A method for adding double-layer watermark to trajectory data

Abstract

The application relates to the field of geographic information security, in particular to a method for adding double-layer watermarks to trajectory data, which comprises the following steps: according to the relationship between the coordinate values and time stamps of the previous trajectory data and the next trajectory data in an original trajectory data sequence, target trajectory data sequences are extracted; according to the polar angles and connection sequences of the first target trajectory data and other trajectory data in the target trajectory data sequences, a convex hull vertex set is formed, three vertices forming the maximum triangular area are determined, and a target edge is determined; according to the angles respectively formed by the second target trajectory data and the two vertices of the target edge, the first layer zero watermark bit value is calculated; according to the distances from the second target trajectory data to the edges of the maximum triangle, the first index value of the first layer zero watermark bit value is calculated; according to the time stamp of the second target trajectory data, the second layer zero watermark bit value is determined; and finally, the double-layer watermarks are added to the trajectory data.

Description

Technical Field

[0001] This application relates to the field of geographic information security, and in particular to a method for adding a double-layer watermark to trajectory data. Background Technology

[0002] With the rapid development of GPS technology, trajectory data has become crucial foundational data for fields such as smart transportation, location services, urban planning, and business analytics. Therefore, establishing an effective copyright protection mechanism for trajectory data, enabling data source authentication and copyright traceability, has become a critical technical issue that urgently needs to be addressed.

[0003] Existing digital rights management (DRM) technologies can be broadly categorized into two types: lossy watermarking and lossless watermarking. Lossy watermarking embeds watermark information by fine-tuning the coordinates or timestamps of trajectory points. While it can resist attacks to a certain extent, it inevitably introduces data distortion, affecting trajectory accuracy and failing to meet the demands of high-precision applications. In contrast, lossless watermarking technology constructs watermarks by extracting inherent features from the data, without modifying the original data. It achieves copyright protection while maintaining data accuracy. Among these, zero-watermarking, a type of lossless watermarking, has become a research focus in recent years.

[0004] However, existing lossless watermarking schemes still have significant shortcomings. First, most studies focus only on the spatial geometric features of the trajectory, neglecting the importance of temporal attributes. In reality, attackers can not only perform geometric transformations such as translation and rotation on the trajectory, but also destroy watermark information through resampling and timestamp tampering. Second, existing methods perform poorly against combined attacks, especially when geometric attacks and temporal attribute attacks occur simultaneously, resulting in a significant drop in watermark detection rate.

[0005] To address the aforementioned issues, there is an urgent need to research a novel zero-watermarking technology for trajectory data that can resist both geometric and temporal attribute attacks while maintaining data accuracy. Summary of the Invention

[0006] This invention provides a method for adding a double-layer watermark to trajectory data, which solves the above-mentioned technical problems in the prior art. The method includes: Based on the relationship between the coordinate values ​​and timestamps of the previous trajectory data and the next trajectory data in the original trajectory data sequence, the target trajectory data sequence is extracted from the original trajectory data sequence; Based on the polar angle and connection order of the first target trajectory data and other trajectory data in the target trajectory data sequence, a convex hull vertex set is formed in space; From the set of convex hull vertices, determine the three vertices that form the largest triangle area, and determine the target edge from them; The first layer of zero watermark bit value is calculated based on the angles formed by the second target trajectory data in the target trajectory data sequence and the two vertices of the target edge. Based on the distances from the second target trajectory data to each side of the largest triangle, calculate the first index value of the first layer of zero watermark bit value; Based on the timestamp of the second target trajectory data, the second layer of zero watermark bit value is determined; Double-layer watermarks are added to the trajectory data sequentially based on the first index value, the first layer zero watermark bit value, and the second layer zero watermark bit value.

[0007] Specifically, extracting the target trajectory data sequence from the original trajectory data sequence based on the relationship between the coordinate values ​​and timestamps of the preceding and following trajectory data in the original trajectory data sequence includes: Based on the relationship between the coordinate values ​​of the previous trajectory data and the next trajectory data and a preset threshold, intermediate trajectory data is determined from the original trajectory data sequence; Based on the difference between the current timestamp and the previous timestamp of the intermediate trajectory data, and the relationship with the preset timestamp, the target trajectory data is determined, and the target trajectory data sequence is obtained.

