Wireless network cooperative positioning method and device for dense to-be-positioned nodes

Abstract

The invention discloses a wireless network cooperative positioning method and device for dense to-be-positioned nodes, and relates to the technical field of communication networks and navigation positioning, and the method comprises the steps that a target node obtains a distance measurement result under a current time slot; constructing a local factor graph calculation model according to the position estimation of the previous time slot, the current internal and external ranging results and the position information of the adjacent nodes; performing approximate processing on the time domain message function and the space domain message function to obtain parameter expressions of corresponding messages; correcting the parameter expression of the airspace message by using a pre-trained graph neural network model; and according to a message passing rule, combining the time domain message with the optimized space domain message, determining position posterior probability distribution of the target node in the current time slot, and outputting a mean value of the position posterior probability distribution as a position estimation result. According to the method, time sequence prior information is fused, parameter expression is carried out on the message by adopting an exponential polynomial, the spatial domain message is corrected by introducing a graph neural network, and both positioning precision and calculation efficiency are considered.

Description

Technical Field

[0001] The present application relates to the technical fields of communication networks and navigation positioning, and particularly to a wireless network cooperative positioning method and device for densely located nodes to be positioned. Background Art

[0002] Cooperative positioning technology is an extension of traditional wireless positioning methods. It not only considers the relationship between anchor nodes and unknown nodes, but also allows any two unknown nodes to obtain measurement data from each other through communication, thereby improving positioning accuracy and robustness. In traditional positioning methods, the position of an unknown node is mainly determined by known nodes, while in cooperative positioning, the nodes are in a peer-to-peer relationship and can jointly participate in measurements, using redundant information to improve the position estimate, thus improving the accuracy of the entire system. Cooperative positioning has important applications in the positioning of wireless sensor network nodes, especially suitable for solving the obstacle problem between mobile terminals and base stations. Cooperative positioning algorithms mainly include centralized positioning and distributed positioning. Centralized positioning is to transmit measurement data to a central node for calculation, with high accuracy but large communication and calculation costs. Distributed positioning is to calculate relative positions using local information and achieve network-wide synchronization through a small amount of communication, which is suitable for large-scale networks. The development of 5G technology also provides strong support for cooperative positioning, enabling it to well solve the problem of network heterogeneity and realize the sharing of positioning results among different devices and networks. Common cooperative positioning technologies include Wi-Fi positioning, Bluetooth positioning, ultra-wideband positioning, etc.

[0003] The prior art with the name of "A Message Passing and Cooperative Positioning Method Based on a Factor Graph Model" constructs a cooperative positioning framework based on positioning reference signals, and the receiving end uses the observed time difference of arrival technology for rough calculation of the initial position. Subsequently, a dimensionality reduction algorithm is used to decompose the three-dimensional positioning problem into parameter estimation problems of three one-dimensional branches, and the factor graph after dimensionality reduction is called a mapped factor graph. Based on the factor graph model, terminal nodes and anchor nodes perform the transmission of position messages and multi-layer iterations to achieve the solution of more terminal positions, effectively overcoming the problem of high interruption probability caused by insufficient positioning nodes.

[0004] However, this technology still has deficiencies in positioning accuracy and calculation efficiency in an environment where nodes are densely distributed. Summary of the Invention

[0005] The purpose of the present application is to provide a wireless network cooperative positioning method and device for densely located nodes to be positioned, which can improve calculation efficiency and achieve high-precision positioning in a dense network.

[0006] To achieve the above object, the present application provides the following solutions:

[0007] In a first aspect, the present application provides a wireless network cooperative positioning method for dense nodes to be located, including:

[0008] The target node obtains the distance measurement results in the current time slot, where the target node refers to any node to be located in the wireless network, the wireless network includes several nodes to be located and anchor nodes, the anchor nodes are nodes with known location information, the distance measurement results include external measurement results and internal measurement results, the external measurement results are the distance measurement values of the cooperative positioning nodes within the communication range of the target node relative to the target node, the internal measurement results are the measurement values of the self-moving distance of the target node from the previous time slot to the current time slot, and the cooperative positioning nodes include other nodes to be located and anchor nodes that communicate with the target node;

[0009] The target node obtains an initial estimated value of the current position according to the internal measurement result and the position parameter value of the previous time slot, and takes the initial estimated value as a reference point to respectively approximate the time-domain message function and the space-domain message function related to the local factor graph, and obtains the time-domain message approximate expression and the space-domain message approximate expression near the initial estimated value, where the time-domain message function is a specific function expression corresponding to the internal measurement result, and the space-domain message function is a specific function expression corresponding to the external measurement result;

[0010] Calculate the time-domain message and the space-domain message respectively according to the time-domain message approximate expression and the space-domain message approximate expression;

[0011] Use the pre-trained graph neural network model to correct the space-domain message to obtain the corrected space-domain message;

[0012] Based on the time-domain message and the corrected space-domain message, construct a local factor graph calculation model of the target node;

[0013] The target node fuses the time-domain message and the corrected space-domain message according to the message passing rule in the local factor graph calculation model to obtain the posterior probability distribution of the current position of the target node;

[0014] Calculate the position estimation result of the target node in the current time slot according to the posterior probability distribution.

[0015] In a second aspect, the present application provides a wireless network cooperative positioning method for dense nodes to be located, including:

[0016] The target node obtains the distance measurement results in the current time slot. Herein, the target node refers to any node to be located in the wireless network. The wireless network includes several nodes to be located and anchor nodes, and the anchor nodes are nodes with known location information. The distance measurement results include external measurement results and internal measurement results. The external measurement results are the distance measurement values of the cooperative positioning nodes within the communication range of the target node relative to the target node, and the internal measurement results are the measurement values of the self-moving distance of the target node from the previous time slot to the current time slot. The cooperative positioning nodes include other nodes to be located and anchor nodes that communicate with the target node;

[0017] The target node obtains an initial estimate value of the current position according to the internal measurement result and the position parameter value of the previous time slot, and takes the initial estimate value as a reference point to respectively approximate the time-domain message function and the space-domain message function related to the local factor graph, and obtains the time-domain message approximate expression and the space-domain message approximate expression near the initial estimate value. Herein, the time-domain message function is a specific function expression corresponding to the internal measurement result, and the space-domain message function is a specific function expression corresponding to the external measurement result;

[0018] Calculate the time-domain message and the space-domain message respectively according to the time-domain message approximate expression and the space-domain message approximate expression;

[0019] Use the pre-trained graph neural network model to correct the time-domain message to obtain the corrected time-domain message;

[0020] Based on the corrected time-domain message and the space-domain message, construct the local factor graph calculation model of the target node;

[0021] The target node fuses the corrected time-domain message and the space-domain message according to the message passing rule in the local factor graph calculation model to obtain the posterior probability distribution of the current position of the target node;

[0022] Calculate the position estimation result of the target node in the current time slot according to the posterior probability distribution.

