Mapping multi-hop positioning method driven by multi-dimensional skeleton information

Abstract

The invention belongs to the technical field of wireless networks, and discloses a multi-dimensional skeleton information driven mapping multi-hop positioning method, which comprises the following steps that: firstly, an anchor node collects actual distances, hop counts, weighted similarity coefficients and node degree variances between the anchor node and other anchor nodes and constructs a distance and multi-dimensional skeleton information matrix; then, centralization processing is carried out on the matrix, and dimensionality reduction is carried out on the matrix through PCA; thirdly, adaptively determining an optimal ridge parameter through an L-curve method by utilizing a ridge regression algorithm, and obtaining an optimal mapping model; acquiring the optimal mapping model by the unknown node through the anchor node with the least hop count, and estimating the distance between the unknown node and each anchor node by taking the multi-dimensional feature vector between the unknown node and each anchor node as input; and finally, improving a myxobacteria optimization algorithm by using staged mixed initialization, and estimating the position of an unknown node by using the improved method. The method provided by the invention is suitable for wireless network positioning tasks in a complex topology environment, and shows higher positioning precision and robustness.

Description

Technical Field

[0001] This invention belongs to the field of wireless network technology, specifically relating to a multi-dimensional skeleton information-driven mapping multi-hop positioning method. Background Technology

[0002] In wireless network applications, location information is not only crucial for efficient data acquisition and stable communication, but also for imbuing sensed data with clear spatial relationships and contextual meaning. Currently, integrating Global Navigation Satellite Systems (GNSS) is one of the mainstream methods for acquiring node location information. However, its applicability is poor in some complex environments, such as urban streets with tall buildings, mountain valleys, underground mines, and caves, where GNSS signals are easily blocked, leading to difficulties in signal reception and a significant decrease in the reliability of traditional positioning. Furthermore, configuring a GNSS receiver module for each node would significantly increase the cost of the positioning system, making it difficult to meet the practical needs of large-scale deployment.

[0003] To address this, the industry has offered a viable alternative: reducing reliance on direct distance measurements and indirectly inferring the relative distances between nodes through multi-hop communication mechanisms to achieve positioning. In the multi-hop positioning technology framework, anchor nodes with known locations are typically relied upon, while the remaining nodes with unknown locations are referred to as unknown nodes. Multi-hop positioning technology estimates the path lengths between nodes and, combined with the locations of the anchor nodes, infers the spatial locations of the unknown nodes, thus achieving autonomous positioning of nodes within a region without relying on external positioning systems. This effectively overcomes the limitations and high costs of GNSS in complex environments.

[0004] Multi-hop localization technology has attracted widespread attention due to its ability to achieve location awareness in complex environments without relying on expensive hardware. However, most existing multi-hop localization methods are based on an idealized assumption: the distance between any two nodes can be estimated by the number of hops in their routing paths. This assumption is reasonable in regular networks with uniform node distribution and near-straight communication paths, such as in open or unobstructed environments. However, in practical applications, such as in mountainous areas, cities, or caves with complex obstacles, the network structure is often highly irregular, and communication paths are greatly affected by terrain and obstructions, leading to a significant increase in the geometric deviation of routing paths between nodes. This severely impacts the accuracy and stability of localization results based on this assumption.

[0005] To alleviate the above problems, various improvement schemes have been proposed in the existing technology. For example, the ProximityDistance Map proposed in Reference 1 (PDM, Lim H, Hou J C. Distributed localization for anisotropic sensor networks[J]. ACM Transactions on Sensor Networks (TOSN), 2009, 5(2):1-26.) first constructs a mapping relationship between the number of hops between anchor nodes and the actual distance, and then estimates the distance between multi-hop nodes using this mapping relationship; finally, the estimated position of unknown nodes is calculated with the help of the least squares method. The PDM method proposed in Reference 1 improves the accuracy of distance measurement and positioning in complex obstacle areas to some extent. However, the PDM algorithm still has many limitations. On the one hand, hop count, as an approximate indicator of distance, suffers from low information granularity and is extremely sensitive to network structure and environment, especially in irregular networks where its accuracy is difficult to guarantee. On the other hand, PDM does not fully consider the difference in dimensions between hop count and distance when establishing the mapping relationship: hop count is a dimensionless topological feature that only reflects the number of connections between nodes, while distance has a definite physical unit. Directly establishing a function mapping can easily introduce modeling errors. In areas with uneven node density or weak connectivity, these errors may be further amplified, affecting the mapping accuracy and model robustness. In addition, in the position estimation stage, PDM and other methods still use the least squares method for coordinate solving, which is easily affected by the distribution of anchor nodes. When anchor nodes are collinear or unevenly distributed, the estimated position is prone to significant deviation, reducing the overall positioning reliability.

