A UUV Cluster Localization Method Based on Merged Enhanced Multidimensional Scale Analysis

Abstract

This invention provides a UUV cluster localization method based on merged enhanced multidimensional scale analysis (MDS), belonging to the field of cluster localization technology. The method includes: acquiring the coordinate information of anchor nodes and the observation distance matrix of the node group; constructing different reference groups based on reference points; for the same reference group, combining the reference group with nodes in the node group that do not belong to the reference group to obtain sub-groups; calculating the relative coordinates of nodes within each sub-group using the MDS algorithm, and then performing rigid body registration to obtain the global relative coordinates corresponding to the reference group; aligning the global relative coordinates based on the coordinate information of the anchor nodes to obtain the absolute coordinate set corresponding to the reference group; and optimizing based on each absolute coordinate set to obtain the localization result of the node to be located. This method fully utilizes the positional information of the reference points, significantly suppresses ranging errors and channel noise, improves the localization effect, and solves the performance degradation problem of traditional MDS in low-connectivity scenarios.

Description

Technical Field

[0001] This invention relates to the field of swarm positioning technology, and is particularly applicable to underwater unmanned vehicle swarm positioning methods based on merging enhanced multidimensional scale analysis. Background Technology

[0002] Underwater unmanned vehicle (UUV) swarms play a vital role in scenarios such as seabed archaeology, underwater resource exploration, and marine development. Since the underwater environment cannot rely on satellite navigation, and high-precision inertial navigation systems are costly and difficult to deploy on a large scale, range-based multidimensional scaling (MDS) positioning methods are gradually becoming the mainstream solution for underwater swarm positioning.

[0003] The classic MDS algorithm constructs a distance matrix by measuring the distance between nodes, transforming it into relative coordinates in a low-dimensional space. However, it has significant limitations in sparse and noisy underwater environments.

[0004] High connectivity requirements: It requires the assumption of a fully connected network, but underwater acoustic channels suffer from severe attenuation, and link interruptions are prone to occur in sparse clusters; High error sensitivity: It is highly sensitive to distance measurement errors, and ranging deviations caused by underwater sound speed fluctuations and multipath effects will seriously reduce positioning accuracy; To address the above problems, existing technologies such as the MDS-MAP method compensate for connectivity deficiencies through shortest path estimation, but in low-density networks, the high attenuation of long-distance links will still lead to a significant performance degradation and reduced positioning accuracy.

[0005] Therefore, there is an urgent need for a positioning method that is adaptable to sparse underwater cluster environments and has strong anti-interference capabilities, in order to solve the problem of excessive positioning errors in existing technologies in low connectivity and high noise scenarios. Summary of the Invention

[0006] To address the shortcomings of large positioning errors and reliance on fully connected underwater sparse swarms in low-connectivity, high-noise scenarios, this invention provides a method for underwater unmanned vehicle (UUV) swarm positioning based on merging enhanced multidimensional scaling analysis, comprising:

[0007] Step S1: Obtain the coordinate information of the anchor node and the observation distance matrix of the node group, wherein the node group includes the anchor node and the underwater unmanned vehicle cluster nodes to be located.

[0008] Step S2: Divide the nodes in the node group into reference points and non-reference points according to the signal-to-noise ratio of the ranging signal;

[0009] Step S3: Based on the divided reference points, construct different reference groups;

[0010] Step S4: For the same reference group, perform the following processing:

[0011] Step S41: Combine the reference group with nodes in the node group that do not belong to the reference group to obtain different sub-combinations;

[0012] Step S42: Calculate the relative coordinates of nodes within each sub-combination using the MDS algorithm;

[0013] Step S43: Perform rigid body registration on the relative coordinates within each sub-group, unify the coordinate system, and obtain the global relative coordinates corresponding to the reference group;

[0014] Step S5: Perform step S4 above on each reference group to obtain the global relative coordinates corresponding to each reference group.

[0015] Step S6: Align the global relative coordinates of each reference group based on the coordinate information of the anchor node to obtain the global absolute coordinates of each reference group.

[0016] Step S7: Optimize based on each global absolute coordinate to obtain the positioning result of the node to be located.

