Trajectory fly point determination method, device and electronic device

Abstract

Embodiments of the present invention provide a method, apparatus, and electronic device for determining trajectory flying points. The method includes: acquiring a sequence of trajectory points from data from a ship's Automatic Identification System (AIS); determining multiple associated feature points corresponding to each undetermined point in the trajectory point sequence based on time parameters; determining a first local steering parameter corresponding to the undetermined point based on position parameters of the undetermined point and position parameters of the associated feature points; determining a second local steering parameter corresponding to the associated feature points based on position parameters of the undetermined point and position parameters of the associated feature points; determining a geometric result corresponding to the undetermined point based on the first and second local steering parameters; determining a direction continuation result based on multiple direction vectors; and determining trajectory flying points in the trajectory point sequence based on the geometric result and the direction continuation result. The solution of the present invention determines trajectory flying points based solely on angle and direction consistency, without relying on absolute thresholds such as speed and distance, thus improving the efficiency of trajectory flying point determination.

Description

Technical Field

[0001] This invention relates to the field of maritime management technology, and more specifically, to a method, apparatus, and electronic device for determining trajectory flying points. Background Technology

[0002] The Automatic Identification System (AIS) is a core technology for modern maritime supervision and navigation safety. It automatically broadcasts and receives static information (such as ship name and size), dynamic information (such as position, speed, and heading), and voyage-related information in the Very High Frequency (VHF) band, enabling real-time monitoring and information exchange of ship navigation status.

[0003] However, in practical applications, AIS data quality is affected by various factors, among which the "flying point" problem is particularly prominent. Flying points refer to abnormal locations in AIS data that deviate significantly from the ship's actual navigation trajectory, disrupting the continuity and reliability of the data. The processing of flying points in ship AIS trajectories mainly relies on methods based on fixed rules. As the number of abnormal scenarios to be identified increases, the rule set expands continuously, leading to high algorithm complexity and insufficient efficiency in determining flying points. Summary of the Invention

[0004] The purpose of this invention is to provide a method, apparatus, and electronic device for determining trajectory flying points, which can solve the problems of high algorithm complexity and insufficient efficiency in determining flying points.

[0005] In view of this, an embodiment of the first aspect of the present invention provides a method for determining trajectory flying points.

[0006] A second aspect of the present invention provides a trajectory flying point determination device.

[0007] An embodiment of the third aspect of the present invention provides an electronic device.

[0008] To achieve the above objectives, an embodiment of the first aspect of the present invention provides a method for determining trajectory flying points, comprising: acquiring a sequence of trajectory points from data of an Automatic Identification System (AIS), the sequence of trajectory points including multiple undetermined points, each undetermined point including a time parameter and a position parameter; determining multiple associated feature points corresponding to each undetermined point in the trajectory point sequence based on the time parameter, wherein the multiple associated feature points and the undetermined point are continuous in the trajectory point sequence; determining a first local steering parameter corresponding to the undetermined point based on the position parameter of the undetermined point and the position parameter of the associated feature points; determining a second local steering parameter corresponding to the associated feature points based on the position parameter of the undetermined point and the position parameter of the associated feature points; determining a geometric result corresponding to the undetermined point based on the first local steering parameter and the second local steering parameter; when both the first local steering parameter and the second local steering parameter are less than a preset steering threshold, determining a direction vector from the undetermined point to the multiple associated feature points based on the position parameter of the undetermined point and the position parameter of the associated feature points; determining a direction continuation result corresponding to the undetermined point based on the multiple direction vectors; and determining trajectory flying points in the trajectory point sequence based on the geometric result and the direction continuation result.

[0009] This invention provides a novel two-level determination system for trajectory flying points. From the original AIS trajectory point sequence, each undetermined point and its adjacent associated feature points are extracted based on temporal continuity. Then, by calculating and analyzing the first and second local turning parameters, a first-level screening is performed based on geometric morphology, identifying clearly normal points and suspicious points. Subsequently, for difficult cases where the geometric results are uncertain, a second-level precise determination is performed from the perspective of motion trend continuity by calculating the direction vector from the undetermined point to multiple subsequent associated feature points and statistically analyzing its consistency with the forward vector of the undetermined point. The combined results of the two-level determination achieve the identification of trajectory flying points.

[0010] Understandably, the trajectory flying point determination method completely abandons the scattered rules that rely on absolute thresholds such as speed and distance in traditional methods. Instead, it uses the two essential physical characteristics of trajectory's inherent angle change and direction consistency for comprehensive reasoning. This not only unifies and simplifies the judgment logic, reduces algorithm complexity and implementation difficulty, but also significantly enhances the adaptability to complex navigation scenarios, thereby fundamentally improving the overall processing efficiency of trajectory flying point recognition.

[0011] In some technical solutions, optionally, a first local turning parameter corresponding to the point to be determined is determined based on the position parameters of the point to be determined and the position parameters of the associated feature points, including: determining a first associated predecessor point located before the point to be determined and a first associated successor point located after the point to be determined based on time parameters; and determining the first local turning parameter based on the position parameters of the first associated predecessor point, the position parameters of the point to be determined, and the position parameters of the first associated successor point.

[0012] In this scheme, the preceding and following trajectory points directly adjacent to the point to be determined are locked based on the time series, and the angle value that accurately represents the local heading change is calculated based on the geometric relationship formed by these three points.

[0013] Understandably, transforming the abstract local turn into an objectively calculable geometric angle provides a stable and reliable quantitative input for the first-level geometric decision.

[0014] In some technical solutions, optionally, a second local turning parameter corresponding to the associated feature point is determined based on the position parameters of the point to be determined and the position parameters of the associated feature point, including: determining a second associated subsequent point located after the first associated subsequent point based on time parameters; and determining the second local turning parameter based on the position parameters of the point to be determined, the position parameters of the first associated subsequent point, and the position parameters of the second associated subsequent point.

[0015] In this scheme, by utilizing the already determined first associated subsequent point, the second associated subsequent point is further located in the time series, and based on the geometric relationship formed by these three points, the local turning angle with the first associated subsequent point as the core is calculated.

[0016] Understandably, the focus of the analysis is naturally extended from the current point to the next adjacent trajectory point, thereby obtaining continuous geometric information of the trajectory instantaneously after the point to be determined. This allows the algorithm to not only focus on the local state of a single point, but also observe the curvature characteristics of the trajectory segment formed by two consecutive points, significantly enhancing the algorithm's ability to analyze complex trajectory patterns and its judgment accuracy.

[0017] In some technical solutions, optionally, determining the geometric result corresponding to the point to be determined based on the first local steering parameter and the second local steering parameter includes: determining a first geometric determination result based on the first local steering parameter when the first local steering parameter is greater than or equal to a preset first feature threshold; determining a second geometric determination result based on the first local steering parameter and the second local steering parameter when the first local steering parameter is less than the first feature threshold and the second local steering parameter is greater than or equal to the first feature threshold; determining a third geometric determination result based on the position parameters of the point to be determined, the position parameters of the first associated preceding point, the position parameters of the first associated subsequent point, and the position parameters of the second associated subsequent point when the first local steering parameter is less than the first feature threshold and the second local steering parameter is less than the first feature threshold; and determining the geometric result corresponding to the point to be determined based on the first geometric determination result, the second geometric determination result, and the third geometric determination result.

[0018] In this scheme, effective points for smooth navigation are quickly screened out by comparing the first local steering parameter with a threshold. Secondly, when the first feature indicates an acute angle, a second feature is introduced for verification, accurately identifying the sharp / blunt pattern representing the normal turning point. For the most complex double-acute angle case, a geometric check is used to accurately locate the true anomaly by comparing the smoothness of the trajectory after removing two suspect points.

[0019] Understandably, by using a progressive decision-making architecture, most simple and straightforward cases are handled with minimal computational cost, while complex computational resources are concentrated on the few most difficult cases. Furthermore, rigorous geometric reasoning fundamentally solves the problem of accurately locating outliers in continuous acute angle scenarios, thus achieving the optimal balance between efficiency and accuracy in flying point recognition.

[0020] In some technical solutions, optionally, a third geometric determination result is determined based on the position parameters of the undetermined point, the position parameters of the first associated preceding point, the position parameters of the first associated subsequent point, and the position parameters of the second associated subsequent point. This includes: determining a first candidate turning feature based on the position parameters of the first associated preceding point, the position parameters of the undetermined point, and the position parameters of the second associated subsequent point; determining a second candidate turning feature based on the position parameters of the first associated preceding point, the position parameters of the first associated subsequent point, and the position parameters of the second associated subsequent point; and determining the third geometric determination result based on the size relationship between the first candidate turning feature and the second candidate turning feature.

[0021] In this scheme, two competing hypotheses are constructed: the undetermined point is a flying point and the subsequent point is a flying point. Based on the corresponding three-point set, the candidate turning features are calculated. Finally, by directly comparing the size of the two feature angles, the true outlier is determined according to the geometric principle that removing true outliers should make the trajectory smoother.

[0022] Understandably, subjective, experience-based rule judgments are transformed into objective, quantifiable geometric result comparisons. This enables the precise identification of a single point of responsibility that disrupts the continuity of a trajectory in complex situations where multiple suspicious points are intertwined, significantly improving the resolution and certainty of the judgment in flypoint identification.