[0006] For example, Reference 2 (i.e., patent application CN113543021A) discloses a multi-hop localization method with resistance to anomaly estimation. In the position estimation stage, this method first analyzes the possible distribution area of ​​unknown nodes based on the bounding-box algorithm. On this basis, it further narrows the bounding box range with the help of virtual anchor nodes. This reduces the geometric ambiguity caused by the collinearity of anchor nodes by limiting the possible area where nodes may exist, thereby reducing the positioning error. However, this method is built on the basis of other algorithms to complete the distance measurement and does not specifically handle the error generated during the ranging process. Therefore, when the distance measurement accuracy of the underlying algorithm is poor, the method has a limited effect on improving the final positioning accuracy. The experimental results in Reference 2 also confirm this problem: for example, it implements position estimation on the ARFL method in the cited Reference 3 (Zaidi S, Assaf AE, Affes S, et al. Accurate Range-Free Localization in Multi-Hop Wireless SensorNetworks[J]. IEEE Transactions on Communications, 2016, 64(9): 3886–3900). Since Reference 3 itself has limitations in ranging accuracy, the improvement in positioning accuracy is not significant when the method proposed in Reference 2 is applied on this basis.

[0007] For example, Reference 4 (i.e., patent application CN115720326A) discloses a non-range-based localization method based on similarity measurement. This method uses the four nearest anchor nodes to construct a rectangular region to correct the geometric ambiguity caused by the collinearity of anchor nodes. Although it innovatively proposes a similarity distance measurement method, its effectiveness is heavily dependent on the distribution quality of the anchor nodes: if the anchor nodes do not tightly surround the unknown node, the ranging error will still increase significantly, and the original paper does not provide an effective countermeasure for this problem. In addition, the Gaussian inertial weighted bat optimization algorithm used in the position estimation stage is an earlier optimization strategy. Its search mechanism is relatively outdated, and its global exploration and local exploitation capabilities are insufficient, resulting in slow convergence speed and limited accuracy improvement in position estimation, which further restricts the improvement of overall localization performance.

[0008] Therefore, there is an urgent need for a robust localization method that can integrate multi-source information and take into account both physical constraints and topological features, in order to improve the performance of multi-hop localization in complex environments. Summary of the Invention

[0009] To address the aforementioned technical problems, this invention provides a multi-dimensional skeleton information-driven mapping multi-hop positioning method, which is suitable for wireless network positioning tasks in complex topology environments and has higher positioning accuracy and robustness.

[0010] The multi-dimensional skeleton information-driven mapping multi-hop localization method of the present invention includes the following steps: Step 1: Deploy several wireless nodes in the area to be located, including anchor nodes and unknown nodes. Set the node communication radius according to the node distribution area and the total number of nodes, and use the signal strength to determine the connectivity between nodes. Step 2: Obtain multi-dimensional skeleton information for anchor nodes, including the actual physical distance between anchor nodes, the corresponding number of hops, the weighted similarity, and the variance of node degree, to form a distance and multi-dimensional skeleton information matrix; Step 3: Center the distance and multidimensional skeleton information matrix data, and use principal component analysis (PCA) to reduce the dimensionality of the multidimensional skeleton information matrix data, taking the first k principal components; Step 4: Construct a multidimensional skeleton information and distance mapping model of the first k principal components using ridge regression, and select the optimal ridge parameters based on the L-curve method to obtain the optimal mapping model; Step 5: The unknown node obtains the optimal mapping model through the anchor node with the fewest hops, and uses the multi-dimensional feature vectors between the unknown node and each anchor node as input to obtain the estimated distance between the unknown node and each anchor node. Step 6: Using the estimated distance between the unknown node and the anchor node and the anchor node position information obtained in Step 5 as constraints, the improved slime mold optimization algorithm is used to predict the position of the unknown node.

[0011] Furthermore, step 1 specifically includes: Consider deploying n wireless nodes in a two-dimensional space, where m nodes have pre-defined location information and serve as anchor nodes, with their coordinates set as follows: The first set consists of nodes A and the second set consists of nodes U, which are unknown nodes to be located. The set U satisfies the following conditions: ; Each node has the same transmit power. The node communication radius *r* is set based on the node distribution area and the total number of nodes. The connectivity between any two nodes is determined using the logarithmic attenuation model, which describes the relationship between the received signal strength and distance between nodes. The logarithmic attenuation model is defined as follows: ,in Indicates the received signal strength. Let d be the signal strength received at a distance of 1 meter, and d be the distance between the two nodes. This is the path loss factor. These are random variables that follow a Gaussian distribution, reflecting the multipath effect; When the signal strength received by the node is higher than the strength corresponding to the set radius r If the two nodes can communicate directly, they are considered to be able to communicate directly; otherwise, they need to communicate indirectly through relay nodes in a multi-hop manner. The number of relay nodes on the communication link between nodes that are far apart is the number of hops between them. In order to ensure that all nodes in the monitoring area are interconnected while avoiding premature battery degradation caused by excessive transmission power, a communication radius is set. ;in, This is the total area of ​​the node deployment area; therefore, the node's transmit power is... .

