Distributed wireless network cooperative positioning method for high-mobility sparse distributed nodes

Abstract

The application is a kind of distributed wireless network cooperative positioning method for high mobility sparse distributed nodes. The method comprises: building a distributed wireless cooperative positioning system comprising a plurality of nodes to be positioned and anchor nodes; each node to be positioned obtains a cooperative positioning node list; the node to be positioned calculates the prior probability distribution of its own position; in a positioning time slot, the node to be positioned obtains the spatial ranging result between the node to be positioned and its cooperative positioning nodes and the time domain ranging result of the node to be positioned; the node to be positioned calculates the posterior probability distribution of its own position through the prior probability distribution of its own position and the parameterized message passing algorithm based on the spatial ranging result and the time domain ranging result; the posterior probability distribution is updated, and the final estimated value of the position of each node to be positioned is calculated. The application reduces the calculation complexity of the node to be positioned, improves the accuracy of cooperative positioning, and reduces the influence of the sparse distribution and high mobility of nodes in the distributed wireless network on the positioning performance.

Description

Technical Field

[0001] This invention relates to the technical fields of next-generation mobile communication networking and communication services, and specifically to a distributed wireless network cooperative positioning method for highly mobile sparsely distributed nodes. Background Technology

[0002] Location awareness plays a crucial role in many emerging applications, and wireless positioning technology has been widely used in various fields such as military, commerce, and public services.

[0003] Currently, wireless positioning technologies are primarily based on space satellite systems and terrestrial wireless networks. In satellite-based wireless positioning technologies, node location information is mainly obtained through the Global Navigation Satellite System (GNSS) and its augmentation systems. However, satellite radio frequency signals have poor penetration capabilities, and satellite signal receivers cannot reliably measure locations in forests, tunnels, underground environments, and dense urban areas, resulting in inaccurate location information. In these satellite signal-blocked environments, cooperative positioning technologies can determine node locations by establishing wireless links between adjacent nodes and transmitting relative distance measurements.

[0004] Traditional terrestrial wireless network positioning technologies typically reduce positioning errors by deploying high-density or high-power anchor nodes and employing centralized cooperative positioning methods. Newer distributed wireless cooperative positioning technologies, however, improve positioning accuracy by establishing peer-to-peer communication links between nodes and utilizing signal measurements between them, thereby enhancing the availability and reliability of positioning services. Furthermore, centralized cooperative positioning methods suffer from drawbacks in large networks, including high communication overhead at the central node, sensitivity to central node failures, and poor network scalability and robustness. Distributed cooperative positioning methods, on the other hand, offer better scalability and robustness, making them more attractive among cooperative positioning technologies.

[0005] Message passing algorithms have significant application prospects in distributed wireless network cooperative localization technology. Research on message passing algorithms in distributed wireless network cooperative localization mainly falls into two directions: First, the core idea is based on a parameterized message representation process. The node to be located uses a specific similarity metric to find a probability distribution to approximate the true posterior probability distribution of its location. Then, the parameters of this approximate distribution are used to replace the parameters of the true distribution. Finally, through message passing between random variables, the positions of each node to be located in the network are calculated. Second, the core idea is based on a particle-based message representation process. The node to be located approximates the true posterior probability distribution of its location by finding a large number of random samples propagating in the state space according to specific rules. This makes the parameters of the approximate posterior probability distribution reconstructed based on the sample set (i.e., the particle set) approximate the parameters of the true posterior probability distribution. Finally, through message passing between random variables, the positions of each node to be located in the network are calculated.

[0006] However, for message-passing distributed cooperative localization algorithms based on parameterized message representation, it is necessary to solve for the optimal parameters of the approximate distribution of the true posterior probability distribution by optimizing a specific similarity metric. This has high computational complexity and may result in multiple local optima.

[0007] For message-passing distributed cooperative localization algorithms based on particle-based message representation, a large number of continuously updated particles are needed to approximate the posterior probability distribution of the node to be located through a specific random sampling method. Since the algorithm's performance is positively correlated with the number of particles, a large number of particles are generally required to approximate the true distribution. Furthermore, the computational complexity of such algorithms is proportional to the square of the number of particles, and their communication overhead is also proportional to the number of particles; therefore, both the computational complexity and communication overhead of these algorithms are very high. Summary of the Invention

[0008] To address the high computational complexity of existing message-passing-based distributed wireless cooperative positioning research, reduce the impact of sparse node distribution and high mobility on positioning performance in distributed wireless networks such as mobile ad hoc networks, and better guarantee high-precision and fast cooperative positioning capabilities for wireless networks, this invention proposes a distributed wireless network cooperative positioning method for highly mobile sparsely distributed nodes.