[0023] In some technical solutions, optionally, the direction continuation result corresponding to the point to be determined is determined based on multiple direction vectors, including: determining multiple associated subsequent points located after the point to be determined based on time parameters; determining the direction vector from the point to be determined to each associated subsequent point based on the position parameters of the point to be determined and the position parameters of the multiple associated subsequent points; obtaining the forward direction vector of the point to be determined; determining multiple directional angle features based on the forward direction vector and each direction vector; determining a quantity feature based on the multiple directional angle features and a preset second feature threshold; and determining the direction continuation result based on the quantity feature.

[0024] In this scheme, an observation window is first defined after the point to be determined and the direction vector pointing to each subsequent point is calculated. Then, the forward direction vector representing the historical movement trend is obtained. The deviation between each subsequent direction and the historical direction is quantified by calculating the angle between the vectors. Finally, the number of subsequent points with a deviation less than the preset tolerance threshold is counted, and this number is used as the direction continuation result.

[0025] Understandably, transforming the fuzzy concept of whether directions are consistent into a quantitative indicator that can be objectively statistically analyzed and compared allows the judgment criteria to be expanded from the instantaneous state of a single point to the short-term continuous motion trend. This effectively distinguishes between changes in direction caused by normal maneuvers and random jumps caused by flying points, significantly enhancing the algorithm's discriminative power and robustness in complex scenarios.

[0026] In some technical solutions, optionally, the trajectory flying points in the trajectory point sequence are determined based on geometric results and direction continuation results, including: determining a primary determination result for the undetermined point based on the geometric results, the primary determination result being used to indicate whether the undetermined point is a valid trajectory point, an abnormal trajectory flying point, or an undetermined state point; when the primary determination result indicates that the undetermined point is an undetermined state point, determining a secondary determination result for the undetermined point based on the direction continuation results, the secondary determination result being used to indicate whether the undetermined point is a valid trajectory point or an abnormal trajectory flying point.

[0027] In this scheme, a primary judgment result is first generated based on the geometric results determined by local geometric analysis. This primary judgment result can clearly classify trajectory points as valid, abnormal, or pending, thus quickly terminating the judgment for most simple and clear cases. The secondary judgment is activated only when a point is marked as pending, that is, the final secondary judgment result is generated using the directional continuation results based on motion trend statistics.

[0028] Understandably, through this decision tree structure that enables rapid initial screening and precise verification, the algorithm can handle the vast majority of normal and obviously abnormal points with extremely low computational overhead, while using complex trend analysis only for the few most difficult cases, thereby achieving overall optimization of processing efficiency.

[0029] In some technical solutions, the trajectory flying point determination method may optionally include: initializing the trajectory point with the earliest time parameter in the trajectory point sequence as a valid trajectory point; taking the next undetermined trajectory point in the trajectory point sequence as an iterative undetermined point; obtaining the judgment result of the iterative undetermined point; updating the judgment state of the trajectory points in the trajectory point sequence according to the judgment result; determining multiple iterative undetermined points according to the judgment state until all trajectory points in the trajectory point sequence have updated their judgment states.

[0030] In this scheme, the earliest trajectory point is initialized as the valid point to establish the processing starting point. Then, the following steps are executed cyclically in chronological order: the next undecided point is selected as the current processing object, the determination logic is called to obtain its valid or abnormal conclusion, and the state of the points in the sequence is updated according to the conclusion. This iterative process continues, and the subsequent processing points are dynamically determined based on the updated state, until all points in the sequence are assigned a final state.

[0031] Understandably, by processing loops, it is ensured that the determination of each point is based on the processed and correct historical trajectory context, thereby realizing automated and reliable flying point identification and labeling of the complete trajectory sequence from beginning to end.

[0032] A second aspect of the present invention provides a trajectory flying point determination device, comprising: a data acquisition module for acquiring a sequence of trajectory points from data of an Automatic Identification System (AIS), the sequence of trajectory points including multiple undetermined points, each undetermined point including a time parameter and a position parameter; a feature association module for determining multiple associated feature points corresponding to each undetermined point in the trajectory point sequence based on the time parameter, the multiple associated feature points and the undetermined point being continuous in the trajectory point sequence; a local steering module for determining a first local steering parameter corresponding to the undetermined point based on the position parameter of the undetermined point and the position parameter of the associated feature points; and an association steering module for determining a first local steering parameter corresponding to the undetermined point based on the position parameter of the undetermined point. The system comprises the following modules: a first local steering parameter and a second local steering parameter; a geometric determination module, which determines the geometric result corresponding to the point to be determined based on the first local steering parameter and the second local steering parameter; a vector determination module, which determines the direction vector pointing from the point to be determined to multiple associated feature points based on the position parameters of the point to be determined and the position parameters of the associated feature points when both the first local steering parameter and the second local steering parameter are less than a preset steering threshold; a direction determination module, which determines the direction continuation result corresponding to the point to be determined based on the multiple direction vectors; and a flying point determination module, which determines the trajectory flying point in the trajectory point sequence based on the geometric result and the direction continuation result.

[0033] An embodiment of the third aspect of this application provides an electronic device, including a processor, a memory, and a program or instructions stored in the memory and executable on the processor, wherein the program or instructions, when executed by the processor, implement the steps of the trajectory flying point determination method as described in the first aspect.

[0034] Additional aspects and advantages of the technical solutions of the present invention will become apparent in the following description or may be learned by practice of the invention. Attached Figure Description

[0035] Figure 1 One of the flowcharts of the trajectory flying point determination method according to this application is shown;

[0036] Figure 2 A second flowchart illustrating the trajectory flying point determination method according to this application is shown;

[0037] Figure 3 The third flowchart illustrates the trajectory flying point determination method according to this application;

[0038] Figure 4 The fourth flowchart illustrates the trajectory flying point determination method according to this application;

[0039] Figure 5 Fifth of the flowcharts illustrating the trajectory flying point determination method according to this application is shown;

[0040] Figure 6 The sixth flowchart of the trajectory flying point determination method according to this application is shown;

[0041] Figure 7 The seventh flowchart illustrates the trajectory flying point determination method according to this application;

[0042] Figure 8 The eighth flowchart illustrates the trajectory flying point determination method according to this application;

[0043] Figure 9 A schematic block diagram of the trajectory flying point determination device according to this application is shown;

[0044] Figure 10 A schematic block diagram of the structure of an electronic device according to this application is shown;

[0045] Figure 11 One of the schematic diagrams of trajectory flypoints according to this application is shown;

[0046] Figure 12 The second schematic diagram of the trajectory flying point according to this application is shown;

[0047] Figure 13 The third schematic diagram of the trajectory flying point according to this application is shown;

[0048] Figure 14 The fourth schematic diagram of the trajectory flying point according to this application is shown.

[0049] Among them, 900: trajectory flying point determination device; 902: data acquisition module; 904: feature association module; 906: local steering module; 908: associated steering module; 910: geometric determination module; 912: vector determination module; 914: direction determination module; 916: flying point determination module;

[0050] 1000: Electronic device; 1109: Memory; 1110: Processor. Detailed Implementation

[0051] To better understand the above-described objectives, features, and advantages of the embodiments of the present invention, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0052] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, embodiments of the invention may also be implemented in other ways different from those described herein. Therefore, the scope of protection of this application is not limited to the specific embodiments disclosed below.

[0053] The Automatic Identification System (AIS), a core technology for modern maritime supervision and navigation safety, automatically broadcasts and receives static information (such as ship name and dimensions), dynamic information (such as position, speed, and heading), and voyage-related information via the VHF band, enabling real-time monitoring and information exchange of ship navigation status. With the rapid development of the global shipping industry, AIS data has become an indispensable basic data source for maritime management, vessel traffic services, maritime search and rescue, shipping logistics optimization, and marine scientific research.

[0054] However, in practical applications, AIS data quality is affected by various factors, among which the "flying points" problem is particularly prominent. Flying points refer to abnormal locations in AIS data that deviate significantly from the ship's actual navigation trajectory, disrupting the continuity and reliability of the data. Based on their generation mechanisms, AIS flying points can be mainly classified into the following categories:

[0055] 1. Latitude and longitude values ​​change irregularly or regularly due to equipment malfunction / interference;

[0056] 2. Inconsistencies in AIS signal reception and transmission delays from different data sources can cause trajectory bounces.

[0057] 3. Counterfeiting: Different physical vessels use the same Maritime Mobile Service Identity (MMSI), causing two tracks to be forcibly merged.

[0058] 4. Error data generated by the software service system;

[0059] 5. Signals were maliciously forged by humans.

[0060] Currently, the main techniques for handling AIS flypoints are rule-based, such as setting fixed distances, setting maximum speed thresholds, handling flypoints based on specific characteristics like deviations between AIS ship position data and the actual calculated results of two consecutive points exceeding a set threshold, and handling bounces. Clearly, the more processing rules involved, the higher the difficulty and complexity of the algorithm's implementation. We aim to design a simpler and more unified processing method that can largely solve the flypoint problem.

[0061] The trajectory flying point determination method, apparatus, and electronic device provided in this application will be described in detail below with reference to specific embodiments and application scenarios.

[0062] This embodiment provides a method for determining trajectory flying points, such as... Figure 1 As shown, the methods for determining the trajectory flying point include:

[0063] Step S100: Obtain the trajectory point sequence from the Automatic Identification System (AIS) data. The trajectory point sequence includes multiple undetermined points, and each undetermined point includes time parameters and position parameters.

