Generalized gdop-based dense uav cluster cooperative positioning method and system

Abstract

This application discloses a method and system for cooperative localization of dense UAV swarms based on generalized GDOP, relating to the field of UAV navigation and positioning technology. The method includes: constructing a set of UAV nodes based on three-dimensional spatial location information; acquiring ranging observation data between the target node to be located and reference nodes through an airborne ranging device, and constructing a ranging observation model; constructing an observation matrix and obtaining an observation noise covariance matrix composed of the standard deviation of measurement noise in the ranging link; calculating a generalized geometrical precision factor (GDP) based on the observation matrix and the observation noise covariance matrix; iteratively selecting reference nodes from the UAV node set with minimizing the GDP as the optimization objective, generating a reference node set; and using the nodes in the reference node set to perform cooperative localization calculations on the target node to be located, obtaining the estimated three-dimensional position of the target node. This application achieves more accurate localization assessment in dense swarms and complex noise environments through the above method.

Description

Technical Field

[0001] This application relates to the field of unmanned aerial vehicle (UAV) navigation and positioning technology, and in particular to a method and system for cooperative positioning of dense UAV swarms based on generalized GDOP. Background Technology

[0002] In environments where GNSS (Global Navigation Satellite System) signals are limited or denied, UAV swarms often rely on inter-UAV relative ranging for cooperative positioning. The Geometric Dilution of Precision (GDOP) is a core indicator for evaluating the quality of positioning geometry and is widely used for reference node configuration optimization. Traditional GDOP methods typically assume that the observation errors of each ranging link are independent and identically distributed, and calculate the geometric attenuation based on the pseudo-inverse of the observation matrix to guide node selection.

[0003] However, existing technologies have the following shortcomings: First, traditional GDOP cannot characterize the noise heterogeneity and correlation between different ranging links in the real environment, resulting in a large deviation between geometric evaluation and actual positioning accuracy; Second, the number of nodes in dense clusters is large and spatially dynamic, and node selection methods based on exhaustive search or empirical thresholds are computationally too complex, making it difficult to achieve real-time adaptive optimization, and easily introducing redundant nodes or geometrically degenerate combinations; Third, traditional least squares positioning models do not consider the error amplification problem under ill-conditioned conditions of the observation equation, and also lack effective error suppression mechanisms when fusing data at multiple time points.

[0004] Based on the above analysis, the problems and shortcomings of the existing technology are as follows: Existing UAV swarm collaborative positioning technologies suffer from several drawbacks, including the lack of fusion of noise characteristics in traditional GDOP, unreasonable selection of reference nodes, ill-conditioned positioning solutions, susceptibility to outlier interference, and low positioning accuracy, poor robustness, and insufficient real-time performance due to the lack of smooth fusion of data from multiple time points. Summary of the Invention

[0005] This application provides a method and system for cooperative localization of dense UAV swarms based on generalized GDOP, which can solve the problems of low positioning accuracy, poor robustness and insufficient real-time performance caused by the lack of fusion of noise characteristics in traditional GDOP in UAV swarm cooperative localization, unreasonable selection of reference nodes, ill-conditioned positioning solution, susceptibility to outlier interference, and lack of smooth fusion of multi-time data in the prior art.

[0006] In a first aspect, embodiments of this application provide a method for cooperative localization of dense UAV swarms based on generalized GDOP. The method includes: acquiring the three-dimensional spatial position information of UAV nodes; constructing a UAV node set based on the three-dimensional spatial position information; acquiring ranging observation data between the target node to be located and reference nodes using an airborne ranging device based on the UAV node set, and constructing a ranging observation model; constructing an observation matrix based on the ranging observation model, and obtaining an observation noise covariance matrix composed of the standard deviation of measurement noise in the ranging link; calculating the generalized geometrical precision factor based on the observation matrix and the observation noise covariance matrix; iteratively selecting reference nodes from the UAV node set with minimizing the generalized geometrical precision factor as the optimization objective, generating a reference node set; and using the nodes in the reference node set to perform cooperative localization calculations on the target node to be located, obtaining the estimated three-dimensional position of the target node to be located.

[0007] In one implementation of this application, with minimizing the generalized geometric precision factor as the optimization objective, reference nodes are iteratively selected from the UAV node set to generate a reference node set. Specifically, this includes: initializing an empty reference node set; selecting any node from the UAV node set and adding it to the reference node set; traversing the remaining candidate nodes in the UAV node set and calculating the generalized geometric precision factor after adding each candidate node to the current reference node set; selecting the candidate node that causes the largest decrease in the generalized geometric precision factor and adding it to the reference node set; repeating the traversal, calculation, and selection steps until the number of nodes in the reference node set reaches a preset threshold.