[0012] Furthermore, step 2 specifically involves: Anchor node a broadcasts its own location to the network. And identification information, when other anchor nodes b (b is an element in set A, but b ≠ a) in the network receive this message, they record the minimum hop count between them. Then, it attached its own location information. The data is sent back to anchor node a; after a period of time, anchor node a can learn about its relationship with the others. The actual distance of each anchor node and corresponding jump number Meanwhile, the weighted similarity between anchor nodes a and b and node degree variance Also retrieved; weighted similarity and node degree variance are defined as follows: , in, This represents the set of relay nodes along the communication path between the anchor node and the node ab. Let i be the set of neighboring nodes of the previous hop of relay node i. This represents the number of common neighbor nodes adjacent to the relay node; Define the degree value of each relay node i in the path. Then the variance of the node degree of the path for: , in, This represents the average degree of the anchor node to the relay nodes along the ab communication path, i.e. .

[0013] In summary, anchor node a obtains the hop count with the other m-1 anchor nodes in the network. Weighted similarity Node degree variance and physical distance Then, construct the multidimensional skeleton vector: ; Subsequently, the anchor nodes exchange various multidimensional vectors to form a multidimensional skeleton information matrix, which is used as the training set, i.e.: and Among them, H, S, Let D be the hop count matrix, weighted similarity matrix, node degree variance matrix, and distance matrix among the m anchor nodes, respectively; their specific representations are as follows: , , , .

[0014] Furthermore, step 3 specifically involves: Step 3-1: Process the multidimensional skeleton information matrix Each column is centered to obtain a centered multidimensional skeleton matrix. : , in, and They represent The mean and standard deviation of the i-th column feature, Representation of the characteristic matrix The i-th column; Step 3-2: For the centralized multidimensional skeleton matrix Principal component analysis was performed, and the top k principal components were extracted as skeleton information. The result Z can be expressed as: ; Step 3-3: Analyze the distance matrix of the training set. Standardization and centralization are performed to obtain the centralized distance matrix. The specific handling method is as follows: , in, express The mean of the j-th column features.

[0015] Furthermore, step 4 specifically involves: Step 4-1: Select the optimal ridge parameters using the L-curve method, including: 1) Construct a candidate ridge parameter set: Define a set of ridge parameters λlist that is uniformly distributed in logarithmic space, with values ​​ranging from... Based on log-uniform selection One point; 2) For each Ridge regression is used to construct a multidimensional skeleton matrix containing a centralization. With the centralized distance matrix mapping model : , Where I is the identity matrix, that is, the elements on the diagonal of the matrix are all 1s. It is a matrix transpose; 3) Calculate the residual sum of squares (RSS) and the Frobenius norm of the model complexity, respectively: , ; 4) Calculate the angle between each candidate point on the L-curve: Based on the sum of squared residuals obtained in the previous step, construct a triplet. , , Constructing vectors in logarithmic coordinates and : , , based on and Calculate the included angle corresponding to this point. : , 5) Determine the optimal ridge parameters: Among all the included angles, select the point corresponding to the largest included angle as the inflection point of the L-curve; the corresponding λ value is the optimal ridge parameter. ; Step 4-2: Based on the obtained optimal ridge parameters To obtain the optimal multidimensional skeleton information and distance mapping model, i.e.: .

[0016] Furthermore, step 5 specifically includes: Step 5-1, Unknown Nodes To the nearest anchor node The application seeks to obtain the optimal multidimensional skeleton information and distance mapping model. ; Step 5-2, Unknown Nodes The multidimensional features collected during the initialization phase and their relationship with each anchor node a are combined into a test vector: , in, This represents the hop count vector from u to each anchor node. This represents the weighted structural similarity vector from u to each anchor node. This represents the variance vector of node degree from u to each anchor node; Step 5-3: Process the multidimensional feature vector After centralization, we get: , in, and Representing the training sample matrix respectively Mean and standard deviation for each column; Step 5-4: The centered test vector Projecting the data onto the low-dimensional principal component space extracted by principal component analysis obtained in step 4, the projection matrix used is the PCA transformation matrix. The projection result is: ; Step 5-5: Utilize the obtained mapping model The dimensionality-reduced feature vector As input, the predicted distances from the centered unknown node u to each anchor node are calculated: ; Steps 5-6: Add the mean of the training distance matrix to the predicted distance. The estimated distances between the unknown node u and each anchor node are obtained by reconstructing the data. , in, This is used to train the mean vector of each column of the distance matrix.

