Multi-agent active radio map estimation method
Through the collaborative work of multiple intelligent agents, the Gaussian process model and trajectory planning algorithm are used to solve the problems of incomplete exploration and low efficiency in existing radio map estimation methods, and high-precision and fast radio map reconstruction is achieved, which is suitable for multi-node systems.
Patent Information
- Application Number
- CN202510930196.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-07
- Publication Date
- 2025-10-03
AI Technical Summary
Existing multi-agent active radio map estimation methods are difficult to ensure the completeness and time efficiency of electromagnetic space exploration under a fixed sampling time. Traditional random sampling ignores the intrinsic connection between electromagnetic wave propagation characteristics and sampling locations, resulting in insufficient estimation accuracy.
Through multi-agent collaboration, the Gaussian process model is used to estimate the radio map, periodically train the mean map and variance map, calculate the centroid of the unknown area, allocate exploration windows and perform neighborhood exploration, optimize sampling trajectory planning, avoid repeated sampling, and improve estimation accuracy and confidence.
It achieves efficient and complete radio map exploration with strong adaptability, can quickly reduce regional uncertainty in any two-dimensional task environment, improve estimation accuracy and exploration efficiency, has strong robustness and self-organization, and is suitable for multi-node scale systems.
Smart Images
Figure CN120740567A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of multi-agent collaborative control technology, and in particular to a multi-agent active radio map estimation method for planning trajectories of multiple agents collecting radio map data and constructing a high-precision radio map. Background Art
[0002] Radio maps, as an important tool for characterizing the electromagnetic environment, map the spatial distribution of multidimensional electromagnetic parameters such as received signal strength, power spectral density, and channel gain by mapping geographic coordinates to electromagnetic parameters. Radio maps are currently widely used in network planning, resource management, and indoor positioning. Furthermore, with the advancement of robotics, radio maps are also being applied to the navigation and control of unmanned systems. It is worth noting that the success of these examples all rely on accurate radio maps. Since radio measurement equipment only has point measurement capabilities, traversing the entire space for data collection is time-consuming and labor-intensive. Therefore, reconstructing high-precision radio maps using a relatively small amount of sampled data is crucial for improving efficiency. Radio map estimation techniques have emerged to reconstruct high-fidelity radio maps using spatially collected discrete signal data and environmental characteristics. Such research often obtains signal data through random sampling, ignoring the inherent relationship between electromagnetic wave propagation characteristics and sampling location. Furthermore, they assume that signals can be collected at any location, neglecting the impact of obstacles. Consequently, these methods are difficult to apply to the real-time, autonomous collection and estimation of the electromagnetic environment.
[0003] To address this problem, the academic community has proposed active radio map estimation methods. In this technology, an intelligent agent proactively plans its next sampling trajectory based on real-time data collection and map estimation to improve estimation accuracy. Multi-agent active radio map estimation involves multiple agents simultaneously performing sampling across different airspaces, effectively accelerating exploration efficiency. However, most existing methods only consider single-machine scenarios or improve estimation accuracy at a fixed sampling rate, failing to guarantee the completeness and time efficiency of electromagnetic space exploration. Summary of the Invention
[0004] The purpose of the present invention is to address the above-mentioned existing problems and provide a multi-agent active radio map estimation method that can improve the estimation accuracy under fixed sampling time, which is the focus of existing work, and can also quickly reduce the overall uncertainty of the region, that is, increase the confidence level of the map estimation, thereby achieving efficient and complete exploration.
[0005] The technical solutions of the present invention are as follows: A multi-agent active radio map estimation method comprises the following steps: Build environmental maps, radio maps, and multi-intelligence sampling trajectory planning models; The map estimation module periodically trains a Gaussian process model based on the wireless map data sampled historically by the agent, outputs a mean map, a variance map, and a variance threshold, and then calculates an uncertain map and marks unknown grids to be sampled. The regional exploration module divides the task environment into multiple Voronoi units, assigns the agent an exploration window, calculates the centroid of the unknown connected area based on the exploration window, and evaluates the centroid with the maximum utility as the waypoint; When the agent reaches the centroid, the neighborhood exploration module calculates the spatial sampling correlation matrix related to the neighborhood sampling density, takes the grid with the lowest sampling density as the waypoint, and performs multiple rounds of exploration to ensure uniform neighborhood.
[0006] Through the above method, through the continuous iteration of "map estimation - region exploration - neighborhood exploration", high-quality data can be efficiently collected and the map estimation accuracy can be improved, thereby realizing multi-agent active radio map estimation.