[0064] Step S102: Determine multiple associated feature points corresponding to each undetermined point in the trajectory point sequence based on the time parameters. The multiple associated feature points and the undetermined point are continuous in the trajectory point sequence.

[0065] Step S104: Determine the first local steering parameter corresponding to the point to be determined based on the position parameters of the point to be determined and the position parameters of the associated feature points;

[0066] Step S106: Determine the second local steering parameters corresponding to the associated feature points based on the position parameters of the point to be determined and the position parameters of the associated feature points;

[0067] Step S108: Determine the geometric result corresponding to the point to be determined based on the first local steering parameters and the second local steering parameters;

[0068] Step S110: When both the first local steering parameter and the second local steering parameter are less than the preset steering threshold, determine the direction vector from the point to be determined to multiple associated feature points based on the position parameters of the point to be determined and the position parameters of the associated feature points.

[0069] Step S112: Determine the direction continuation result corresponding to the point to be determined based on multiple direction vectors;

[0070] Step S114: Determine the trajectory flying points in the trajectory point sequence based on the geometric results and direction continuation results.

[0071] This invention provides a novel two-level determination system for trajectory flying points. From the original AIS trajectory point sequence, each undetermined point and its adjacent associated feature points are extracted based on temporal continuity. Then, by calculating and analyzing the first and second local turning parameters, a first-level screening is performed based on geometric morphology, identifying clearly normal points and suspicious points. Subsequently, for difficult cases where the geometric results are uncertain, a second-level precise determination is performed from the perspective of motion trend continuity by calculating the direction vector from the undetermined point to multiple subsequent associated feature points and statistically analyzing its consistency with the forward vector of the undetermined point. The combined results of the two-level determination achieve the identification of trajectory flying points.

[0072] For example, the first local turning parameter is a quantitative index calculated with the point to be determined as the core, used to characterize the degree of directional change exhibited by the point to be determined in its local trajectory segment. The first local turning parameter is calculated based on the position parameters of the point to be determined itself and the position parameters of the associated feature points that are adjacent to it in the time series, through specific geometric relationships.

[0073] The second local steering parameter is another quantitative indicator calculated using a specific associated feature point corresponding to the point to be determined as the core. It is used to characterize the degree of directional change of the associated feature point within its own local trajectory segment. The second local steering parameter is calculated based on the position parameters of the point to be determined and the associated feature point.

[0074] The geometric result is a comprehensive criterion, jointly determined by the first and second local steering parameters calculated above. By analyzing the degree of local steering at the point to be determined and its immediate neighbors, the geometry of the current trajectory segment is comprehensively evaluated and classified, thus providing primary, morphological evidence for determining whether the point to be determined is abnormal.

[0075] The direction continuation result is a supplementary judgment index activated when both the first and second local steering parameters indicate that the trajectory local steering is smooth (i.e., both are less than the preset steering threshold). It is used to evaluate whether the direction of motion is maintained or continued over a subsequent period of time after starting from the point to be determined. The direction continuation result determines whether the motion trend of a point that appears smooth in local geometry is consistent with the subsequent trajectory, in order to identify abnormal points that appear straight but are actually caused by jumps.

[0076] Understandably, the trajectory flying point determination method completely abandons the scattered rules that rely on absolute thresholds such as speed and distance in traditional methods. Instead, it uses the two essential physical characteristics of trajectory's inherent angle change and direction consistency for comprehensive reasoning. This not only unifies and simplifies the judgment logic, reduces algorithm complexity and implementation difficulty, but also significantly enhances the adaptability to complex navigation scenarios, thereby fundamentally improving the overall processing efficiency of trajectory flying point recognition.

[0077] Specifically, the trajectory flying point determination method provided by the present invention aims to automatically and accurately identify and remove abnormal trajectory flying points from the Automatic Identification System (AIS) data of ships, thereby obtaining a clean trajectory that can truly reflect the continuous and smooth motion law of ships.

[0078] First, obtain the sequence of trajectory points composed of the ship's AIS reports.

[0079] Each point in the trajectory point sequence is considered a candidate point, meaning it needs to be determined as either a normal valid point or an anomalous flying point. Each candidate point contains its reported time parameters and latitude and longitude location parameters. Based on the order of the time parameters, multiple temporally adjacent related feature points can be dynamically determined for each candidate point in the sequence.

[0080] The first trajectory point received in the trajectory point sequence is directly marked as a valid point and used as the benchmark for subsequent judgments.

[0081] Based on the position parameters of the undetermined point and its associated feature points, two key local steering features are calculated.

[0082] The first is the first local steering parameter, which represents the local steering angle with the point to be determined as the vertex;

[0083] The second is the second local steering parameter, which represents the local rotation angle with the next associated feature point immediately adjacent to the point to be determined as the vertex.

[0084] These two angular features together describe the geometry of the trajectory in the local region.

[0085] Based on the comparison between these two feature values ​​and the preset steering threshold, a geometric result corresponding to the point to be determined can be comprehensively determined.

[0086] The geometric results directly lead to a preliminary judgment: if the local turning is gentle, it indicates that the point to be determined is in a straight section of navigation and can be determined as a valid point; if there is a significant obtuse angle turn, it indicates that the ship may be starting a normal turn, and the point to be determined as the starting point of the turn is also determined as a valid point; if there are continuous sharp acute angle turns, it indicates that the trajectory has an unnatural and violent bend at this point, and the possibility of an abnormal flypoint in the area is extremely high. In this case, the geometric results will mark the point to be determined as a pending state that requires further review.

[0087] When the first-level determination marks the point to be determined as pending, the method automatically initiates the second-level determination, which is based on the continuity of motion direction. This level aims to resolve complex situations that the first level cannot distinguish, such as whether consecutive acute angles are caused by abnormal ship bouncing or by the ship performing high-frequency zigzag maneuvers. In this case, the method examines whether the motion trend of the point to be determined continues over a subsequent period of time.

[0088] The specific process involves selecting several consecutive related subsequent points in time sequence after the point to be determined, and calculating the direction vector from the position of the point to be determined to the positions of these subsequent points.

[0089] At the same time, obtain the forward motion direction vector of the point to be determined in the trajectory.

[0090] By comparing the forward direction vector with each subsequent direction vector and calculating the angle difference between them, multiple directional angle features are obtained.

[0091] By counting the number of these included angle features that are less than a preset abnormal direction threshold, a quantitative feature can be obtained, which is defined as the direction continuation result.

[0092] If, among subsequent points, a sufficient number of points move in a direction that is essentially consistent with the forward direction of the point to be determined, it indicates that the movement trend of the point to be determined has continued, and the point to be determined is a valid point; otherwise, it indicates that the movement direction after the point to be determined is chaotic, and the point to be determined may be an abnormal flying point.

[0093] By combining the geometric results from the first-level judgment with the directional continuation results from the second-level judgment, a final decision is made on each undetermined point in the trajectory point sequence, accurately identifying any trajectory flying points. The entire judgment process is logically clear, with the two levels of features complementing each other. The first level quickly filters out obviously normal and abnormal cases based on static geometric shapes, while the second level resolves difficult cases based on dynamic motion trends. This significantly improves the accuracy and adaptability of the algorithm while maintaining a high recall rate.

[0094] For example, the first local steering parameter can be calculated using the position coordinates of the point to be determined, its preceding associated point, and its subsequent associated point. Specifically, it is represented by the angle formed by the line segments from the preceding point to the point to be determined, and from the point to the subsequent point. The steering threshold can be set comprehensively based on the ship's maneuverability and AIS reporting error, for example, using 150 degrees as a boundary to distinguish between a gentle turn and an acute turn. The size of the observation window in the direction continuity determination is configurable. For example, considering five subsequent points, if at least three of these points have an angle of less than 20 degrees with the forward direction of the point to be determined, then the direction is determined to be continuous.

[0095] In some embodiments, the preset steering threshold is optionally not a fixed value, but is dynamically adjusted based on the ship's historical average sailing speed or ship type reflected in the trajectory point sequence. By matching the judgment benchmark with the ship's actual maneuverability, the algorithm's adaptability and judgment accuracy for ships with different performance characteristics are improved.

[0096] Optionally, after updating the state of the trajectory points in the trajectory point sequence according to the judgment result, points identified as abnormal trajectory flying points are immediately removed from the currently processed sequence. This allows the subsequent processing of the next undetermined point to be based on a cleaner trajectory context, avoiding interference from identified flying points on subsequent geometric result calculations, thereby improving the robustness and efficiency of the overall processing flow.

[0097] In some embodiments, optionally, the number of associated subsequent points used in determining the direction continuation result is a parameter that can dynamically change with the ship's speed relative to the ground. A larger number is used at higher speeds to observe longer-term trends, while a smaller number is used at lower speeds. This allows the observation window for direction continuation to adapt to the ship's motion state, enabling timely responses even in low-speed scenarios with frequent ship maneuvers.

[0098] In some embodiments, optionally, external environmental data corresponding to the time parameters is acquired simultaneously when acquiring the trajectory point sequence. The step of determining the direction continuation result also references the external environmental data to assist in interpreting the rationality of the direction change.

[0099] In some embodiments, the method output may include not only the identified anomalous trajectory flying points, but also an anomalous confidence label for each point determined to be anomalous. The anomalous confidence label is a quantitative value calculated based on the statistical characteristics in the direction continuation results, used to indicate the reliability of the flying point determination, and providing a grading basis for subsequent manual review or differentiated processing for different application scenarios.