[0017] Furthermore, step 6 specifically includes: Step 6-1: Construct an optimization function with the objective of minimizing the deviation between the estimated distance and the actual distance; let the position of the unknown node u be... The position of anchor node a is The objective function is as follows: , in, and Let u represent the actual distance and the estimated distance from the unknown node u to the anchor node a, respectively. Step 6-2: Predict the location of unknown nodes using an improved slime mold optimization algorithm, including: 1) Generate an initial solution that accounts for 80% of the total population using a spatially uniform sampling method, and denote the lower boundary of the node distribution region as... The upper boundary is Then the coordinates of an individual in the population in the dim dimension Represented as: , in, Indicates the population size; Here, `dim` is the spatial uniformity sampling generation function; `dim` is the dimension. To round down, i.e., take the integer part that is not greater than... The largest integer; 2) Introduce chaotic sampling for local exploitation, generating local samples that account for 20% of the total population, including: Initialize a seed vector of dimension dim. , as the initial value of the chaotic mapping; using a chaotic iteration method, x is processed... In the next iteration, multiple chaotic perturbation vectors are generated. Where t is the number of iterations, To round up; In each iteration, the mean of the samples is sampled with spatial uniformity. Centered on, with Within a hypercube local search region of side length, generate chaotic sampling points: , in, Indicates product by components; Boundary corrections are applied to chaotic sampling points to ensure they remain within the domain: ; Step 6-3: Based on the initial position, iterative updates are performed using the food-approaching, food-enveloping, and oscillation mechanisms to search for the optimal position of unknown nodes; simultaneously, a convergence factor is used to balance local and global searches; the specific operations of food-approaching, food-enveloping, and oscillation mechanisms are as follows: 1) Approaching food: Individuals move towards food sources based on their fitness and the location of the globally optimal individual, thus achieving pheromone-guided searching; 2) Encapsulating food: Simulating slime molds to explore food sources by encapsulating them enhances the search for local regions in the solution space; 3) The oscillation mechanism introduces positional perturbations, enhancing the ability to escape local optima and increasing population diversity; Step 6-4: When the preset threshold is reached in the previous step, or when the fitness function value changes less than the threshold for several consecutive generations, the algorithm terminates; finally, it returns the position corresponding to the individual with the best fitness. , which serves as the estimated coordinates of the unknown node u.

[0018] The beneficial effects of this invention are as follows: The method described in this invention first constructs an anchor node structure feature matrix that comprehensively reflects the global topological characteristics of the network by collecting multi-dimensional skeleton information. This matrix not only depicts the connection relationships between nodes but also integrates multi-source information such as hop count, weighted similarity, and node degree variance in a high-dimensional feature space. This information effectively characterizes the connectivity and geometric distribution of nodes in the deployment area, thereby achieving accurate and effective modeling and estimation of distances between nodes. Subsequently, the matrix is ​​centered and dimensionality is reduced using principal component analysis (PCA), effectively removing redundant correlations between features, alleviating the ill-conditioned problem of high-dimensionality, and making the distance estimation results more stable and reliable. Through the above steps, this invention can obtain more accurate and less erroneous distance information between nodes while maintaining the integrity of the global network topology, providing a more accurate input basis for subsequent location estimation and global optimization. In the location estimation stage, this invention employs an improved slime mold optimization algorithm (SFO), which introduces a phased hybrid initialization strategy, combining globally uniform initialization with a perturbation enhancement mechanism. This strategy expands the search range and enhances global exploration capabilities in the initial stage, and converges to a refined solution region in the later stage, thereby significantly improving search stability and optimization accuracy. This approach effectively reduces the risk of the algorithm getting trapped in local optima. In summary, this invention achieves high-precision estimation of unknown node locations in complex topological environments through a collaborative design of structural feature modeling and intelligent optimization. Compared to traditional methods, this invention maintains high positioning accuracy and robustness in networks with uneven obstacle distribution, sparse nodes, or irregular topologies, demonstrating greater adaptability and practical value. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method described in this invention; Figure 2 This is a node distribution diagram; Figure 3 To utilize the neighbor relationship graph obtained in step 1 of this invention; Figure 4 for Figure 3 A diagram illustrating the process of selecting ridge parameters for L-curves under neighbor relationships; Figure 5 for Figure 3 A diagram showing the positioning results of the method proposed in this invention under neighbor relationships; Figure 6 for Figure 3 The localization result diagram of the method proposed in prior art literature 1 under the neighbor relationship; Figure 7 for Figure 3 The localization results of the algorithm in existing technical literature 2 and improved literature 3 under the neighbor relationship; Figure 8 for Figure 3 The localization results of the method proposed in existing technical literature 4 under the neighbor relationship; Figure 9 In order to be in Figure 3 Under the neighbor relationship shown, the distribution of the distance measurement error from the unknown node to the anchor node in the method proposed in this invention, the improved method of reference 3 in reference 1 and reference 2, and the method in reference 4 are as follows: Figure 10 In order to be in Figure 3 The diagram shows the localization completion rates of the method proposed in this invention, the improved methods of the algorithm in reference 3 in references 1 and 2, and the method proposed in reference 4, under the neighbor relationships presented. Figure 11 In order to be in Figure 3 The location error (RMSE) distribution of the proposed method, the improved algorithm of reference 3 in references 1 and 2, and the proposed method in reference 4 are shown under the neighbor relationship and the number of anchor nodes changes. Detailed Implementation