[0009] The distributed wireless network cooperative localization method for highly mobile sparsely distributed nodes of the present invention includes the following steps:

[0010] Step 1: Construct a distributed wireless cooperative positioning system consisting of several nodes to be located and several anchor nodes; the nodes to be located and the anchor nodes are distributed in an arbitrary topology within a spatial area to form a distributed wireless self-organizing network; for each node to be located, the other nodes to be located and the anchor nodes that communicate with that node are collectively referred to as the cooperative positioning nodes of that node.

[0011] Step 2: Each node to be located broadcasts a cooperative positioning request signal, saving the identification information of the cooperative positioning nodes that return a response within its communication range to its respective cooperative list. The cooperative positioning nodes that return a response include the anchor node with a known actual location within the communication range of the node to be located, and the other nodes to be located with unknown actual locations within the communication range of the node to be located.

[0012] Step 3: Calculate the prior probability distribution of the random vector of the position of each node to be located. For each node to be located, based on the posterior probability distribution of its random vector of position at the previous time step, and according to the prediction steps of the Extended Kalman Filter (EKF) algorithm, calculate the prior probability distribution of the random vector of the position of the node to be located at the current time step.

[0013] Step 4: During the time slot where positioning is required, each node to be positioned sends a ranging request to each node in its respective collaboration list. Each node in the list returns its own prior probability distribution information of its position to the corresponding node to be positioned. Each node to be positioned obtains the ranging result between itself and its collaborating positioning nodes, i.e., the spatial ranging result. Each node to be positioned measures its own distance traveled from the previous time to the current time, i.e., the time domain ranging result.

[0014] Step 5: Each node to be located calculates the posterior probability distribution of its own position random vector using its prior probability distribution information and a parameterized message passing algorithm based on spatial and temporal ranging results.

[0015] Each node i to be located performs the following: (501) Calculates the time-domain message corresponding to the time-domain ranging result based on its time-domain ranging result, and approximates the nonlinear term in the time-domain message using a second-order Taylor polynomial; calculates the spatial-domain message corresponding to the spatial-domain ranging result between each cooperative positioning node based on its spatial-domain ranging result, and approximates the nonlinear term in the spatial-domain message using a second-order Taylor polynomial; (502) Iteratively updates the spatial-domain message with each cooperative positioning node; in each iteration, each positioning node multiplies its own position prior probability distribution information, time-domain message and all spatial-domain messages called in this iteration to obtain the probability distribution of its own position random vector after this iteration, and broadcasts the probability distribution after this iteration to the positioning nodes in the cooperative list of the positioning node; finally, after reaching the maximum number of iterations set or determined by the iteration convergence threshold, each positioning node multiplies its own position prior probability distribution information, each spatial-domain message and time-domain message to obtain the posterior probability distribution of its own position random vector at the current time.

[0016] Step 501 includes: (1) The target node i calculates the time-domain message corresponding to the time-domain ranging result at the current time. The time-domain message is a function composed of the posterior probability distribution of the position vector of the target node i at the previous time and the observation likelihood function corresponding to the distance measurement result of the target node i from the previous time to the current time according to a specific rule; (2) The target node i calculates the spatial message corresponding to the spatial ranging result between it and each anchor node in its cooperative list. Each spatial message of this type is a function composed of the prior probability distribution of the position vector of its corresponding cooperative anchor node at the current time and the observation likelihood function corresponding to the spatial ranging result between the target node i and the cooperative anchor node according to a specific rule; (3) The target node i calculates the spatial message corresponding to the spatial ranging result between it and each target node i in its cooperative list. Each spatial message of this type is a function composed of the probability distribution of the position vector provided by its corresponding cooperative target node in this iteration and the observation likelihood function corresponding to the spatial ranging result between the target node i and the cooperative target node according to a specific rule.