[0008] Specifically, determining intermediate trajectory data from the original trajectory data sequence based on the relationship between the coordinate values ​​of the previous and subsequent trajectory data and a preset threshold includes: The intermediate trajectory data is determined from the original trajectory data sequence according to the following formula (I). : Formula (1); in, For the intermediate trajectory data Previous data, For point coordinates For point coordinates , For the preset threshold, .

[0009] Specifically, the step of determining the target trajectory data and obtaining the target trajectory data sequence based on the relationship between the difference between the current timestamp and the previous timestamp of the intermediate trajectory data and a preset timestamp includes: The difference in timestamps is calculated using the following formula (II): Formula (II); in, To obtain the intermediate trajectory data The previous timestamp, To obtain the previous trajectory data of the intermediate trajectory data timestamp, Preset timestamp; The intermediate trajectory data that satisfies Formula (II) is taken as the target trajectory data, and at the same time deleted. and The target trajectory data sequence is obtained by analyzing the data between the points in between.

[0010] Specifically, based on the polar angles formed in space by the first target trajectory data and the order of connections with other trajectory data in the target trajectory data sequence, a convex hull vertex set is formed, including: Using the first target trajectory data as the pole, other trajectory data are sequentially connected to the first target trajectory data to form polar angles. The data in the target trajectory data sequence are sorted in ascending order of the polar angles formed. If the polar angles are the same, the data closest to the first target trajectory data is sorted first. The target trajectory data that has completed the sorting operation is sequentially connected to the second vertex and the stack vertex in the pre-created empty stack. The target trajectory data that form counterclockwise or collinear connections are pushed onto the stack, and finally the convex hull vertex set is obtained.

[0011] Specifically, determining the three vertices forming the largest triangle area from the set of convex hull vertices, and determining the target edge from them, includes: Find the largest triangle formed by any three target trajectory data points from the set of convex hull vertices; Calculate the distance from the second target trajectory data in the target trajectory data sequence to the three sides of the largest triangle, and take the side with the second longest distance as the target side.

[0012] Specifically, the step of calculating the first-layer zero-watermark bit value based on the angles formed by the second target trajectory data in the target trajectory data sequence and the two vertices of the target edge includes: When the formed angle is less than or equal to 45 degrees, the first layer of zero watermark bit value is 0; When the angle formed is greater than 45 degrees, the first layer of zero watermark bit value is 1.

[0013] Specifically, calculating the first index value of the first layer of zero watermark bit value based on the distance from the second target trajectory data to each side of the largest triangle includes: The first index value is calculated according to the following formula (iii). : Formula (III); Where α, k, and r are preset keys, and >> indicates right shift. This indicates the length of the first layer of zero watermark bit values. The longest distance from the second target trajectory data to the three sides of the largest triangle is given by [reference to a specific location]. The shortest distance from the second target trajectory data to the three sides of the largest triangle.

[0014] Specifically, determining the second-layer zero-watermark bit value based on the timestamp of the second target trajectory data includes: The timestamps of the second target trajectory data are converted into Chinese character sequences, and the word vectors of each calculated Chinese character are summed to obtain an array. ; calculate With the pre-constructed projection matrix The product of the products is used to obtain the array according to the following formula (iv). : Formula (IV); When array If the value is greater than 0.5, assign a value of 1; otherwise, assign a value of 0. The value is then determined based on the assigned value. The second layer of zero watermark bit value is obtained.

[0015] Specifically, adding a double-layer watermark to the trajectory data sequentially based on the first index value, the first layer zero watermark bit value, and the second layer zero watermark bit value includes: Count the number of times "1" and "0" appear in the first layer zero watermark bit values ​​with the same first index value; when the number of occurrences is the same, take the bit value as "1" to complete the first zero watermark addition operation on the target trajectory data; Count the number of times "1" and "0" appear in the second-layer zero watermark bit values ​​with the same second-layer index value; when the number of occurrences is the same, take the bit value as "1" to complete the second zero watermark addition operation on the target trajectory data.

[0016] The method provided in this invention is a dual zero-watermarking method for trajectory data that can resist both geometric and temporal attribute attacks. Compared with the prior art, this invention constructs two different zero-watermarks based on the geometric features and temporal attributes of trajectory data, respectively. This overcomes the problem of poor robustness of traditional methods when facing geometric and temporal attribute attacks, improves the robustness of trajectory data digital watermarking algorithms against complex attacks, and effectively protects the copyright of trajectory data. Attached Figure Description

[0017] Figure 1The flowchart illustrates a method for adding a double-layer watermark to trajectory data, as provided in an embodiment of the present invention.