[0017] Optionally, step S2 includes:

[0018] Step S21: Based on the observation distance matrix, calculate the signal power attenuation between nodes according to the following formula:

[0019] ,

[0020] Where TL represents the signal power attenuation between node i and node j; This represents the observation distance between node i and node j. For parameter items;

[0021] Step S22: Calculate the signal-to-noise ratio of signal propagation between nodes based on the signal power attenuation;

[0022] Step S23: Based on the signal-to-noise ratio of signal propagation between the nodes, the nodes in the node group are divided into reference points and non-reference points using a signal-to-noise ratio threshold.

[0023] Optionally, step S42 includes:

[0024] The observation distance matrix corresponding to the sub-combination is obtained based on the observation distance matrix of the node group;

[0025] The observation distance matrix corresponding to the sub-combination is double-centered according to the following formula:

[0026] ,

[0027] in, This represents the quadratic centered matrix corresponding to the nth sub-combination obtained based on the mth reference group; This represents the observation distance matrix corresponding to the nth sub-combination obtained based on the mth reference group. Represents a centered matrix; "Indicates the Hadamardi accumulation;

[0028] The quadratic centered matrix is ​​subjected to eigenvalue decomposition to obtain a preset number of eigenvalues ​​and corresponding eigenvectors;

[0029] Calculate the relative coordinates of nodes within a sub-combination using the following formula:

[0030] ,

[0031] in, This represents the relative coordinates of the nodes within the nth sub-combination obtained based on the mth reference group; This represents a diagonal matrix composed of a predetermined number of eigenvalues. This represents the matrix formed by the eigenvectors corresponding to the eigenvalues.

[0032] Optionally, step S7 includes:

[0033] The positioning result of the point to be located is obtained by performing least squares optimization based on each global absolute coordinate according to the following formula:

[0034] ,

[0035] Where Z represents the sum of squared residuals; This represents a parameter function minimized with respect to X as the optimization objective, where X represents the absolute coordinates of each node in the node group, including the absolute coordinates of the node to be located. Represents the absolute coordinates of the nth node in the node group; This represents the absolute coordinates of the nth node in the global absolute coordinates corresponding to the kth reference group; K represents the number of reference groups, and N represents the number of nodes in the node group.

[0036] Optionally, step S7 includes:

[0037] The positioning result of the point to be located is obtained by optimizing each global absolute coordinate according to the following formula:

[0038] ,

[0039] in, Represents the absolute coordinates of the nth node in the node group; , , These represent the coordinates of the nth node in the global absolute coordinates corresponding to the kth reference group in the x, y, and z directions, respectively; K represents the number of reference groups.

[0040] Furthermore, the present invention also proposes an electronic device and a readable storage medium:

[0041] An electronic device includes a processor and a memory, the memory being used to store one or more programs; characterized in that: when the one or more programs are executed by the processor, the above-described method is implemented.

[0042] A readable storage medium storing a computer program, characterized in that: when the computer program is executed by a processor, the above-described method is implemented.

[0043] The embodiments described in this invention have the following advantages:

[0044] This invention provides a method for swarm localization of underwater unmanned vehicles (UUVs) based on merging enhanced multidimensional scale analysis. The method involves acquiring the coordinate information of anchor nodes and the observation distance matrix of the node swarm. Based on the signal-to-noise ratio of the ranging signals, the nodes in the swarm are divided into reference points and non-reference points. Different reference groups are constructed based on these reference points. For each reference group, the reference group is combined with nodes in the node swarm that do not belong to the reference group, resulting in different sub-combinations. The relative coordinates of nodes within each sub-combination are calculated using the MDS algorithm. Then, the relative coordinates within each sub-combination are rigidly registered to unify the coordinate system, obtaining the global relative coordinates corresponding to the reference group. The above steps are performed on each reference group to obtain the global relative coordinates corresponding to each reference group. Based on the coordinate information of the anchor nodes, the global relative coordinates corresponding to each reference group are aligned to obtain the global absolute coordinates corresponding to each reference group. Finally, optimization processing is performed based on the global absolute coordinates to obtain the localization result of the node to be located.