[0017] In step 502, the random vector of the current position of the target node i to be located. The posterior probability distribution is expressed as

[0018]

[0019] in, The vector represents all observations of the target node i at time t, including spatial ranging results and temporal ranging results; l max Indicates the maximum number of iterations; express The prior probability distribution; Indicates the first time max In this iteration, the target node i receives the spatial message corresponding to the node j in its collaborating list; Indicates the first time max In this iteration, the target node i to be located receives the spatial message corresponding to the anchor node k in its collaboration list; Let be the set of nodes to be located and the set of anchor nodes in the collaborative list of node i to be located at time t, respectively.

[0020] Step 6: Using the EKF update step, update the posterior probability distribution of the random vector of the location of the node to be located obtained in Step 5 to further improve the accuracy of the posterior probability distribution.

[0021] Step 7: For each node to be located, take the mean of the random vector in the posterior probability distribution of the node's position after the update process in Step 6, and use it as the final estimated value of the node's position vector at the current time.

[0022] The advantages and positive effects of this invention are as follows: The cooperative localization method for distributed wireless networks with highly mobile sparsely distributed nodes proposed in this invention employs a parameterized message passing algorithm based on second-order Taylor polynomials, which reduces the computational complexity of each node to be located during the distributed cooperative localization process based on message passing algorithms. Furthermore, it uses an extended Kalman filter algorithm to predict the prior probability of the node's location and update the posterior probability, thereby improving the accuracy of cooperative localization. In addition, this invention reduces the impact of sparse distribution and high mobility of nodes in distributed wireless networks such as mobile ad hoc networks on localization performance, and can better guarantee high-precision and rapid cooperative localization capabilities for wireless networks. Attached Figure Description

[0023] Figure 1 This is a flowchart of the distributed wireless network cooperative localization method for highly mobile sparsely distributed nodes according to the present invention.

[0024] Figure 2 This is a diagram of the device for locating the node used in this invention;

[0025] Figure 3 This is a diagram of the anchor node device used in this invention;

[0026] Figure 4 This is a diagram illustrating the effect of the collaborative positioning method of the present invention. Detailed Implementation

[0027] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0028] This invention addresses systems and application scenarios comprised of randomly arranged wireless sensors or mobile nodes, and proposes a distributed wireless network cooperative positioning method for highly mobile, sparsely distributed nodes. For example... Figure 1 As shown, the method includes the following seven steps, and the implementation of each step is explained below.

[0029] Step 1: Build a distributed wireless cooperative positioning system that includes several nodes to be located and several anchor nodes.

[0030] In this embodiment, each node to be located and each anchor node are distributed in the spatial area according to any topology, forming a distributed wireless self-organizing network.

[0031] The node to be located is a node whose location information is unknown and needs to be estimated. For example... Figure 2 As shown, each node to be located has a first wireless communication unit, a first storage unit, a first control unit, and a first computing unit. The first wireless communication unit is responsible for communicating with other nodes within the communication range of the node to be located. The first storage unit is responsible for storing the list of cooperative positioning nodes of the node to be located, the probability distribution information of the state random vector of the node to be located (which may include, but is not limited to, position, velocity, direction of movement, and acceleration), the probability distribution information of the position random vectors of the cooperative positioning nodes, the ranging results between the node to be located and each cooperative positioning node (i.e., spatial ranging results), and the distance the node to be located has moved from the previous time to the current time (i.e., time-domain ranging results). The first control unit is responsible for controlling the movement trajectory of the node to be located. The first computing unit is responsible for calculating the prior probability distribution of the state random vector of the node to be located at each time, the spatial message corresponding to each spatial ranging result, the time-domain message corresponding to each time-domain ranging result, and the posterior probability distribution of the state random vector of the node to be located at each time.

[0032] Anchor nodes are nodes whose location information is precise and known prior to the information. For example... Figure 3 As shown, each anchor node has a second wireless communication unit, a second storage unit, and a second control unit. The second wireless communication unit is responsible for communication between the anchor node and its cooperating nodes to be located; the second storage unit is responsible for storing the anchor node's own position information and a list of cooperating nodes to be located; the second control unit is responsible for controlling the movement trajectory of the anchor node.