[0100] In some embodiments, optionally, such as Figure 2As shown, step S104: Determine the first local steering parameter corresponding to the point to be determined based on the position parameters of the point to be determined and the position parameters of the associated feature points, including:

[0101] Step S1042: Determine the first associated predecessor point before the undetermined point and the first associated successor point after the undetermined point based on the time parameters;

[0102] Step S1044: Determine the first local turning parameters based on the position parameters of the first associated preceding point, the position parameters of the undetermined point, and the position parameters of the first associated subsequent point.

[0103] In this embodiment, the preceding and following trajectory points directly adjacent to the point to be determined are locked based on the time series, and the angle value that accurately represents the local heading change is calculated based on the geometric relationship formed by these three points.

[0104] Understandably, transforming the abstract local turning point into an objectively calculable geometric angle provides a stable and reliable quantitative input for the first-level geometric determination. This calculation method, based on the instantaneous relationship between three adjacent points, is not only logically simple and computationally efficient, capable of processing data streams in real time, but more importantly, it directly reflects the microscopic continuity of ship motion. This allows the algorithm to keenly detect any unnatural, minute bends in the trajectory, laying a solid feature foundation for accurately distinguishing between normal navigation and abnormal jumps.

[0105] Specifically, determining the first local steering parameters begins with the use of time series data. The data points in the Automatic Identification System (AIS) report naturally carry time parameters, which can be used to uniquely determine the adjacent relationships of any point to be determined within the complete trajectory point sequence.

[0106] For each undetermined point, a point needs to be located before it based on the time parameter, called the first associated predecessor point, and a point needs to be located after it, called the first associated successor point.

[0107] The first associated preceding point is the trajectory point reported immediately before the point to be determined in time sequence, while the first associated subsequent point is the trajectory point reported immediately after the point to be determined in time sequence.

[0108] These three points form a minimal trajectory segment that is continuous in time and adjacent in space.

[0109] The first associated preceding point, the undetermined point, and the first associated subsequent point all contain their latitude and longitude location parameters.

[0110] These positional parameters allow us to construct two directed line segments.

[0111] The first line segment points from the position of the first associated preceding point to the position of the undetermined point, and the second line segment points from the position of the undetermined point to the position of the first associated subsequent point.

[0112] The essence of the first local steering parameter is to calculate the angle between two line segments.

[0113] The size of this angle directly reflects the degree to which the ship's trajectory changes direction when passing through the point to be determined.

[0114] If the included angle is close to 180 degrees, it means that the two line segments are almost on the same straight line, the ship's course hardly changes, and the local trajectory is straight.

[0115] If the included angle is significantly less than 180 degrees, it indicates that the ship has undergone a significant turn at the point to be determined.

[0116] By using trigonometric functions and vector operations, the value of the included angle can be accurately calculated using the latitude and longitude coordinates of the three points. The calculated angle value is then defined as the specific numerical representation of the first local steering parameter.

[0117] For example, assuming the latitude and longitude coordinates of the first associated preceding point, the undetermined point, and the first associated subsequent point are known, the first local steering parameter can be obtained by calculating the azimuth angle from the preceding point to the undetermined point and the azimuth angle from the undetermined point to the subsequent point, then obtaining the absolute value of the difference between the two azimuth angles, and normalizing it to an angle between zero and 180 degrees.

[0118] In some embodiments, optionally, when determining the first associated preceding point and the first associated subsequent point based on the time parameter, if the point to be determined is the starting point or ending point of the trajectory point sequence, resulting in no available trajectory points before or after it, a virtual associated feature point is assigned to the special location point by a preset rule to ensure the integrity of the calculation of the first local turning parameter and the continuity of the process, and to avoid algorithm interruption due to missing boundary data.

[0119] In some embodiments, optionally, a data preprocessing step is introduced before calculating the first local steering parameters. The position parameters of the first associated preceding point, the point to be determined, and the first associated subsequent point are smoothed and filtered to suppress angle calculation disturbances caused by measurement noise from the AIS receiver itself or minor positioning fluctuations. This makes the calculated first local steering parameters more reflective of the ship's macroscopic maneuvering intentions, rather than minor measurement errors, thus enhancing the stability of the feature.

[0120] In some embodiments, optionally, such as Figure 3 As shown, step S106: Determine the second local turning parameter corresponding to the associated feature point based on the position parameters of the point to be determined and the position parameters of the associated feature point, including:

[0121] Step S1062: Determine the second associated successor point located after the first associated successor point based on the time parameter;

[0122] Step S1064: Determine the second local steering parameters based on the position parameters of the point to be determined, the position parameters of the first associated subsequent point, and the position parameters of the second associated subsequent point.

[0123] In this embodiment, by utilizing the already determined first associated subsequent point, the second associated subsequent point is further located in the time series, and based on the geometric relationship formed by these three points, the local turning angle with the first associated subsequent point as the core is calculated.

[0124] Understandably, the focus of the analysis is naturally extended from the current point to the next adjacent trajectory point, thereby obtaining continuous geometric information about the trajectory instantaneously after the point. This allows the algorithm to not only focus on the local state of a single point, but also observe the curvature characteristics of the trajectory segment formed by two consecutive points. By continuously calculating the first and second local steering parameters, the method achieves coherent detection of potentially abnormal regions (such as consecutive acute angles), providing indispensable paired geometric evidence for accurately distinguishing normal turning points from abnormal flight point sequences, significantly enhancing the algorithm's analytical ability and judgment accuracy for complex trajectory patterns.

[0125] Specifically, the process of determining the second local steering parameters is logically consistent with that of determining the first local steering parameters, but the core focus of the calculation has changed.

[0126] First, it needs to be clarified that the object of the calculation is the first associated subsequent point.

[0127] After the first associated successor point, continue searching for the next trajectory point that is immediately adjacent in time sequence. This point is defined as the second associated successor point.

[0128] Thus, we have obtained three points that form the basis of the calculation: the undetermined point, the first associated subsequent point, and the second associated subsequent point.

[0129] It is worth noting that these three points are also arranged continuously according to the time parameter. The undetermined point and the first associated subsequent point constitute the previous displacement, while the first associated subsequent point and the second associated subsequent point constitute the next displacement.

[0130] After identifying the three points, geometric calculations are performed based on their position parameters. The goal of the calculation is to determine the angle between the direction from the undetermined point to the first associated subsequent point and the direction from the first associated subsequent point to the second associated subsequent point.

[0131] Treat the first associated subsequent point as a vertex and calculate the angle formed by the two displacement vectors before and after it.

[0132] This angle value is defined as the second local steering parameter, which characterizes the degree of course change that occurs at the position of the first associated subsequent point when the ship leaves the pending point, passes the first associated subsequent point, and continues to move towards the second associated subsequent point.

[0133] The second local steering parameter is calculated in this way, allowing the algorithm to observe the trajectory curvature at positions immediately following the point to be determined. By combining the first and second local steering parameters, the algorithm can determine from the continuous geometric shape whether the current trajectory segment is in a straight section, a single-point turning point, or a continuous, complex curved region.

[0134] In some embodiments, optionally, a dynamic search strategy is employed when determining the second associated successor point following the first associated successor point based on time parameters. If the second associated successor point cannot be found immediately according to the standard time series, a forward search is allowed within a set time tolerance window, using the temporally closest trajectory point as an effective replacement. This strategy ensures that the feature calculation process can continue even when there are minor gaps in AIS data or slight fluctuations in the reporting timestamps, thereby improving the robustness of the entire flying point recognition algorithm when dealing with incomplete data.

[0135] In some embodiments, optionally, such as Figure 4 As shown, step S108: Determine the geometric result corresponding to the point to be determined based on the first local steering parameters and the second local steering parameters, including:

[0136] Step S1082: When the first local steering parameter is greater than or equal to the preset first feature threshold, determine the first geometric determination result based on the first local steering parameter;

[0137] Step S1084: When the first local steering parameter is less than the first feature threshold and the second local steering parameter is greater than or equal to the first feature threshold, determine the second geometric determination result based on the first local steering parameter and the second local steering parameter;

[0138] Step S1086: When the first local steering parameter is less than the first feature threshold and the second local steering parameter is less than the first feature threshold, determine the third geometric determination result based on the position parameters of the undetermined point, the position parameters of the first associated preceding point, the position parameters of the first associated subsequent point, and the position parameters of the second associated subsequent point.

[0139] Step S1088: Determine the geometric result corresponding to the point to be determined based on the first geometric determination result, the second geometric determination result, and the third geometric determination result.

[0140] In this embodiment, effective points for smooth navigation are quickly screened out by comparing the first local steering parameter with a threshold. Secondly, when the first feature indicates an acute angle, a second feature is introduced for verification, accurately identifying the sharp / blunt pattern representing the normal turning point. For the most complex double-acute angle case, a geometric check is used, comparing the smoothness of the trajectory after removing two suspect points to accurately locate the true anomaly.

[0141] Understandably, by using a progressive decision-making architecture, most simple and straightforward cases are handled with minimal computational cost, while complex computational resources are concentrated on the few most difficult cases. Furthermore, rigorous geometric reasoning fundamentally solves the problem of accurately locating outliers in continuous acute angle scenarios, thus achieving the optimal balance between efficiency and accuracy in flying point recognition.

[0142] First, the calculated first local steering parameters are compared with a preset first feature threshold.

[0143] The first characteristic threshold is a key angular boundary value used to geometrically distinguish between gentle turns and sharp turns. For example, a typical value for the first characteristic threshold can be set based on common sense regarding ship handling, including but not limited to ninety degrees.