[0045] Using the above method, the positioning method of this invention achieves underwater swarm positioning of unmanned aerial vehicles based on two loops. The first loop iteration decomposes a single positioning operation into multiple parallel positioning groups. This approach helps to fully utilize the unique topological distribution of different reference groups when limited observation information is available. The second loop iteration incorporates different child nodes through the same reference node to construct sub-positioning results at the same level, achieving a gradual reduction in error, significantly suppressing ranging errors and channel noise, and improving positioning accuracy.

[0046] Therefore, the aforementioned dual-loop positioning method can fully utilize the location information of reference points, reduce the interference of low signal-to-noise ratio nodes in low connectivity and high noise environments on the positioning results, improve the positioning effect, and solve the performance degradation problem of traditional MDS in low connectivity scenarios. Furthermore, it reduces the dependence on anchor nodes, and the positioning of underwater unmanned vehicle clusters can be achieved with a small number of anchor nodes, making it more suitable for sparse cluster environments underwater, with good anti-interference effect and applicability. At the same time, merging the global absolute coordinates corresponding to each reference group to obtain the absolute coordinates of the point to be positioned further reduces the positioning error.

[0047] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0048] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0049] Figure 1 A flowchart of a swarm localization method for underwater unmanned vehicles (UUVs) based on merging enhanced multidimensional scale analysis is provided for embodiments of the present invention.

[0050] Figure 2 Flowchart of another underwater unmanned vehicle (UUV) swarm localization method based on merging enhanced multidimensional scale analysis provided in this embodiment of the invention;

[0051] Figure 3 This is a comparison chart of positioning results under a rectangular cuboid region when the cluster size is 17, provided by an embodiment of the present invention.

[0052] Figure 4 This is a comparison chart of positioning results for a cluster of 17 centered cuboid regions, provided as an embodiment of the present invention.

[0053] Figure 5 This is a comparison chart of positioning results under a C-shaped polyhedron region when the cluster size is 17, provided as an embodiment of the present invention.

[0054] Figure 6 A comparison chart of the relationship between positioning error and number of points in a rectangular cuboid region when the maximum reference combination limit is 200 and 400, provided for an embodiment of the present invention;

[0055] Figure 7 A comparison chart of the relationship between positioning error and number of points in a centered cuboid region when the maximum reference combination limit is 200 and 400, provided for embodiments of the present invention;

[0056] Figure 8A comparison chart of the relationship between positioning error and number of points in a C-shaped polyhedron region when the maximum reference combination limit is 200 and 400, provided for embodiments of the present invention;

[0057] Figure 9 This is a comparison chart showing the relationship between positioning error and number of points in a rectangular cuboid region when the ranging error and variance are 0.02 and 0.05, respectively, as provided in an embodiment of the present invention.

[0058] Figure 10 This is a comparison chart showing the relationship between positioning error and number of points in a centered cuboid region when the ranging error and variance are 0.02 and 0.05, respectively, as provided in an embodiment of the present invention.

[0059] Figure 11 This is a comparison chart showing the relationship between positioning error and number of points in a C-shaped polyhedron region when the ranging error and variance are 0.02 and 0.05, respectively, as provided in an embodiment of the present invention. Detailed Implementation

[0060] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0061] Reference Figure 1 The present invention provides a flowchart of a method for swarm localization of underwater unmanned vehicles (UUVs) based on merging enhanced multidimensional scale analysis, comprising:

[0062] Step S1: Obtain the coordinate information of the anchor node and the observation distance matrix of the node group, wherein the node group includes the anchor node and the underwater unmanned vehicle cluster nodes to be located.

[0063] The underwater drone swarm consists of anchor nodes and cluster nodes of underwater drones to be located. Each node represents an underwater drone, and the position coordinates of the nodes are represented by a three-dimensional coordinate system. Anchor nodes are nodes with known absolute coordinates, which can be obtained through a high-precision inertial navigation system. The observation distance matrix is ​​used to record the observation distance between two nodes and can be obtained through signal ranging. In the simulation process, it can be obtained by adding the actual distance between the generated points and the ranging error matrix to simulate the error offset in actual observation.