[0020] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0021] like Figure 1 As shown, this invention provides a multi-dimensional skeleton information-driven mapping multi-hop localization method, comprising the following steps: Step 1: Deploy several wireless nodes in the area to be located, including anchor nodes and unknown nodes. Then, set the node communication radius based on the node distribution area and the total number of nodes, and use the signal strength to determine the connectivity between nodes. Step 2: During the network initialization phase, anchor nodes acquire multi-dimensional skeleton information, including the actual physical distance between anchor nodes, the corresponding number of hops, the weighted similarity, and the variance of node degree, to form a distance and multi-dimensional skeleton information matrix. Step 3: Center the distance and multidimensional skeleton information matrix data, and use principal component analysis to reduce the dimensionality of the multidimensional skeleton information matrix data, taking the first k principal components; Step 4: Construct a multidimensional skeleton information and distance mapping model of the first k principal components using ridge regression, and select the optimal ridge parameters based on the L-curve method to obtain the optimal mapping model; Step 5: The unknown node obtains the optimal mapping model obtained in Step 4 through the anchor node with the fewest hops, and uses the multi-dimensional feature vector between it and each anchor node as input to obtain the estimated distance between it and each anchor node. Step 6: Using the estimated distance between the unknown node and the anchor node and the anchor node position information obtained in Step 5 as constraints, the improved slime mold optimization algorithm with a phased hybrid initialization scheme is used to predict the position of the unknown node.

[0022] like Figure 2 and Figure 3 As shown, a 400m × 400m area was selected, and 400 wireless nodes were randomly deployed. Due to obstacles in the area, a Z-shaped network topology was ultimately formed. Figure 2 , Figure 3 The "rectangle" markers represent anchor nodes, i.e., nodes with known locations, totaling 20; while the "solid circles" represent ordinary nodes with unknown actual locations, totaling 380. All nodes are equipped with omnidirectional antennas, and due to energy constraints, the communication radius of all nodes is set to be consistent, and the following conditions are met: . Figure 3 Showing based on Figure 2 The diagram shows the network connection structure formed by node distribution and communication radius limitations. A "connection" indicates that the physical distance between two nodes does not exceed the communication radius, enabling direct communication. If the distance between nodes is greater, relay nodes are needed to complete information transmission in a multi-hop manner.

[0023] In step 2, anchor nodes acquire multi-dimensional information during network initialization, including the actual physical distance between them, the corresponding hop count, weighted similarity, and node degree variance. Combined with... Figure 2 , Figure 3 The example shown is a matrix. The size is 20×20; multidimensional information matrix The size is 20×60.

[0024] In step 3, principal component analysis (PCA) is used to reduce the dimensionality of the multidimensional information between the anchor nodes, and the first k=10 principal components are selected, that is, the size of the matrix Z obtained after PCA is 20×10.

[0025] Step 4, the process of selecting the optimal ridge parameters using the L-curve method, includes setting a set of ridge regression parameters that are uniformly distributed in logarithmic space. The value range is

[10] . -3 , 10 +3 Based on a logarithmically uniform selection of 100 points, the selected results... =0.61, the selected range and selection results are as follows Figure 4 As shown.

[0026] In step 5, the unknown node obtains a multidimensional information matrix with the anchor node during network initialization. Its size is 1×3, and it is then centered, projected to a low-dimensional principal component space, and input into the optimal model. Obtain the predicted distance and add the mean. Restore the estimated distance from the unknown node to the anchor node. Figure 9 Error distribution diagram for estimating the distance from the unknown node to the anchor node.

[0027] In step 6, an improved slime mold optimization algorithm is used to predict the location of unknown nodes. The population size in the algorithm... Maximum number of iterations Spatial homogeneity sampling was performed using Latin Hypercube Sampling (LHS), while chaotic sampling was performed using Tent. Figure 3 The location results of the distribution are as follows Figure 5 As shown. Figure 5 The "hollow circles" represent the estimated positions of unknown nodes, and the length of the connecting lines between them and the corresponding "solid circles" represents the estimation error. A longer connecting line indicates a larger error, and vice versa. For With 2 sampling points in a two-dimensional space (dim=2), the sample points generated by LHS can be represented as follows: , in, for A random permutation (corresponding to the interval order of the j-th dimension). For uniform random perturbation, .