[0008] In one implementation of this application, the method further includes: when a change in the spatial location of a node in the UAV cluster or a change in the communication link status is detected, determining the local region where the changed node is located; and calculating a generalized geometric precision factor for a subset of candidate reference nodes within the local region to update the reference node set.

[0009] In one implementation of this application, the method further includes: calculating the decrease in the generalized geometric precision factor after each new node is added to the reference node set; determining whether the decrease in the generalized geometric precision factor for a consecutive preset number of times is lower than a preset marginal revenue threshold; if it is lower than the preset marginal revenue threshold, terminating the iteration in advance, and using the current reference node set as the final reference node set.

[0010] In one implementation of this application, before calculating the generalized geometrical precision factor based on the observation matrix and the observation noise covariance matrix, the method further includes: acquiring measurement noise data of at least two different ranging links; performing correlation analysis on the measurement noise data to determine whether there is a correlation between the noise of the at least two ranging links; and when a correlation is determined to exist, setting the off-diagonal elements in the observation noise covariance matrix corresponding to the at least two ranging links to non-zero values ​​to characterize the impact of the correlation on the calculation of the generalized geometrical precision factor.

[0011] In one implementation of this application, the nodes in the reference node set are used to perform cooperative localization calculation on the target node to be located to obtain the three-dimensional position estimate of the target node to be located. Specifically, this includes: constructing the observation matrix and ranging observation vector corresponding to the reference node set; determining whether the observation matrix is ​​ill-conditioned; if it is determined to be ill-conditioned, introducing a regularization term into the least squares estimation containing the observation matrix and ranging observation vector to form a regularized least squares estimation formula; solving the regularized least squares estimation formula to obtain the three-dimensional position estimate of the target node to be located.

[0012] In one implementation of this application, collaborative localization is performed on the target node to be located using nodes in a reference node set to obtain a three-dimensional position estimate of the target node. Specifically, this includes: dividing the reference node set into a first subset and a second subset, wherein the first subset and the second subset do not overlap and the difference in the number of nodes does not exceed 1; performing least squares localization on the target node to be located based on the first subset to obtain a first position estimate; performing least squares localization on the target node to be located based on the second subset to obtain a second position estimate; calculating the Euclidean distance between the first position estimate and the second position estimate; and when the Euclidean distance is greater than a preset consistency threshold, determining that there are abnormal ranging values ​​in the current reference node set, removing the node that contributes the most to the localization results of the first subset and the second subset, and performing cross-validation on the remaining nodes.

[0013] In one implementation of this application, before performing cooperative localization calculation on the target node to be located using nodes in the reference node set, the method further includes: acquiring ranging observation data for K consecutive time steps prior to the current time step, where K≥2; combining the ranging observation data for K+1 time steps with the same reference node set to construct a multi-time observation equation set; introducing a smoothing constraint term into the multi-time observation equation set, the smoothing constraint term being used to suppress abrupt changes in position estimates between adjacent time steps; and using the least squares method to solve for the three-dimensional position estimate of the target node to be located at the current time step based on the observation equation set after introducing the smoothing constraint term.

[0014] Secondly, embodiments of this application also provide a dense UAV swarm cooperative positioning system based on generalized GDOP. The system includes: a data acquisition module: acquiring the three-dimensional spatial position information of UAV nodes and constructing a UAV node set based on the three-dimensional spatial position information; a ranging calculation module: acquiring ranging observation data between the target node to be positioned and reference nodes through an airborne ranging device based on the UAV node set, and constructing a ranging observation model; an observation matrix and covariance construction module: constructing an observation matrix based on the ranging observation model, and acquiring an observation noise covariance matrix composed of the standard deviation of the measurement noise of the ranging link; a G-GDOP calculation module: calculating the generalized geometrical precision factor based on the observation matrix and the observation noise covariance matrix; a node optimization module: iteratively selecting reference nodes in the UAV node set with the goal of minimizing the generalized geometrical precision factor, and generating a reference node set; and a cooperative positioning calculation module: using the nodes in the reference node set to perform cooperative positioning calculation on the target node to be positioned, and obtaining the three-dimensional position estimate of the target node to be positioned.

[0015] Thirdly, embodiments of this application also provide a non-volatile computer storage medium for cooperative localization of dense UAV swarms based on generalized GDOP, which stores computer-executable instructions, configured to execute any one of the steps of a cooperative localization method for dense UAV swarms based on generalized GDOP.

