A method for inferring wireless network topology based on spatio-temporal features

Abstract

The present invention relates to a method for inferring a wireless network topology based on spatio-temporal characteristics, including: setting up a sensor network in a target area; detecting the power of a non-cooperative network; dividing the target area into M preset grids; inputting the power of the preset grids into a neural network model to obtain the coordinates of non-cooperative nodes; obtaining the distance between two non-cooperative nodes according to the coordinates of the non-cooperative nodes; obtaining the start time and end time of the transmission information of each non-cooperative node according to the time information of the interaction between non-cooperative nodes; obtaining the mean value of the frame intervals and the variance of the frame intervals of each node pair; inputting the mean value of the frame intervals, the variance of the frame intervals, and the distance information of the node pairs into a trained classification model to obtain the connectivity relationship of each node pair. The method for inferring a wireless network topology based on spatio-temporal characteristics in the present invention combines node positioning and topology inference into a system to achieve topology inference when the positions of target nodes are unknown.

Description

Technical Field

[0001] The present invention belongs to the technical field of positioning and topology inference, and relates to a method for inferring a wireless network topology based on spatio-temporal features. Background Art

[0002] With the rapid development of information technology, everything has entered the era of interconnection, and the scale of the network is growing day by day, which makes network management difficult. Therefore, the intelligent analysis of network behavior is becoming more and more important.

[0003] In order to understand the structure of a communication network, a promising technology is to identify the structure of the network through sensing and inference. Topology inference can help identify network traffic, master the degree of user connection, and optimize and improve network security. For non-cooperative wireless networks, topology inference can mine intelligence and gain information advantages.

[0004] However, most of the existing topology inference algorithms infer the topology based on the known node positions, and the topology inference for unknown nodes has become a problem to be solved. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a method for inferring a wireless network topology based on spatio-temporal features. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0006] An embodiment of the present invention provides a method for inferring a wireless network topology based on spatio-temporal features. The non-cooperative topology inference method includes:

[0007] Step 1: Set up a sensor network in the target area, where the sensor network includes M sensor nodes randomly distributed;

[0008] Step 2: Use the sensor network to detect the power of the non-cooperative network in the target area, where the non-cooperative network includes N non-cooperative nodes;

[0009] Step 3: Divide the target area into M preset grids equal to the number of the sensor nodes, and determine the power of each preset grid by using the power detected by the sensor network;

[0010] Step 4: Input the power of the preset grid obtained in Step 3 into a trained neural network model to obtain the coordinate information of the non-cooperative nodes;

[0011] Step 5: Obtain the distance information between two non-cooperative nodes according to the coordinate information of the non-cooperative nodes determined in Step 4;

[0012] Step 6: Obtain the start time and end time of the transmission information of each non - cooperative node according to the time information of the interaction between the non - cooperative nodes in the target area detected by the sensor network;

[0013] Step 7: Obtain the mean value of the frame intervals and the variance of the frame intervals of each node pair according to the start time and end time of the transmission information of the non - cooperative nodes;

[0014] Step 8: Input the mean value of the frame intervals, the variance of the frame intervals, and the distance information of the node pairs into the trained classification model to obtain the connectivity relationship of each node pair.

[0015] In an embodiment of the present invention, the power detected by the i - th sensor node is:

[0016]

[0017] where p i,j represents the power detected by the i - th sensor node for the j - th non - cooperative node, p i,j =p j G t G r (λ / 4πR i,j ) 2 , where 1 ≤ i ≤ M, 1 ≤ j ≤ N, G t represents the antenna gain of the transmitting antenna, G r represents the antenna gain of the receiving antenna, λ represents the wavelength, and R i,j represents the distance between the i - th sensor node and the j - th non - cooperative node.

[0018] In an embodiment of the present invention, the power of the m - th preset grid is:

[0019]

[0020] where represents the power of the m - th preset grid, and B represents the number of sensors included in the m - th preset grid, where 1 ≤ m ≤ M.