[0028] The individual coordinates mapped to the actual coordinate boundary node deployment area are: , Building upon LHS sampling, Tent mapping sampling is further introduced for local development. The number of samples in this mapping sampling is... .

[0029] Initialize a dimension as seed vector It uses Tent mapping for iteration, mapping each component independently (represented component-by-component as...). , )conduct In the next iteration, the mapping is defined as: , Commonly used parameters are taken Therefore, the denominators are 0.7 and 0.3 respectively.

[0030] The result Mapped to the spatially uniform sample mean Centered on, with side length as Within the hypercube local region: , in, Indicates product by components;

[0031] Finally, boundary corrections are applied to the generated points to ensure they fall within the defined domain: .

[0032] To quantitatively and objectively assess positioning performance, the case study uses Root Mean Square Error (RMSE) to quantify positioning error. The formula for RMSE is as follows: , in, and These are the actual location and the estimated location of the node to be located, respectively.

[0033] based on Figure 3 The network configuration, and the positioning results obtained by the method proposed in this invention are as follows: Figure 5 As shown, its RMS is 30.55.

[0034] The localization results obtained by the PDM method proposed by Lim et al. in Reference 1 are as follows: Figure 6 Its RMSE is 64.89. Figure 6 The positioning results within the Chinese box deviate significantly from the actual positions of the corresponding unknown nodes because the least squares method used in this approach is highly sensitive to the spatial distribution of anchor nodes. When unknown nodes are approximately collinear with the anchor nodes used for positioning, the positioning results often become unstable, resulting in the less-than-ideal positioning results in Reference 1.

[0035] Reference 2 improves upon the algorithm in Reference 3 to obtain the localization results, as shown below. Figure 7 Its RMSE is 90.74. This method only improves the unknown node estimation process of existing algorithms, but when the measurement distance error from the unknown node to the anchor node is large, the method in reference 2 has limited improvement on the final positioning.

[0036] The localization results in Reference 4 are as follows Figure 8 Its RMSE is 43.16. Reference 4 defines a sub-region for each unknown node based on the inventors' empirical values. This sub-region is smaller than the entire node deployment area, thus making the Gaussian inertial weight-based bat optimization search for unknown node locations more accurate. However, the search optimization method used, namely Gaussian inertial weight-based bat optimization, is an earlier proposed optimization strategy. Its search mechanism is relatively outdated, lacking global exploration and local development capabilities, resulting in slow convergence speed and limited accuracy improvement in location estimation. Figure 8 The location found by node 94 is far from its true location.

[0037] Figure 9 In order to be in Figure 3Under the neighbor relationships shown, the distribution of ranging errors from unknown nodes to anchor nodes is compared between the proposed method of this invention, the improved methods of Reference 3 in References 1 and 2, and the method in Reference 4. It is evident that the error distribution of the proposed method is more concentrated. For quantitative analysis, Table 1 presents two quantitative analysis parameters—standard deviation and mean absolute error—to measure the four positioning methods. The mean absolute error reflects the typical magnitude of the ranging error, while the standard deviation reveals the degree of error dispersion and the risk of outliers. The proposed method maintains a low mean absolute error while also exhibiting a significantly lower standard deviation than the comparative algorithms. This indicates that the proposed algorithm not only has high ranging accuracy but also good stability and stronger robustness to outliers, laying a reliable foundation for subsequent high-precision position estimation.

[0038] Table 1 Statistical Data

[0039] Figure 10 In order to be in Figure 3 The diagram shows the localization completion rates of the proposed method, the improved methods of Reference 3 (based on Reference 1 and Reference 2), and the method proposed in Reference 4, under the neighbor relationships presented. For qualitative analysis, two evaluation metrics are introduced:

[0040] Relative Positioning Error (RPE): This metric represents the deviation between the predicted and actual positions of an unknown node, and is normalized by the node's communication radius r, defined as follows: ; Complete Positioning Ratio (CPR): This metric represents the predicted position. With real location The number of unknown nodes whose deviation does not exceed the communication radius r accounts for a certain percentage of the total number of unknown nodes. The ratio is defined as: , in, It is a counter function.

[0041] Figure 10 Show, when When the proportion of unknown nodes whose positioning error RMSE is less than the communication radius r is reached, the proportion of unknown nodes in the method proposed in this invention is 79.21%, which is significantly higher than the improved methods of Reference 1 and Reference 2 on Reference 3, and the method in Reference 4. Specifically, the RPE of Reference 1 is 27.37%, the RPE of the improved method of Reference 2 on Reference 3 is 13.95%, and the RPE of Reference 1 is 65.79%. This also demonstrates that the method proposed in this invention achieves faster positioning convergence and higher positioning accuracy.