[0023] In a third aspect, the present application provides a wireless network cooperative positioning method for dense nodes to be located, including:

[0024] The target node obtains the distance measurement results in the current time slot. Here, the target node refers to any node to be located in the wireless network. The wireless network includes several nodes to be located and anchor nodes. The anchor nodes are nodes with known location information. The distance measurement results include external measurement results and internal measurement results. The external measurement results are the distance measurement values of the cooperative positioning nodes within the communication range of the target node relative to the target node. The internal measurement results are the measurement values of the self-movement distance of the target node from the previous time slot to the current time slot. The cooperative positioning nodes include other nodes to be located and anchor nodes that communicate with the target node;

[0025] The target node obtains an initial estimate of the current position based on the internal measurement results and the position parameter values of the previous time slot, and takes the initial estimate as a reference point to approximately process the time-domain message function and the space-domain message function related to the local factor graph respectively, obtaining the time-domain message approximate expression and the space-domain message approximate expression near the initial estimate. Here, the time-domain message function is a specific function expression corresponding to the internal measurement results, and the space-domain message function is a specific function expression corresponding to the external measurement results;

[0026] Calculate the time-domain message and the space-domain message respectively according to the time-domain message approximate expression and the space-domain message approximate expression;

[0027] Use the pre-trained graph neural network model to correct the time-domain message and the space-domain message respectively, obtaining the corrected time-domain message and the corrected space-domain message;

[0028] Based on the corrected time-domain message and the corrected space-domain message, construct a local factor graph calculation model of the target node;

[0029] The target node fuses the corrected time-domain message and the corrected space-domain message according to the message passing rules in the local factor graph calculation model, obtaining the posterior probability distribution of the current position of the target node;

[0030] Calculate the position estimation result of the target node in the current time slot according to the posterior probability distribution.

[0031] In a fourth aspect, the present application provides a computer device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor. The processor executes the computer program to implement the wireless network cooperative positioning method for dense nodes to be located described in the first aspect above, or the wireless network cooperative positioning method for dense nodes to be located described in the second aspect above, or the wireless network cooperative positioning method for dense nodes to be located described in the third aspect above.

[0032] Fifth aspect, the present application provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the wireless network cooperative positioning method for dense nodes to be located described in the first aspect above, or the wireless network cooperative positioning method for dense nodes to be located described in the second aspect above, or the wireless network cooperative positioning method for dense nodes to be located described in the third aspect above.

[0033] Sixth aspect, the present application provides a computer program product, including a computer program. When the computer program is executed by a processor, it implements the wireless network cooperative positioning method for dense nodes to be located described in the first aspect above, or the wireless network cooperative positioning method for dense nodes to be located described in the second aspect above, or the wireless network cooperative positioning method for dense nodes to be located described in the third aspect above.

[0034] According to the specific embodiments provided by the present application, the following technical effects are disclosed in the present application:

[0035] The present application provides a wireless network cooperative positioning method for dense nodes to be located, including: the target node obtains the distance measurement results in the current time slot; approximates the time-domain message function and the space-domain message function to calculate the time-domain message and the space-domain message; uses a pre-trained graph neural network model to correct the space-domain message, and constructs a local factor graph calculation model of the target node in combination with the time-domain message; determines the position estimation result of the target node in the current time slot according to the message passing rule in the local factor graph calculation model. Since the present application uses the estimated result of the target node's own position at the past moment as prior information, and combines the ranging information between the cooperative positioning nodes to calculate the posterior probability distribution of the target node's position, it reduces the error accumulation in a single time slot, and the positioning accuracy is more accurate; uses a pre-trained graph neural network model to optimize the message passing process on the factor graph, can obtain the model parameters through training and learning, avoids solving the complex expression of the space-domain message, avoids complex closed-form derivation, improves the calculation speed, reduces the calculation complexity, and is suitable for dense networks. Description of the Drawings

[0036] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required to be used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0037] Figure 1 It is a schematic flowchart of a wireless network cooperative positioning method for dense nodes to be located in Embodiment 1 of the present application;

[0038] Figure 2 Schematic diagram of the construction of the local factor graph calculation model and the calculation of time-domain messages in Embodiment 1 of the present application;

[0039] Figure 3 Local factor graph calculation model of the target node in Embodiment 1 of the present application;

[0040] Figure 4 Schematic diagram of the process of calculating spatial-domain messages using GNN in Embodiment 1 of the present application;

[0041] Figure 5 Equivalent graph of GNN in Embodiment 1 of the present application;

[0042] Figure 6 Schematic diagram of the process of updating the posterior probability distribution of the target node's own position according to the time-domain message and the spatial-domain message in Embodiment 1 of the present application;

[0043] Figure 7 Schematic diagram of the framework of a distributed wireless network cooperative positioning system for densely distributed nodes provided in Embodiment 2 of the present application. Detailed implementation manners

[0044] Through research, it is found that the related technology with the invention name of "An Enhanced UAV Cooperative Positioning Method Based on Position Message Passing and Merging" proposes a message passing and cooperative positioning method based on a factor graph model. Although it realizes precise positioning based on position message passing, reduces the complexity of position calculation and the system resource overhead at the same time, this technical solution has the following disadvantages:

[0045] 1. High computational complexity and low positioning accuracy in a dense network: This technical solution uses a factor graph to describe the message passing process between nodes. However, in a dense network, the factor graph or other probabilistic graph models usually contain many loop structures, which will introduce uncertainty in the confidence result inference process and make the convergence complex, thus significantly reducing the positioning accuracy and convergence speed of the distributed cooperative positioning algorithm.