[0033] Step 2: Each node to be located broadcasts a cooperative positioning request signal through the first wireless communication unit, and saves the list of cooperative positioning nodes that return a response within its communication range to its own first storage unit;

[0034] In this embodiment, each cooperative positioning node that returns a response includes the anchor node that responds within the communication range of the node to be positioned and the remaining nodes to be positioned that respond within the communication range of the node to be positioned.

[0035] Step 3: Each node to be located calculates its prior probability distribution of its own position random vector through the first computing unit. For the target node i to be located, based on the posterior probability distribution of its position random vector at time t-1, and according to the prediction steps of the extended Kalman filter algorithm, the first computing unit calculates its prior probability distribution of its position random vector at time t.

[0036] In a two-dimensional scenario, the state vector of node i at time t is represented as: in and Let represent the position vector and velocity vector of node i in two-dimensional space, respectively. T This indicates the transpose operation.

[0037] Based on the prediction steps of the extended Kalman filter algorithm, we can obtain:

[0038]

[0039]

[0040] Where F is the state transition matrix, Let represent the posterior estimate of the state vector of the target node i at time t-1. This represents the prior estimate of the state vector of the target node i at time t. This represents the prior estimate of the covariance matrix of the state vector of the target node i at time t. Let represent the posterior estimate of the covariance matrix of the state vector of the target node i at time t-1. Let be the covariance matrix of the state transition noise vector of the target node i at time t.

[0041] At time t, the random vector representing the position of the target node i to be located. Prior probability distribution This can be expressed as the mean. Covariance is The Gaussian distribution, i.e. Corresponding to Positional components in It is based on elements and Let be a two-dimensional diagonal matrix with diagonal elements, where and These are the covariance matrices. The position component corresponding to the target node i to be located and The variance.

[0042] Step 4: During the time slot where positioning is required, each node to be positioned sends a ranging request to each node in the cooperative list stored in its first storage unit through its first wireless communication unit. 1) Each node in the list returns its prior probability distribution information of its position to the corresponding node to be positioned through its first wireless communication unit; 2) Each node to be positioned obtains the ranging result between itself and its cooperative positioning nodes, i.e., the spatial ranging result; 3) Each node to be positioned measures its own moving distance from time t-1 to time t, i.e., the instantaneous ranging result; Each node to be positioned stores the above three types of observation data in its first storage unit.

[0043] Step 5: Each node to be located calculates the posterior probability distribution of its own position random vector through its own first computing unit, based on the prior probability distribution information of its own position and the parameterized message passing algorithm based on the spatial ranging results and the temporal ranging results.

[0044] Each node to be located calculates the corresponding time-domain message based on its time-domain ranging result using its own first computing unit, approximating the nonlinear terms in the time-domain message using a second-order Taylor polynomial. Based on its spatial ranging result, it calculates the corresponding spatial message for the spatial ranging result between itself and each cooperating positioning node using its own first computing unit, approximating the nonlinear terms in the spatial message using a second-order Taylor polynomial. It then iteratively updates the spatial message with each cooperating node to be located via a first wireless communication unit and a first computing unit. In each iteration, each node to be located multiplies its prior probability distribution information, the time-domain message, and all spatial messages invoked in that iteration using its own first computing unit to obtain the probability distribution of its own position random vector after that iteration. This probability distribution is then broadcast to the cooperating nodes in the node to be located's list via the first wireless communication unit. Finally, after reaching the maximum number of iterations set or determined by the iteration convergence threshold, each node to be located multiplies its own prior probability distribution information, each spatial message, and the temporal message through its own first computing unit to obtain the posterior probability distribution of its own position random vector at the current time.

[0045] In this embodiment, for the target node i to be located, its position vector is calculated. Taking the components as an example, the calculation steps are as follows: Steps 501 onwards, the position vector... The components can be solved in a similar way.

[0046] Step 501: The target node i to be located calculates the time domain message corresponding to the time domain ranging result and the spatial domain message corresponding to each spatial domain ranging result through its first calculation unit.

[0047] 1) Calculate the time-domain message corresponding to the time-domain ranging result of the target node to be located at the current time. This message is a function composed of the posterior probability distribution of the position vector of the target node to be located at the previous time and the observation likelihood function corresponding to the measured distance of the target node from the previous time to the current time, according to a specific rule.