[0007] Furthermore, the map estimation module is constructed as follows: The map estimation module will be triggered periodically to sample data with the signal As input; set the trigger period to , at each triggering moment , the historical sampling positions and data of the agent will be aggregated to obtain the data set ,in, is the sampling location, is the signal strength, is the number of samples in the dataset; Using Gaussian process regression theory, based on the data set Train the Gaussian process model and set the model's hyperparameter variables to , the specific value will be obtained by optimizing the likelihood function as follows: , in, , Represents the kernel function, which is used to measure the correlation between two variables. Considering that the signal strength usually decays quadratically with respect to the distance, the square exponential kernel function is used, that is: , Based on the trained Gaussian process, the radio map to be estimated The coordinate set of all grids in , calculate the estimated value The posterior distribution of : , in, is the mean, which can be calculated as: , in, is the covariance matrix, whose diagonal elements are given by composition; Based on the trained Gaussian process model, this module will output a mean map , variance map ; Using threshold Update the uncertainty map matrix .
[0008] Furthermore, the It can be calculated as: .
[0009] Furthermore, the method for constructing the area exploration module includes: Setting up the Agent The area exploration is completed with the identifier , whose initial value is ,when for Enter the module when Setting up the Agent The current target waypoint is ,by Agent target waypoints As the spawn point, the task environment Divide into non-overlapping Voronoi unit , each Voronoi unit Formally: , in, is the vector norm. At the beginning of the mission, since the target waypoints are all empty, that is, , at this time ; Set the minimum bounding rectangle of the Voronoi cell As an intelligent agent The exploration window, set the exploration window In the uncertainty map matrix The slice on , the 0-1 matrix Treat it as a binary image, use image processing algorithm to find connected areas, and get a series of unknown connected areas. The area is ; For the agent , calculate each connected area Generalized quality and centroid : , Traverse all connected areas Calculate its center of mass. If the center of mass Located outside the Vinod unit, i.e. , then remove the centroid; if the centroid is within the obstacle, project it to the nearest free grid position, that is, , Thus, a set of candidate centroids is formed ; Constructing utility function to evaluate centroid : , in, , traverse all centroids , the centroid with the maximum utility will be selected as the current waypoint of the agent, that is: , When the candidate centroid is an empty set , the agent will include the candidate centroids of other agents and exclude the target waypoints of other agents, that is, , Then select the target waypoint; Calculate the target waypoint through trajectory planning algorithm The trajectory of the agent Arrival at the destination waypoint ,but , and exit the current module.
[0010] Furthermore, the trajectory planning algorithm is an A star algorithm.
[0011] This method uses a Voronoi diagram to divide the environment into non-overlapping regions. Each agent is responsible for one unit. The generalized centroid of the unknown connected region is used as a navigation point. The centroid position of each unknown region is calculated (accounting for obstacle projections). The optimal navigation point is dynamically selected based on a utility function that considers distance and region size. This avoids the exploration blind spots caused by traditional random sampling and ensures complete global coverage.
[0012] Furthermore, the method for constructing the neighborhood exploration module includes: when Enter the module when Set the spatial sampling correlation matrix , whose elements are determined by the sampling density of the neighborhood: , For the agent , the current grid row and column pair is , target waypoint The grid around it will be selected In the neighborhood The grid with the largest element value is the grid with the lowest neighborhood sampling density: , Calculate the target waypoint through trajectory planning algorithm trajectory.
[0013] Furthermore, the neighborhood exploration module will execute multiple rounds, setting the maximum number of rounds to , the termination round number is , which can be calculated as: , in, Representing an agent The Unknown areas In an uncertain map Slice on, set the current round number to , the initial value is 0; when the agent reaches the waypoint hour, ,like , then return to the step of setting the spatial sampling correlation matrix, otherwise let , , exit the module.
[0014] Through this method, after reaching the centroid, the agent selects a local sampling point based on the spatial sampling correlation matrix, prioritizes exploring surrounding grids with lower sampling density, and sets rounds to ensure uniform local coverage. This prevents repeated sampling in local areas and improves data collection efficiency.