[0046] 2. Failure to utilize time-domain messages: This technical solution only utilizes the ranging information between nodes, that is, the spatial-domain message, without considering the estimation results of the node's own position in the past time slots, that is, the time-domain message.

[0047] To overcome the above technical deficiencies, this embodiment provides a wireless network cooperative positioning method and device for dense nodes to be located. By using the estimated results of the node's own position in the past time slots as prior information and combining the ranging information between nodes, the posterior distribution of the target node's position is calculated using the local factor graph calculation model and the GNN (Graph Neural Network) calculation model, and the positioning accuracy is more accurate; the efficiency of the message passing process on the factor graph is optimized through the graph neural network, thereby reducing the computational complexity while ensuring the accuracy.

[0048] Next, the technical solutions in the embodiments of the present application will be clearly and completely described with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0049] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0050] Embodiment 1

[0051] This embodiment provides a wireless network cooperative positioning method for dense nodes to be located, as Figure 1 shown, including the following steps a to g, where:

[0052] Step a, the target node obtains the distance measurement result in the current time slot. The target node refers to any node to be located in the wireless network. The wireless network includes several nodes to be located and anchor nodes. The anchor nodes are nodes with known position information. The distance measurement result includes an external measurement result and an internal measurement result. The external measurement result is the distance measurement value of the cooperative positioning nodes within the communication range of the target node relative to the target node. The internal measurement result is the measurement value of the self-moving distance of the target node from the previous time slot to the current time slot. The cooperative positioning nodes include other nodes to be located and anchor nodes that communicate with the target node.

[0053] Step b, the target node obtains the initial estimated value of the current position according to the internal measurement result and the position parameter value of the previous time slot, and uses the initial estimated value as a reference point to approximate the time-domain message function and the space-domain message function related to the local factor graph respectively, and obtains the time-domain message approximation expression and the space-domain message approximation expression near the initial estimated value. The time-domain message function is a specific function expression corresponding to the internal measurement result, and the space-domain message function is a specific function expression corresponding to the external measurement result.

[0054] Step c: Calculate the time-domain message and the space-domain message respectively according to the approximate expressions of the time-domain message and the space-domain message, where the space-domain message includes the space-domain messages transmitted from other nodes to be located to the target node and the space-domain messages transmitted from the anchor nodes to the target node.

[0055] The time-domain message is a functional expression constructed based on the internal measurement results of the target node between two adjacent time slots. Its form is an exponential polynomial expression obtained by performing a second-order Chebyshev polynomial expansion on the position variable of the target node at the initial estimate value. The coefficients of this exponential polynomial expression are related to the internal measurement results and their error variances.

[0056] The position information provided by other nodes to be located to the target node is the position estimate value and its covariance at the current time slot. The target node performs an approximate expansion of the ranging function at the initial estimate value of the current position according to this position information and the external measurement results, and obtains the space-domain message transmitted from other nodes to be located to the target node. This space-domain message is parameterized in the form of an exponential polynomial and is used to describe the spatial position constraint relationship between the target node and the neighboring nodes to be located.

[0057] The target node performs an approximate expansion of the ranging function at the initial estimate value of the current position according to the known positions of the anchor nodes and the external measurement results at the current time slot, and obtains the space-domain message transmitted from the anchor nodes to the target node. This space-domain message is parameterized in the form of an exponential polynomial and is used to describe the spatial position constraint relationship between the target node and the anchor nodes.

[0058] Step d: Use the pre-trained graph neural network model to correct the space-domain message to obtain the corrected space-domain message.

[0059] Step e: Based on the time-domain message and the corrected space-domain message, construct a local factor graph calculation model for the target node. This model is used to simultaneously represent the ranging constraint relationship between the target node and the neighboring nodes, and the continuous motion constraint relationship of the target node in the time dimension.

[0060] Step f: The target node fuses the time-domain message and the corrected space-domain message according to the message passing rules in the local factor graph calculation model to obtain the posterior probability distribution of the current position of the target node.

[0061] Step g: Calculate the position estimate result of the target node at the current time slot according to the posterior probability distribution.

[0062] In this embodiment, the target node uses the estimation result of its own position at a past moment as prior information, and combines the ranging information among cooperative nodes to calculate the posterior probability distribution of the target node's position, with higher positioning accuracy.

[0063] To make those skilled in the art more clearly understand the specific implementation process of the above-mentioned wireless network cooperative positioning method for dense nodes to be located in this embodiment, the following is a specific explanation.

[0064] Build the system environment: The wireless network cooperative positioning method of this embodiment is applied to a distributed communication system, which consists of several nodes to be located and several anchor nodes. Specifically:

[0065] Each node is distributed in a spatial area according to an arbitrary topology to form an ad hoc network. Randomly select one of the nodes to be located as the target node. The remaining nodes to be located and anchor nodes that communicate with the target node are collectively referred to as the cooperative positioning nodes of the target node.

[0066] The target node obtains all cooperative positioning nodes within its communication range and saves them in the cooperative positioning node list; and receives the cooperative positioning response signal, the arrival time of the ranging signal, the response time of the ranging signal, and the position information of the cooperative positioning nodes.

[0067] The anchor node obtains all nodes to be located that communicate with it and saves them in the node-to-be-located list; at the same time, receives the cooperative positioning request and the ranging request, and sends its own position information to the nodes to be located that communicate with this anchor node.

[0068] The main process of this embodiment is as follows: First, the target node constructs a local factor graph calculation model according to the ranging information and its own historical state, including the spatial position constraint constructed based on the external measurement result and the time position constraint constructed based on the internal measurement result; then, approximate and expand the above-mentioned ranging function at the initial estimated value of the current position respectively to obtain the corresponding time-domain message and space-domain message, and the forms of the time-domain message and the space-domain message are both exponential polynomials; then, use the graph neural network to optimize and correct the space-domain message to improve the accuracy of the parametric expression; finally, jointly use the time-domain message and the optimized space-domain message to infer the posterior probability distribution of the target node's position in the current time slot, and use the mean value of this distribution as the position estimation result of the target node.

[0069] The specific process of this main process is as follows:

[0070] 1. The target node sends a cooperative positioning request in a broadcast manner and obtains the response information of each cooperative positioning node within its communication range, including the prior information of the position of the cooperative positioning node itself, the time when the ranging request is received, and the time when the ranging response message is sent. Factorize the posterior probability of the target node's own position based on the above information, and establish a local factor graph calculation model that describes the message passing process between the target node and its cooperative positioning nodes. The construction process of the local factor graph calculation model and the calculation process of the time-domain message are as Figure 2 shown.