[0048] Time-domain ranging result of target node i at time t Corresponding time-domain message It can be represented as:

[0049]

[0050] in, Represents the position component of the target node i to be located. The posterior probability distribution at time t-1 This represents the noisy measurement value received by the node i to be located at time t-1, including the temporal ranging result measured by the node i and the spatial ranging result obtained with each cooperating positioning node; f i t|t-1 f represents the observation likelihood function corresponding to the measured distance traveled by the target node i from time t-1 to time t. i t|t-1 satisfy

[0051]

[0052] in, express The variance of , ||·||2 represents the Euclidean norm, and exp(·) represents an exponential function with the natural constant e as the base.

[0053] The first computational unit of the target node i to be located will use time-domain information. Nonlinear terms in exist and A second-order Taylor polynomial approximation is performed at the point, where, Let represent the posterior estimate of the position of the target node i at time t-1. This represents the prior estimate of the position of the target node i at time t. The obtained time-domain message... The expression satisfies

[0054]

[0055] Where “∝” indicates that it is proportional to, and the parameters satisfy

[0056]

[0057] in, Let y be the final estimated position of the target node i at time t-1. for The variance.

[0058] 2) Calculate the spatial message corresponding to the spatial ranging result between the target node to be located and each anchor node in its cooperative list. Each message of this type is a function composed of the prior probability distribution of the position vector of its corresponding cooperative anchor node at the current time and the observation likelihood function corresponding to the spatial ranging result between the target node to be located and the cooperative anchor node, according to a specific rule.

[0059] In the l-th iteration, the spatial ranging results between the target node i and its cooperating anchor node k Corresponding airspace message It can be represented as:

[0060]

[0061] in, Represents the two positional component variables of anchor node k. and Let represent the probability distributions corresponding to the two components of the position vector of anchor node k, and let δ(·) represent the impulse function. and These represent the values ​​of the two positional components of anchor node k. This represents the spatial ranging result between the target node i and the anchor node k. The corresponding observation likelihood function, satisfy:

[0062]

[0063] in, express The variance.

[0064] The spatial message is processed through the first computing unit of the target node i. Nonlinear terms in exist A second-order Taylor polynomial approximation is performed at the point, where, Let represent the mean parameter in the probability distribution function of the target node i in the l-th iteration, that is, to obtain the position estimate of the target node i after the l-th iteration at time t; in the l-th iteration... max In this iteration, the spatial message obtained The expression satisfies

[0065]

[0066] The parameters are as follows:

[0067]

[0068] in, This indicates that at time t, the target node i to be located is at the lth position. max The mean parameter of the probability distribution function in the -1th iteration.

[0069] 3) Calculate the spatial messages corresponding to the spatial ranging results between the target node to be located and each node to be located in its collaborating list. Each message of this type is a function composed of the probability distribution of the position vector provided by its corresponding collaborating node to be located in this iteration, and the observation likelihood function corresponding to the spatial ranging results between the target node to be located and the collaborating node to be located, according to a specific rule.

[0070] In the l-th iteration, the spatial ranging results between the target node i and its collaborating nodes j in the collaborating list are... Corresponding airspace messages It can be represented as:

[0071]

[0072] in

[0073]

[0074]

[0075] Let represent the probability distributions corresponding to the two components of the position vector of the node j to be located in the cooperative operation. Represents the two positional component variables of the node j to be located. and Let and represent the mean parameters of the probability distribution functions of the two position components of the node j to be located after the (l-1)th iteration. This represents the observation likelihood function corresponding to the spatial ranging results between target node i and target node j. satisfy:

[0076]

[0077] in, express The variance. The spatial information is processed through the first computational unit of the target node i. Nonlinear terms in exist and A second-order Taylor polynomial approximation is performed at the point, where, This represents the prior position estimate of the target node i at time t. This represents the estimated position of node j after the (l-1)th iteration; in the lth iteration... max In this iteration, the spatial message obtained The expression satisfies

[0078]

[0079] The intermediate parameters in the above formula are as follows:

[0080]

[0081] in, and These represent the positions of nodes i and j to be located at time t, respectively, at the lth time. max Position estimate after -1 iterations; This indicates that at time t, the node j to be located is at the lth node. max The y-axis component of the final position estimate after -1 iterations; express The variance.