[0144] When the first local steering parameter is greater than or equal to the first feature threshold, it indicates that the local turning angle with the point to be determined as the vertex is an obtuse angle or a straight angle.

[0145] The ship's trajectory changes gently at this point, consistent with the characteristics of straight-line navigation or large-radius constant-speed turning.

[0146] In this case, a determination can be made directly based on this single feature, and the determined first geometric determination result indicates that the point to be determined is a valid trajectory point.

[0147] When the first local steering parameter is less than the first feature threshold, it indicates that a sharp steering, i.e. an acute angle, has occurred at the point to be determined.

[0148] This immediately triggered further scrutiny of the trajectory's continuous morphology.

[0149] At this point, a second local steering parameter needs to be introduced for the first associated subsequent point. This second local steering parameter is compared with the same first feature threshold. If the second local steering parameter is greater than or equal to the first feature threshold, it means that although an acute angle appears at the point to be determined, the curvature of the trajectory quickly returns to a gentler shape at the next point. This continuous pattern of initial sharpness followed by bluntness perfectly matches the physical process of a ship initiating a normal maneuvering turn, with the point to be determined precisely being the starting point of this turn.

[0150] Therefore, the second geometric determination result based on these two features also indicates that the point to be determined is a valid trajectory point and identifies it as a normal turning point.

[0151] When both the first local steering parameter and the second local steering parameter are less than the first feature threshold, it indicates that the trajectory has two consecutive acute angles at the point to be determined and the next point immediately following it.

[0152] The double acute angle pattern is one of the most prominent features of abnormal flight points, but it may also be part of complex maneuvers, thus constituting the most difficult and delicate situation in the first-level judgment.

[0153] At this point, the method no longer simply draws a conclusion based on the angle threshold, but instead initiates a more in-depth geometric analysis subprocess to determine the third geometric decision result.

[0154] The subprocess requires the positional parameters of four points: the undetermined point, its preceding point (i.e., the first associated predecessor point), the first associated successor point, and the second associated successor point. Its core idea is to perform a hypothesis test: to determine whether the undetermined point or the first associated successor point is more likely to be an outlier that disrupts trajectory smoothness.

[0155] Specifically, we first assume that the first associated subsequent point is an outlier and temporarily remove it from the geometric structure. Then, connecting the first associated preceding point, the undetermined point, and the second associated subsequent point will form a new turning point, which is defined as the first candidate turning feature.

[0156] Next, assuming the undetermined point is an outlier and is temporarily removed, connecting the first associated preceding point, the first associated subsequent point, and the second associated subsequent point will form another new turning point, which is defined as the second candidate turning feature.

[0157] Then, the magnitudes of the two candidate inflection features are compared.

[0158] The underlying logic is that a true trajectory should become smoother after removing real outliers, meaning that the resulting turns should be larger.

[0159] Therefore, if the first candidate turning point feature is smaller than the second candidate turning point feature, it indicates that the trajectory is smoother after removing the first associated subsequent point, so the undetermined point is determined to be valid, and the first associated subsequent point is an anomaly; conversely, it indicates that the trajectory is smoother after removing the undetermined point, so the undetermined point is determined to be an anomaly.

[0160] Ultimately, the first geometric decision result, the second geometric decision result, or the third geometric decision result determined by one of the three branch logics mentioned above are comprehensively determined into a unified geometric result corresponding to the point to be determined.

[0161] In some embodiments, the preset first feature threshold is optionally not a globally fixed value, but is dynamically configured based on the ship type or historical average speed reflected in the trajectory point sequence. For example, a smaller threshold can be used for ships with high maneuverability or low-speed navigation to detect more subtle turns; a larger threshold is used for large ships or high-speed navigation to avoid misjudging normal large-radius turns as suspicious situations. This allows the sensitivity of the first-level geometric determination to adapt to the navigation characteristics of the target ship, improving the accuracy of the determination.

[0162] In some embodiments, optionally, such as Figure 5 As shown, in step S1086, the third geometric determination result is determined based on the position parameters of the point to be determined, the position parameters of the first associated preceding point, the position parameters of the first associated subsequent point, and the position parameters of the second associated subsequent point, including:

[0163] Step S10862: Determine the first candidate turning feature based on the position parameters of the first associated preceding point, the position parameters of the undetermined point, and the position parameters of the second associated subsequent point;

[0164] Step S10864: Determine the second candidate turning feature based on the position parameters of the first associated preceding point, the position parameters of the first associated subsequent point, and the position parameters of the second associated subsequent point;

[0165] Step S10866: Determine the third geometric judgment result based on the size relationship between the first candidate turning feature and the second candidate turning feature.

[0166] In this embodiment, two competing hypotheses are constructed: the undetermined point is a flying point and the subsequent point is a flying point. Based on the corresponding three-point set, the candidate turning features are calculated. Finally, by directly comparing the size of the two feature angles, the true outlier is determined according to the geometric principle that removing true outliers should make the trajectory smoother.

[0167] Understandably, subjective, experience-based rule judgments are transformed into objective, quantifiable geometric result comparisons. This enables the precise identification of a single point of responsibility that disrupts the continuity of a trajectory in complex situations where multiple suspicious points are intertwined, significantly improving the resolution and certainty of the judgment in flypoint identification.

[0168] Specifically, when the decision logic enters this branch, it means that four key points have been confirmed: the first associated preceding point, the undetermined point, the first associated subsequent point, and the second associated subsequent point, and it is known that the local turning angles at the undetermined point and the first associated subsequent point are both acute angles.

[0169] At this point, both the point to be determined and the first associated subsequent point become suspicious points.

[0170] First, we can tentatively consider the subsequent points of the first association as abnormal data and remove them from the trajectory segments currently being analyzed.

[0171] Connect the first associated predecessor point, the undetermined point, and the second associated successor point. Using the positional parameters (latitude and longitude coordinates) of these three points, we can construct two vectors: the first vector points from the first associated predecessor point to the undetermined point, and the second vector points from the undetermined point to the second associated successor point.

[0172] These two vectors represent the continuous displacement direction of the ship from the first associated preceding point, through the undetermined point, to the second associated subsequent point in the absence of interference from the first associated subsequent point.

[0173] Next, calculate the angle between the two vectors.

[0174] The size of this angle quantifies the degree of curvature of the trajectory at the point to be determined, under the assumption of eliminating the first associated subsequent points, i.e., the first candidate turning feature.

[0175] Connect the remaining first associated predecessor point, the first associated successor point, and the second associated successor point.

[0176] Based on the positional parameters of these three points, two new vectors are constructed: the first vector points from the first associated predecessor point to the first associated successor point, and the second vector points from the first associated successor point to the second associated successor point.

[0177] Calculate the angle between these two vectors. The magnitude of this angle quantifies the curvature of the trajectory at the first associated subsequent point, under the assumption of eliminating undetermined points, which is the second candidate turning feature.

[0178] Removing a genuine anomalous flight point from a normal, smooth flight path should result in a reduced curvature of the remaining path, i.e., an increased turning angle and a smoother trajectory. Therefore, the core of the decision is to directly compare the angle values ​​of the two candidate turning features.

[0179] If the angle value of the first candidate turning feature is less than the angle value of the second candidate turning feature, it indicates that under the assumption of eliminating the first associated subsequent point, the remaining turning angle (smaller) of the trajectory at the undetermined point is still sharper than under the assumption of "eliminating the undetermined point", the remaining turning angle (larger) of the trajectory at the first associated subsequent point.

[0180] According to the principle of smoothness, removing true outliers should result in a larger angle (a smoother trajectory). Therefore, a larger "second candidate turning point feature" means that the hypothesis of "removing undetermined points" is more likely to hold. Thus, the decision is: the undetermined point is an outlier.

[0181] Conversely, if the angle value of the "first candidate turning point feature" is greater than the angle value of the "second candidate turning point feature", it indicates that "removing the first associated subsequent point" can produce a smoother trajectory. Therefore, the decision is: the first associated subsequent point is an outlier, while the undetermined point is a valid point.

[0182] In some embodiments, optionally, a tolerance threshold is introduced when determining the third geometric determination result based on the magnitude relationship between the first candidate turning feature and the second candidate turning feature. If the absolute difference between the two feature values ​​is less than the tolerance threshold, the double acute angle case is determined to be an ambiguous state. Instead of immediately ruling out an outlier, the current undetermined point is marked as an undetermined state point that needs to be submitted to the subsequent second-level directional continuity test for final determination. This avoids making arbitrary decisions on boundary cases where feature values ​​are extremely close due to measurement noise, and improves the decision reliability of the algorithm in critical states.

[0183] In some embodiments, optionally, such as Figure 6 As shown, step S112: Determine the direction continuation result corresponding to the point to be determined based on multiple direction vectors, including:

[0184] Step S1120: Determine multiple associated subsequent points located after the point to be determined based on the time parameters;

[0185] Step S1122: Determine the direction vector from the point to be determined to each associated subsequent point based on the position parameters of the point to be determined and the position parameters of multiple associated subsequent points;

[0186] Step S1124: Obtain the forward direction vector of the point to be determined;

[0187] Step S1126: Determine multiple directional angle features based on the forward direction vector and each direction vector;

[0188] Step S1128: Determine the quantity features based on the angle features of multiple directions and the preset second feature threshold; determine the direction continuation result based on the quantity features.