[0021] In an embodiment of the present invention, the training method of the neural network model includes:

[0022] S1: Obtain a training set, and the training set includes a number of non - cooperative training nodes;

[0023] S2: Divide the area where the non - cooperative training nodes are located into H training grids of the same size, where H > M;

[0024] S3: Calculate the distance R i,j';

[0025] S4. According to the distance R i,j ', obtain the training power of the i-th sensor training node to the j-th non-cooperative training node;

[0026] S5. Input a number of input-output pairs (p (i) , x (i) ) into the neural network model to train the neural network model and obtain a trained neural network model, where p (i) is the training power of the non-cooperative training node, and x (i) is the training grid where the true position of the non-cooperative training node is located.

[0027] In an embodiment of the present invention, step 4 includes:

[0028] Step 4.1. Input the power of each preset grid into the trained neural network model to obtain the positioning result of the non-cooperative node, so as to determine the preset grid where the non-cooperative node is located.

[0029] Step 4.2. Take the center position of the preset grid where the non-cooperative node is located as the coordinate position of the non-cooperative node.

[0030] In an embodiment of the present invention, the distance information between two non-cooperative nodes is:

[0031]

[0032] Wherein, is the coordinate of the p-th non-cooperative node, is the coordinate of the q-th non-cooperative node, and d p,q represents the distance between the p-th non-cooperative node and the q-th non-cooperative node.

[0033] In an embodiment of the present invention, the data obtained by the sensor network detecting the p-th non-cooperative node is:

[0034]

[0035] Wherein, n represents the number of signals included in F p T represents the transpose of the matrix, represents the set of real numbers, represents a real matrix with n rows and 2 columns;

[0036] The i-th signal of the p-th non-cooperative node is:

[0037]

[0038] Wherein, represents the start time of the i-th signal transmission of the p-th non-cooperating node, represents the duration of the i-th signal of the p-th non-cooperating node.

[0039] In an embodiment of the present invention, the mean value of the frame interval is:

[0040]

[0041]

[0042] wherein, represents the mean value of the frame interval between the p-th non-cooperating node and the q-th non-cooperating node, represents the frame interval between the p-th non-cooperating node and the q-th non-cooperating node, represents the start time of the i-th signal transmission of the q-th non-cooperating node.

[0043] In an embodiment of the present invention, the variance of the frame interval is:

[0044]

[0045] wherein, represents the variance of the frame interval between the p-th non-cooperating node and the q-th non-cooperating node.

[0046] In an embodiment of the present invention, the connectivity relationship of each node pair is represented by an adjacency matrix A, and the adjacency matrix A is:

[0047] A = [a ij

[0048] wherein, non-cooperating node v i and non-cooperating node v j the link connection situation a ij is:

[0049]

[0050] wherein, 1 indicates that there is a connectivity relationship between non-cooperating node v i and non-cooperating node v j 0 indicates that there is no connectivity relationship between non-cooperating node v i and non-cooperating node v j does not exist.

[0051] Compared with the prior art, the beneficial effects of the present invention:

[0052] The wireless network topology inference method based on spatio-temporal characteristics of the present invention combines node positioning and topology inference into a system to achieve topology inference when the position of the target node is unknown.

[0053] ​The positioning method of the present invention uses machine learning to achieve the positioning of target nodes.

[0054] The topology inference method of the present invention proposes spatio-temporal features (the mean, variance of frame intervals, and distance between node pairs) as the basis for judging whether there is a communication relationship between nodes, and uses machine learning methods to quickly obtain the topology inference result.

[0055] Through the following detailed description with reference to the accompanying drawings, other aspects and features of the present invention become apparent. However, it should be understood that the drawings are only designed for the purpose of explanation and not as a limitation of the scope of the present invention, as it should refer to the appended claims. It should also be understood that, unless otherwise indicated, the drawings are not necessarily drawn to scale, and they are only intended to conceptually illustrate the structures and processes described herein. Description of the Drawings

[0056] Figure 1 It is a schematic flowchart of a wireless network topology inference method based on spatio-temporal features provided by an embodiment of the present invention;

[0057] Figure 2 It is a schematic diagram of a target topology with a sensor network provided by an embodiment of the present invention;