[0082] Step 502: The target node i to be located performs iterative updates of spatial domain messages with each cooperating node to be located. In each iteration, each node to be located multiplies its own prior probability distribution, temporal message, and all spatial messages called in this iteration to obtain the probability distribution of its own position random vector after this iteration, and broadcasts the probability distribution after this iteration to the nodes to be located in its cooperative list; finally, after reaching the maximum number of iterations set or determined by the iteration convergence threshold, each node to be located multiplies its own prior probability distribution information, each spatial message, and temporal message to obtain the posterior probability distribution of its own position random vector at the current time.

[0083] After l max After the iteration, the position components of the target node i at time t The posterior probability distribution satisfies:

[0084]

[0085] in, Let represent the set of nodes to be located and the set of anchor nodes in the cooperative list of the target node i at time t, respectively.

[0086] Finally, the target node i to be located obtains its random position vector at time t through its first computing unit. The posterior probability distribution of the components is as follows:

[0087]

[0088] The mean and variance are as follows:

[0089]

[0090]

[0091] The target node i to be located can be obtained using a similar calculation method through its first calculation unit. Posterior probability distribution of components Finally, the random vector of the position of the target node i at time t is obtained. The posterior probability distribution follows a mean. Covariance Matrix The Gaussian distribution, where

[0092]

[0093] diag(a,b) represents a diagonal matrix with elements a and b on the diagonal; the target node i to be located will... and Stored in the first storage unit.

[0094] Step 6: Each node to be located processes the posterior probability distribution obtained in Step 5 through its first computing unit using the update step of EKF, further improving the accuracy of the posterior probability distribution of the random vector of the target node i at time t, and stores the probability distribution in its respective first storage unit.

[0095] Each node to be located calculates its measurement residual vector through its first computing unit. and its covariance matrix

[0096]

[0097]

[0098] Where H is the observation matrix, the approximate optimal Kalman gain can be expressed as:

[0099]

[0100] Finally, the mean and covariance matrix of the posterior probability distribution of the target node i at time t are obtained as follows:

[0101]

[0102]

[0103] Step 7: For the posterior probability distribution of the random vector of the location of each node to be located after processing in Step 6, take its mean as the final estimated value of the location vector of the corresponding node to be located at the current time, so as to realize distributed wireless cooperative positioning.

[0104] like Figure 4 The diagram shows the cooperative localization effect of the present invention, compared with EKF, particle method, and neural network-based method, in a scenario with high node mobility and sparse distribution in a two-dimensional plane. Specifically, on a 3000m × 3000m plane, 13 anchor nodes and 40 nodes to be located are deployed; the moving speed of the nodes to be located follows a Gaussian distribution with a mean of 50 m / s and a standard deviation of 5 m / s; in each time slot, the direction of movement of the nodes to be located is selected according to a uniform distribution in [0, 2π); the spatial and temporal ranging errors of the nodes to be located follow a Gaussian distribution with a mean of 0 and a standard deviation of 1 meter; max The value is set to 30; the root mean square error (RMSE) is used to represent the positioning accuracy, with the horizontal axis representing the observation time slot and the vertical axis representing RMSE. From Figure 4 As can be seen, for a node to be located, in the third to fifth time slots, the number of neighbors of the node to be located is less than the minimum value of 3 that can accurately determine its own position in a two-dimensional plane. Under this environmental configuration, compared with the other positioning methods mentioned above, the cooperative positioning method of the present invention has the smallest positioning error. At the same time, in time slots where the number of neighbors of the node to be located is ≥3, the cooperative positioning method of the present invention still has the smallest positioning error.

[0105] Except for the technical features described in the specification, all other technologies are known to those skilled in the art. Descriptions of well-known components and technologies are omitted in this invention to avoid redundancy and unnecessary limitation. The embodiments described above do not represent all embodiments consistent with this application. Various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this invention are still within the protection scope of this invention.