[0064] Step S2: Divide the nodes in the node group into reference points and non-reference points according to the signal-to-noise ratio of the ranging signal.

[0065] Signal-to-noise ratio (SNR) can reflect the effectiveness of ranging results. Therefore, nodes can be screened using SNR. For example, nodes at both ends of a link with an SNR below the threshold can be marked as non-reference points, while nodes at both ends of a link with an SNR greater than or equal to the threshold can be marked as reference points. This allows for subsequent positioning calculations and reduces the interference of ranging errors on the positioning results.

[0066] Specifically, step S2 may include:

[0067] Step S21: Based on the observation distance matrix, calculate the signal power attenuation between nodes according to the following formula:

[0068] (1)

[0069] Where TL represents the signal power attenuation between node i and node j; This represents the observation distance between node i and node j. For parameter items;

[0070] Step S22: Calculate the signal-to-noise ratio of signal propagation between nodes based on the signal power attenuation;

[0071] Step S23: Based on the signal-to-noise ratio of signal propagation between the nodes, the nodes in the node group are divided into reference points and non-reference points using a signal-to-noise ratio threshold.

[0072] in, , Indicates the center frequency of the ranging signal used.

[0073] The signal-to-noise ratio (SNR) of a signal reflects its propagation quality. Therefore, in this invention, the SNR of the ranging signal propagation between nodes is used to filter reference points and non-reference points. It is understood that during the transmission, propagation, and reception of the ranging signal, the transmitted signal power, propagation loss (i.e., signal power attenuation), other losses, and noise power all affect the SNR. When the changes in transmitted signal power, other losses, and noise power are relatively small, propagation loss can be used alone as a metric to filter reference points, thereby improving positioning efficiency. For example, in simulated or relatively stable marine environments, the propagation loss can be calculated in step S21, and reference points can be directly delineated based on the propagation loss.

[0074] Furthermore, to ensure the simulation closely approximates the sparse cluster scenario, an adaptive signal-to-noise ratio (SNR) threshold can be employed in the simulation experiments to adjust connectivity. Specifically, when the cluster has a small number of points and a sparse distribution within a limited area, the average distance between nodes is large. In this case, lowering the threshold ensures that at least one set of usable reference points exists within the cluster. Conversely, as the cluster density increases, the average distance between nodes decreases. To ensure that disconnected links still exist within the cluster, the SNR threshold is increased to limit the number of connected links. Using an adaptive SNR threshold in the simulation helps improve the adaptability of this method to sparse cluster environments. Of course, in practical applications, setting an adaptive SNR threshold can also be used to filter reference points and improve the localization effect.

[0075] Step S3: Based on the divided reference points, construct different reference groups.

[0076] Different reference points are combined to obtain different reference groups. The number of reference groups can be expressed by the following formula:

[0077] (2)

[0078] Where K represents the number of reference groups, i.e., K reference groups; This represents the number of different ways to select 4 reference points from H reference points to form a reference group. In this example, the preset reference group contains 4 nodes, and to ensure real-time performance when dealing with large-scale clusters, an upper limit of 400 is set for the number of reference combinations participating in the calculation. The upper limit of the reference group and the number of nodes in the reference group can be determined according to the actual situation.

[0079] If the number of reference points is insufficient, the signal-to-noise ratio threshold can be adaptively lowered to increase the number of reference points and meet the positioning requirements. If all nodes meet the reference point criteria, the threshold can be increased to enhance node discrimination, thereby improving the positioning effect. This approach can significantly improve the engineering applicability of underwater unmanned vehicle swarm positioning.

[0080] Step S4: For the same reference group, perform the following processing:

[0081] Step S41: Combine the reference group with nodes in the node group that do not belong to the reference group to obtain different sub-combinations;

[0082] Step S42: Calculate the relative coordinates of nodes within each sub-combination using the MDS algorithm;

[0083] Step S43: Perform rigid body registration on the relative coordinates within each sub-group, unify the coordinate system, and obtain the global relative coordinates corresponding to the reference group.