[0016] This application provides a method and system for collaborative positioning of dense UAV swarms based on generalized GDOP. By introducing the observation noise covariance matrix to construct the generalized GDOP index, the accuracy of positioning accuracy assessment in complex environments is significantly improved. An iterative node selection strategy aimed at minimizing the generalized GDOP is adopted, combined with early termination due to marginal benefits and local incremental update mechanisms, which reduces computational complexity and improves system real-time performance while ensuring positioning accuracy. Regularization is used to suppress the solution divergence problem caused by ill-conditioned matrices, and subset cross-validation is combined to effectively eliminate abnormal ranging and interference nodes, enhancing the positioning robustness. By using multi-time observation data fusion and smoothing constraints, the positioning results are made continuous and stable, greatly reducing positional abrupt changes and jitter. This enables UAV swarms to maintain high-precision and high-robust collaborative positioning performance even in GNSS-constrained scenarios, making it more suitable for engineering applications of dense dynamic swarms. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 A flowchart illustrating a dense UAV swarm cooperative localization method based on generalized GDOP, provided for embodiments of this application; Figure 2 A schematic diagram of the UAV swarm topology network for a dense UAV swarm cooperative localization method based on generalized GDOP provided in this application embodiment; Figure 3 A comparison diagram of GDOP and G-GDOP for a dense UAV swarm cooperative localization method based on generalized GDOP provided in this application embodiment; Figure 4 This is a schematic diagram comparing the positioning errors of a dense UAV swarm cooperative positioning method based on generalized GDOP, provided in an embodiment of this application. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] This application provides a method and system for cooperative localization of dense UAV swarms based on generalized GDOP, which solves the problems of low positioning accuracy, poor robustness and insufficient real-time performance caused by the lack of fusion of noise characteristics in traditional GDOP in the existing UAV swarm cooperative localization, unreasonable selection of reference nodes, ill-conditioned positioning solution, susceptibility to outlier interference, and lack of smooth fusion of multi-time data.

[0020] The technical solutions proposed in the embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0021] Figure 1 A flowchart illustrating a dense UAV swarm cooperative localization method based on generalized GDOP, provided for embodiments of this application. Figure 1 As shown in the figure, the method for cooperative localization of dense UAV swarms based on generalized GDOP provided in this application specifically includes the following steps: Step 10: Obtain the three-dimensional spatial location information of the drone nodes, and construct a drone node set based on the three-dimensional spatial location information.

[0022] In this step, the spatial position status information of each node in the drone swarm is first obtained through the drone's onboard sensors or communication module. Assuming the drone swarm contains N drone nodes, the three-dimensional spatial position of the i-th drone is represented as:

[0023] in, Let x be the x-axis coordinate of the UAV in three-dimensional space; Let y be the y-axis coordinate of the UAV in three-dimensional space; The height coordinates of the UAV in three-dimensional space.

[0024] In the system, all drones establish an information sharing mechanism through a wireless communication network. Each drone node can send its location status information to the data acquisition module, which then uniformly constructs the spatial topology of the drone cluster.

[0025] Construct a set of drone nodes based on the above location information: It is used for subsequent distance measurement calculations and geometric structure analysis.

[0026] Step 20: Based on the UAV node set, acquire the ranging observation data between the target node to be located and the reference node through the airborne ranging equipment, and construct the ranging observation model.

[0027] In this step, after obtaining the spatial location information of the UAV, the distance observation information between the UAVs is obtained through a relative ranging device between the UAVs. Let's assume the position of the target UAV to be located is represented as:

[0028] Under good line-of-sight conditions, the UWB ranging value between the i-th reference UAV and the target UAV can be expressed as:

[0029] in, This represents the distance measured from the i-th UAV to the target UAV; This indicates ranging error noise; Ranging error noise typically follows a Gaussian distribution:

[0030] In the system implementation, the above distance calculation is completed by the distance calculation module, and the distance calculation result is sent to the geometric evaluation module.

[0031] By ranging all reference UAVs, the ranging observation vector can be obtained:

[0032] Where M is the number of reference nodes participating in the positioning.

[0033] In one embodiment, 100 drone nodes are randomly generated within a 100m × 100m × 100m space to construct a cluster topology network, such as... Figure 2 As shown in the figure, the dots represent UAV nodes, and the lines represent the ranging links between nodes.

[0034] Step 30: Based on the ranging observation model, construct the observation matrix and obtain the observation noise covariance matrix composed of the standard deviation of the ranging link's measurement noise.

[0035] In this step, after obtaining the UAV ranging observation data, the impact of the UAV node spatial geometry on positioning accuracy is evaluated. An observation matrix H is constructed based on the ranging equation, and the observation matrix is ​​defined as follows:

[0036] in , which represents the actual distance between the drones.

[0037] After obtaining the observation matrix H, assume that the observation error follows a zero-mean Gaussian distribution, and the observation noise covariance matrix R is expressed as:

[0038] in To measure the standard deviation of noise, It is an identity matrix.

