node in the suboptimal anchor node pair and unknown nodes Distance estimates between : ； in, and Representing anchor nodes To unknown node and anchor node arrive The minimum jump value, Represents anchor node and The distance between them; (3) Criteria for determining unusable anchor node pairs: Anchor node pairs that are neither optimal nor suboptimal are classified as unusable anchor pairs in two ways: First, the distance between the two anchor nodes is very small, and both anchor nodes are located in overlapping areas; this situation is usually caused by large coverage gaps in the network that bypass most of the routing paths between nodes; Second, the maximum potential coverage areas of the anchor nodes do not overlap at all; irregularity in communication range is the main cause of this situation. Unusable anchor node pairs cannot provide reliable information, and the above judgment conditions are not met. Therefore, they will not be used in our plan.

6. The non-ranging node localization method under irregular network node distribution according to claim 1, characterized in that: The unknown node coordinates in step 4 of the iterative convex optimization problem are calculated using the following method: Step 4.1: Relax the non-convex objective function into a constrained convex objective function by introducing auxiliary variables. Specifically: Based on the objective function of the weighted minimum-maximum residual optimization problem constructed in step 3, since the objective function is non-convex, let... To maximize the weighted residual, the original problem can be transformed into the following optimization problem: ； in, express Norm, Indicates unknown nodes to be optimized Location, It is a weighting factor. This represents the position offset error of the unknown node. This represents the maximum weighted residual representing the distance from the unknown node to the anchor node. Indicates the first The location of each anchor node Indicates the first Anchor nodes and unknown nodes The estimated distance between them Indicates the number of anchor nodes; Step 4.2: Iterative optimization using continuous convex approximation to estimate the location of unknown nodes, specifically: Following step 4.1, the non-convex constraints are relaxed to convex constraints, given the unknown nodes. Optimization initial value Iterative solution yields and will The initial value obtained from the optimization solution for the next iteration is... Iterate and optimize in this way until... Meets the accuracy threshold This leads to the following convex optimization problem: ； in, express Norm, Indicates transpose. Indicates unknown nodes to be optimized Location, It is a weighting factor. This represents the position offset error of the unknown node. This represents the maximum weighted residual representing the distance from the unknown node to the anchor node. Indicates the first The location of each anchor node Indicates unknown nodes to be optimized Initial position value, Indicates the first Anchor nodes and unknown nodes The estimated distance between them Indicates the number of anchor nodes.

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