[0084] For the same reference group, the reference group is combined with the nodes in the remaining node group after removing the reference group to obtain different sub-combinations. Multidimensional scaling (MDS) is then used for dimensionality reduction to obtain the relative coordinates of the nodes within each sub-combination. Rigid body registration is then used to unify the coordinates within each sub-combination to the same coordinate system, thus obtaining the set of relative coordinates of the node group. By combining the reference group (composed of nodes with high signal-to-noise ratio, i.e., reference points) with the remaining nodes, the relative coordinates within the sub-combinations are first calculated. Then, rigid body registration is used to obtain the set of relative coordinates of the node group corresponding to the reference group. This fully utilizes the positional information of the reference points with high signal-to-noise ratio and gradually reduces the interference of nodes with low signal-to-noise ratio (i.e., low connectivity) on the positioning results.

[0085] While ensuring that the global relative coordinates can include the coordinate information of all nodes in the node group, the number of reference groups, the number of nodes in the reference groups, the number of subgroups, and the number of nodes in the subgroups can be adjusted according to the actual situation.

[0086] As an example, Figure 2 A flowchart of another underwater unmanned vehicle swarm localization method based on merging enhanced multidimensional scale analysis provided by an embodiment of the present invention is given. The reference group contains 4 nodes, and the sub-group formed by the reference group and the remaining nodes contains 5 nodes. For... Figure 2 -(B) shows The reference group is formed by combining the P1 reference group with the remaining nodes to obtain a sub-combination. N represents the number of nodes in the node group; the MDS algorithm is used to calculate and generate subgraphs under different coordinate bases. That is, the relative coordinates of the nodes within each sub-combination, and then using rigid body registration to unify the subgraphs to a unified coordinate system, merging them into global relative coordinates. The reference group can then be obtained. Corresponding global relative coordinates .

[0087] Specifically, step S42 includes:

[0088] The observation distance matrix corresponding to the sub-combination is obtained based on the observation distance matrix of the node group;

[0089] The observation distance matrix corresponding to the sub-combination is double-centered according to the following formula:

[0090] (3)

[0091] in, This represents the quadratic centered matrix corresponding to the nth sub-combination obtained based on the mth reference group; This represents the observation distance matrix corresponding to the nth sub-combination obtained based on the mth reference group. Represents a centered matrix; "Indicates the Hadamardi accumulation;

[0092] The quadratic centered matrix is ​​subjected to eigenvalue decomposition to obtain a preset number of eigenvalues ​​and corresponding eigenvectors;

[0093] Calculate the relative coordinates of nodes within a sub-combination using the following formula:

[0094] (4)

[0095] in, This represents the relative coordinates of the nodes within the nth sub-combination obtained based on the mth reference group; This represents a diagonal matrix composed of a predetermined number of eigenvalues. This represents the matrix formed by the eigenvectors corresponding to the eigenvalues.

[0096] in, ,in It is a column vector of all 1s. This represents the identity matrix. The eigenvalues ​​can be extracted by taking the three largest eigenvalues ​​and their corresponding eigenvectors for subsequent calculations; the specific method can be determined based on the actual situation.

[0097] Taking a reference group with 4 nodes and a sub-combination with 5 nodes as an example, the nth sub-combination is obtained based on the mth reference group. , It can be expressed by the following formula:

[0098] (5)

[0099] in, Let i represent the i-th node within the m-th reference group, where i = 1, 2, 3, 4. This represents the nth node in the node group excluding the current reference group; This represents the observation distance between the i-th node and the j-th node within the m-th reference group, where i = 1, 2, 3, 4, j = 1, 2, 3, 4, and i ≠ j. and Both represent the observation distance between the i-th node in the m-th reference group and the n-th node in the node group other than the current reference group, i=1,2,3,4, which can be obtained from the observation matrix obtained in step S1.