[0039] Step 40: Calculate the generalized geometric precision factor based on the observation matrix and the observation noise covariance matrix.

[0040] In this step, the generalized geometrical precision factor G-GDOP (Generalized Geometric Dilution of Precision) is defined as follows:

[0041] in: The observation matrix; This is the matrix transpose. Represents the matrix trace operation; This is the ranging observation noise covariance matrix, used to describe the noise characteristics of different ranging links.

[0042] G-GDOP is used to evaluate the impact of UAV node spatial geometry on positioning accuracy. The smaller the G-GDOP value, the better the UAV node geometry and the higher the positioning accuracy.

[0043] Step 50: With minimizing the generalized geometric accuracy factor as the optimization objective, iteratively select reference nodes from the UAV node set to generate a reference node set.

[0044] In this step, not all UAV nodes in the UAV swarm participate in the positioning calculation. Therefore, it is necessary to select some nodes from the UAV node set P as reference nodes to participate in the positioning calculation. In order to obtain the optimal positioning geometry, this application proposes a reference node selection optimization method based on G-GDOP minimization.

[0045] As an optional embodiment, with minimizing the generalized geometric accuracy factor as the optimization objective, reference nodes are iteratively selected from the UAV node set to generate a reference node set, which may specifically include: Step 501: Initialize an empty reference node set.

[0046] In this step, the reference node set is initialized. If the set is empty, select any node from the set of drone nodes P as the initial reference node and add it. .

[0047] Step 502: Select any node from the UAV node set and add it to the reference node set; Step 503: Traverse the remaining candidate nodes in the UAV node set and calculate the generalized geometric precision factor after adding each candidate node to the current reference node set; In this step, each of the remaining candidate nodes is added to the current reference node set one by one. Construct the corresponding observation matrix H and calculate the G-GDOP value after adding the node.

[0048] Step 504: Select the candidate node that causes the largest decrease in the generalized geometric precision factor and add it to the reference node set.

[0049] In this step, the changes in G-GDOP after the addition of each candidate node are compared, and the node that causes the largest decrease in G-GDOP is selected to be added to the reference node set. .

[0050] Step 505: Repeat the traversal, calculation and selection steps until the number of nodes in the reference node set reaches the preset threshold.

[0051] In this step, steps 503 to 504 are repeated until the reference node set is reached. When the number of nodes reaches the preset number M, output the final set of reference nodes:

[0052] In this way, the node selection process based on the greedy strategy described above avoids exhaustive calculation of all node combinations. Considering that the number of node combinations increases exponentially with the node size, in actual engineering implementation, heuristic search or approximate optimization methods can also be used to screen the candidate node set, thereby reducing computational complexity and improving the real-time performance of the algorithm while ensuring positioning accuracy.

[0053] Furthermore, a model was built in the simulation software MATLAB, and the simulation results are as follows: Figure 3As shown, experimental results demonstrate that, compared to the traditional GDOP method, the G-GDOP values ​​of clusters at different sizes are significantly reduced using the method of this invention. This indicates that the proposed method effectively considers observation noise characteristics, thereby improving the accuracy of positioning geometry evaluation. Furthermore, the system's geometric stability is further enhanced as the number of UAVs increases.

[0054] As an optional embodiment, the method may further include: step 506: when a change in the spatial location of a node in the UAV cluster or a change in the communication link status is detected, determining the local area where the changed node is located.

[0055] In this step, the real-time status monitoring mechanism of the UAV swarm continuously monitors the three-dimensional spatial position of each node, as well as the status information such as the connectivity and signal strength of the communication links between nodes. When any node is detected to have moved or updated its position, or when the corresponding communication link is interrupted, restored, or weakened, the local area is determined based on the preset spatial range or topological relationship, taking the changed node as the center, so as to accurately locate the range of influence of the change.

[0056] Step 507: Calculate the generalized geometric precision factor for the subset of candidate reference nodes in the local region to update the reference node set.

[0057] In this step, after determining the local region, only the candidate reference nodes within that local region are extracted to form a subset, and traversal calculations are no longer performed on all UAV nodes globally. Based on this subset of local candidate reference nodes, the observation matrix and observation noise covariance matrix are reconstructed, and the corresponding generalized geometric precision factor is calculated. Local nodes are screened and replaced according to the optimization objective of minimizing the generalized geometric precision factor, and the global reference node set is updated incrementally. While ensuring the optimal positioning geometry configuration, the computational overhead caused by global reconstruction is significantly reduced, and the real-time response capability of the system in dynamic scenarios is improved.