[0071] 1.1. At time slot t, the target node i sends a cooperative positioning request and obtains the response information of each cooperative positioning node within its communication range. The set of anchor nodes among the cooperative positioning nodes is denoted as The set of nodes to be located among the cooperative positioning nodes is denoted as The true position of the target node i at time slot t is where (·) T represents the transpose operation.

[0072] 1.2. At time slot t, the target node i obtains the Euclidean distance measurement results (external measurement results) and the distance measurement results for itself (internal measurement results). Considering the influence of Gaussian white noise during the signal transmission process, where represents the true distance between the target node i and the cooperative positioning node j at time slot t, represents the distance measurement error, which follows a zero-mean Gaussian distribution with variance ; similarly, the internal measurement result follows a zero-mean Gaussian distribution with variance .

[0073] 1.3. Define the vector to represent all the distance measurement results obtained by the target node i within time slot t. The following steps are to infer the posterior probability distribution of the position vector of the target node i based on this vector

[0074] 1.4. In order to calculate using the message passing method on the factor graph, first factorize

[0075]

[0076] 1.5. According to the factorization result of , construct the local factor graph calculation model of the target node i, as Figure 3 shown, where

[0077]

[0078] 1.6. According to the message passing on the factor graph, the posterior distribution of can be represented by the confidence result:

[0079]

[0080] where represents the confidence result of represents the time-domain message passed from the factor node f i t|t-1 to the variable and represents the spatial-domain message passed from the factor node f j→i to the variable .

[0081] 1.7. Obtaining the time-domain message : The result of is obtained by using the following formula (i.e., the specific functional expression corresponding to the internal measurement result):

[0082]

[0083] where ||·||2 represents the Euclidean norm, represents the estimation result of. Further, the second-order Chebyshev polynomial is used to approximate ξ1 (note: any approximation method can be used here, such as the second-order Taylor expansion, the third-order Taylor expansion, the third-order Chebyshev polynomial, the second-order Padé approximation, etc. In this embodiment, the second-order Chebyshev polynomial is taken as an example for illustration), as shown in the following formula:

[0084]

[0085]

[0086] where c nm represents the coefficient of the Chebyshev polynomial, m ∈ [0, 2], n ∈ [0, 2], T n (x) and T m (x) respectively represent and the polynomial bases of, satisfying T0(x) = 1, T1(x) = x, T n+1 (x) = 2xT n (x) - T n-1 ; ​

[0087] In summary, the time-domain message is calculated by the following formula (i.e., the approximate expression of the spatial-domain message):

[0088]

[0089] ω i = [ω i1 , ω i2 , ω i3 , ω i4 , ω i5 T ;

[0090]

[0091]

[0092]

[0093] where is the time-domain message; is the factor node in the local factor graph calculation model; is the position of the target node i at time slot t; is the internal measurement result; is the variance of the internal measurement result; c nm is the coefficient of the Chebyshev polynomial, m ∈ [0, 2], n ∈ [0, 2]; is 's estimation result; is the position of the target node i at time slot (t - 1).

[0094] 1.8. Obtaining the spatial-domain message transmitted from the anchor node to the target node i: Use the following formula (i.e., the specific function expression corresponding to the external measurement result of the anchor node - target node) to obtain 's result:

[0095]

[0096] where

[0097] is the same as the approximation method in step 1.7. Use the second-order Chebyshev polynomial to approximate ξ1, and finally obtain (the approximate expression corresponding to the spatial-domain message transmitted from the anchor node to the target node).

[0098] 1.9. By the node to be located ​Airspeed message transmitted to target node i is obtained in two cases as follows:

[0099] ① When the probability distribution of the position of the node j to be located is unimodal, the following formula (i.e., a specific function expression corresponding to the external measurement result of the node to be located - target node when unimodal) is used to obtain the result of:

[0100]

[0101] Among them,

[0102] is the same as the approximation method in step 1.7. The second-order Chebyshev polynomial is used to approximate ξ1, and finally (approximate expression corresponding to the airspeed message transmitted from the node to be located to the target node when unimodal);

[0103] ② When the probability distribution of the position of the node j to be located is bimodal, and the positions x1 = [x1, y1] and x2 = [x2, y2] are two peak points, the following formula (i.e., a specific function expression corresponding to the external measurement result of the node to be located - target node when bimodal) is used to obtain the result of:

[0104]

[0105] is the same as the approximation method in step 1.7. The second-order Chebyshev polynomial is used to approximate and and finally (approximate expression corresponding to the airspeed message transmitted from the node to be located to the target node when bimodal).

[0106] The above uses the local factor graph calculation model to describe the airspeed message transmission process between nodes, which risks reducing the positioning accuracy and convergence speed of the distributed cooperative positioning algorithm. In this regard, in this embodiment, the graph neural network is used to optimize the efficiency of the airspeed message transmission process on the local factor graph calculation model, thereby reducing the computational complexity while ensuring the accuracy.

[0107] 2. Use the graph neural network to optimize the factor graph to improve the convergence speed and reduce the computational complexity. The specific process of using the GNN (Graph Neural Network, GNN) to optimize the airspeed message is as Figure 4 shown.

[0108] The Graph Neural Network (GNN) is a type of deep learning model used to process graph-structured data, capturing complex dependencies in the graph through information transmission between network nodes. Traditional neural networks are mainly used to process vectorized data, while the emergence of GNNs provides innovative solutions for processing unstructured data. In a GNN, each node carries a feature vector reflecting its attribute information. Through the interconnection relationships between nodes, the GNN can spread and aggregate information, thereby updating the representation of the target node. By learning the representation vectors of nodes, the GNN can capture the features of nodes and the surrounding local topological structures. By learning the representation vectors of all nodes, the representation vector of the entire graph can be obtained, capturing the relationship between the global topological structure and local information of the graph. This ability enables the GNN to effectively process various types of graph-structured data, demonstrating powerful modeling and prediction capabilities in various fields. Classic graph neural network models include GCN (Graph Convolutional Network), GAT (Graph Attention Network), GraphSAGE, etc.