[0058] Figure 3 It is a system working block diagram of a wireless network topology inference method based on spatio-temporal features provided by an embodiment of the present invention;

[0059] Figure 4 It is a spatio-temporal feature map of a wireless network topology inference method based on spatio-temporal features provided by an embodiment of the present invention;

[0060] Figure 5 It is a CDF error cumulative distribution diagram of target node positioning in an embodiment of the present invention;

[0061] Figure 6 It is a schematic diagram of the inference accuracy of a topology inference algorithm in an embodiment of the present invention. Detailed Embodiments

[0062] The following further describes the present invention in detail with specific embodiments, but the embodiments of the present invention are not limited thereto.

[0063] Embodiment 1

[0064] Please refer to Figure 1 , Figure 1 It is a schematic flowchart of a wireless network topology inference method based on spatio-temporal features provided by an embodiment of the present invention. The present invention provides a wireless network topology inference method based on spatio-temporal features. The wireless network topology inference method includes steps 1 - step 8, where:

[0065] Step 1. Set up a sensor network in the target area. The sensor network includes M sensor nodes randomly distributed, where the positions of the sensor nodes are known.

[0066] Use the sensor network composed of M sensor nodes randomly distributed in the target area L to detect the power of the non - cooperative network in the target area L. The non - cooperative network includes N non - cooperative nodes.

[0067] In a specific embodiment, Step 1 may specifically include Step 1.1 - Step 1.2, where:

[0068] Step 1.1. Randomly set M sensor nodes in the target area L, where the positions of the sensor nodes are known

[0069] Specifically, please refer to Figure 2 , a schematic diagram of a non - cooperative network including sensor nodes provided by an embodiment of the present invention. The non - cooperative network is composed of N non - cooperative nodes, and the sensor network is composed of M sensor nodes and a sink node (the sink node is used to collect data sent by all other nodes and perform related processing, etc.). The M sensor nodes are randomly scattered in the target area, and the coordinates of the sensor nodes are T represents the transpose of a matrix, represents the set of real numbers, represents a real - valued matrix with M rows and 2 columns. The coordinates of the i - th sensor are

[0070] Step 2. Use the sensor network to detect the power of the non - cooperative network in the target area. The non - cooperative network includes N non - cooperative nodes.

[0071] Specifically, according to the energy distribution in the target area detected by M sensor nodes, each sensor node obtains the received power at its location.

[0072] In this embodiment, the sensor detects the power of the non - cooperative nodes and obtains p = [p 1 , p 2 , …, p i , …, p M . The power detected by the i - th sensor node is:

[0073]

[0074] where p i,j represents the power detected by the i - th sensor node for the j - th non - cooperative node, p i,j = p j G t G r (λ / 4πR i,j ) 2, where 1 ≤ i ≤ M, 1 ≤ j ≤ N, N represents the total number of non - cooperative nodes in the non - cooperative network, G t represents the antenna gain of the transmitting antenna, G r represents the antenna gain of the receiving antenna, λ represents the wavelength, R i,j represents the distance between the i - th sensor node and the j - th non - cooperative node.

[0075] Step 3: Divide the target area into M preset grids equal in number to the number of sensor nodes, and determine the power of each preset grid using the power detected by the sensor network.

[0076] Specifically, according to the number of sensors, divide the target area into M equal - sized preset grids, and then, based on the power data obtained by each sensor above and the known sensor position information, obtain the power data of each preset grid.

[0077] In this embodiment, from the power data detected by each sensor obtained above, obtain the power distribution of the M preset grids, that is The power of the m - th preset grid is expressed as: B represents the number of sensors included in the m - th preset grid, where 1 ≤ m ≤ M.

[0078] Step 4: Input the power of the preset grid obtained in Step 3 into the trained neural network model to obtain the coordinate information of the non - cooperative nodes.

[0079] In this embodiment, the training method of the neural network model includes:

[0080] S4.1: Obtain a training set, which includes a number of non - cooperative training nodes, and the non - cooperative training nodes are non - cooperative nodes for training.