[0058] As an optional embodiment, the method may further include: calculating the decrease in the generalized geometric precision factor after each new node is added to the reference node set; determining whether the decrease in the generalized geometric precision factor for a consecutive preset number of times is lower than a preset marginal revenue threshold; if it is lower than the preset marginal revenue threshold, terminating the iteration in advance, and using the current reference node set as the final reference node set.

[0059] In this step, after each new node is added to the reference node set, the decrease in the generalized geometric precision factor (GMP) caused by this addition is calculated. The difference between the GMP value before adding the new node and the value after adding the new node is used to obtain the benefit value of the current iteration. Following the iteration order, the decrease in the GMP after adding new nodes is recorded multiple times. It is determined whether the decrease for a preset number of consecutive times is lower than the preset marginal benefit threshold. If the decrease for a preset number of consecutive times is lower than the preset marginal benefit threshold, it indicates that adding more reference nodes can no longer significantly improve the positioning geometric performance. To reduce the system's computational load and redundancy, the iteration selection process is terminated early, and the currently formed reference node set is directly used as the final optimal reference node set for subsequent collaborative positioning solutions.

[0060] Step 60: Use the nodes in the reference node set to perform cooperative localization calculation on the target node to be located, and obtain the three-dimensional position estimate of the target node to be located.

[0061] In this step, the ranging observation model is linearized and the positioning equation is established based on the least squares estimation principle:

[0062] in, This is the distance measurement observation vector; The observation matrix; denoted as the target UAV position; e represents the measurement error.

[0063] The position estimate of the target UAV can be obtained using the least squares estimation method:

[0064] in, This indicates the estimated location of the target drone.

[0065] Positioning error:

[0066] The root mean square error of UAV positioning was statistically analyzed, and the positioning accuracy of three methods—least square method, random topology method, and G-GDOP-based method—was compared and analyzed. The simulation results are as follows: Figure 4 As shown, Figure 4 The results show the comparison of the root mean square error of the three algorithms under different cluster sizes. The simulation was repeated 300 times using the Monte Carlo method and the average value was taken. The results show that the method of the present invention achieves the lowest positioning error under all scales.

[0067] Furthermore, to verify the performance of the proposed method, multiple Monte Carlo experiments were conducted in a simulation environment. Experimental results show that, compared with traditional methods, the proposed UAV swarm cooperative localization method based on generalized GDOP has significant advantages in both positioning accuracy and stability, and demonstrates good applicability under different noise conditions and swarm sizes.

[0068] As an optional embodiment, the nodes in the reference node set are used to perform cooperative localization calculation on the target node to be located to obtain the three-dimensional position estimate of the target node to be located. Specifically, it may include: Step 601: Construct the observation matrix and ranging observation vector corresponding to the reference node set; In this step, based on the selected optimal set of reference nodes, the positioning equation is linearized using the ranging observation model to construct the observation matrix H corresponding to the current reference node. Then, based on the measured ranging data between each reference node and the target node to be positioned, a ranging observation vector d is generated. The observation matrix and the ranging observation vector correspond one-to-one, forming the basis for the least-squares positioning solution.

[0069] Step 602: Determine whether the observation matrix is ​​ill-conditioned.

[0070] By calculating the condition number, rank, or determinant variation trend of the observation matrix, it can be determined whether the current observation matrix exhibits ill-conditioned characteristics. An observation matrix is ​​considered ill-conditioned when it approaches singularity, its column vectors are approximately linearly dependent, or its geometric structure is severely degraded. Ill-conditioned matrices can cause drastic fluctuations, error amplification, and even positioning divergence in traditional least squares solutions. The ill-conditioned threshold can be set based on the actual sensor's measurement noise level and the system's positioning accuracy requirements.

[0071] Step 603: If the matrix is ​​determined to be ill-conditioned, a regularization term is introduced into the least squares estimate containing the observation matrix and the ranging observation vector to form a regularized least squares estimate.

[0072] In this step, when the observation matrix is ​​determined to be ill-conditioned, a regularization term is introduced into the standard least squares objective function to constrain the magnitude of the localization solution in order to suppress the amplification of the solution error. The observation matrix, the ranging observation vector, and the regularization term are substituted into the objective function to form a stable regularized least squares estimate, ensuring that the localization solution remains convergent and stable even under unfavorable matrix conditions.

[0073] Step 604: Solve the regularized least squares estimation formula to obtain the three-dimensional position estimate of the target node to be located.

[0074] In this step, based on the constructed regularized least squares estimation formula, matrix inversion or iterative optimization methods are used to solve the problem and obtain a stable and convergent 3D position estimate. By introducing regularization constraints, the positioning mutations and error propagation caused by ill-conditioned matrices are effectively avoided, ensuring that the positioning results maintain high accuracy and robustness in complex geometric configurations and dense cluster environments.