[0189] In this embodiment, an observation window is first defined after the point to be determined and the direction vector pointing to each subsequent point is calculated. Then, the forward direction vector representing the historical movement trend is obtained. The deviation between each subsequent direction and the historical direction is quantified by calculating the angle between the vectors. Finally, the number of subsequent points with a deviation less than a preset tolerance threshold is counted, and this number is used as the direction continuation result.

[0190] Understandably, transforming the fuzzy concept of whether directions are consistent into a quantitative indicator that can be objectively statistically analyzed and compared allows the judgment criteria to be expanded from the instantaneous state of a single point to the short-term continuous motion trend. This effectively distinguishes between changes in direction caused by normal maneuvers and random jumps caused by flying points, significantly enhancing the algorithm's discriminative power and robustness in complex scenarios.

[0191] After the point to be determined, a series of consecutive trajectory points are selected sequentially. These selected points are defined as multiple associated subsequent points in the current analysis. The number of these points constitutes an observation window, and the size of the window (e.g., selecting 5 subsequent points) is a configurable parameter that determines the length of the time span considered in the trend analysis.

[0192] For each selected associated successor point, using its location parameters (latitude and longitude) and the location parameters of the point to be determined, a vector pointing from the location of the point to be determined to the location of the associated successor point can be determined through vector operations.

[0193] To assess whether the direction has been maintained, a reference direction is needed for comparison. This reference direction is called the forward direction vector. The forward direction vector represents the instantaneous direction of motion of the ship before reaching the point to be determined.

[0194] The forward direction vector is typically obtained based on the positional relationship between the point to be determined and its preceding valid trajectory point (e.g., a valid preceding point confirmed in the first-level determination). Based on the positional parameters of these two valid points, a vector pointing from the preceding point to the point to be determined is calculated; this vector is defined as the forward direction vector.

[0195] After obtaining the baseline forward direction vector and a set of future-oriented direction vectors, for each calculated direction vector, the angle between it and the forward direction vector is calculated. This angle value is called a direction angle feature. That is, how many degrees the instantaneous direction required to move from the point to be determined to a subsequent point deviates from the ship's historical direction of motion when it reached the point to be determined.

[0196] The second feature threshold is an angle value, such as 20 degrees or 30 degrees, used to define the permissible deviation range for consistent orientation.

[0197] The value of each directional angle feature is compared with this second feature threshold. The number of directional angle feature values ​​that are less than (i.e., closer to) this threshold is counted. This count is defined as the quantitative feature. The quantitative feature intuitively represents how many subsequent points' movement directions can be considered a reasonable continuation of the current point's forward direction within a preset time window.

[0198] Finally, the statistically derived quantitative features are directly used as the direction continuation result for judgment. This feature is an integer. This direction continuation result is compared with another preset quantitative threshold (e.g., requiring at least 3 subsequent points to have the same direction). If the direction continuation result reaches or exceeds the quantitative threshold, the direction of the point to be determined is considered to have been effectively continued, and it is judged as a valid point; otherwise, its direction is considered to lack subsequent support, and it is judged as an abnormal flying point.

[0199] For example, if the observation window consists of 5 subsequent points, and the second feature threshold is set to 25 degrees, the calculated directional angle features are 10 degrees, 50 degrees, 15 degrees, 5 degrees, and 30 degrees. Upon comparison, points 1, 3, and 4 have angles less than 25 degrees, a total of 3. Therefore, the quantity feature is 3, which represents the direction continuation result. If the preset pass threshold requires at least 3 points to have the same direction, then the current point to be determined passes this second-level test and is judged as a valid point.

[0200] In some embodiments, optionally, when determining multiple associated subsequent points located after the point to be determined based on time parameters, the number of determined subsequent points is not a fixed value, but is dynamically calculated based on the ship's speed relative to ground or rate of change of course at the point to be determined. For example, when the speed is high or the course is stable, a larger observation window is used to observe long-term trends; when the speed is low or the course changes drastically, a smaller window is used to ensure timely response. This allows the observation scale of directional continuity to adapt to the real-time motion state of the ship, improving the adaptability and accuracy of the determination.

[0201] In some embodiments, the preset second feature threshold can be dynamically adjusted according to the navigation environment or external conditions of the point to be determined. For example, in open waters or good weather conditions, a smaller threshold can be used for more stringent consistency judgment; in narrow channels, complex sea conditions, or areas with dense traffic flow, a larger threshold is automatically adopted to tolerate greater directional fluctuations caused by reasonable maneuvers such as avoidance and steering. This enhances the applicability and rationality of the algorithm in different actual navigation scenarios.

[0202] In some embodiments, optionally, such as Figure 7 As shown, step S114: Determine the trajectory flying points in the trajectory point sequence based on the geometric results and direction continuation results, including:

[0203] Step S1142: Determine the primary judgment result of the undetermined point based on the geometric results. The primary judgment result is used to indicate whether the undetermined point is a valid trajectory point, an abnormal trajectory flying point, or an undetermined state point.

[0204] Step S1144: When the first-level judgment result indicates that the point to be determined is a point in a state to be determined, the second-level judgment result of the point to be determined is determined according to the direction continuation result. The second-level judgment result is used to indicate whether the point to be determined is a valid trajectory point or an abnormal trajectory flying point.

[0205] In this embodiment, a primary judgment result is first generated based on the geometric results determined by local geometric analysis. This primary judgment result can clearly classify the trajectory points as valid, abnormal, or pending, thereby quickly terminating the judgment of most simple and clear cases. The secondary judgment is activated only when a point is marked as pending, that is, the final secondary judgment result is generated using the direction continuation results based on motion trend statistics.

[0206] Understandably, through this decision tree structure that enables rapid initial screening and precise verification, the algorithm can handle the vast majority of normal and obviously abnormal points with extremely low computational overhead, while using complex trend analysis only for the few most difficult cases, thereby achieving overall optimization of processing efficiency.

[0207] Meanwhile, the mutual verification and supplementation of the two levels of evidence fundamentally solves the problem that a single judgment rule is prone to misjudgment or omission when facing complex navigation scenarios, and significantly improves the overall accuracy of flight point recognition and the reliability of the system.

[0208] First, the process executes the first-level decision. The input to the decision is the geometric result, and based on this geometric result, the first-level judgment result is determined.

[0209] When the local trajectory morphology reflected by the input geometry indicates that the point to be determined is in a straight flight segment or at the starting point of a reasonable turning maneuver, the system generates a first-level judgment result indicating this state. This means that geometric morphology analysis alone is sufficient to confirm that the point to be determined is a normal point. Once this result is generated, the processing flow for the point to be determined immediately terminates, it is marked as a normal point, and no further directional continuity analysis will be performed on it.

[0210] When the input geometric result originates from specific geometric analysis logic and explicitly indicates that the point to be determined is an outlier that disrupts trajectory smoothness, the system generates this state as its primary judgment result. Once this result is generated, the processing of the point to be determined immediately terminates, and it is directly marked as an anomalous flying point.

[0211] When the input geometric results indicate that the point to be determined and its subsequent points form a continuous, sharp turning pattern, making it impossible for the system to distinguish from an anomalous jump or a complex maneuver solely from a geometric perspective, the generated first-level decision result is this state. This state is a non-final intermediate instruction, marking the end of the first-level decision and the triggering of the second-level decision.

[0212] Next, the process moves to the second level of decision-making, which is conditionally enforceable.

[0213] The system is activated only when the first-level decision result is clearly "pending state point". The input for the second-level decision is the direction continuation result, which is a statistical value representing the degree to which the movement direction of the pending point is continued over a subsequent period of time. Based on this direction continuation result, the system determines the final second-level decision result.

[0214] If the numerical results of the direction continuation result indicate that a sufficient number of subsequent motion directions are consistent with the historical directions of the point to be determined, then the secondary determination result is a valid trajectory point. This means that although the geometry is questionable, its motion trend is consistent, and therefore it is more likely to be a valid trajectory point.

[0215] Conversely, if the numerical result of the direction continuation indicates that the subsequent motion direction lacks consistency, the secondary judgment result is an abnormal trajectory flying point. This means that the point not only has an abnormal geometric shape, but its motion trend cannot be continued, and therefore it is ultimately judged as a flying point.

[0216] In some embodiments, the decision may take effect only when the secondary decision result and the primary decision result determine that the point to be determined is a trajectory flying point.

[0217] In some embodiments, optionally, such as Figure 8 As shown, the trajectory flying point determination method also includes:

[0218] Step S1160: Initialize the trajectory point with the earliest time parameter in the trajectory point sequence as a valid trajectory point;

[0219] Step S1162: Take the next undetermined trajectory point in the trajectory point sequence as the point to be determined in the iteration;

[0220] Step S1164: Obtain the judgment result of the iterative undetermined point;

[0221] Step S1166: Update the judgment status of trajectory points in the trajectory point sequence according to the judgment result;

[0222] Step S1168: Determine multiple iterative undetermined points based on the determination state until all trajectory points in the trajectory point sequence have updated their determination states.

[0223] In this embodiment, the earliest trajectory point is initialized as a valid point to establish the processing starting point. Then, the following steps are executed cyclically in chronological order: the next undecided point is selected as the current processing object; the determination logic is called to obtain a valid or abnormal conclusion; and the state of points in the sequence is updated based on the conclusion. This iterative process continues, dynamically determining subsequent processing points based on the updated states, until all points in the sequence are assigned a final state.