[0081] Specifically, the training set consists of data that can monitor some non - cooperative nodes and obtain their positions.

[0082] S4.2: Divide the area where the non - cooperative training nodes are located into H training grids of the same size, where H > M.

[0083] S4.3: Calculate the distance R i,j ' between the i - th sensor training node and the j - th non - cooperative training node.

[0084] Specifically, the training set consists of data that can monitor some non - cooperative nodes and obtain their positions. Assume the coordinate of the j - th non - cooperative training node is z=(x j ,y j); Then calculate the distance between each non - cooperative training node and each sensor training node (i.e., the sensor nodes used for training). The distance \(R_{ij}\) between the \(i\) - th sensor training node and the \(j\) - th non - cooperative training node is: i,j ' is:

[0085]

[0086] Where: is the coordinate of the \(i\) - th sensor training node.

[0087] S4.4. According to the distance \(R_{ij}\) i,j ', obtain the training power of the \(i\) - th sensor training node to the \(j\) - th non - cooperative training node.

[0088] Specifically, substitute the distance \(R_{ij}\) i,j ' into the power formula in step 2 to obtain the received power of the \(i\) - th sensor training node to the \(j\) - th non - cooperative training node.

[0089] S4.5. Input a number of input - output pairs \((p_j,x_j)\) (i) , \(x_j\) (i) ) into the neural network model to train the neural network model and obtain a trained neural network model, where \(p_j\) (i) is the training power of the non - cooperative training node, and \(x_j\) (i) is the training grid where the true position of the non - cooperative training node is located.

[0090] Specifically, create combinations of non - cooperative training nodes. Suppose there are \(n\) non - cooperative training nodes, then the total number of possible combinations of non - cooperative training nodes appearing in each training grid is:

[0091]

[0092] Input the training set \(\{(p,x)\}=\{(p_{j_1},x_{j_1}),(p_{j_2},x_{j_2}),\cdots,(p_{j_m},x_{j_m})\}\) into the neural network model, where \((p_j,x_j)\) is an input - output pair, (1) , \(x_j\) (1) ), \((p_{j_2},x_{j_2})\) (2) , \(x_j\) (2) ), \(\cdots\), \((p_{j_m},x_{j_m})\) (n) , \(x_j\) (n) )} into the neural network model, where \((p_j,x_j)\) is an input - output pair, (i) , \(x_j\) (i) ) is the input - output pair, is the obtained power data, \(x_j\) (i) \(\in[0,1]\) H is the training grid where the true position of the non - cooperative node is located, and train the weight parameters of the neural network model to obtain a trained neural network model.

[0093] In a specific embodiment, step 4 may specifically include steps 4.1 - 4.2, where:

[0094] Step 4.1: Input the power of each preset grid into the trained neural network model to obtain the positioning result of the non-cooperative node, so as to determine the preset grid where the non-cooperative node is located.

[0095] Step 4.2: Take the center position of the preset grid where the non-cooperative node is located as the coordinate position of the non-cooperative node.

[0096] Specifically, when the sensor network detects the target area, power data p = [p 1 , p 2 , …, p i , …, p M of a scene to be measured is obtained. This data is used as the input of the trained neural network model. The neural network model outputs the positioning result of the non-cooperative node, that is, the non-cooperative node is located in a certain preset grid, and then the center position of the preset grid is used as the coordinate of the non-cooperative node, where r i = (x i , y i ) represents the coordinate of the i-th node.

[0097] Step 5: Obtain the distance information between two non-cooperative nodes according to the coordinate information of the non-cooperative nodes determined in Step 4.

[0098] Specifically, according to the positioning result of the target node (the target node is a non-cooperative node), the distance information between each non-cooperative node can be obtained. Taking the p-th non-cooperative node and the q-th non-cooperative node as an example, the distance between the two non-cooperative nodes is:

[0099]

[0100] Among them, is the coordinate of the p-th non-cooperative node, is the coordinate of the q-th non-cooperative node, and d p,q represents the distance between the p-th non-cooperative node and the q-th non-cooperative node.