Claims

1. A cooperative localization method for distributed wireless networks with highly mobile sparsely distributed nodes, comprising the following steps: Step 1: Construct a distributed wireless self-organizing network containing several nodes to be located and several anchor nodes; in, The nodes to be located and the anchor nodes are distributed in an arbitrary topology within the spatial region; the positions of the anchor nodes are known. For each node to be located, the other nodes to be located that communicate with that node, as well as the anchor node, are called the cooperative positioning nodes of that node. Step 2: Each node to be located broadcasts a cooperative positioning request signal and saves the identity information of the cooperative positioning nodes that return a response within their respective communication range to their respective cooperative list. Step 3: Calculate the prior probability distribution of the random vector of each node to be located; For each node i to be located, based on the posterior probability distribution of the random vector of the node i's position at the previous time step, the prior probability distribution of the random vector of the node i's position at the current time step is calculated according to the prediction steps of the extended Kalman filter algorithm; i is a positive integer. Step 4: During the time slot where positioning is required, each node to be positioned sends a ranging request to each cooperative positioning node in its respective cooperative list. Each node in the cooperative list returns its prior probability distribution of its position to the corresponding node to be positioned. Each node to be positioned obtains the ranging result between itself and its cooperative positioning nodes, thus obtaining the spatial ranging result. Each node to be positioned measures the distance it has moved from the previous time to the current time, thus obtaining the temporal ranging result. Step 5: Each node to be located calculates its posterior probability distribution using the prior probability distribution of its own position random vector and a parameterized message passing algorithm based on spatial and temporal ranging results; each node i to be located executes: Step 501) Calculate the time-domain message corresponding to the time-domain ranging result, and the spatial-domain message corresponding to the spatial-domain ranging result between each cooperative positioning node, using a second-order Taylor polynomial to approximate the nonlinear terms in the time-domain message and the spatial-domain message; wherein, the time-domain message is a function composed of the posterior probability distribution of the position of the node to be positioned i at the previous time step and the observation likelihood function corresponding to the time-domain ranging result measured by the node i; the spatial-domain message corresponding to the spatial-domain ranging result between the node to be positioned i and an anchor node in the cooperative list is a function composed of the prior probability distribution of the anchor node's position vector at the current time step and the observation likelihood function corresponding to the corresponding spatial-domain ranging result; the spatial-domain message corresponding to the spatial-domain ranging result between the node to be positioned i and a node to be positioned in the cooperative list is a function composed of the probability distribution of the position vector provided by the node to be positioned in this iteration and the observation likelihood function corresponding to the corresponding spatial-domain ranging result. Step 502) Iteratively update the spatial domain messages with each cooperating node to be located; in each iteration, each node to be located multiplies its own prior probability distribution, time domain message, and all spatial domain messages called in this iteration to obtain the probability distribution of its own position random vector after this iteration, and broadcasts the probability distribution after this iteration to the nodes to be located in the cooperating list of the node to be located; finally, after reaching the maximum number of iterations set or determined by the iteration convergence threshold, each node to be located multiplies its own prior probability distribution information, each spatial domain message, and time domain message to obtain the posterior probability distribution of its own position random vector at the current time; Step 6: Update the posterior probability distribution of the random vector of the location of the node to be located obtained in Step 5 using the update step of the extended Kalman filter algorithm. Step 7: For each node to be located, take the mean of the random vector in the posterior probability distribution of the node's position after the update process in Step 6, and use it as the final estimated value of the node's position vector at the current time.

2. The method according to claim 1, characterized in that, In step one, each node to be located has a first wireless communication unit, a first storage unit, a first control unit, and a first computing unit. The first storage unit stores the node's cooperative list, the probability distribution information of the node's state vector, the probability distribution information of the random vectors of the cooperative positioning nodes, the ranging results between the node and each cooperative positioning node, and the distance the node has moved from the previous moment to the current moment. The first control unit controls the movement trajectory of the node. The first computing unit calculates the prior probability distribution of the node's random state vector at each moment, the spatial message corresponding to each spatial ranging result, the temporal message corresponding to each temporal ranging result, and the posterior probability distribution of the node's random state vector at each moment.

3. The method according to claim 1, characterized in that, In step one, each anchor node has a second wireless communication unit, a second storage unit, and a second control unit; wherein, the second storage unit stores the anchor node's own position and a list of nodes to be located that have a cooperative relationship with the anchor node; the second control unit is used to control the movement trajectory of the anchor node.