[0109] 2.1. GNN equivalent graph representation of the factor graph: The GNN is used to optimize the efficiency of the spatial message passing process in the local factor graph calculation model. The GNN equivalent graph of the corresponding part in the local factor graph calculation model is as Figure 5 shown, where m j→i represents the message transmitted to k→i and m represents the message

[0110] transmitted to These two types of messages need to be obtained through the learning of the GNN. k,l and ω j,l , where represents the position estimation result of the target node at the (l - 1)-th iteration, represents the covariance of the posterior probability distribution at the (l - 1)-th iteration, and ω j,l and ω k,l respectively represent the first edge attribute vector ω j and the second edge attribute vector ω k calculated at the l-th iteration., the position estimation result of the target node at the (l - 1)-th iteration is the mean of the posterior probability distribution at the (l - 1)-th iteration. The posterior probability distribution at the (l - 1)-th iteration is a variable value calculated based on the time-domain message and the spatial-domain message at the (l - 1)-th iteration. The initial spatial-domain message is a message calculated based on the local factor graph calculation model. The first edge attribute vector is the attribute information of the edge used to connect other nodes to be located and the target node in the equivalent graph of the graph neural network. The second edge attribute vector is the attribute information of the edge used to connect the anchor node and the target node in the equivalent graph of the graph neural network.

[0111] 2.3. Calculation of node embedding vectors and edge embedding vectors at the l-th iteration on the GNN: Create node embedding vectors for each other node to be located and anchor node on the GNN graph. The node embedding vectors include the embedding vector h j,l = g1(a j,l ) of other nodes to be located and the embedding vector h k,l = g1(a k,l ), where and represent the attribute vectors of other nodes to be located and anchor nodes respectively. g1(·) is the first model parameter, representing a function inside the GNN, which needs to be obtained through model training. The specific network structure is not limited. For example, a fully connected neural network can be used. l represents the l-th iteration. Create edge embedding vectors for each edge on the GNN graph, including the first edge embedding vector (the embedding vector of the edge connecting other nodes to be located and the target node) and the second edge embedding vector (the embedding vector of the edge connecting the anchor node and the target node). The first edge embedding vector h j→i,l = g2(a j→i,l ), where a j→i,l = ω j,l represents the first edge attribute vector with a dimension of 5. g2(·) is the second model parameter, representing a function inside the GNN, which needs to be obtained through model training. The specific network structure is not limited. For example, a fully connected neural network can be used. The second edge embedding vector h k→i,l = g2(a k→i,l ), a k→i,l = ω k,l .

[0112] 2.4. Calculation of message passing m j→i,l and m k→i,l on the GNN: The message m j→i,l (i.e., the first transmitted message) passed from the node to be located j to the target node i on the GNN graph is expressed as where the symbol denotes element-wise multiplication; similarly, the message m passed from the anchor node k to the target node i on the GNN graph k→i,l (i.e., the second message passing) is denoted as where g3(·) is the third model parameter, representing a function inside the GNN, which needs to be obtained through model training, and the specific network structure is not restricted. For example, a fully connected neural network can be used.

[0113] 2.5. Utilize m j→i,l and m k→i,l to optimize the process of passing the spatial domain message on the factor graph: construct the first parameter matrix where g4(·) and g5(·) are the fourth model parameter and the fifth model parameter respectively, both representing functions inside the GNN, which need to be obtained through model training, and the specific network structure is not restricted. For example, a fully connected neural network can be used. The optimized spatial domain message passed from the to-be-localized node j to the target node i is denoted as Similarly, construct the second parameter matrix φ k,l =[φ k1 , φ k2 , φ k3 , φ k4 , φ k5 T =ω k,l g4(m k→i,l ) + g5(m k→i,l ), and the optimized spatial domain message passed from the anchor node k to the target node i is denoted as

[0114] Input the above parameters ω k,l and ω j,l After that, the GNN will automatically complete the internal operations, and the final output result is the spatial domain message and

[0115] 2.6. Model parameter training process: First, a training set needs to be obtained. The specific content includes the position information and distance measurement information of the anchor nodes and the to-be-localized nodes within a certain period of time. The acquisition time length and the number of nodes are not specifically required in this embodiment. The more the number of samples, the higher the positioning accuracy. Determine the model parameters g1(·), g2(·), g3(·), g4(·), and g5(·) through training.

[0116] The calculation formula for the spatial domain message passed from other to-be-localized nodes to the target node is:

[0117]

[0118] φ j =[φ j1 ​, φ j2 , φ j3 , φ j4 , φ j5 T = ω j g4(m j→i ) + g5(m j→i );

[0119]

[0120] ω j = [ω j1 , ω j2 , ω j3 , ω j4 , ω j5 T ;

[0121]

[0122] Among them, is the airspace message transmitted from other to-be-located node j to the target node i; f j→i is the factor node in the local factor graph calculation model; is the position of the target node i at time slot t, φ j is the first parameter matrix; φ j1 , φ j2 , φ j3 , φ j4 , φ j5 are respectively the elements within the first parameter matrix; ω j is the first edge attribute vector; ω j1 , ω j2 , ω j3 , ω j4 , ω j5 are respectively the 5 attribute information of the edges connecting other to-be-located nodes and the target node; m j→i is the first transmitted message; g4(·) and g5(·) are respectively the fourth model parameter and the fifth model parameter; is the distance measurement value of other to-be-located node j to the target node i; c nm is the coefficient of the Chebyshev polynomial, m ∈ [0, 2], n ∈ [0, 2]; is the standard deviation of the distance measurement value of other to-be-located node j to the target node i at time slot t; is the position estimation result of the target node i at time slot t,

[0123] The calculation formula for the airspace message transmitted from the anchor node to the target node is: ​​

[0124]

[0125] φ k = [φ k1 , φ k2 , φ k3 , φ k4 , φ k5 T = ω k g4(m k→i ) + g5(m k→i );

[0126]

[0127] ω k = [ω k1 , ω k2 , ω k3 , ω k4 , ω k5 T ;

[0128]