[0100] For example, the first sub-combination corresponding to the m-th reference group Relative coordinates of internal nodes Based on this, step S43 may include:

[0101] Calculate the nth sub-combination corresponding to the mth reference group. Relative coordinates of internal nodes and Cross covariance matrix and its singular value decomposition The optimal rotation matrix is ​​calculated. :

[0102] (6)

[0103] and translation vector :

[0104] (7)

[0105] use and Will Transform to Under the corresponding coordinate base:

[0106] (8)

[0107] in, express The relative coordinates after coordinate system transformation. After rigid body registration is completed for each sub-group, the global relative coordinates corresponding to the m-th reference group can be obtained. .

[0108] Step S5: Perform step S4 above on each reference group to obtain the global relative coordinates corresponding to each reference group.

[0109] Dividing reference groups and incorporating different nodes through the same reference node to construct sub-positioning results at the same level helps to make full use of the unique topological distribution of different reference groups when the observation information is limited. This approach also makes full use of the location information of reference points with high signal-to-noise ratios, reduces interference from ranging errors and channel noise, and improves the accuracy of positioning results under low connectivity and high noise conditions.

[0110] like Figure 2As shown in the example, the positioning method described in this invention is based on two loops. The first loop iterates by decomposing a single positioning operation into multiple parallel positioning groups. The size of the loop depends on the distribution of the nodes. For example, when the nodes are relatively concentrated, there are more available reference combinations, so the loop size will be larger. This approach helps to make full use of the unique topological distribution of different reference groups as the core, even with limited observation information, and solves the performance degradation problem of traditional MDS in low connectivity scenarios. The second loop iterates by incorporating different child nodes through the same reference node to construct sub-positioning results at the same level, thereby gradually reducing the error, significantly suppressing ranging errors and channel noise, and improving positioning accuracy.

[0111] Step S6: Align the global relative coordinates of each reference group based on the coordinate information of the anchor node to obtain the global absolute coordinates of each reference group.

[0112] Alignment can be performed using rigid body registration. Using the coordinates of the anchor node as a reference, the global relative coordinates of each reference group are converted to absolute coordinates, thus obtaining the global absolute coordinates of each reference group, as shown in the figure. .

[0113] Step S7: Optimize based on each global absolute coordinate to obtain the positioning result of the node to be located.

[0114] In order to integrate all the positioning results obtained from the first loop and reduce the positioning result offset caused by the random distribution of the reference group, it is necessary to optimize each global absolute coordinate, such as least squares optimization and mean optimization, so as to obtain the positioning result with positioning nodes.

[0115] Optionally, step S7 may include:

[0116] The positioning result of the point to be located is obtained by performing least squares optimization based on each global absolute coordinate according to the following formula:

[0117] (9)

[0118] Where Z represents the sum of squared residuals; This represents a parameter function minimized with respect to X as the optimization objective, where X represents the absolute coordinates of each node in the node group, including the absolute coordinates of the node to be located. Represents the absolute coordinates of the nth node in the node group; This represents the absolute coordinates of the nth node in the global absolute coordinates corresponding to the kth reference group; K represents the number of reference groups, and N represents the number of nodes in the node group.

[0119] By using least squares optimization to process each global absolute coordinate, it has strong adaptability to complex environments, and is especially suitable for problems such as high noise and low connectivity in underwater sparse cluster environments, which helps to further reduce positioning errors.

[0120] Optionally, step S7 includes:

[0121] The positioning result of the point to be located is obtained by optimizing each global absolute coordinate according to the following formula:

[0122] (10)

[0123] in, Represents the absolute coordinates of the nth node in the node group; , , These represent the coordinates of the nth node in the global absolute coordinates corresponding to the kth reference group in the x, y, and z directions, respectively; K represents the number of reference groups.

[0124] Optimization by directly averaging the global absolute coordinates of each reference group helps to effectively improve positioning efficiency and achieve an effective balance between positioning efficiency and positioning accuracy.