[0015] Furthermore, the establishment of a multi-intelligent sampling trajectory planning model includes the following steps: Set the An intelligent agent in The coordinates of the moment are , and set the agent to move only to the neighborhood grid of 3×3 at each moment, the corresponding kinematic constraints The calculation method is: , in, Represents the mapping function from grid coordinates to grid row and column pairs, represents the infinite norm; Set the 0-1 sampling matrix , Indicates that the corresponding grid has been sampled, otherwise, Indicates that it has not been sampled; if the position of the agent at a certain moment is in a certain grid, the grid is considered to have been sampled; Radio Map By Gaussian process approximation, the following posterior Gaussian distribution can be constructed: , in, represents a sampled data set, is the mean function, indicating the position The estimated signal strength at ; represents the variance function; in the Gaussian process, the point Variance With confidence interval satisfy ,in, Indicates confidence Corresponding Score; from the perspective of parameter estimation, the maximum error tolerance ratio is given When the confidence interval is within the error tolerance range, the area can be considered "known". Otherwise, the area is uncertain or "unknown" and further sampling is required. The corresponding threshold is: , in, express The maximum value of the function; set the 0-1 uncertainty map matrix ,like OK The grid of the column is the free grid, that is , and the variance Greater than a given threshold ,matrix The corresponding element will be marked as 1, otherwise it will be marked as 0; It can be expressed as: , The goal of sampling trajectory planning for a multi-agent system is to reduce the proportion of unknown areas to a preset ratio in the shortest possible time. , which can be formally expressed as the following optimization problem model:
[0016]
[0017] , in, Indicates the task completion time. is the Frobenius norm, for any 0-1 matrix , Equivalent to The number of non-zero grids in yes The number of unknown grids at the time, is the number of free grids in the task environment.
[0018] Furthermore, the It can be constructed as follows: , in, It is the rounding operator towards negative infinity.
[0019] Furthermore, the establishment of the environment map and the radio map includes the following steps: Set up the multi-agent task environment and the corresponding environment map matrix ; Set the radiation source parameters and the corresponding radio map matrix ; The task environment is a two-dimensional plane space, represented as a set , task environment Existence Incoherent radiation source, any position The received signal strength at is modeled as: , in, Represents the received signal components of each radiation source ; Divide the task environment evenly into grid, for OK The grid coordinates of the columns are expressed as the coordinates of the grid center point: , Represents the mapping function from grid rows and columns to grid coordinates: , in, , are the X-axis and Y-axis coordinate ranges of the task environment, is the origin coordinate of the task environment; Set up a 0-1 environment map matrix ,That OK Column Elements Indicates that the corresponding grid is occupied by an obstacle, otherwise Indicates that it is free space; sets the radio map matrix ,element The received intensity at the grid coordinates of the corresponding grid is recorded, that is, .
[0020] Compared with the existing technology, the beneficial effects of the present invention are: 1. Strong adaptability and scalability: This application estimates radio maps using a Gaussian process model, without any restrictions on environment size, obstacle distribution, or the number, type, and distribution of electromagnetic radiation sources. It is applicable to the acquisition and estimation of radio maps for any radiation source configuration in any two-dimensional task environment. Furthermore, the present invention allocates exploration windows using the Voronoi partitioning method, allowing each agent to collect non-overlapping areas in parallel. Provided communication and computing power allow, the present invention can be expanded to multi-agent systems of any node size. 2. Complete and efficient exploration: This application quickly detects and locates unknown areas by calculating the centroid of connected regions, ensuring complete exploration. Furthermore, after the agent reaches the region centroid, the invention adds neighboring exploration to achieve uniform sampling of the unknown area, avoiding secondary exploration of the area.
[0021] 3. Strong robustness and self-organization: By periodically broadcasting sampling data and sharing location data in real time, the present invention can be distributed and deployed on each intelligent agent to run independently. The failure of some intelligent agents will not affect the task execution of other intelligent agents. BRIEF DESCRIPTION OF THE DRAWINGS
[0022] Figure 1 Flowchart of the present application method.
[0023] Figure 2 Scene graph for multi-agent sampling trajectory planning tasks.
[0024] Figure 3 Schematic diagram of the agent extracting the centroid from the exploration window.
[0025] Figure 4 The sampled trajectories and final deployment positions of the intelligent agent using the algorithm proposed in this application.
[0026] Figure 5 This is the final radio map estimation result using the algorithm proposed in this application.
[0027] Figure 6 The estimation error of the algorithm proposed in this application and the comparison algorithm under fixed sampling time is shown. DETAILED DESCRIPTION
[0028] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.
[0029] The features and performance of the present invention are further described in detail below with reference to the embodiments.