[0129] Among them, is the spatial domain message transmitted from the anchor node k to the target node i; f k→i is the factor node in the local factor graph calculation model; is the position of the target node i at time slot t; φ k is the second parameter matrix; φ k1 , φ k2 , φ k3 , φ k4 , φ k5 are respectively the elements within the second parameter matrix; ω k is the second edge attribute vector; ω k1 , ω k2 , ω k3 , ω k4 , ω k5 are respectively the 5 attribute information of the edge connecting the anchor node and the target node; m k→i is the second transmitted message; g4(·) and g5(·) are respectively the fourth model parameter and the fifth model parameter; is the distance measurement value of the anchor node k to the target node i; c nm is the coefficient of the Chebyshev polynomial, m ∈ [0, 2], n ∈ [0, 2]; is the standard deviation of the distance measurement value of the anchor node k to the target node i at time slot t; is the position estimation result of the target node i at time slot t, ​​

[0130] 3. Update the posterior probability distribution of the target node's own position according to the time-domain message in Step 1 and the space-domain message in Step 2. The specific process is as Figure 6 shown, including:

[0131] 3.1 Calculate the posterior probability distribution at the l-th iteration in the current time slot according to the posterior probability distribution of the target node at the (l - 1)-th iteration in the current time slot, the time-domain message obtained in Step 1.7, and the space-domain message at the l-th iteration in the current time slot obtained in Step 2.4. Finally, use the mean of the posterior probability distribution as the position estimation result of the target node in this time slot.

[0132] The confidence result of the target node i updating its own position in the l-th iteration at time slot t is expressed as:

[0133]

[0134] where represents the confidence result of represents the time-domain message passed from the factor node f i t|t-1 to the variable and represents the space-domain message passed from the factor node f j→i to the variable at the l-th iteration.

[0135] 3.2 Use the mean of the posterior distribution of the position of the target node i at the l-th iteration in the current time slot as its minimum mean square error estimate of the position.

[0136] 3.3 Repeat the above steps iteratively until the maximum number of iterations l max is reached. Finally, the posterior probability distribution of the target node can be expressed as:

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143]

[0144] where is the posterior probability distribution of the target node i at the time slot t position; is the position of the target node i at the time slot t; is the distance measurement result obtained by the target node i at the time slot t; φ j1 , φ j2 , φ j3 , φ j4 , φ j5 are the respective elements within the first parameter matrix; ω i1 , ω i2 , ω i3 , ω i4 , ω i5 are intermediate variables respectively; is the internal measurement result; is the variance of the internal measurement result; c nm are the coefficients of the Chebyshev polynomial, m ∈ [0, 2], n ∈ [0, 2]; is the estimation result of; is the position of the target node i at the time slot (t - 1).

[0145] The present inventor also found that in a dense network, due to the large number of cooperative positioning nodes, loop structures will appear on the factor graph, which will lead to a slow convergence speed and low positioning accuracy; in addition, for the message passing process on the factor graph, even if an approximate method is used to obtain a closed-form expression, the computational complexity is still large.

[0146] Therefore, in this embodiment, GNN (GNN can not only effectively handle the loop structure of the factor graph, but also obtain model parameters through training and learning, avoiding the solution of complex expressions) is combined with the message passing algorithm based on the factor graph, which can improve the convergence speed of the cooperative positioning algorithm and improve the positioning accuracy, realizing high-precision and low-complexity cooperative positioning in a dense network.

[0147] The key of this embodiment lies in: 1) Using GNN to optimize the message passing process on the factor graph, which can obtain model parameters through training and learning, can avoid the solution of complex expressions of spatial domain messages, improve the convergence speed, and reduce the computational complexity; 2) It is not necessary to obtain the global factor graph structure, and only need to construct the local factor graph calculation model corresponding to the target node.

[0148] Compared with the prior art, this embodiment can:

[0149] 1) Achieving high-precision positioning in a dense network while maintaining low computational complexity: Existing technologies usually implement cooperative positioning based on a factor graph model. However, when the node density is high, a large number of short-loop structures are likely to appear in the factor graph, resulting in repeated message propagation in the graph, causing confidence inflation and difficulty in the convergence of the inference process, thereby reducing the positioning accuracy. In this embodiment, based on constructing a local factor graph and generating parameterized airspace messages, a GNN is used to optimize and correct the expression of airspace messages. This method obtains parameters through training and can improve the inference efficiency and convergence speed while maintaining the advantages of closed-form expression without using high-complexity numerical methods such as particle filtering.

[0150] 2) Making full use of the prior information of the target node's position for higher positioning accuracy: Existing technologies only use the ranging information between cooperative positioning nodes and the target node for positioning. The proposed solution in this application takes the estimation result of the target node at a past moment as prior information and combines it with the ranging information to obtain a more accurate position estimation result.

[0151] 3) By performing a second-order Chebyshev polynomial expansion on the ranging function at the initial estimated value of the current position, obtaining a structurally stable exponential polynomial form message expression: In this embodiment, aiming at the non-linear ranging function characteristics between nodes, a second-order Chebyshev polynomial expansion method centered on the initial estimated value of the current position is adopted when constructing local messages to obtain a parameterized expression in the form of an exponential polynomial. Compared with traditional particle filter approximation, this method not only has a closed-form expression and does not require a large number of samples, but also has advantages such as good numerical stability, controllable error, and can be directly used as the input of a neural network, significantly improving the accuracy and efficiency of message construction and laying a good foundation for the subsequent optimization of the graph neural network.

[0152] Embodiment 2

[0153] Based on the same inventive concept, this embodiment also provides a distributed wireless network cooperative positioning system for dense distribution nodes for implementing the above-mentioned wireless network cooperative positioning method for dense nodes to be located, as Figure 7 shown, including:

[0154] A factor graph construction module, a graph neural network optimization module, and a positioning module.

[0155] The factor graph construction module is used to construct a local factor graph calculation model of the target node according to the input ranging information and output the time-domain message passing result and the constructed local factor graph calculation model.

[0156] The graph neural network optimization module is used to optimize the airspace message passing process on the factor graph using a GNN according to the input local factor graph calculation model.

[0157] The positioning module is used to calculate the posterior probability distribution of the target node position based on the time-domain message passing result output by the factor graph construction module and the optimized space-domain message passing result output by the graph neural network optimization module, and use the mean value of the distribution as the position estimation result of the target node.

[0158] The implementation solution provided by this system for solving problems is similar to the implementation solution described in Embodiment 1. For the implementation process of the specific solution, please refer to Embodiment 1 and will not be elaborated here.