[0224] Understandably, by processing loops, it is ensured that the determination of each point is based on the processed and correct historical trajectory context, thereby realizing automated and reliable flying point identification and labeling of the complete trajectory sequence from beginning to end.

[0225] Specifically, the iterative process begins with the initialization of the processing context. Since the first point in the trajectory point sequence is the earliest in time, there are no other points preceding it that can provide historical motion information as a basis for judgment. In order to start the entire processing chain, a definite initial state must be assigned to this point.

[0226] Therefore, the trajectory point with the earliest time parameter in the trajectory point sequence is initialized as a valid trajectory point. Initialization means directly assigning a valid identity based on the initial assumptions of the algorithm design without undergoing complete decision-making calculations.

[0227] After initialization, the system enters the main body of the iterative loop. The first step is to determine the target object to be processed, that is, to take the next undetermined trajectory point in the trajectory point sequence as the iteration undetermined point.

[0228] The determination state is a dynamically maintained attribute of the trajectory points as processing progresses. Each point is initially undetermined. The determination of the next point usually follows the order of time parameters, sequentially scanning the trajectory point sequence and selecting the first undetermined point as the core of the current iteration, i.e., the iterative undetermined point.

[0229] After selecting the target, the judgment result of the iterative undetermined point needs to be obtained. The two-level judgment logic determines whether the iterative undetermined point is a valid trajectory point or an abnormal trajectory flying point.

[0230] After obtaining the judgment result, update the judgment status of the trajectory points in the trajectory point sequence according to the judgment result.

[0231] If the judgment result is a valid trajectory point, the state of the undetermined point is updated from never having been judged to valid. If the judgment result is an abnormal trajectory flying point, its state is updated to abnormal. The state update has important implications: a point being marked as valid means that it becomes part of the trajectory history, and subsequent points will use it as a valid preceding reference point when calculating their own features (such as the forward direction vector). A point being marked as abnormal means that it is excluded from the valid trajectory, and subsequent processing will skip it when searching for associated preceding points.

[0232] After updating the state of a point, the overall state of the sequence is re-evaluated. It scans the sequence again from the beginning, searching for the next point whose state is still undecided. Since the state of a point is updated in each iteration, the next point found each time is the subsequent point in the time sequence.

[0233] This process repeats continuously, with each iteration processing the current highest-ranking unresolved point. The loop terminates when the status of all points has been updated from unresolved to valid or abnormal.

[0234] For example, for a trajectory sequence containing 100 points, the first point is first initialized as valid. In the first iteration, the second point (the first undecided point at this point) is selected as the iteration pending point, the complete determination logic is executed, and its determination result (e.g., valid) is obtained. Then, the state of the second point is updated to valid. In the second iteration, since the states of the first and second points are determined, the system selects the third point as the iteration pending point, processes it, and updates its state. This process is repeated until the 100th point is processed and its state is updated. At this point, all 100 points have either a valid or abnormal state, the iteration ends, and the final, fully labeled trajectory sequence is output. This iterative mechanism ensures the orderliness of the processing and guarantees that the determination of each point can be performed in the correct historical trajectory context (based on the states of already determined points).

[0235] In one specific embodiment, the present invention optionally provides an efficient AIS trajectory flying point processing algorithm based on the smoothing concept. Its core lies in adaptively distinguishing between normal navigation points and abnormal flying points by combining local geometric results with short-term motion trends.

[0236] The most prominent issue with the flight point display function is its unsmoothness, which is easily detected and identified. The most obvious problem is its lack of smoothness. Smoothness is the intuitive understanding of good trajectory quality and a normal characteristic of trajectories generated by ship navigation. Describing smoothness in terms of the angular magnitude of consecutive trajectory points involves quantifying and constraining the degree of change in ship heading reflected by adjacent trajectory points, ensuring that it conforms to the physical laws of ship maneuvering and common sense of navigation.

[0237] The key to setting smoothness rules is to solve the problems of determining directional continuity and recognizing normal turns.

[0238] For example, the trajectory point sequence: P0, P1, ... P n These are AIS location points arranged in chronological order, with each point containing information such as latitude and longitude, and a timestamp.

[0239] A valid point is a point that is determined to truly reflect the trajectory of the ship's movement;

[0240] Anomalies (flying points) are points that are determined to be inconsistent with the laws of ship motion and deviate from the true trajectory;

[0241] Points pending determination are points that have not yet been determined as valid or abnormal and are in a pending processing state;

[0242] The forward vector V1 is derived from the previous valid point P. kPoint to the current undetermined point P i The vector reflects the direction of movement of the current point relative to the confirmed trajectory;

[0243] The preset angle threshold (e.g., 90°) for the abnormal direction threshold α is used to determine whether the directions are consistent. If the angle between two vectors is less than α, they are considered to be consistent.

[0244] The direction continuation window N is used to count the number of consecutive subsequent points for the direction continuation test (configurable, e.g., N=5).

[0245] The direction continuation count C is the number of points within the direction continuation window whose angle with the forward vector of the current point is less than α.

[0246] The direction continuation determination threshold T is the minimum direction continuation count used to determine whether the current point is a valid point (e.g., T=3).

[0247] Flying point identification and decision process: The algorithm uses a sequential sliding window approach to perform two-level decisions for each point to be determined.

[0248] 1) Initialization:

[0249] The first received trajectory point P0 is directly marked as a valid point and used as the benchmark for subsequent judgments.

[0250] 2) First level: Judgment of basic geometric results:

[0251] For the current undetermined point P i (i≥1):

[0252] a) Calculate the local steering angle θ i (by P) i-1 ,P i ,P i+1 constitute);

[0253] b) If P exists i+1 Calculate its local steering angle θ i+1 .

[0254] Judgment rules:

[0255] If θ i If the angle is obtuse: Determine P i This is a valid point.

[0256] like Figure 11 As shown, if θ i An acute angle and θ i+1 If the angle is obtuse: Determine P i This is the valid point (the starting point of a normal turn).

[0257] If θ i With θ i+1 All angles are acute; proceed to the anomaly detection logic:

[0258] Calculate two candidate turning angles:

[0259] A = ∠P i+1 P i P i+2 (A is the turning angle at P after assuming the removal of P i+1 ); i at the turning angle);

[0260] B = ∠P i-1 P i+1 P i+2 (B is the turning angle at P after assuming the removal of P i ); i+1 at the turning angle).

[0261] Compare A and B:

[0262] If A < B, as shown in Figure 12 , then determine that P i is a valid point and P i+1 is an abnormal point;

[0263] If B < A, as shown in Figure 13 , then determine that P i is an abnormal point and P i+1 remains to be determined.

[0264] The second level: Motion direction continuity test:

[0265] When the previous point of the pending point P j is determined to be a valid point and its local turning angle is acute (i.e., it may be in the turning or abnormal interval), start this step, as shown in Figure 14 :

[0266] 1. Select N consecutive points (N can be configured, for example, N = 5) after P j as the observation window W = {P j+1 , P j+2 , …, P j+N}.

[0267] 2. Calculate the direction vectors U1, U2, …, U j pointing from P N to each point in the window respectively (vectors).

[0268] 3. Compare these direction vectors with the forward vector V j of P<​​​​​​​​

[0271] If C ≥ T (e.g., T = 3), then P is considered to be... j The direction is continued, and it is determined to be a valid point;

[0272] Otherwise, determine P. j This is an outlier.

[0273] Iterative execution:

[0274] After making a decision on the current point, the next undetermined point is taken as the processing object, and the first and second level decision processes are repeated until the entire trajectory sequence is traversed.

[0275] In practice, once an acute angle appears, the same goal can be achieved by simply checking if the subsequent trajectory continues in the direction of the line that caused the acute angle. However, this solution does not use such a rule. Instead, it first uses geometric results to filter out most obviously normal points, identifying only the most difficult-to-determine cases of "continuous acute angles," and then uses the "direction continuation" approach for precise location. This method is more efficient and targeted.

[0276] like Figure 9 As shown in the figure, this application embodiment also provides a trajectory flying point determination device 900, which includes: a data acquisition module 902, used to acquire a trajectory point sequence from the ship automatic identification system data, the trajectory point sequence including multiple undetermined points, each undetermined point including time parameters and position parameters; a feature association module 904, used to determine multiple associated feature points corresponding to each undetermined point in the trajectory point sequence according to the time parameters, the multiple associated feature points and the undetermined points being continuous in the trajectory point sequence; a local steering module 906, used to determine a first local steering parameter corresponding to the undetermined point according to the position parameters of the undetermined point and the position parameters of the associated feature points; and an association steering module 908, used to determine the position of the undetermined point according to the position of the undetermined point. The parameters and position parameters of associated feature points determine the second local steering parameters corresponding to the associated feature points; the geometry determination module 910 is used to determine the geometric result corresponding to the point to be determined based on the first local steering parameters and the second local steering parameters; the vector determination module 912 is used to determine the direction vector from the point to be determined to multiple associated feature points based on the position parameters of the point to be determined and the position parameters of the associated feature points when both the first local steering parameters and the second local steering parameters are less than a preset steering threshold; the direction determination module 914 is used to determine the direction continuation result corresponding to the point to be determined based on multiple direction vectors; and the flying point determination module 916 is used to determine the trajectory flying point in the trajectory point sequence based on the geometric result and the direction continuation result.

