Low-altitude unmanned aerial vehicle trajectory clustering method and system based on weighted multi-dimensional dynamic time warping

Abstract

The application discloses a low-altitude unmanned aerial vehicle trajectory clustering method and system based on weighted multi-dimensional dynamic time warping, and the method comprises the following steps: preprocessing original trajectories to obtain normalized and simplified four-dimensional trajectory sequences; defining a weighted point-to-point distance function, introducing a dimension weight vector of longitude, latitude, height and speed; constructing a cumulative cost matrix, and obtaining a global similarity by performing path length normalization on the cumulative cost of an optimal alignment path; adopting a DBSCAN algorithm to perform clustering by taking the global similarity as a distance measure, and a trajectory neighborhood is composed of trajectories with a similarity not exceeding a neighborhood radius threshold; configuring a weight vector according to an application scenario; and determining an optimal neighborhood radius by multi-index collaborative optimization of a silhouette coefficient, a Davies-Bouldin index, a Calinski-Harabasz index and a noise rate. The application realizes multi-dimensional weighted similarity measurement, and effectively distinguishes heterogeneous operation modes such as the same path with different speeds and the same path with different layers.

Description

Technical Field

[0001] This invention relates to the fields of unmanned aerial vehicle (UAV) trajectory analysis and low-altitude traffic management, specifically to a UAV trajectory clustering method and system based on weighted multidimensional dynamic time warping. Background Technology

[0002] With the explosive growth of urban drone applications, the operating environment of urban low-altitude airspace is becoming increasingly complex, posing severe challenges to low-altitude traffic management. Trajectory behavior pattern recognition, as a core technology for sensing the operational status of drones, can deeply characterize the kinematic characteristics and behavioral mechanisms of drones. Through clustering and analysis of massive trajectory data, management systems can effectively extract operational patterns, which has significant application value and practical implications in key areas such as abnormal behavior detection, traffic guidance strategy formulation, refined path planning, and flight safety assurance.

[0003] Current trajectory clustering techniques are mainly divided into three categories: First, Euclidean distance clustering, represented by DBSCAN or K-means, relies heavily on simple two-dimensional geographic coordinates, making it difficult to characterize alignment differences in the time dimension and unable to effectively distinguish heterogeneous operating patterns caused by different speeds or altitudes under the same path; Second, clustering based on dynamic time warping (DTW), which can handle the problem of varying trajectory lengths, but mostly uses single-dimensional or equally weighted multi-dimensional features, ignoring the differences in the contribution of physical dimensions such as latitude, longitude, altitude, and speed under different task scenarios; Third, pure geospatial clustering, which divides routes based solely on two-dimensional spatial distribution and cannot reveal the three-dimensional, kinematic airspace utilization structure such as altitude stratification and speed gradation.

[0004] In summary, existing clustering methods have limitations when dealing with complex UAV trajectories, including limited feature fusion dimensions, lack of physical meaning, and inability to adapt to diverse task requirements. In particular, when trajectories exhibit fine-grained distributions such as "different speeds along the same route" or "different altitudes along the same route," traditional algorithms struggle to accurately identify and classify them. Therefore, constructing a trajectory clustering method that can integrate multi-dimensional kinematic features, support task-oriented dynamic weighting, and effectively distinguish heterogeneous operating modes has become a critical technical problem urgently needing to be solved in current low-altitude traffic behavior analysis. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a low-altitude UAV trajectory clustering method and system based on weighted multidimensional dynamic time warping, which addresses the limitations of existing trajectory clustering methods such as single feature dimension, equal weighting of physical features, and insufficient ability to distinguish heterogeneous patterns.

[0006] This method and system quantifies trajectory similarity within a four-dimensional feature space comprised of longitude, latitude, altitude, and speed. It supports flexible adjustment of the contribution weights of each dimension based on specific task scenarios and utilizes path length normalization technology to eliminate interference from differences in trajectory sampling lengths in similarity evaluation. Its core objective is to effectively identify refined heterogeneous operating patterns such as "different speeds along the same path" and "layered operation along the same path" while maintaining high-precision geographic route identification. This provides crucial technical support for the refined management of low-altitude traffic and the scientific allocation of airspace resources.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A low-altitude UAV trajectory clustering method based on weighted multidimensional dynamic time warping includes the following steps:

[0009] Step 1: Preprocess the original UAV flight trajectory and configure the dimension weight vector according to the application scenario to obtain the normalized and simplified four-dimensional trajectory sequence and the set of trajectories to be clustered.