[0030] See also Figure 1-6 , a multi-agent active radio map estimation method, e.g. Figure 1 and Figure 2 As shown, the following steps are included: S1. Build environment maps, radio maps, and multi-agent sampling trajectory planning models; S1.1. Setting up the multi-agent task environment and the corresponding environment map matrix In this embodiment, the side length is set to The rectangular area is divided into Raster maps of size, such as Figure 1 As shown in Figure 1. Black grids represent obstacle grids, and colored grids represent idle grids. Construct an environment map matrix based on the obstacle distribution. , the size is .
[0031] S1.2. Set the radiation source parameters and the corresponding radio map matrix In this embodiment, the number of radiation sources is , the coordinates are , the operating frequency of the radiation source is , No. The total radio propagation loss of a radiating source is modeled as: , in, is the signal frequency , is the distance power attenuation coefficient, and are the distance between the radiation source and the receiving terminal and the number of walls, is the wall penetration loss coefficient. The radiation source, take the empirical value as well as Based on this, the received signal components of each radiation source are calculated as follows: , in, For the The transmission power (dBm) of each radiation source. In this embodiment, the transmission power is Calculate each grid The received signal strength at ,like Figure 1 As shown. The normalized value of the received signal strength corresponding to the color grid is represented by the color scale in the figure. According to the received signal strength of each grid , construct the radio map matrix , the size is .
[0032] S1.3. Set up the multi-agent trajectory planning model, including the number of nodes in the multi-agent system , confidence , Maximum error tolerance ratio and the scaling factor In this embodiment, the multi-agent system consists of three agents. , query the Z score comparison table of the standard Gaussian distribution to obtain the confidence level The Z score is . , Therefore, when the ratio of the number of grids in the environment that satisfy (6) is reduced to After the following, the task is considered completed. .
[0033] S2. Set the radio map estimation and neighborhood exploration module parameters; S2.1. Setting the trigger period in the radio map estimation module In this embodiment, .
[0034] S2.2. Set the maximum number of rounds in the neighborhood exploration module In this embodiment, .
[0035] S3, execute the radio map estimation module and update the map; S3.1. Get the current time value .like If true, randomly sample 1% of the radio map grid using grid coordinates. and sampling data Building a dataset In this embodiment, the number of grids collected is 21. Set the sampled grid coordinates to , the raster data is .definition ,in, , .make when If it is false, go to S3.2.
[0036] S3.2. Calculate the corresponding grid coordinates based on the positions of all agents In this embodiment, the coordinates of all agents are , corresponding to the grid coordinates .
[0037] S3.3. Construction Sampling dataset at time ,in, are the grid coordinates of all agents, is the collected data of all agents. join in In this embodiment, , .
[0038] S3.4, according to Update spatial sampling correlation matrix .
[0039] S3.5, when If true, go to S3.6; otherwise, go to S4.
[0040] S3.6. Optimize the likelihood function to obtain hyperparameters , further based on and , calculate the posterior distribution model of the estimated value.
[0041] S3.7, based on the posterior distribution model, traverse all grid coordinates , calculate the mean map , variance map . And calculate the corresponding threshold , further update the uncertainty map matrix .
[0042] S3.8, if If is true, the task is completed. If it is false, go to S4.
[0043] S4, execute area exploration module; S4.1. If True, set the The region exploration completion identifier of the agent is , set the The target waypoint of the agent . judge Is it true? If true, go to S5. If false, go to S4.2.
[0044] S4.2, according to Agent target waypoints ,get Voronoi unit and use Calculate the bounding rectangle to get the exploration window , get exist Slices on , and use image processing algorithms to calculate The unknown connected area on The connected regions are In this embodiment, the calculation of the connected area calls the bwconncomp function in MATLAB.
[0045] S4.3, according to Calculate the center of mass. Set up the agent The set of candidate centroids . Traverse all the centroids, if If it is within the obstacle, then according to Calculate the center of mass after projection .like ,but The centroid extraction process from the exploration window is as follows Figure 3 shown.
[0046] S4.4, if Not an empty set, according to Obtain target waypoint .like If it is an empty set, then add the candidate centroids of other agents to obtain the target waypoint .
[0047] S4.5. Calculate arrival using trajectory planning algorithm In this embodiment, the trajectory planning algorithm adopts the A star algorithm.
[0048] S4.6, judge the Agent positions Arrival If true, then .
[0049] S5, executing the neighborhood exploration module; S5.1. Judgment Is it true? If true, calculate the termination round number , set the current round number , go to S5.2. If false, go to S5.4.
[0050] S5.2. Calculate the The target waypoint of the agent , using trajectory planning algorithm to calculate the arrival path and execute it.