[0075] As an optional embodiment, the nodes in the reference node set are used to perform cooperative localization calculation on the target node to be located, to obtain the three-dimensional position estimate of the target node to be located. Specifically, this may include: Step 605: Divide the reference node set into a first subset and a second subset, wherein the first subset and the second subset do not overlap and the difference in the number of nodes does not exceed 1.

[0076] In this step, to verify the consistency of the positioning results, the selected set of reference nodes is divided into two non-overlapping subsets based on the principle of balanced number. The two subsets have no shared nodes, and the difference in the number of nodes does not exceed 1, ensuring that the conditions for the two sets of positioning solutions are basically consistent and improving the reliability of subsequent consistency judgments.

[0077] Step 606: Perform least squares localization on the target node to be located based on the first subset to obtain the first position estimate; Step 607: Perform least squares localization on the target node to be located based on the second subset to obtain the second position estimate; In this step, based on the reference nodes in the first subset, the corresponding observation matrix and ranging observation vector are constructed, and the standard least squares method is used to perform the positioning solution to obtain the first position estimate of the target node to be positioned, which is used as the first set of positioning results; keeping the positioning model and solution parameters unchanged, independent least squares positioning solution is performed only on the reference nodes in the second subset to obtain the second position estimate of the target node to be positioned, which is used as the second set of positioning results.

[0078] Step 608: Calculate the Euclidean distance between the first position estimate and the second position estimate.

[0079] In this step, the spatial distance between the first and second position estimates is calculated using the three-dimensional Euclidean distance formula. This distance is used to quantify the consistency between the two sets of positioning results. The smaller the distance, the more consistent the two sets of positioning results are, and the higher the system reliability. The larger the distance, the more significant the deviation between the two sets of results is, and the higher the possibility of abnormal observations.

[0080] Step 609: When the Euclidean distance is greater than the preset consistency threshold, it is determined that there are abnormal ranging values ​​in the current reference node set, the node that contributes the most to the contradiction of the positioning results of the first subset and the second subset is removed, and the remaining nodes are cross-validated.

[0081] In this step, when the Euclidean distance between two sets of position estimates exceeds a preset consistency threshold, it is determined that the current reference node set contains abnormal ranging values ​​or faulty nodes. Further analysis is conducted to determine the impact of each node on the two sets of positioning results, and the nodes that cause the greatest discrepancy between the two sets of results are removed. After removing abnormal nodes, the subset partitioning, independent calculation, and consistency verification process is repeated using the remaining reference nodes until the two sets of positioning results meet the consistency requirements, thereby improving the anti-interference capability and reliability of collaborative positioning.

[0082] As an optional embodiment, before calculating the generalized geometrical precision factor based on the observation matrix and the observation noise covariance matrix, the method may further include: acquiring measurement noise data from at least two different ranging links; performing correlation analysis on the measurement noise data to determine whether there is a correlation between the noise of the at least two ranging links; and, if a correlation is determined to exist, setting the off-diagonal elements in the observation noise covariance matrix corresponding to the at least two ranging links to non-zero values ​​to characterize the impact of the correlation on the calculation of the generalized geometrical precision factor.

[0083] In this step, measurement noise data from at least two different ranging links are acquired. In actual flight environments, ranging signals between different UAV nodes and target nodes may be subject to the same environmental interference, such as obstruction, multipath effects, and electromagnetic interference, causing the measurement noise of multiple ranging links to fluctuate synchronously and not be completely independent. Correlation analysis is performed on the acquired noise data from multiple ranging links. By calculating the correlation coefficient between noise sequences, it is determined whether the measurement noise of different links has a common trend, thereby determining whether there is a statistical correlation between the links. When it is determined that there is a noise correlation between two or more ranging links, the off-diagonal elements in the observed noise covariance matrix corresponding to these links are set to non-zero values. Traditional covariance matrices only record the independent noise variance of each link at the diagonal position, while the off-diagonal elements are zero, assuming that the noise is independent. By setting the off-diagonal elements to non-zero, the correlation characteristics between noises can be accurately reflected, making the calculation of the generalized geometrical precision factor more consistent with the real environment and improving the reliability of positioning accuracy assessment.

[0084] As an optional embodiment, before performing cooperative localization calculations on the target node using nodes in the reference node set, the method may further include: acquiring ranging observation data for K consecutive time intervals prior to the current time interval, where K ≥ 2.

[0085] In this step, ranging observation data of the current time and the K consecutive times before the current time are obtained, where K≥2, that is, the ranging information of the current time and the most recent multiple frames are used at once, instead of using only single-time data for positioning; By combining the ranging observation data at K+1 time points with the same set of reference nodes, a multi-time observation equation system is constructed.