[0042] Figure 11 The simulation results (based on step 1) are presented with 400 nodes randomly distributed multiple times in a Z-shaped network. The figure shows the distribution of the localization error (RMSE) after running the method of this invention, the improved method of reference 1, the improved method of reference 2 to reference 3, and the method of reference 4 a total of 120 times under different anchor node ratios. Figure 11 A composite chart combining half-violin plots, scatter plots, and box plots was used to illustrate the RMSE distribution of each method. It can be observed that the RMSE value distribution of the method of this invention is more concentrated and the median is lower, indicating that it possesses both higher positioning accuracy and stability. This conclusion is further supported by the specific statistical characteristics in Table 2: in both the median reflecting accuracy and the quartile interval reflecting stability, the present invention outperforms the other three comparative methods.

[0043] Table 2 Statistical characteristics

[0044] The above description is merely a preferred embodiment of the present invention and is not intended to further limit the present invention. All equivalent changes made based on the description and drawings of the present invention are within the protection scope of the present invention.

Claims

1. A multi-dimensional skeleton information-driven mapping multi-hop localization method, characterized in that, Includes the following steps: Step 1: Deploy several wireless nodes in the area to be located, including anchor nodes and unknown nodes. Set the node communication radius according to the node distribution area and the total number of nodes, and use the signal strength to determine the connectivity between nodes. Step 2: Obtain multi-dimensional skeleton information for anchor nodes, including the actual physical distance between anchor nodes, the corresponding number of hops, the weighted similarity, and the variance of node degree, to form a distance and multi-dimensional skeleton information matrix; Step 3: Center the distance and multidimensional skeleton information matrix data, and use principal component analysis to reduce the dimensionality of the multidimensional skeleton information matrix data, taking the first k principal components; Step 4: Construct a multidimensional skeleton information and distance mapping model of the first k principal components using ridge regression, and select the optimal ridge parameters based on the L-curve method to obtain the optimal mapping model; Step 5: The unknown node obtains the optimal mapping model through the anchor node with the fewest hops, and uses the multi-dimensional feature vectors between the unknown node and each anchor node as input to obtain the estimated distance between the unknown node and each anchor node. Step 6: Using the estimated distance between the unknown node and the anchor node and the anchor node position information obtained in Step 5 as constraints, the improved slime mold optimization algorithm is used to predict the position of the unknown node.

2. The multi-dimensional skeleton information-driven mapping multi-hop localization method according to claim 1, characterized in that, Step 1 is as follows: Consider deploying n wireless nodes in a two-dimensional space, where m nodes have pre-defined location information and serve as anchor nodes, with their coordinates set as follows: This forms set A; The remaining unknown nodes to be located form a set U, and satisfy the following condition: ; Each node has the same transmit power. The node communication radius r is set based on the node distribution area and the total number of nodes. The relationship between the received signal strength and distance between nodes is described by the logarithmic attenuation model. The connectivity between any two nodes is then determined. If the signal strength received by a node is higher than the signal strength received at a set radius r, then the two are considered to be able to communicate directly. Otherwise, indirect communication must be achieved through relay nodes in a multi-hop manner.

3. The multi-dimensional skeleton information-driven mapping multi-hop localization method according to claim 2, characterized in that, Step 2 is as follows: Anchor node a broadcasts its own location to the network. The message includes identification information, and other anchor nodes (b) in the network receive the message and record the minimum hop count between them. Then, it attached its own location information. Return the result to anchor node a; where b is an element in set A, b ≠ a; the actual distance between anchor node a and anchor node b is: ， Weighted similarity between anchor nodes a and b for: ， in, This represents the set of relay nodes along the communication path between the anchor node and the node ab. Let i be the set of neighboring nodes of the previous hop of relay node i. This represents the number of common neighbor nodes adjacent to the relay node; Define the degree value of each relay node i in the path. Then the variance of the node degree of the path for: ， in, This represents the average degree of the anchor node to the relay nodes along the ab communication path, i.e. ; Anchor node 'a' obtains the hop count between itself and the other m-1 anchor nodes in the network. Weighted similarity Node degree variance and physical distance Construct a multidimensional skeleton vector: ； Anchor nodes exchange various multidimensional vectors to form a multidimensional skeleton information matrix, which is then used as the training set. and Among them, H, S, Let D be the hop count matrix, weighted similarity matrix, node degree variance matrix, and distance matrix among the m anchor nodes, respectively; the specific representation is as follows: ， ， ， 。 4. The multi-dimensional skeleton information-driven mapping multi-hop localization method according to claim 2, characterized in that, Step 3 specifically involves: Step 3-1: Process the multidimensional skeleton information matrix Each column is centered to obtain a centered multidimensional skeleton matrix. : ， in, and They represent The mean and standard deviation of the i-th column feature, Representation of the characteristic matrix The i-th column; Step 3-2: For the centralized multidimensional skeleton matrix Principal component analysis was performed, and the top k principal components were extracted as skeleton information. The result Z can be expressed as: ； Step 3-3: Analyze the distance matrix of the training set. Standardization and centralization are performed to obtain the centralized distance matrix. The specific handling method is as follows: ， in, express The mean of the j-th column features.