[0101] Step 6: Obtain the start time and end time of the transmission information of each non-cooperative node according to the time information of the interaction between the non-cooperative nodes detected by the sensor network within the target area.

[0102] Specifically, after obtaining the positions of the target nodes in step 4, radio "fingerprint" recognition means can be applied in combination with information such as the frequency and interception time of the signals to distinguish the communication signals between the target nodes and determine which non-cooperating node emits the detected signal. Detecting non-cooperating nodes can effectively detect the start time and signal duration of the signals sent by the target nodes within a given area. The data obtained by detecting all non-cooperating nodes is represented as F = {F 1 , F 2 , …, F p , …, F N}, and the data obtained by detecting the p-th non-cooperating node is represented as:

[0103]

[0104] where n represents the number of signals included in F p .

[0105] The i-th signal of the p-th non-cooperating node is:

[0106]

[0107] where represents the start time of the i-th signal sent by the p-th non-cooperating node, represents the duration of the i-th signal of the p-th non-cooperating node.

[0108] Step 7: Obtain the mean and variance of the frame intervals of each node pair based on the start time and end time of the transmission information of the non-cooperating nodes. The mean and variance of the frame intervals and the distance between the node pairs are used as features to determine whether the node pairs are connected, where a node pair consists of two non-cooperating nodes.

[0109] Specifically, taking the p-th non-cooperating node and the q-th non-cooperating node as an example, the frame interval between the i-th signal of the p-th non-cooperating node and the i-th signal of the q-th non-cooperating node is represented as and its calculation formula is:

[0110]

[0111] The mean of the frame intervals between the p-th non-cooperating node and the q-th non-cooperating node is represented as and its calculation formula is:

[0112]

[0113] The variance of the frame intervals between the p-th non-cooperating node and the q-th non-cooperating node is represented as and its calculation formula is:

[0114]

[0115] Among them, represents the variance of the frame interval between the p-th non-cooperating node and the q-th non-cooperating node.

[0116] After that, the mean of the frame interval, the variance of the frame interval, and the distance between node pairs obtained in step 5 are used as features to determine whether the non-cooperating node pairs are connected. where C p = [c 1→p , c 2→p , …, c N→p T represents the spatio-temporal characteristics of the nodes other than the p-th non-cooperating node and the p-th non-cooperating node. The characteristics of the p-th non-cooperating node and the q-th non-cooperating node are

[0117] Step 8: Input the mean of the frame interval, the variance of the frame interval, and the distance information of the node pairs into the trained classification model to obtain the connectivity relationship of each node pair.

[0118] Specifically, the classification model is trained with a known training set, and then the mean of the frame interval, the variance, and the distance between the node pairs are used as features and put into the trained classification model to obtain the connectivity relationship of the node pairs, that is, the topological inference result of the entire network is obtained.

[0119] In this embodiment, the training method of the classification model includes:

[0120] The training set consists of data with known connectivity relationships of node pairs. The mean of the frame interval, the variance, and the distance between the node pairs in the training set are used as feature data, and the connectivity relationship of the node pairs is used as a label to obtain the trained classification model.

[0121] Specifically, the scenario with known non-cooperating node connectivity is used as the training scenario, and (C, A) = ((C 1 , A 1 ), (C 2 , A 2 ), …, (C i , A i ), …, (C I , A I )) is input into the classification model to be trained as the training set. Among them, (C i , A i ) is a set of training data, C i is the feature data of the i-th scenario, and A i is the adjacency matrix of the network topology in this scenario, and thus the trained classification model is obtained.

[0122] In a specific embodiment, the data of the non - cooperative network to be measured is fed into the trained classification model to obtain the connectivity relationship of each node pair, that is, the adjacency matrix A of the entire network is obtained.

[0123] Specifically, the adjacency matrix of the network is expressed as A = [a ij , where the link connection situation a i between the non - cooperative node v j and the non - cooperative node v ij is as follows:

[0124]

[0125] Among them, 1 indicates that there is a connectivity relationship between the non - cooperative node v i and the non - cooperative node v j , and 0 indicates that there is no connectivity relationship between the non - cooperative node v i and the non - cooperative node v j .