[0010] Step 2: Define a weighted point-to-point distance function, construct a cumulative cost matrix, obtain the global similarity between trajectories by normalizing the cumulative cost of the optimal alignment path to the path length, and traverse all trajectory pairs to construct a similarity matrix.

[0011] Step 3: The density-based DBSCAN clustering algorithm is used to cluster trajectories with the global similarity between trajectories obtained in Step 2 as the distance metric, and the neighborhood radius is optimized by multiple indicators to output the clustering results.

[0012] Furthermore, step 1 specifically includes the following sub-steps:

[0013] Step 11: Extract the four-dimensional features of longitude, latitude, altitude and speed of the original UAV flight trajectory, map each dimension to the [0,1] interval using minimum-maximum normalization, and simplify the trajectory using an adaptive threshold-based trajectory simplification method or an equivalent method to obtain a normalized and simplified four-dimensional trajectory sequence.

[0014] Step 12: Configure dimension weight vectors according to the application scenario. ,in The weights correspond to longitude, latitude, altitude, and speed, respectively.

[0015] Step 13: Establish a simplified set of trajectories to be clustered. .

[0016] Furthermore, in step 12, the configuration method of the dimension weight vector includes:

[0017] Pure geographic clustering adopts Only longitude and latitude are considered;

[0018] Kinematic enhancement clustering adopts Reduce the height weight to weaken vertical noise, and increase the speed weight to distinguish different speed patterns on the same path.

[0019] Furthermore, step 2 specifically includes the following sub-steps:

[0020] Step 21, Define the weighted point-to-point distance function For the two simplified trajectories , Any two points , ,calculate:

[0021]

[0022] in , For each point at the 1st The normalized value of the dimension, For dimension weight vectors;

[0023] Step 22, construct based on point-to-point distance Cumulative cost matrix ,boundary recursive formula ;

[0024] Step 23: The global similarity between the two trajectories is obtained by normalizing the cumulative cost of the optimal alignment path using the path length: This eliminates the impact of trajectory length differences on similarity assessment.

[0025] Step 24: Traverse all trajectory pairs in the trajectory set and construct a complete similarity matrix.

[0026] Furthermore, step 3 specifically includes the following sub-steps:

[0027] Step 31: Set the minimum cluster size MinPts, and determine the neighborhood radius based on the normalized feature scale. The effective search range;

[0028] Step 32, for each candidate Values, perform DBSCAN clustering: based on global similarity between trajectories As a distance metric, if but belong of - Neighborhood; determine core points, boundary points, and noise points based on neighborhood density to form cluster partitions;

[0029] Step 33: Calculate multiple indicators for each clustering result and plot the above indicators as a function of clustering. The changing co-evolution curve;

[0030] Step 34: Use the elbow method to identify the critical inflection point where the rate of change tends to stabilize, and determine the optimal neighborhood radius. ;

[0031] Step 35, adopt the optimal Perform DBSCAN clustering, output the trajectories of each cluster and its members, and evaluate the clustering quality.

[0032] Furthermore, in step 31, for pure geographic clustering, The search interval is [0.01, 0.04]; for kinematic enhancement clustering, The search range has been expanded accordingly.

[0033] Furthermore, in step 33, the multiple indicators include the profile coefficient, the Davidson-Bolding index, the Calinski-Harabasz index, and the noise rate.

[0034] In step 34, the elbow method is used to analyze the multi-index co-evolution curve and determine the critical inflection point where the rate of change tends to stabilize as the optimal neighborhood radius.

[0035] Furthermore, in step 35, the silhouette coefficient, the Davidsonburgin index, and the Calinski-Harabasz index are used to evaluate the clustering quality. A silhouette coefficient close to 1 indicates a clear cluster structure, a lower Davidsonburgin index indicates a more compact cluster structure and better separation between clusters, and a higher Calinski-Harabasz index indicates better clustering performance.

[0036] Furthermore, after obtaining the clustering results in step 3, the clustering results are exported as at least one of the following formats: cluster labels, cluster center trajectories, and intra-cluster trajectory lists, for use by downstream applications.

[0037] A low-altitude UAV trajectory clustering system based on weighted multidimensional dynamic time warping includes:

[0038] The trajectory preprocessing and weight configuration module is used to preprocess the original trajectory and configure the dimension weight vector to obtain a normalized and simplified four-dimensional trajectory sequence and a set of trajectories to be clustered.