5. The multi-dimensional skeleton information-driven mapping multi-hop localization method according to claim 2, characterized in that, Step 4 is as follows: Step 4-1: Select the optimal ridge parameters using the L-curve method, including: 1) Construct a candidate ridge parameter set: Define a set of ridge parameters λlist that is uniformly distributed in logarithmic space, with values ​​ranging from... Based on log-uniform selection One point; 2) For each Ridge regression is used to construct a multidimensional skeleton matrix containing a centralization. With the centralized distance matrix mapping model : ， Where I is the identity matrix, that is, the elements on the diagonal of the matrix are all 1s. It is a matrix transpose; 3) Calculate the residual sum of squares (RSS) and the Frobenius norm of the model complexity, respectively: ， ； 4) Calculate the angle between each candidate point on the L-curve: Based on the sum of squared residuals obtained in the previous step, construct a triplet. , , Constructing vectors in logarithmic coordinates and : ， ， based on and Calculate the included angle corresponding to this point. : ， 5) Determine the optimal ridge parameters: Among all the included angles, select the point corresponding to the largest included angle as the inflection point of the L-curve; the corresponding λ value is the optimal ridge parameter. ; Step 4-2: Based on the obtained optimal ridge parameters To obtain the optimal multidimensional skeleton information and distance mapping model, i.e.: 。 6. The multi-dimensional skeleton information-driven mapping multi-hop localization method according to claim 5, characterized in that, Step 5 specifically involves: Step 5-1, Unknown Nodes To the nearest anchor node The application seeks to obtain the optimal multidimensional skeleton information and distance mapping model. ; Step 5-2, Unknown Nodes The multidimensional features collected during the initialization phase and their relationship with each anchor node a are combined into a test vector: ， in, This represents the hop count vector from u to each anchor node. This represents the weighted structural similarity vector from u to each anchor node. This represents the variance vector of node degree from u to each anchor node; Step 5-3: Process the multidimensional feature vector After centralization, we get: ， in, and Representing the training sample matrix respectively Mean and standard deviation for each column; Step 5-4: The centered test vector Projecting the data onto the low-dimensional principal component space extracted by principal component analysis obtained in step 4, the projection matrix used is the PCA transformation matrix. The projection result is: ， Step 5-5: Utilize the obtained mapping model The dimensionality-reduced feature vector As input, the predicted distances from the centered unknown node u to each anchor node are calculated: ， Steps 5-6: Add the mean of the training distance matrix to the predicted distance. The estimated distances between the unknown node u and each anchor node are obtained by reconstructing the data. ， in, This is used to train the mean vector of each column of the distance matrix.

7. The multi-dimensional skeleton information-driven mapping multi-hop localization method according to claim 1, characterized in that, Step 6 specifically involves: Step 6-1: Construct an optimization function with the objective of minimizing the deviation between the estimated distance and the actual distance; let the position of the unknown node u be... The position of anchor node a is The objective function is as follows: ， in, and Let u represent the actual distance and the estimated distance from the unknown node u to the anchor node a, respectively. Step 6-2: Predict the location of unknown nodes using an improved slime mold optimization algorithm, including: 1) Generate an initial solution that accounts for 80% of the total population using a spatially uniform sampling method, and denote the lower boundary of the node distribution region as... The upper boundary is Then the coordinates of an individual in the population in the dim dimension Represented as: ， in, Indicates the population size; Here, `dim` is the spatial uniformity sampling generation function; `dim` is the dimension. To round down, i.e., take the integer part that is not greater than... The largest integer; 2) Introduce chaotic sampling for local exploitation, generating local samples that account for 20% of the total population, including: Initialize a seed vector of dimension dim. , as the initial value of the chaotic mapping; using a chaotic iteration method, x is processed... In the next iteration, multiple chaotic perturbation vectors are generated. Where t is the number of iterations, To round up; In each iteration, the mean of the samples is sampled with spatial uniformity. Centered on, with Within a hypercube local search region of side length, generate chaotic sampling points: ， in, Indicates product by components; Boundary corrections are applied to chaotic sampling points to ensure they remain within the domain: ； Step 6-3: Based on the initial position, iteratively update the search for the optimal position of the unknown node by considering the food-oriented, food-enveloping, and oscillation mechanisms; at the same time, combine the convergence factor to regulate the balance between local and global search. Step 6-4: When the preset threshold is reached in the previous step, or when the fitness function value changes less than the threshold for several consecutive generations, the algorithm terminates; finally, it returns the position corresponding to the individual with the best fitness. , which serves as the estimated coordinates of the unknown node u.

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