[0126] The characteristic data of the wireless network detected by the sensor is C pre , and it is input into the trained classification model to obtain the adjacency matrix A of the entire network.

[0127] The effectiveness of the wireless network topology inference method based on spatio - temporal features in this embodiment is verified through experiments below.

[0128] Specifically, please refer to Figure 3 , Figure 3 which is the system working block diagram of a wireless network topology inference method based on spatio - temporal features provided by an embodiment of the present invention. First, the energy distribution in the target area is detected by sensors to roughly locate the target nodes. Specifically, the power data detected by each sensor is put into the trained neural network model to obtain the positioning result of the target nodes. Then, through the effective detection of the target nodes, the start time and duration of the information sent by the target nodes are extracted, and the mean, variance of the frame interval between each node pair and the distance between node pairs are calculated as the features indicating whether there is a connectivity relationship between node pairs. The spatio - temporal feature map is as Figure 4 shown. The data of this network is input into the trained classification model to obtain the topology inference result of the entire network.

[0129] In this simulation, the antenna type of the target node is set as an omnidirectional antenna, the given area is divided into grids with the same number as the number of sensors, and the positioning error finally output by the trained network is as Figure 5 shown. The error is measured in units of the side length of the divided grid to obtain the CDF positioning error of the nodes. Figure 6 represents the inference accuracy of the target node topology inference algorithm.

[0130] The present invention proposes a method for inferring the wireless network topology based on spatio-temporal features. When the positions of non-cooperative nodes are determined, sensor nodes collect the power distribution in the target area and feed it into a trained neural network model to obtain the positioning results of the target nodes. The distance and frame interval information between nodes are used as features to judge whether there is a connectivity relationship between nodes, and then fed into a trained classification model to obtain the inferred topology.

[0131] The method for inferring the wireless network topology based on spatio-temporal features in the present invention combines node positioning and topology inference into a system to achieve topology inference when the position of the target node is unknown.

[0132] The positioning method of the present invention uses a machine learning method to achieve the positioning of the target node.

[0133] The topology inference method of the present invention proposes spatio-temporal features (the mean, variance of the frame interval, and the distance between node pairs) as the basis for judging whether there is a communication relationship between nodes, and uses a machine learning method to quickly obtain the topology inference result.

[0134] Embodiment 2

[0135] Another aspect of the present invention provides an electronic device, including a memory and a processor. A computer program is stored in the memory, and when the processor calls the computer program in the memory, the steps of the non-cooperative topology inference method based on the unknown node position as described in any one of the above embodiments are implemented.

[0136] In the description of the present invention, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, "a plurality" means two or more unless otherwise specifically defined.

[0137] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials, or characteristic data points described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic descriptions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristic data points described can be combined in a suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.

[0138] The above content is a further detailed description of the present invention in combination with specific preferred embodiments. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as falling within the protection scope of the present invention.

Claims

1. A method for inferring the wireless network topology based on spatio-temporal features, characterized in that, the method includes: Step 1: Set up a sensor network in the target area, where the sensor network includes M randomly distributed sensor nodes; Step 2: Use the sensor network to detect the power of the non-cooperative network in the target area, where the non-cooperative network includes N non-cooperative nodes; Step 3: Divide the target area into M preset grids equal to the number of sensor nodes, and determine the power of each preset grid using the power detected by the sensor network; Step 4: Input the power of the preset grids obtained in Step 3 into the trained neural network model to obtain the coordinate information of the non-cooperative nodes; Step 5: Obtain the distance information between two non-cooperative nodes according to the coordinate information of the non-cooperative nodes determined in Step 4; Step 6: According to the time information of the interaction between the non-cooperative nodes detected by the sensor network in the target area, obtain the start time and end time of the transmission information of each non-cooperative node; Step 7: Obtain the mean value of the frame interval and the variance of the frame interval of each node pair according to the start time and end time of the transmission information of the non-cooperative nodes; Step 8: Input the mean value of the frame interval, the variance of the frame interval, and the distance information of the node pairs into the trained classification model to obtain the connectivity relationship of each node pair.