[0039] The WMD-DTW similarity calculation and similarity matrix construction module is used to define the weighted point-to-point distance function, construct the cumulative cost matrix, calculate the global similarity between trajectories, and traverse all trajectory pairs to construct the complete similarity matrix;

[0040] The DBSCAN clustering and neighborhood radius optimization module is used to perform DBSCAN clustering with global similarity as the distance metric, and uses multi-index collaborative optimization to determine the optimal neighborhood radius, and outputs the trajectory of each cluster and its members.

[0041] Beneficial Effects: This invention incorporates UAV flight trajectories into a four-dimensional feature space (longitude, latitude, altitude, and speed), defines a weighted multidimensional dynamic time warping (WMD-DTW) similarity metric, and combines it with a density-based DBSCAN clustering algorithm to achieve route corridor identification and heterogeneous behavior pattern mining. It supports task-oriented dimensional weighting configuration and multi-indicator collaborative neighborhood radius optimization. Compared with existing technologies, it has the following advantages:

[0042] (1) Multidimensional weighted similarity: Through WMD-DTW and dimensional weight vector, a balanced measurement of geometric shape and kinematic features is achieved, which supports flexible configuration according to task scenarios and adapts to different application needs;

[0043] (2) Differentiation of heterogeneous patterns: Compared with pure two-dimensional geographic clustering, sub-patterns such as "different speeds along the same path" and "layering along the same path" can be identified in the same location. Experiments show that kinematic enhancement clustering can identify 27 heterogeneous behavior clusters, while pure geographic clustering can only identify 11 basic routes;

[0044] (3) Path length invariance: By normalizing the path length, the influence of trajectory length differences on similarity is eliminated, ensuring the objective comparability of trajectories of different scales;

[0045] (4) Multi-indicator synergistic optimization: through , , Collaborative analysis of noise rate is used to determine the optimal neighborhood radius, achieving a balance between clustering accuracy and route extraction completeness. Optimal geographic clustering... optimal kinematic clustering ;

[0046] (5) Scalability: The method is applicable to large-scale trajectory data and can be used in combination with trajectory simplification methods to support offline analysis and online application expansion of urban low-altitude traffic management. Attached Figure Description

[0047] Figure 1 This is a flowchart illustrating the UAV trajectory clustering method based on weighted multidimensional dynamic time warping.

[0048] Figure 2 This is a graph showing the variation of evaluation indicators with neighborhood radius under pure geographical clustering.

[0049] Figure 3 This is a schematic diagram of the geographic clustering results;

[0050] Figure 4 A graph showing the variation of evaluation metrics with neighborhood radius under kinematic clustering;

[0051] Figure 5 This is a schematic diagram of the kinematic clustering results. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the examples described herein are only used to explain the core principles of the present invention, but are not intended to limit the present invention.

[0053] Example 1

[0054] Figure 1 This is a flowchart illustrating the UAV trajectory clustering method based on weighted multidimensional dynamic time warping, demonstrating the complete execution flow from input preprocessed trajectories to output clustering results, including weight configuration, WMD-DTW similarity calculation, and similarity matrix construction. Parameter scanning, DBSCAN clustering, multi-index evaluation, and elbow method for determining the optimal solution. Key steps, etc. Figure 2 For pure geographic clustering ( The evaluation index varies with the neighborhood radius. The variation curves show the changes in parameters such as silhouette coefficient (SC), Davidson-Bolding index (DBI), Calinski-Harabasz index (CHI), noise rate, and cluster number as a function of time. Co-evolution, optimal labeling . Figure 3 This is a schematic diagram of the geographic clustering results, showing Longhua District. Spatial distribution of the air route corridor. Figure 4 For kinematic clustering ( The following evaluation indicators follow Change curve, optimal labeling . Figure 5 This is a schematic diagram of the kinematic clustering results, showing... This includes heterogeneous behavioral clusters and phenomena such as "different speeds on the same path" and "layering on the same path".

[0055] We selected drone flight trajectory data collected in a certain city and performed a trajectory clustering process based on weighted multidimensional dynamic time warping. An example calculation is shown below:

[0056] Step 1: Perform trajectory preprocessing and weight configuration. This involves preprocessing the high-density urban low-altitude UAV flight trajectory data and setting the mission-oriented dimensional contributions. The specific steps are as follows:

[0057] (1.1) The original UAV flight trajectories are preprocessed to extract the four-dimensional features (longitude, latitude, altitude, and velocity) of each trajectory. For data lacking velocity, the displacement and time difference between adjacent points are estimated. Min-max normalization is used to map each dimension to the [0,1] interval. A trajectory simplification method based on adaptive threshold is used to compress the number of trajectory points by about 96% while maintaining an energy retention rate of about 99%, resulting in a normalized and simplified four-dimensional trajectory sequence. The data contains more than 130,000 flight trajectories, collected from January to April 2025, covering various task types such as infrastructure inspection, logistics distribution, aerial sightseeing, and film and television aerial photography.