[0086] In this step, all ranging observation data at these K+1 times are combined with the same optimized set of reference nodes to construct a large set of observation equations containing observation information at multiple times, making full use of data redundancy at different times to improve positioning stability. A smoothing constraint term is introduced into the multi-time observation equations to suppress abrupt changes in the position estimates between adjacent time points.

[0087] In this step, a smoothing constraint term is introduced into the multi-time observation equations. This constraint term is used to enforce restrictions: the position estimates between two adjacent times cannot change too much, so as to avoid problems such as instantaneous movement, jitter, and jagged trajectory of the UAV due to noise interference.

[0088] Based on the observation equations with the introduction of smoothing constraints, the least squares method is used to solve for the estimated three-dimensional position of the target node to be located at the current time.

[0089] In this step, based on the multi-time observation equations with added smoothing constraints, the least squares method is used for overall solution to finally obtain the three-dimensional position estimate of the target node to be located at the current time, making the positioning results smoother, more continuous and more resistant to interference.

[0090] The above are embodiments of the method proposed in this application. Based on the same inventive concept, embodiments of this application also provide a dense UAV swarm cooperative positioning system based on generalized GDOP. The system includes: a data acquisition module: acquiring the three-dimensional spatial position information of UAV nodes and constructing a UAV node set based on the three-dimensional spatial position information; a ranging calculation module: acquiring ranging observation data between the target node to be positioned and reference nodes through an airborne ranging device based on the UAV node set, and constructing a ranging observation model; an observation matrix and covariance construction module: constructing an observation matrix based on the ranging observation model, and acquiring an observation noise covariance matrix composed of the standard deviation of the measurement noise of the ranging link; a G-GDOP calculation module: calculating the generalized geometrical precision factor based on the observation matrix and the observation noise covariance matrix; a node optimization module: iteratively selecting reference nodes in the UAV node set with the goal of minimizing the generalized geometrical precision factor, and generating a reference node set; and a cooperative positioning calculation module: using the nodes in the reference node set to perform cooperative positioning calculation on the target node to be positioned, and obtaining the three-dimensional position estimate of the target node to be positioned.

[0091] Some embodiments of this application provide corresponding to Figure 1A non-volatile computer storage medium for cooperative localization of dense UAV swarms based on generalized GDOP stores computer-executable instructions, which are configured to execute any one of the steps of a cooperative localization method for dense UAV swarms based on generalized GDOP.

[0092] The various embodiments in this application are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the embodiments for IoT devices and media are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0093] The systems, media, and methods provided in this application are one-to-one correspondences. Therefore, the systems and media also have similar beneficial technical effects as their corresponding methods. Since the beneficial technical effects of the methods have been described in detail above, the beneficial technical effects of the systems and media will not be repeated here.

[0094] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0095] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0096] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.

[0097] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0098] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0099] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0100] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0101] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0102] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for cooperative localization of dense UAV swarms based on generalized GDOP, characterized in that, The method includes: Obtain the three-dimensional spatial location information of the UAV nodes, and construct a set of UAV nodes based on the three-dimensional spatial location information; Based on the UAV node set, the ranging observation data between the target node to be located and the reference node is obtained through the airborne ranging device, and a ranging observation model is constructed. Based on the ranging observation model, an observation matrix is ​​constructed, and the observation noise covariance matrix composed of the standard deviation of the ranging link's measurement noise is obtained. Calculate the generalized geometric precision factor based on the observation matrix and the observation noise covariance matrix; With minimizing the generalized geometric accuracy factor as the optimization objective, reference nodes are iteratively selected from the UAV node set to generate a reference node set; By using the nodes in the reference node set to perform cooperative localization calculation on the target node to be located, the three-dimensional position estimate of the target node to be located is obtained.

2. The method for cooperative localization of dense UAV swarms based on generalized GDOP as described in claim 1, characterized in that, The step of iteratively selecting reference nodes from the UAV node set to generate a reference node set, with the optimization objective of minimizing the generalized geometric accuracy factor, specifically includes: Initialize an empty set of reference nodes; Select any node from the drone node set and add it to the reference node set; Traverse the remaining candidate nodes in the UAV node set and calculate the generalized geometric precision factor after adding each candidate node to the current reference node set; Select the candidate node that causes the largest decrease in the generalized geometric precision factor and add it to the reference node set; Repeat the steps of traversal, calculation and selection until the number of nodes in the reference node set reaches a preset threshold.

3. The method for cooperative localization of dense UAV swarms based on generalized GDOP as described in claim 2, characterized in that, The method further includes: When a change in the spatial location of a node or a change in the communication link status is detected in a drone swarm, the local area where the changed node is located is determined. A generalized geometric precision factor is calculated for a subset of candidate reference nodes within the local region to update the reference node set.