[0159] Embodiment 3

[0160] This embodiment provides another wireless network cooperative positioning method for densely located nodes to be located. Different from Embodiment 1, it uses a pre-trained graph neural network model to only correct the time-domain message. Since the implementation manners of other steps in this embodiment are similar to the implementation solution described in Embodiment 1, for the implementation process of the specific solution provided in this embodiment, please refer to Embodiment 1 and will not be elaborated here.

[0161] Embodiment 4

[0162] A wireless network cooperative positioning method for densely located nodes to be located provided in this embodiment is different from Embodiment 1 in that it uses a pre-trained graph neural network model to correct the time-domain message and the space-domain message. Since the implementation manners of other steps in this embodiment are similar to the implementation solution described in Embodiment 1, for the implementation process of the specific solution provided in this embodiment, please refer to Embodiment 1 and will not be elaborated here.

[0163] Embodiment 5

[0164] This embodiment provides a computer device, which can be a server or a terminal. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O), and a communication interface. Among them, the processor, the memory, and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store data in the wireless network cooperative positioning method for densely located nodes to be located. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with external terminals through a network connection. When the computer program is executed by the processor, it implements a wireless network cooperative positioning method for densely located nodes to be located in Embodiment 1.

[0166] Example 6

[0167] This embodiment provides a computer device, including a memory and a processor. A computer program is stored in the memory. When the processor executes the computer program, it implements a wireless network cooperative positioning method for dense nodes to be located in Embodiment 1.

[0168] Example 7

[0169] This embodiment provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements a wireless network cooperative positioning method for dense nodes to be located in Embodiment 1.

[0170] Example 8

[0171] This embodiment provides a computer program product including a computer program. When the computer program is executed by a processor, it implements a wireless network cooperative positioning method for dense nodes to be located in Embodiment 1.

[0172] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0173] Specific examples are used in this article to elaborate on the principles and implementation manners of the present application. The descriptions of the above embodiments are only used to help understand the method and its core idea of the present application; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present application.

Claims

1. A wireless network cooperative positioning method for dense nodes to be located, characterized in that, Including: The target node obtains the distance measurement results in the current time slot. Herein, the target node refers to any node to be located in the wireless network. The wireless network includes several nodes to be located and anchor nodes, and the anchor nodes are nodes with known location information. The distance measurement results include external measurement results and internal measurement results. The external measurement results are the distance measurement values of the cooperative positioning nodes within the communication range of the target node relative to the target node, and the internal measurement results are the measurement values of the self-moving distance of the target node from the previous time slot to the current time slot. The cooperative positioning nodes include other nodes to be located and anchor nodes that communicate with the target node; The target node obtains the initial estimated value of the current position according to the internal measurement result and the position parameter value of the previous time slot, and takes the initial estimated value as a reference point to approximately process the time-domain message function and the space-domain message function related to the local factor graph respectively, and obtains the time-domain message approximate expression and the space-domain message approximate expression near the initial estimated value. Herein, the time-domain message function is a specific function expression corresponding to the internal measurement result, and the space-domain message function is a specific function expression corresponding to the external measurement result; Calculate the time-domain message and the space-domain message respectively according to the time-domain message approximate expression and the space-domain message approximate expression; Use the pre-trained graph neural network model to correct the space-domain message to obtain the corrected space-domain message; Based on the time-domain message and the corrected space-domain message, construct the local factor graph calculation model of the target node; The target node fuses the time-domain message and the corrected space-domain message according to the message passing rule in the local factor graph calculation model to obtain the posterior probability distribution of the current position of the target node; Calculate the position estimation result of the target node in the current time slot according to the posterior probability distribution.

2. The wireless network cooperative positioning method for dense nodes to be located according to claim 1, characterized in that Calculating the position estimation result of the target node in the current time slot according to the posterior probability distribution specifically includes: Obtain the target input parameters at the l-th iteration in the current time slot, where l>1. The target input parameters include the position estimation result of the target node at the (l - 1)-th iteration, the covariance of the posterior probability distribution at the (l - 1)-th iteration, the first edge attribute vector at the l-th iteration, and the second edge attribute vector at the l-th iteration. The first edge attribute vector is the attribute information of the edge used to connect other nodes to be located and the target node in the equivalent graph of the graph neural network, and the second edge attribute vector is the attribute information of the edge used to connect the anchor node and the target node in the equivalent graph of the graph neural network. The equivalent graph of the graph neural network is an equivalent graph obtained according to the local factor graph calculation model; Take the target input parameters as inputs and use the trained graph neural network model to obtain the corrected space-domain message at the l-th iteration in the current time slot; Calculate the posterior probability distribution at the l-th iteration in the current time slot according to the corrected space-domain message at the l-th iteration in the current time slot, the time-domain message, and the posterior probability distribution at the (l - 1)-th iteration in the current time slot; Take the mean of the posterior probability distribution at the \(l\)-th iteration in the current time slot as the position estimation result of the target node at the \(l\)-th iteration in the current time slot; When the preset number of iterations is reached, take the mean of the posterior probability distribution at the last iteration as the final position estimation result of the target node in the current time slot.

3. The wireless network cooperative positioning method for dense nodes to be located according to claim 2, wherein The airspace messages include the airspace messages transmitted from other nodes to be located to the target node and the airspace messages transmitted from the anchor nodes to the target node; Taking the target input parameters as the input, use the trained graph neural network model to obtain the corrected airspace messages at the \(l\)-th iteration in the current time slot, specifically including: Determine the node embedding vector at the \(l\)-th iteration in the current time slot according to the node attribute vector and the first model parameters, where the node attribute vector is the attribute information of each other node to be located and the anchor node at the \(l\)-th iteration in the current time slot in the equivalent graph of the graph neural network, and the node attribute vector is a variable value determined according to the position estimation result of the target node at the \((l - 1)\)-th iteration in the current time slot. The node embedding vector includes the embedding vectors of other nodes to be located and the embedding vectors of the anchor nodes; Determine the first edge embedding vector at the \(l\)-th iteration according to the first edge attribute vector and the second model parameters at the \(l\)-th iteration; Determine the second edge embedding vector at the \(l\)-th iteration according to the second edge attribute vector and the second model parameters at the \(l\)-th iteration; Determine the first transfer message at the \(l\)-th iteration according to the third model parameters, the embedding vectors of other nodes to be located at the \(l\)-th iteration, and the first edge embedding vector, where the first transfer message is the message transmitted from other nodes to be located to the target node; Determine the second transfer message at the \(l\)-th iteration according to the third model parameters, the embedding vectors of the anchor nodes at the \(l\)-th iteration, and the second edge embedding vector, where the second transfer message is the message transmitted from other anchor nodes to the target node; Construct the first parameter matrix at the \(l\)-th iteration according to the first transfer message, the fourth model parameters, and the fifth model parameters at the \(l\)-th iteration; Construct the second parameter matrix at the \(l\)-th iteration according to the second transfer message, the fourth model parameters, and the fifth model parameters at the \(l\)-th iteration; Correct the airspace messages transmitted from other nodes to be located to the target node at the \(l\)-th iteration according to the first parameter matrix at the \(l\)-th iteration; Correct the airspace messages transmitted from the anchor nodes to the target node at the \(l\)-th iteration according to the second parameter matrix at the \(l\)-th iteration.