[0058] (1.2) Configure dimension weight vectors according to application scenarios Pure geographical route extraction adopts Only longitude and latitude are considered; kinematic pattern mining adopts... Reduce the height weight to weaken vertical noise, and increase the speed weight to distinguish different speed patterns on the same path.

[0059] (1.3) Establish a simplified set of trajectories to be clustered .

[0060] Step two involves calculating WMD-DTW similarity and constructing a similarity matrix to quantify and store the spatiotemporal similarity between trajectories. The specific steps are as follows:

[0061] (2.1) For any two simplified trajectories , (lengths are respectively) , Define weighted point-to-point distance ,in Pick to ;

[0062] (2.2) Construction Cumulative cost matrix ,boundary recursive formula ;

[0063] (2.3) Global Similarity The influence of trajectory length differences is eliminated by path length normalization;

[0064] (2.4) Traverse all trajectory pairs in the trajectory set and construct a complete similarity matrix for use in step three clustering.

[0065] Set minimum cluster size They were clustered using pure geographic clustering ( ) and kinematic clustering ( Taking two weight configurations as examples, regarding the neighborhood radius... Perform parameter scanning within the valid interval and calculate each... Corresponding contour coefficient Davidson-Borgin Din Index Calinski-Harabasz index ., noise rate, number of clusters, etc., to obtain such Figure 2 and Figure 4 The evaluation indicators shown follow Change curves. Analysis revealed that pure geographic clustering... hour Stay However, the number of clusters is too large. This can easily trigger a "chain reaction," leading to route merging; kinematic clustering, due to the introduction of the velocity dimension, makes the feature space sparser, resulting in optimal... Move right .

[0066] Step 3: Perform DBSCAN clustering and neighborhood radius optimization, extract flight path patterns, and adaptively determine clustering parameters. The specific steps are as follows:

[0067] (3.1) For each candidate Values, perform DBSCAN clustering: with global similarity As a distance metric, if but belong of - Neighborhood; determine core points, boundary points, and noise points based on neighborhood density to form cluster partitions;

[0068] (3.2) For each clustering result, calculate the silhouette coefficient (SC), Davidson-Bolding index (DBI), Calinski-Harabasz index (CHI), and noise rate. Use the elbow method to identify the critical inflection point where the rate of change tends to stabilize, and determine the optimal clustering. Pure geographical clustering is optimal. optimal kinematic clustering ;

[0069] (3.3) Adopt the optimal Perform DBSCAN clustering and output the trajectories of each cluster and its members;

[0070] (3.4) Export the clustering results as cluster labels, cluster center trajectories, intra-cluster trajectory lists, etc., for downstream applications such as route planning, anomaly detection, and fine-grained allocation of airspace resources.

[0071] Use the optimal After performing clustering, for The clustering results are as follows Figure 3 As shown, it forms on the geographical plane of Longhua District. A clearly identifiable airway corridor, with trajectory flows exhibiting radial or point-to-point configurations; for The clustering results are as follows Figure 5 As shown, increased to A heterogeneous behavior cluster can be decomposed into multiple sub-clusters in the same geographical location, effectively revealing phenomena such as "different speeds on the same path" and "layering on the same path".

[0072] An effectiveness analysis of clustering results for low-altitude UAV trajectories in high-density cities was conducted, taking the number of clusters and noise rate as examples, and analyzing their variation with neighborhood radius. The evolution was examined, and the results were as follows: Figure 2 , Figure 4 The evaluation index co-evolution curve is shown. It can be seen that at the optimal... Down, To reach a local minimum, Maintaining a high level of cluster structure and achieving a balance between cluster structure and route integrity; combining geographical clustering and kinematic clustering can reveal the operational patterns of UAVs from different dimensions, proving that urban low-altitude operations are highly procedural and repetitive. The clustering results can be applied to scenarios such as route planning, anomaly detection, and refined allocation of airspace resources; in actual deployment, adjustments can be made based on data scale and trajectory density. The search interval, and the minimum cluster size, can generally be taken as a fraction of the total number of trajectories. to For reference, the similarity matrix can be pre-computed and cached to support incremental clustering.