[0018] Figure 2 The resulting image shows the trajectory data sequence after compression. Figure 3 A schematic diagram of the vertex set of the convex hull; Figure 4 A schematic diagram for determining the triangle with the largest area from the set of convex hull vertices. Detailed Implementation

[0019] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0020] In the description of this application, it should be understood that if terms such as "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential" appear, these terms indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0021] Furthermore, where the terms "first" and "second" appear, these terms are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, where the term "multiple" appears, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0022] This invention provides a method for adding a double-layer watermark to trajectory data. In this embodiment, the original trajectory data sequence is: Trajectory data refers to the continuous or discrete location records of moving entities within the spatial-temporal domain. Each trajectory data point consists of a series of geographic coordinates arranged in chronological order. Composition, in which Indicates the first The coordinates of each sampling time point on the spatial x-axis and y-axis. This indicates that the corresponding timestamp of the sampling point is obtained, such as... Figure 1 As shown, the specific process is as follows: Step 11: Based on the relationship between the coordinate values ​​and timestamps of the preceding and following trajectory data in the original trajectory data sequence, extract the target trajectory data sequence from the original trajectory data sequence; this step specifically includes: Step A: Based on the relationship between the coordinate values ​​of the previous and subsequent trajectory data and a preset threshold, determine the intermediate trajectory data from the original trajectory data sequence; this step includes: According to the following formula (I), the original trajectory data sequence ,Pick from Begin by iterating through the original trajectory data sequence and determining the intermediate trajectory data from it. : Formula (1); in, For the intermediate trajectory data Previous data, For point coordinates For point coordinates , For the preset threshold, .

[0023] Step B, based on the acquired intermediate trajectory data Current timestamp and trajectory data from the previous moment The difference in timestamps, and its relationship with a preset timestamp, are used to determine the target trajectory data, thus obtaining the target trajectory data sequence. Specifically, the difference in timestamps is calculated according to the following formula (II): Formula (II); in, To obtain the intermediate trajectory data The previous timestamp, To obtain the previous trajectory data of the intermediate trajectory data timestamp, Preset timestamp; The intermediate trajectory data that satisfies Formula (II) is taken as the target trajectory data, and at the same time deleted. and The data between, at this time let Repeat steps A and B, retaining the data that satisfies formulas (I) and (II), and finally obtain the compressed target trajectory data sequence. The effect of the trajectory data sequence after compression is as follows: Figure 2 As shown.

[0024] Step 12: Based on the polar angles formed in space by the first target trajectory data and the other trajectory data in the target trajectory data sequence, and the order of the connecting lines, a convex hull vertex set is formed; a schematic diagram of the convex hull vertex set is shown below. Figure 3 As shown, this step specifically includes: Using the first target trajectory data As the extreme point, the other trajectory data are sequentially compared with the first target trajectory data. Connecting the polar angles forms a polar angle, and sorting the data in the target trajectory data sequence in ascending order of the polar angle; if the polar angles are the same, the data closest to the first target trajectory data is sorted first; for example, when and The polar angle formed by the connection is less than and When connected to form a polar angle, the order is as follows: , , If when and The polar angle formed by connecting them is equal to and When connected to form a polar angle, arrive The distance is less than The distance is then sorted as follows: , , .

[0025] The target trajectory data that has undergone sorting is sequentially connected to the second vertex and the stack vertex in a pre-created empty stack. Target trajectory data forming counter-clockwise or collinear connections are pushed onto the stack, ultimately obtaining the convex hull vertex set. The specific process includes: first, creating an empty stack, then... The first sorted point is pushed onto the stack. The next point in the target trajectory data sequence is then retrieved sequentially. Connect the second vertex in the stack and the top vertex of the stack. ,point If the connection direction is clockwise, pop the top of the stack and repeat the check; if the connection direction is counterclockwise or collinear, then... Push the data onto the stack and repeat the steps until all data in the target trajectory data sequence has been processed. The points in the stack, arranged in order, form the convex hull vertex set. .