4. The method according to claim 1, characterized in that, In step five, the time-domain message corresponding to the time-domain ranging result calculated by the node to be located is as follows: Let the time-domain ranging result of the node i to be located at time t be: Corresponding time-domain message Represented as: in, This represents the position component of the node i to be located at time t-1. The posterior probability distribution, f represents a vector consisting of all observations of the node i to be located at time t-1, including time-domain ranging results and spatial-domain ranging results; i t|t-1 This represents the time-domain ranging result with respect to the node i to be located. The corresponding observation likelihood functions are as follows: in, express The variance of , ||·||2 represents the Euclidean norm, and exp(·) represents an exponential function with the natural constant e as the base; Time domain messages Nonlinear terms in exist and A second-order Taylor polynomial approximation is performed at the point, where, Let represent the posterior estimate of the position of node i to be located at time t-1. Let represent the prior estimate of the position of node i to be located at time t, then the obtained time-domain message is... The expression satisfies: Where ∝ represents proportionality, and the intermediate parameters are as follows: in, Let y be the final estimated position of node i to be located at time t-1. for The variance.

5. The method according to claim 1, characterized in that, In step five, the node to be located calculates the spatial message corresponding to the spatial ranging result between each cooperative anchor node, as follows: In the l-th iteration, let the spatial ranging result between the node to be located i and the cooperating anchor node k be . Corresponding airspace message Represented as: in, Represents the two positional component variables of anchor node k. and Let represent the probability distributions corresponding to the two positional components of anchor node k, respectively. and Let δ(·) represent the values ​​of the two positional components of anchor node k, and let δ(·) represent the impulse function. Indicates the results of spatial ranging. The corresponding observation likelihood function is as follows: in, express variance Let i and k represent the random vectors of the positions of the node to be located and the anchor node k at time t, respectively. airspace message Nonlinear terms in exist Perform a second-order Taylor polynomial approximation at the l-th position; max In this iteration, the spatial message obtained as follows: The intermediate parameters are as follows: in, This represents the estimated position of node i to be located at time t after the l-th iteration.

6. The method according to claim 1, characterized in that, In step five, the spatial messages corresponding to the spatial ranging results between the node to be located and each cooperating node to be located are calculated as follows: In the l-th iteration, let the spatial ranging result between the node to be located i and the cooperative node to be located j in the cooperative list be... and Corresponding airspace messages Represented as: in, The probability distributions corresponding to the two positional components of node j are shown below: in, Let the random variable represent the two positional components of node j. and represent the mean parameters in the probability distribution functions of the two positional components of node j after the (l-1)th iteration; Indicates airspace message The corresponding observation likelihood function is as follows: in, express The variance; Let i and j represent the random vectors of the positions of nodes i and j to be located at time t, respectively. airspace message Nonlinear terms in exist and A second-order Taylor polynomial approximation is performed at the point, where, This represents the prior estimate of the position of node i to be located at time t. This represents the estimated position of node j after the (l-1)th iteration; in the lth iteration... max In this iteration, the spatial message obtained The expression satisfies The intermediate parameters are as follows: in, and They represent the nodes i and j to be located at time t at the lth time. max Position estimate after -1 iterations; This indicates that at time t, the node j to be located is at the lth position. max The y-axis component of the final position estimate after -1 iterations; for The variance.

7. The method according to claim 1, characterized in that, In step 502, the random vector x of the position of the node i to be located at the current time t is calculated. i t The posterior probability distribution is expressed as: in, express The prior probability distribution, Let be the time-domain message of node i to be located at time t. Let be the set of nodes to be located and the set of anchor nodes in the collaboration list of node i to be located at time t, respectively. To achieve the maximum number of iterations l max The spatial message corresponding to the spatial ranging result between the node i to be located and the cooperating anchor node k. To obtain the spatial message corresponding to the spatial ranging result between the node i to be located and the cooperating node j to be located after the maximum number of iterations; This represents a vector consisting of all observations of the node i to be located at time t, including spatial ranging results and temporal ranging results.

8. The method according to claim 1, characterized in that, The processing procedure in step six includes: Step five yields the posterior probability distribution of the random vector representing the position of the node i to be located. This distribution follows the mean. Covariance Matrix Gaussian distribution; calculate the measurement residual vector for each node to be located. and its covariance matrix as follows: Where H is the observation matrix, This represents the prior estimate of the state vector of the node i to be located at time t; This represents the prior estimate of the state vector covariance matrix of the node i to be located at time t; The approximate optimal Kalman gain is expressed as: Finally, the mean of the posterior probability distribution of the node i to be located at time t is obtained. Covariance Matrix as follows: The superscript T indicates the transpose operation.

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