[0073] Example 2

[0074] This embodiment provides a low-altitude UAV trajectory clustering system based on weighted multidimensional dynamic time warping, used to implement the method described in Embodiment 1. The system includes the following modules:

[0075] (I) Trajectory Preprocessing and Weight Configuration Module

[0076] This module is used to preprocess the original UAV flight trajectory and configure the dimension weight vector according to the application scenario to obtain a normalized and simplified four-dimensional trajectory sequence and a set of trajectories to be clustered.

[0077] Specifically, this module performs the following operations: extracts the four-dimensional features of longitude, latitude, altitude, and speed from the original UAV flight trajectory; maps each dimension to a normalization interval using min-max normalization; and simplifies the trajectory using an adaptive threshold-based trajectory simplification method to obtain a normalized and simplified four-dimensional trajectory sequence; configures dimension weight vectors according to the application scenario, corresponding to the weights of longitude, latitude, altitude, and speed, where pure geographic clustering only considers longitude and latitude, and kinematic augmentation clustering reduces the weight of altitude and increases the weight of speed; and establishes a set of simplified trajectories to be clustered for use by subsequent modules.

[0078] (II) WMD-DTW Similarity Calculation and Similarity Matrix Construction Module

[0079] This module is used to define a weighted point-to-point distance function, construct a cumulative cost matrix, obtain the global similarity between trajectories by normalizing the cumulative cost of the optimal alignment path to the path length, and traverse all trajectory pairs to construct a similarity matrix.

[0080] Specifically, this module performs the following operations: For any two simplified trajectories, a weighted point-to-point distance function is defined to calculate the four-dimensional weighted Euclidean distance of longitude, latitude, altitude, and speed; a cumulative cost matrix is ​​constructed based on the point-to-point distance, and the minimum cumulative cost is calculated recursively using dynamic programming; the cumulative cost of the optimal alignment path is normalized by path length to eliminate the influence of trajectory length differences on similarity evaluation, thereby obtaining the global similarity between trajectories; all trajectory pairs in the trajectory set are traversed to construct a complete similarity matrix, which is then stored as input for the subsequent clustering module.

[0081] (III) DBSCAN Clustering and Neighborhood Radius Optimization Module

[0082] This module is used to perform DBSCAN clustering with global similarity as the distance metric, uses multi-index collaborative optimization to determine the optimal neighborhood radius, and outputs the trajectories of each cluster and its members.

[0083] Specifically, this module performs the following operations: It sets a minimum cluster size and establishes an effective search interval for the neighborhood radius based on a normalized feature scale; it performs DBSCAN clustering on each candidate neighborhood radius value, using global similarity as a distance metric, and determines core points, boundary points, and noise points based on neighborhood density to form cluster partitions; it calculates multiple indicators (including silhouette coefficient, Davidsonburgin index, Calinski-Harabasz index, and noise rate) for each clustering result and plots the co-evolution curves of these indicators with neighborhood radius changes; it uses the elbow method to identify the critical inflection point where the rate of change tends to stabilize and determines the optimal neighborhood radius; it performs DBSCAN clustering using the optimal neighborhood radius, outputs the trajectories of each cluster and its members, and evaluates the clustering quality using the silhouette coefficient, Davidsonburgin index, and Calinski-Harabasz index; and it exports the clustering results in at least one format: cluster labels, cluster center trajectories, or intra-cluster trajectory lists, for use by downstream applications (such as route planning, anomaly detection, and refined allocation of airspace resources).

[0084] The system in this embodiment corresponds to the method steps in Embodiment 1, with three modules implementing steps one, two, and three respectively. Through the deployment and operation of this system, heterogeneous operating modes such as "different speeds along the same path" and "layered operation along the same path" can be effectively distinguished, enabling refined clustering analysis of low-altitude UAV trajectories.

[0085] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A low-altitude UAV trajectory clustering method based on weighted multidimensional dynamic time warping, characterized in that: Includes the following steps: Step 1: Preprocess the original UAV flight trajectory and configure the dimension weight vector according to the application scenario to obtain the normalized and simplified four-dimensional trajectory sequence and the set of trajectories to be clustered. Step 2: Define a weighted point-to-point distance function, construct a cumulative cost matrix, obtain the global similarity between trajectories by normalizing the cumulative cost of the optimal alignment path to the path length, and traverse all trajectory pairs to construct a similarity matrix. Step 3: The density-based DBSCAN clustering algorithm is used to cluster trajectories with the global similarity between trajectories obtained in Step 2 as the distance metric, and the neighborhood radius is optimized by multiple indicators to output the clustering results.