[0051] S5.3, judge the Agent positions Arrival If true, . Further, judge Is true. If true, then .
[0052] S5.4, Order , return to S3.
[0053] At this point, the multi-agent active radio map estimation method has been implemented.
[0054] Experimental verification: Through MATLAB simulation experiments, Figure 4 The sampling trajectory and final deployment position of the intelligent agent using the algorithm proposed in this invention are shown. Figure 5 The final radio map estimation results are shown. It can be seen that the trajectories planned by this application are evenly distributed across all "rooms" in the scene, balancing the completeness of global exploration with the accuracy of local exploration, directly verifying the regional and neighborhood exploration capabilities. After 10 Monte Carlo experiments, this application achieved a 100% mission success rate, an average completion time of 365 steps, an average sampling rate of 43%, and a root mean square error (RMSE) of 5.1886 dB for map estimation. To demonstrate the advantages of this application in map estimation, an algorithm with only neighborhood exploration capabilities was used as a comparison algorithm. Figure 6 The proposed algorithm and the comparison algorithm show the estimation errors at a fixed sampling time. As the sampling time increases, the estimation accuracy of all algorithms improves. The proposed algorithm significantly improves the estimation accuracy, reducing the error by 28% and 20%, respectively, while the comparison algorithm only reduces it by 12%.
[0055] The above-described embodiments merely represent specific implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of protection of the present application. It should be noted that a person skilled in the art would be able to make various modifications and improvements without departing from the technical concept of the present application, and these modifications and improvements are all within the scope of protection of the present application.
Claims
1. A multi-agent active radio map estimation method, characterized in that: The following steps are involved: Build environmental maps, radio maps, and multi-intelligence sampling trajectory planning models; The map estimation module periodically trains a Gaussian process model based on the wireless map data sampled historically by the agent, outputs a mean map, a variance map, and a variance threshold, and then calculates an uncertain map and marks unknown grids to be sampled. The regional exploration module divides the task environment into multiple Voronoi units, assigns the agent an exploration window, calculates the centroid of the unknown connected area based on the exploration window, and evaluates the centroid with the maximum utility as the waypoint; When the agent reaches the centroid, the neighborhood exploration module calculates the spatial sampling correlation matrix related to the neighborhood sampling density, takes the grid with the lowest sampling density as the waypoint, and performs multiple rounds of exploration to ensure uniform neighborhood.
2. A multi-agent active radio map estimation method according to claim 1, characterized in that: The construction method of the map estimation module is as follows: The map estimation module will be triggered periodically to sample data with the signal As input; set the trigger period to , at each triggering moment , the historical sampling positions and data of the agent will be aggregated to obtain the data set ,in, is the sampling location, is the signal strength, is the number of samples in the dataset; Using Gaussian process regression theory, based on the data set Train the Gaussian process model and set the model's hyperparameter variables to , the specific value will be obtained by optimizing the likelihood function as follows: ， in, , Represents the kernel function, which is used to measure the correlation between two variables. Considering that the signal strength usually decays quadratically with respect to the distance, the square exponential kernel function is used, that is: ， Based on the trained Gaussian process, the radio map to be estimated The coordinate set of all grids in , calculate the estimated value The posterior distribution of : ， in, is the mean, which can be calculated as: ， in, is the covariance matrix, whose diagonal elements are given by composition; Based on the trained Gaussian process model, this module will output a mean map , variance map ; Using threshold Update the uncertainty map matrix .
3. A multi-agent active radio map estimation method according to claim 2, characterized in that: described It can be calculated as: 。 4. The multi-agent active radio map estimation method according to claim 1, characterized in that: The method for constructing the area exploration module includes: Setting up the Agent The area exploration is completed with the identifier , whose initial value is ,when for Enter the module when Setting up the Agent The current target waypoint is ,by Agent target waypoints As the spawn point, the task environment Divide into non-overlapping Voronoi unit , each Voronoi unit Formally: ， in, is the vector norm. At the beginning of the mission, since the target waypoints are all empty, that is, , at this time ; Set the minimum bounding rectangle of the Voronoi cell As an intelligent agent The exploration window, set the exploration window In the uncertainty map matrix The slice on , the 0-1 matrix Treat it as a binary image, use image processing algorithm to find connected areas, and get a series of unknown connected areas. The area is ; For the agent , calculate each connected area Generalized quality and centroid : ， Traverse all connected areas Calculate its center of mass. If the center of mass Located outside the Vinod unit, i.e. , then remove the centroid; if the centroid is within the obstacle, project it to the nearest free grid position, that is, ， Thus, a set of candidate centroids is formed ; Constructing utility function to evaluate centroid : ， in, , traverse all centroids , the centroid with the maximum utility will be selected as the current waypoint of the agent, that is: ， When the candidate centroid is an empty set , the agent will include the candidate centroids of other agents and exclude the target waypoints of other agents, that is, ， Then select the target waypoint; Calculate the target waypoint through trajectory planning algorithm The trajectory of the agent Arrival at the destination waypoint ,but , and exit the current module.