4. The method for cooperative localization of dense UAV swarms based on generalized GDOP as described in claim 2, characterized in that, The method further includes: After each new node is added to the reference node set, the decrease in the generalized geometric precision factor is calculated. Determine whether the decrease rate for a preset number of consecutive preset times is lower than a preset marginal revenue threshold; If all values ​​are below the preset marginal revenue threshold, the iteration is terminated early, and the current set of reference nodes is used as the final set of reference nodes.

5. The method for cooperative localization of dense UAV swarms based on generalized GDOP as described in claim 1, characterized in that, Before calculating the generalized geometric precision factor based on the observation matrix and the observation noise covariance matrix, the method further includes: Acquire measurement noise data from at least two different ranging links; Correlation analysis is performed on the measured noise data to determine whether there is a correlation between the noise of at least two ranging links; When a correlation is determined to exist, the off-diagonal elements in the observation noise covariance matrix corresponding to the at least two ranging links are set to non-zero values ​​to characterize the impact of the correlation on the calculation of the generalized geometric precision factor.

6. The method for cooperative localization of dense UAV swarms based on generalized GDOP as described in claim 1, characterized in that, The step of using nodes in the reference node set to perform cooperative localization calculation on the target node to be located, and obtaining the three-dimensional position estimate of the target node to be located, specifically includes: Construct the observation matrix and ranging observation vector corresponding to the reference node set; Determine whether the observation matrix is ​​ill-conditioned; If the matrix is ​​determined to be ill-conditioned, a regularization term is introduced into the least squares estimate containing the observation matrix and the ranging observation vector to form a regularized least squares estimate. Solve the regularized least squares estimation formula to obtain the three-dimensional position estimate of the target node to be located.

7. The method for cooperative localization of dense UAV swarms based on generalized GDOP as described in claim 1, characterized in that, The step of using nodes in the reference node set to perform cooperative localization calculation on the target node to be located, and obtaining the three-dimensional position estimate of the target node to be located, specifically includes: The reference node set is divided into a first subset and a second subset, wherein the first subset and the second subset do not overlap and the difference in the number of nodes does not exceed 1; Based on the first subset, the target node to be located is located by least squares to obtain a first position estimate. Based on the second subset, the target node to be located is located by least squares to obtain a second position estimate. Calculate the Euclidean distance between the first position estimate and the second position estimate; When the Euclidean distance is greater than a preset consistency threshold, it is determined that there are abnormal ranging values ​​in the current reference node set. The node that contributes the most to the positioning results of the first subset and the second subset is removed, and the remaining nodes are cross-validated.

8. The method for cooperative localization of dense UAV swarms based on generalized GDOP according to claim 1, characterized in that, Before performing cooperative localization calculation on the target node to be located using nodes in the reference node set, the method further includes: Obtain ranging observation data for the K consecutive time steps prior to the current time step, where K ≥ 2; By combining the ranging observation data at K+1 time points with the same set of reference nodes, a multi-time observation equation system is constructed. A smoothing constraint term is introduced into the multi-time observation equation set to suppress abrupt changes in the position estimate between adjacent time points. Based on the observation equations after introducing the smoothing constraint term, the least squares method is used to solve for the estimated three-dimensional position of the target node to be located at the current time.

9. A dense UAV swarm cooperative positioning system based on generalized GDOP, characterized in that, The system includes: Data acquisition module: acquires the three-dimensional spatial location information of UAV nodes, and constructs a set of UAV nodes based on the three-dimensional spatial location information; Ranging calculation module: Based on the UAV node set, it acquires ranging observation data between the target node to be located and the reference node through the airborne ranging device, and constructs a ranging observation model; Observation matrix and covariance construction module: Based on the ranging observation model, construct the observation matrix and obtain the observation noise covariance matrix composed of the standard deviation of the measurement noise of the ranging link; G-GDOP calculation module: Calculates the generalized geometric precision factor based on the observation matrix and the observation noise covariance matrix; Node optimization module: With minimizing the generalized geometric accuracy factor as the optimization objective, iteratively selects reference nodes from the UAV node set to generate a reference node set; Cooperative positioning calculation module: Utilizes the nodes in the reference node set to perform cooperative positioning calculation on the target node to be positioned, and obtains the three-dimensional position estimate of the target node to be positioned.

10. A non-volatile computer storage medium for cooperative localization of dense UAV swarms based on generalized GDOP, storing computer-executable instructions, characterized in that, The computer-executable instructions are set as follows: Perform the steps of the dense UAV swarm cooperative localization method based on generalized GDOP as described in any one of claims 1-8.

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