2. The method according to claim 1, characterized in that: Step 1 specifically includes the following sub-steps: Step 11: Extract the four-dimensional features of longitude, latitude, altitude and speed of the original UAV flight trajectory, map each dimension to the [0,1] interval using minimum-maximum normalization, and simplify the trajectory using an adaptive threshold-based trajectory simplification method or an equivalent method to obtain a normalized and simplified four-dimensional trajectory sequence. Step 12: Configure dimension weight vectors according to the application scenario. ,in The weights correspond to longitude, latitude, altitude, and speed, respectively. Step 13: Establish a simplified set of trajectories to be clustered. .

3. The method according to claim 2, characterized in that: In step 12, the configuration methods for the dimension weight vector include: Pure geographic clustering adopts Only longitude and latitude are considered; Kinematic enhancement clustering adopts Reduce the height weight to weaken vertical noise, and increase the speed weight to distinguish different speed patterns on the same path.

4. The method according to claim 1, characterized in that: Step 2 specifically includes the following sub-steps: Step 21, Define the weighted point-to-point distance function For the two simplified trajectories , Any two points , ,calculate: in , For each point at the 1st The normalized value of the dimension, For dimension weight vectors; Step 22, construct based on point-to-point distance Cumulative cost matrix ,boundary recursive formula ; Step 23: The global similarity between the two trajectories is obtained by normalizing the cumulative cost of the optimal alignment path using the path length: This eliminates the impact of trajectory length differences on similarity assessment. Step 24: Traverse all trajectory pairs in the trajectory set and construct a complete similarity matrix.

5. The method according to claim 1, characterized in that: Step 3 specifically includes the following sub-steps: Step 31: Set the minimum cluster size MinPts, and determine the neighborhood radius based on the normalized feature scale. The effective search range; Step 32, for each candidate Values, perform DBSCAN clustering: based on global similarity between trajectories As a distance metric, if but belong of - Neighborhood; determine core points, boundary points, and noise points based on neighborhood density to form cluster partitions; Step 33: Calculate multiple indicators for each clustering result and plot the above indicators as a function of clustering. The changing co-evolution curve; Step 34: Use the elbow method to identify the critical inflection point where the rate of change tends to stabilize, and determine the optimal neighborhood radius. ; Step 35, adopt the optimal Perform DBSCAN clustering, output the trajectories of each cluster and its members, and evaluate the clustering quality.

6. The method according to claim 5, characterized in that: In step 31, for pure geographic clustering, The search interval is [0.01, 0.04]; for kinematic enhancement clustering, The search range has been expanded accordingly.

7. The method according to claim 5, characterized in that: In step 33, the multiple indicators include the profile coefficient, the Davidson-Bolding index, the Calinski-Harabasz index, and the noise rate. In step 34, the elbow method is used to analyze the multi-index co-evolution curve and determine the critical inflection point where the rate of change tends to stabilize as the optimal neighborhood radius.

8. The method according to claim 5, characterized in that: In step 35, the silhouette coefficient, the Davidson-Bourdin index, and the Calinski-Harabasz index are used to evaluate the clustering quality. A silhouette coefficient close to 1 indicates a clear cluster structure. A lower Davidson-Bourdin index indicates a compact cluster structure and better separation between clusters. A higher Calinski-Harabasz index indicates better clustering performance.

9. The method according to claim 5, characterized in that: After obtaining the clustering results in step 3, the clustering results are exported as at least one of the following formats: cluster labels, cluster center trajectories, and intra-cluster trajectory lists, for use by downstream applications.

10. A low-altitude UAV trajectory clustering system based on weighted multidimensional dynamic time warping, used to implement the method of claim 1, characterized in that: include: The trajectory preprocessing and weight configuration module is used to preprocess the original trajectory and configure the dimension weight vector to obtain a normalized and simplified four-dimensional trajectory sequence and a set of trajectories to be clustered. The WMD-DTW similarity calculation and similarity matrix construction module is used to define the weighted point-to-point distance function, construct the cumulative cost matrix, calculate the global similarity between trajectories, and traverse all trajectory pairs to construct the complete similarity matrix; The DBSCAN clustering and neighborhood radius optimization module is used to perform DBSCAN clustering with global similarity as the distance metric, and uses multi-index collaborative optimization to determine the optimal neighborhood radius, and outputs the trajectory of each cluster and its members.

Images