5. A multi-agent active radio map estimation method according to claim 4, characterized in that: The trajectory planning algorithm is the A star algorithm.
6. The multi-agent active radio map estimation method according to claim 1, characterized in that: The method for constructing the neighborhood exploration module includes: when Enter the module when Set the spatial sampling correlation matrix , whose elements are determined by the sampling density of the neighborhood: ， For the agent , the current grid row and column pair is , target waypoint The grid around it will be selected In the neighborhood The grid with the largest element value is the grid with the lowest neighborhood sampling density: ， Calculate the target waypoint through trajectory planning algorithm trajectory.
7. A multi-agent active radio map estimation method according to claim 6, characterized in that: The neighborhood exploration module will execute multiple rounds, setting the maximum number of rounds to , the termination round number is , which can be calculated as: ， in, Representing an agent The Unknown areas In an uncertain map On the slice, is the Frobenius norm, set the current round number to , the initial value is 0; when the agent reaches the waypoint hour, ,like , then return to the step of setting the spatial sampling correlation matrix, otherwise let , , exit the module.
8. The multi-agent active radio map estimation method according to claim 1, characterized in that: The establishment of the multi-intelligent sampling trajectory planning model includes the following steps: Set the An intelligent agent in The coordinates of the moment are , and set the agent to move only to the neighborhood grid of 3×3 at each moment, the corresponding kinematic constraints The calculation method is: ， in, Represents the mapping function from grid coordinates to grid row and column pairs, represents the infinite norm; Set the 0-1 sampling matrix , Indicates that the corresponding grid has been sampled, otherwise, Indicates that it has not been sampled; if the position of the agent at a certain moment is in a certain grid, the grid is considered to have been sampled; Radio Map By Gaussian process approximation, the following posterior Gaussian distribution can be constructed: ， in, represents a sampled data set, is the mean function, indicating the position The estimated signal strength at ; represents the variance function; in the Gaussian process, the point Variance With confidence interval satisfy ,in, Indicates confidence Corresponding Score; from the perspective of parameter estimation, the maximum error tolerance ratio is given When the confidence interval is within the error tolerance range, the area can be considered "known". Otherwise, the area is uncertain or "unknown" and further sampling is required. The corresponding threshold is: ， in, express The maximum value of the function; set the 0-1 uncertainty map matrix ,like OK The grid of the column is the free grid, that is , and the variance Greater than a given threshold ,matrix The corresponding element will be marked as 1, otherwise it will be marked as 0; It can be expressed as: ， The goal of sampling trajectory planning for a multi-agent system is to reduce the proportion of unknown areas to a preset ratio in the shortest possible time. , which can be formally expressed as the following optimization problem model: ， in, Indicates the task completion time. is the Frobenius norm, for any 0-1 matrix , Equivalent to The number of non-zero grids in yes The number of unknown grids at the time, is the number of free grids in the task environment.
9. The multi-agent active radio map estimation method according to claim 8, characterized in that: described It can be constructed as follows: ， in, It is the rounding operator towards negative infinity.
10. The multi-agent active radio map estimation method according to claim 1, characterized in that: The establishment of the environment map and the radio map comprises the following steps: Set up the multi-agent task environment and the corresponding environment map matrix ; Set the radiation source parameters and the corresponding radio map matrix ; The task environment is a two-dimensional plane space, represented as a set , task environment Existence Incoherent radiation source, any position The received signal strength at is modeled as: ， in, Represents the received signal components of each radiation source ; Divide the task environment evenly into grid, for OK The grid coordinates of the columns are expressed as the coordinates of the grid center point: , Represents the mapping function from grid rows and columns to grid coordinates: ， in, , are the X-axis and Y-axis coordinate ranges of the task environment, is the origin coordinate of the task environment; Set up a 0-1 environment map matrix ,That OK Column Elements Indicates that the corresponding grid is occupied by an obstacle, otherwise Indicates that it is free space; sets the radio map matrix ,element The received intensity at the grid coordinates of the corresponding grid is recorded, that is, .