4. The wireless network cooperative positioning method for dense nodes to be located according to claim 1, characterized in that The time domain message is a functional expression constructed according to the internal measurement results of the target node between two adjacent time slots. The functional expression is an exponential polynomial expression obtained by performing a second-order Chebyshev polynomial expansion on the position variable of the target node at the initial estimate value. The coefficients of the exponential polynomial expression are related to the internal measurement results and their error variances.

5. The wireless network cooperative positioning method for dense nodes to be located according to claim 3, characterized in that, The airspace message transmitted by the anchor node to the target node is a function expression obtained by approximately expanding the ranging function at the initial estimated value of the current position according to the known position of the anchor node and the external measurement results in the current time slot. The function expression is parameterized in the form of an exponential polynomial and is used to describe the spatial position constraint relationship between the target node and the anchor node; The airspace messages transmitted by other to-be-located nodes to the target node are function expressions obtained by approximately expanding the ranging function at the initial estimated value of the current position according to the position information and external measurement results. The function expressions are parameterized in the form of an exponential polynomial and are used to describe the spatial position constraint relationship between the target node and neighboring to-be-located nodes. Among them, the position information is the position estimate value and its covariance in the current time slot provided by other to-be-located nodes to the target node.

6. A wireless network cooperative positioning method for dense nodes to be located, characterized in that, Including: The target node obtains the distance measurement results in the current time slot. Here, the target node refers to any to-be-located node in the wireless network. The wireless network includes several to-be-located nodes and anchor nodes. The anchor nodes are nodes with known position information. The distance measurement results include external measurement results and internal measurement results. The external measurement results are the distance measurement values of the cooperative positioning nodes within the communication range of the target node relative to the target node. The internal measurement results are the measurement values of the moving distance of the target node itself from the previous time slot to the current time slot. The cooperative positioning nodes include other to-be-located nodes and anchor nodes that communicate with the target node; The target node obtains the initial estimated value of the current position according to the internal measurement results and the position parameter values of the previous time slot, and takes the initial estimated value as a reference point to approximately process the time-domain message function and the airspace message function related to the local factor graph respectively, and obtains the time-domain message approximate expression and the airspace message approximate expression near the initial estimated value. Among them, the time-domain message function is a specific function expression corresponding to the internal measurement results, and the airspace message function is a specific function expression corresponding to the external measurement results; Calculate the time-domain message and the airspace message respectively according to the time-domain message approximate expression and the airspace message approximate expression; Use the pre-trained graph neural network model to correct the time-domain message to obtain the corrected time-domain message; Based on the corrected time-domain message and the airspace message, construct a local factor graph calculation model of the target node; The target node, according to the message passing rules in the local factor graph calculation model, fuses the corrected time-domain message and the airspace message to obtain the posterior probability distribution of the current position of the target node; According to the posterior probability distribution, calculate the position estimation result of the target node in the current time slot.

7. A wireless network cooperative positioning method for dense nodes to be located, characterized in that Including: The target node obtains the distance measurement results in the current time slot, where the target node refers to any node to be located in the wireless network. The wireless network includes several nodes to be located and anchor nodes. The anchor nodes are nodes with known location information. The distance measurement results include external measurement results and internal measurement results. The external measurement results are the distance measurement values of the cooperative positioning nodes within the communication range of the target node relative to the target node. The internal measurement results are the measurement values of the self-movement distance of the target node from the previous time slot to the current time slot. The cooperative positioning nodes include other nodes to be located and anchor nodes that communicate with the target node; The target node obtains an initial estimate of the current position based on the internal measurement results and the position parameter values of the previous time slot, and uses the initial estimate as a reference point to approximate the time-domain message function and the space-domain message function related to the local factor graph respectively, obtaining an approximate expression of the time-domain message near the initial estimate and an approximate expression of the space-domain message. Among them, the time-domain message function is a specific function expression corresponding to the internal measurement results, and the space-domain message function is a specific function expression corresponding to the external measurement results; Calculate the time-domain message and the space-domain message respectively according to the approximate expression of the time-domain message and the approximate expression of the space-domain message; Use the pre-trained graph neural network model to correct the time-domain message and the space-domain message respectively, obtaining the corrected time-domain message and the corrected space-domain message; Based on the corrected time-domain message and the corrected space-domain message, construct a local factor graph calculation model of the target node; The target node fuses the corrected time-domain message and the corrected space-domain message according to the message passing rules in the local factor graph calculation model, obtaining the posterior probability distribution of the current position of the target node; According to the posterior probability distribution, calculate the position estimation result of the target node in the current time slot.

8. A computer device, comprising: A memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to implement the wireless network cooperative positioning method for dense nodes to be located according to any one of claims 1-5, or the wireless network cooperative positioning method for dense nodes to be located according to claim 6, or the wireless network cooperative positioning method for dense nodes to be located according to claim 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the wireless network cooperative positioning method for dense nodes to be located according to any one of claims 1-5, or the wireless network cooperative positioning method for dense nodes to be located according to claim 6, or the wireless network cooperative positioning method for dense nodes to be located according to claim 7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the wireless network cooperative positioning method for dense nodes to be located according to any one of claims 1-5, or the wireless network cooperative positioning method for dense nodes to be located according to claim 6, or the wireless network cooperative positioning method for dense nodes to be located according to claim 7.

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