[0125] In summary, this invention provides a method for underwater unmanned vehicle (UAV) swarm localization based on merging enhanced multidimensional scale analysis. The method involves acquiring the coordinate information of anchor nodes and the observation distance matrix of the node swarm. Based on the signal-to-noise ratio (SNR) of the ranging signals, the nodes in the swarm are divided into reference points and non-reference points. Different reference groups are constructed based on these reference points. For each reference group, the reference group is combined with nodes in the swarm that do not belong to the reference group to obtain different sub-combinations. The relative coordinates of nodes within each sub-combination are calculated using the MDS algorithm. Then, the relative coordinates within each sub-combination are rigidly registered to unify the coordinate system, obtaining the global relative coordinates corresponding to the reference group. The above steps are performed on each reference group to obtain the global relative coordinates corresponding to each reference group. Based on the coordinate information of the anchor nodes, the global relative coordinates corresponding to each reference group are aligned to obtain the global absolute coordinates corresponding to each reference group. Finally, optimization processing is performed based on the global absolute coordinates to obtain the localization result of the node to be located.

[0126] Using the above method, the positioning method of this invention achieves underwater swarm positioning of unmanned aerial vehicles based on two loops. The first loop iteration decomposes a single positioning operation into multiple parallel positioning groups. This approach helps to fully utilize the unique topological distribution of different reference groups when limited observation information is available. The second loop iteration incorporates different child nodes through the same reference node to construct sub-positioning results at the same level, achieving a gradual reduction in error, significantly suppressing ranging errors and channel noise, and improving positioning accuracy.

[0127] Therefore, the aforementioned dual-loop positioning method can fully utilize the location information of reference points, reduce the interference of low signal-to-noise ratio nodes in low connectivity and high noise environments on the positioning results, improve the positioning effect, and solve the performance degradation problem of traditional MDS in low connectivity scenarios. Furthermore, it reduces the dependence on anchor nodes, and the positioning of underwater unmanned vehicle clusters can be achieved with a small number of anchor nodes, making it more suitable for sparse cluster environments underwater, with good anti-interference effect and applicability. At the same time, merging the global absolute coordinates corresponding to each reference group to obtain the absolute coordinates of the point to be positioned further reduces the positioning error.

[0128] To better explain the underwater unmanned vehicle swarm localization method based on merging enhanced multidimensional scale analysis of the present invention, the present invention provides, as follows: Figures 3-11 The simulation results of the three localization methods are shown in Table 1. The simulation parameters are as follows: Classic MDS algorithm, Multidimensional Scaling-MAP (MDS-MAP) algorithm, and Merging Enhanced-MDS algorithm, which are the localization methods provided in this invention.

[0129] Table 1 Simulation Parameters

[0130]

[0131] Figure 3 , Figure 4 , Figure 5 The diagram shows top-down views of three different distribution areas when the cluster size is 17 points, visually illustrating the characteristics of the cluster under each distribution. Figure 3 The distribution is relatively even. Figure 4 The overall situation presents an encirclement. Figure 5 It presents a semi-encircling shape. Overall, Figure 4 Figure 5 The resulting topological structure exhibits strong hollowing characteristics, indicating that the system has a high tolerance for structures with relatively poor connectivity.

[0132] Figure 6, 7 Figure 8 primarily illustrates the changes in localization error magnitudes for the classic MDS method, the MDS-MAP method, and the ME-MDS method with restrictions on the selection upper limits of different reference groups. The horizontal axis represents the number of nodes from small to large, and the vertical axis represents the average Euclidean distance (Localization Error) between the localization results of all nodes and the actual location. As can be seen from the figure, the localization accuracy of ME-MDS is less affected by changes in the number of nodes, maintaining superior accuracy even with a small number of nodes and a sparse cluster distribution. Furthermore, as the number of nodes increases, the ME-MDS method described in this invention can adaptively increase the upper limit of the reference group selection, further reducing the localization error at the cost of increased computational complexity.

[0133] Figure 9 , Figure 10 , Figure 11 This figure primarily illustrates the changes in positioning error magnitude of the classical MDS method, the MDS-MAP method, and the ME-MDS method proposed in this invention under different observation distance errors and standard deviations. The horizontal axis represents the number of nodes from small to large, and the vertical axis represents the average Euclidean distance (Localization Error) of the positioning results of all nodes relative to the true location. Dashed lines represent larger ranging errors, and solid lines represent smaller ranging errors. As can be seen from the figure, the positioning accuracy obtained by the ME-MDS method remains superior even when the error increases. That is, under conditions of higher ranging errors, based on the same observations, the ME-MDS method exhibits better suppression of ranging errors.