2. The method for inferring the wireless network topology based on spatio-temporal features according to claim 1, characterized in that, the power detected by the i-th sensor node is: Among them, p i,j represents the power of the j-th non-cooperating node detected by the i-th sensor node, p i,j = p j G t G r (λ4πR i,j ) 2 , where 1 ≤ i ≤ M, 1 ≤ j ≤ N, G t represents the antenna gain of the transmitting antenna, G r represents the antenna gain of the receiving antenna, λ represents the wavelength, and R i,j represents the distance between the i-th sensor node and the j-th non-cooperating node detected.

3. The method for inferring the wireless network topology based on spatio-temporal features according to claim 2, characterized in that, the power of the m-th preset grid is: Among them, represents the power of the m-th preset grid, and B represents the number of sensors included in the m-th preset grid, where 1 ≤ m ≤ M.

4. The method for inferring the wireless network topology based on spatio-temporal features according to claim 1, characterized in that, the training method of the neural network model includes: S1: Obtain a training set, where the training set includes several non-cooperative training nodes; S2: Divide the area where the non-cooperative training nodes are located into H training grids of the same size, where H > M; S3. Calculate the distance R between the i-th sensor training node and the j-th non-cooperative training node i,j '; S4. According to the distance R i,j 'obtain the training power from the i-th sensor training node to the j-th non-cooperative training node; S5. Input a number of input-output pairs (p (i) , x (i) ) into the neural network model to train the neural network model and obtain a trained neural network model, where p (i) is the training power of the non-cooperative training node, and x (i) is the training grid where the true location of the non-cooperative training node is located.

5. The method for inferring the wireless network topology based on spatio-temporal features according to claim 1, characterized in that, Step 4 includes: Step 4.1: Input the power of each preset grid into the trained neural network model to obtain the positioning result of the non-cooperative nodes, so as to determine the preset grid where the non-cooperative nodes are located; Step 4.2: Take the center position of the preset grid where the non-cooperative nodes are located as the coordinate position of the non-cooperative nodes.

6. The method for inferring the wireless network topology based on spatio-temporal features according to claim 1, characterized in that, the distance information between two non-cooperative nodes is: Among them, is the coordinate of the p-th non-cooperating node, is the coordinate of the q-th non-cooperating node, and d p,q represents the distance between the p-th non-cooperating node and the q-th non-cooperating node.

7. The method for inferring the wireless network topology based on spatio-temporal features according to claim 1, characterized in that, the data obtained by the sensor network detecting the p-th non-cooperative node is: where n represents the number of signals contained in F p , T represents the transpose of the matrix, represents the set of real numbers, represents a real matrix with n rows and 2 columns; the i-th signal of the p-th non-cooperative node is: Among them, represents the start time of the i-th signal transmission of the p-th non-cooperating node, represents the duration of the i-th signal of the p-th non-cooperating node.

8. The method for inferring the wireless network topology based on spatio-temporal features according to claim 7, characterized in that, the mean value of the frame interval is: Among them, represents the mean of the frame intervals between the p-th non-cooperating node and the q-th non-cooperating node, represents the frame interval between the p-th non-cooperating node and the q-th non-cooperating node, represents the start time of the i-th signal transmission of the q-th non-cooperating node.

9. The method for inferring a wireless network topology based on spatio-temporal features according to claim 8, characterized in that, the variance of the frame interval is: Among them, represents the variance of the frame interval between the p-th non-cooperating node and the q-th non-cooperating node.

10. The method for inferring a wireless network topology based on spatio-temporal features according to claim 1, characterized in that, the connectivity relationship of each node pair is represented by an adjacency matrix A, and the adjacency matrix A is: A = [a ij ​ Among them, the non-cooperating node v i and the non-cooperating node v j 's link connection situation a ij is as follows: Among them, 1 indicates non - cooperative node v i There is a connectivity relationship with non - cooperative node v j and 0 indicates non - cooperative node v i There is no connectivity relationship with non - cooperative node v j ​

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