[0277] like Figure 10As shown, this application embodiment also provides an electronic device 1000, including a processor 1110, a memory 1109, and a program or instructions stored in the memory 1109 and executable on the processor 1110. When the program or instructions are executed by the processor 1110, they implement the various processes of the above-described trajectory flying point determination method embodiment and achieve the same technical effect. To avoid repetition, they will not be described again here.

[0278] Optionally, the processor 1110 is used to acquire a sequence of trajectory points in the data of the Automatic Identification System for ships, the sequence of trajectory points including multiple undetermined points, each undetermined point including time parameters and position parameters;

[0279] Optionally, the processor 1110 is further configured to determine multiple associated feature points corresponding to each undetermined point in the trajectory point sequence based on time parameters, wherein the multiple associated feature points and the undetermined point are continuous in the trajectory point sequence;

[0280] Optionally, the processor 1110 is further configured to determine a first local steering parameter corresponding to the point to be determined based on the position parameters of the point to be determined and the position parameters of the associated feature points;

[0281] Optionally, the processor 1110 is further configured to determine a second local turning parameter corresponding to the associated feature point based on the position parameters of the point to be determined and the position parameters of the associated feature point;

[0282] Optionally, the processor 1110 is further configured to determine the geometric result corresponding to the point to be determined based on the first local steering parameters and the second local steering parameters;

[0283] Optionally, the processor 1110 is further configured to determine a direction vector pointing from the point to be determined to multiple associated feature points based on the position parameters of the point to be determined and the position parameters of the associated feature points when both the first local steering parameter and the second local steering parameter are less than a preset steering threshold.

[0284] Optionally, the processor 1110 is also configured to determine the direction continuation result corresponding to the point to be determined based on multiple direction vectors;

[0285] Optionally, the processor 1110 is also configured to determine trajectory flying points in the trajectory point sequence based on geometric results and direction continuation results.

[0286] The memory 1109 can be used to store software programs and various data. The memory 1109 may primarily include a first storage area for storing programs or instructions and a second storage area for storing data. The first storage area may store the operating system, application programs or instructions required for at least one function (such as sound playback, image playback, etc.). Furthermore, the memory 1109 may include volatile memory or non-volatile memory, or both. The non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory can be random access memory (RAM), static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous link dynamic random access memory (SLDRAM), and direct memory bus RAM (DRRAM). The memory 1109 in this embodiment includes, but is not limited to, these and any other suitable types of memory.

[0287] In this invention, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance; the term "multiple" refers to two or more unless otherwise explicitly defined. The terms "install," "connect," "link," and "fix" should be interpreted broadly. For example, "connect" can be a fixed connection, a detachable connection, or an integral connection; "link" can be a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0288] In the description of this invention, it should be understood that the terms "upper," "lower," "left," "right," "front," "rear," 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 unit 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.

[0289] In the description of this specification, the terms "one embodiment," "some embodiments," "specific embodiment," etc., refer to specific features, structures, materials, or characteristics described in connection with an embodiment or example that are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0290] The above are merely preferred embodiments of the present invention and are not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for determining the trajectory flying point, characterized in that, The method comprises: acquiring a sequence of trajectory points in a vessel automatic identification system data, the sequence of trajectory points comprising a plurality of undetermined points, each of the undetermined points comprising a time parameter and a position parameter; determining a plurality of associated feature points corresponding to each of the undetermined points in the sequence of trajectory points according to the time parameter, the plurality of associated feature points and the undetermined point being continuous in the sequence of trajectory points; determining a first local turning parameter corresponding to the undetermined point according to the position parameter of the undetermined point and the position parameter of the associated feature point; determining a second local turning parameter corresponding to the associated feature point according to the position parameter of the undetermined point and the position parameter of the associated feature point; determining a geometric result corresponding to the undetermined point according to the first local turning parameter and the second local turning parameter; when the first local turning parameter and the second local turning parameter are both less than a preset turning threshold, determining a direction vector of the undetermined point pointing to the plurality of associated feature points according to the position parameter of the undetermined point and the position parameter of the associated feature point; determining a direction continuation result corresponding to the undetermined point according to the plurality of direction vectors; determining a trajectory fly point in the sequence of trajectory points according to the geometric result and the direction continuation result.

2. The trajectory flypoint determination method of claim 1, wherein, The method comprises: determining a first associated previous point located before the undetermined point and a first associated subsequent point located after the undetermined point according to the time parameter; determining the first local turning parameter according to the position parameter of the first associated previous point, the position parameter of the undetermined point and the position parameter of the first associated subsequent point.

3. The trajectory flypoint determination method of claim 2, wherein, The method comprises: determining a second associated subsequent point located after the first associated subsequent point according to the time parameter; determining the second local turning parameter according to the position parameter of the undetermined point, the position parameter of the first associated subsequent point and the position parameter of the second associated subsequent point.

4. The trajectory flypoint determination method of claim 3, wherein, The method comprises: when the first local turning parameter is greater than or equal to a preset first feature threshold, determining a first geometric determination result according to the first local turning parameter; when the first local turning parameter is less than the first feature threshold and the second local turning parameter is greater than or equal to the first feature threshold, determining a second geometric determination result according to the first local turning parameter and the second local turning parameter; when the first local turning parameter is less than the first feature threshold and the second local turning parameter is less than the first feature threshold, determining a third geometric determination result according to the position parameter of the undetermined point, the position parameter of the first associated previous point, the position parameter of the first associated subsequent point and the position parameter of the second associated subsequent point. The geometric result corresponding to the point to be determined is determined based on the first geometric determination result, the second geometric determination result, and the third geometric determination result.

5. The trajectory flypoint determination method of claim 4, wherein, The step of determining the third geometric determination result based on the position parameters of the undetermined point, the position parameters of the first associated preceding point, the position parameters of the first associated subsequent point, and the position parameters of the second associated subsequent point includes: Based on the position parameters of the first associated preceding point, the position parameters of the undetermined point, and the position parameters of the second associated subsequent point, a first candidate turning feature is determined; The second candidate turning feature is determined based on the position parameters of the first associated preceding point, the position parameters of the first associated subsequent point, and the position parameters of the second associated subsequent point. The third geometric determination result is determined based on the size relationship between the first candidate turning feature and the second candidate turning feature.

6. The trajectory flypoint determination method of claim 1, wherein, The step of determining the direction continuation result corresponding to the point to be determined based on multiple direction vectors includes: Based on the time parameters, determine a number of associated subsequent points located after the point to be determined; Based on the position parameters of the undetermined point and the position parameters of the plurality of associated subsequent points, determine the direction vector from the undetermined point to each of the associated subsequent points; Obtain the forward direction vector of the point to be determined; Multiple directional angle features are determined based on the forward direction vector and each of the direction vectors; The quantity features are determined based on the multiple directional angle features and a preset second feature threshold. The direction continuation result is determined based on the quantitative characteristics.

7. The trajectory flypoint determination method of claim 1, wherein, Determining the trajectory flying points in the trajectory point sequence based on the geometric results and the direction continuation results includes: Based on the geometric results, a primary determination result is determined for the undetermined point. The primary determination result is used to indicate whether the undetermined point is a valid trajectory point, an abnormal trajectory flying point, or an undetermined state point. When the first-level determination result indicates that the undetermined point is an undetermined state point, the second-level determination result of the undetermined point is determined according to the direction continuation result. The second-level determination result is used to indicate whether the undetermined point is a valid trajectory point or an abnormal trajectory flying point.

8. The trajectory flypoint determination method of claim 7, wherein, The trajectory flying point determination method also includes: The trajectory point with the earliest time parameter in the trajectory point sequence is initialized as a valid trajectory point; The next undetermined trajectory point in the trajectory point sequence is taken as the iterative undetermined point; Obtain the judgment result of the iterative undetermined point; Update the determination status of the trajectory points in the trajectory point sequence according to the determination result; Based on the determination state, multiple iterative undetermined points are determined until all trajectory points in the trajectory point sequence update the determination state.

9. A trajectory flypoint determination apparatus characterized by comprising: include: The data acquisition module is used to acquire a sequence of trajectory points in the data of the Automatic Identification System for ships. The sequence of trajectory points includes multiple undetermined points, and each undetermined point includes time parameters and position parameters. The feature association module is used to determine multiple associated feature points corresponding to each undetermined point in the trajectory point sequence based on the time parameters, wherein the multiple associated feature points and the undetermined point are continuous in the trajectory point sequence; A local steering module is used to determine a first local steering parameter corresponding to the point to be determined based on the position parameters of the point to be determined and the position parameters of the associated feature points; The associated steering module is used to determine a second local steering parameter corresponding to the associated feature point based on the position parameters of the point to be determined and the position parameters of the associated feature point; A geometry determination module is used to determine the geometric result corresponding to the point to be determined based on the first local steering parameters and the second local steering parameters. The vector determination module is used to determine the direction vector from the undetermined point to multiple associated feature points based on the position parameters of the undetermined point and the position parameters of the associated feature points when both the first local steering parameter and the second local steering parameter are less than a preset steering threshold. A direction determination module is used to determine the direction continuation result corresponding to the point to be determined based on multiple direction vectors; The flying point determination module is used to determine the trajectory flying point in the trajectory point sequence based on the geometric results and the direction continuation results.

10. An electronic device, comprising: It includes a processor, a memory, and a program or instructions stored in the memory and executable on the processor, wherein the program or instructions, when executed by the processor, implement the steps of the trajectory flying point determination method as described in any one of claims 1 to 8.

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