[0134] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0135] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0136] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A UUV swarm positioning method based on merging enhanced multidimensional scaling analysis, characterized in that, The method comprises: Step S1, obtaining coordinate information of anchor nodes and an observation distance matrix of a node group, the node group comprising anchor nodes and a cluster of underwater unmanned vehicle nodes to be positioned; Step S2, dividing nodes in the node group into reference points and non-reference points according to a signal-to-noise ratio of a ranging signal; Step S3, constructing different reference groups based on the divided reference points; Step S4, for the same reference group, performing the following processing: Step S41, combining the reference group with nodes in the node group that do not belong to the reference group to obtain different subgroups; Step S42, calculating relative coordinates of nodes in each subgroup by using an MDS algorithm; Step S43, rigidly registering the relative coordinates in each subgroup to unify the coordinate system and obtain global relative coordinates corresponding to the reference group; Step S5, performing the above step S4 on each reference group to obtain global relative coordinates corresponding to each reference group, respectively; Step S6, aligning the global relative coordinates corresponding to each reference group based on the coordinate information of the anchor nodes to obtain global absolute coordinates corresponding to each reference group, respectively; Step S7, performing optimization processing based on each global absolute coordinate to obtain a positioning result of the node to be positioned.

2. The method of claim 1, wherein, The step S2 comprises: Step S21, calculating signal power attenuation between nodes based on the observation distance matrix according to the following formula: ， where TLrepresents the signal power attenuation between node i and node j; represents the observed distance between node i and node j, is a parameter term; Step S22, calculating a signal-to-noise ratio of signal propagation between nodes based on the signal power attenuation; Step S23, dividing nodes in the node group into reference points and non-reference points by using a signal-to-noise ratio threshold based on the signal-to-noise ratio of signal propagation between nodes.

3. The method of claim 1, wherein, The step S42 comprises: Obtaining an observation distance matrix corresponding to the subgroup from the observation distance matrix of the node group; Performing double-centering processing on the observation distance matrix corresponding to the subgroup according to the following formula: ， wherein, denotes the second centralised moment matrix corresponding to the nth sub-combination based on the mth reference set; denotes the observed distance matrix corresponding to the nth sub-combination based on the mth reference set, denotes the centralised matrix; denotes the Hadamard product; Performing eigenvalue decomposition on the twice-centered matrix to obtain a preset number of eigenvalues and corresponding eigenvectors; Calculating the relative coordinates of nodes in the subgroup according to the following formula: ， wherein, represents the relative coordinates of the nodes in the nthsub-combination based on the mthreference group; represents a diagonal matrix composed of preset numbers of eigenvalues, represents a matrix composed of eigenvectors corresponding to the eigenvalues.

4. The method of claim 1, wherein, The step S7 comprises: Performing least squares optimization processing based on each global absolute coordinate according to the following formula to obtain a positioning result of the node to be positioned: ， wherein Z represents a residual sum of squares; represents a minimization parameter function with X as the optimization target, X represents the absolute coordinates of each node in the node group, including the absolute coordinates of the node to be positioned, represents the absolute coordinates of the n th node in the node group; represents the absolute coordinates of the n th node in the global absolute coordinates corresponding to the k th reference group; K represents the number of reference groups, and N represents the number of nodes in the node group.

5. The method of claim 1, wherein, The step S7 comprises: Performing optimization processing based on each global absolute coordinate according to the following formula to obtain a positioning result of the node to be positioned: ， wherein, represents the absolute coordinates of the nth node in the node group; , , respectively represent the coordinate values of the nth node in the x, y, z directions in the global absolute coordinates corresponding to the kth reference group; K represents the number of reference groups. 6.An electronic device, comprising a processor, a memory storing one or more programs; characterized in that: When the one or more programs are executed by the processor, the method of any one of claims 1-5 is implemented.

7. A readable storage medium, storing a computer program, characterized in that: When the computer program is executed by the processor, the method of any one of claims 1-5 is implemented.

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