[0026] Step 13: Determine the three vertices forming the largest triangle area from the convex hull vertex set, and determine the target edge from them; a schematic diagram of the triangle with the largest area determined from the convex hull vertex set is shown below. Figure 4 As shown, it specifically includes: Find the largest triangle formed by any three target trajectory data points from the convex hull vertex set. This can be achieved by traversing every three vertices of the convex hull vertex set and calculating their areas. The optimal solution is updated when the area exceeds the current maximum value, and finally, the three target trajectory data points corresponding to the triangle with the largest area are retained. At this point, the vertices of the triangle with the largest area are... .

[0027] Calculate the second target trajectory data in the target trajectory data sequence. To the three sides of the largest triangle , , The distance is used to determine the second longest edge as the target edge. .

[0028] Step 14: Calculate the first-layer zero-watermark bit value based on the angles formed by the second target trajectory data in the target trajectory data sequence and the two vertices of the target edge; that is, calculate the point... ,point ,point corner of the construction end And then according to The size is quantized into the watermark bit value of the first layer of zero watermark. That is, when the formed angle is less than or equal to 45 degrees, the first layer of zero watermark bit value is 0; when the formed angle is greater than 45 degrees, the first layer of zero watermark bit value is 1. Formula (V) is as follows; Formula (5); Step 15, based on the second target trajectory data The distance to each side of the largest triangle is used to calculate the first index value of the first layer of zero watermark bits; specifically, this includes first calculating the longest distance from the second target trajectory data to the three sides of the largest triangle. The shortest distance from the second target trajectory data to the three sides of the largest triangle. Then, calculate the first index value according to the following formula (iii). : Formula (3); Where α, k, and r are preset keys, and >> indicates right shift. This indicates the length of the first layer of zero watermark bit values.

[0029] Step 16: Determine the second-layer zero-watermark bit value based on the timestamp of the second target trajectory data, specifically including: Read the timestamp of the second target trajectory data in the format YYYY:MM:DD:hh:mm:ss, and divide the timestamp string into several fields using the colon ":". Iterate through each field, split each numeric character in each field individually, and concatenate them in their original order to form a complete character sequence. Establish a fixed mapping table 1 for each Arabic numeral character to convert the sequence of numeral characters into a sequence of Chinese characters. ; Table 1

[0030] Traversal For each Chinese character in the dataset, a word vector is calculated using the BERT model. The calculated word vectors for each character are then summed to obtain an array. .

[0031] Construct a watermark length that is equal to the second-layer zero watermark bit value. projection matrix ; calculate The product of the projection matrix and the pre-constructed projection matrix is ​​obtained according to the following formula (iv) to obtain a length of... array : Formula (IV); When array If the value is greater than 0.5, assign a value of 1; otherwise, assign a value of 0. The value is then determined based on the assigned value. , length is of Second layer zero watermark bit value .

[0032] right Except and For all points outside the first layer, repeat steps 11 to 16 to obtain the first layer zero watermark bit value, the first index value of the first layer zero watermark, and the second layer zero watermark bit value for each point.

[0033] Step 17: Add a double-layer watermark to the trajectory data sequentially according to the first index value, the first-layer zero-watermark bit value, and the second-layer zero-watermark bit value. Specifically, this includes: counting the number of times "1" and "0" appear in the first-layer zero-watermark bit values ​​with the same first index value; when the number of occurrences is the same, set the bit value to "1", completing the first zero-watermark addition operation on the target trajectory data; Count the number of times "1" and "0" appear in the second-layer zero watermark bit values ​​with the same second-layer index value; when the number of occurrences is the same, take the bit value as "1" to complete the second zero watermark addition operation on the target trajectory data.

[0034] The corresponding zero-watermark detection steps for this solution are as follows: For the trajectory sequence to be detected Following the above process, the compressed target trajectory data sequence is obtained. And the vertex of the largest area triangle ; right Except and For all points outside the first layer, repeat steps 11-16 above to extract the first layer zero watermark index value, the first layer zero watermark bit value, and the second layer zero watermark bit value for each point. Propose the trajectory sequence to be detected The first layer of zero watermark bit group and the second layer of zero watermark bit value; Calculate the cosine similarity between the detected first-layer zero-watermark bit value and the generated first-layer zero-watermark bit value, and between the detected second-layer zero-watermark bit value and the generated second-layer zero-watermark bit value. If the cosine similarity is greater than a threshold... If the zero watermarks are the same, the data to be detected is consistent with the original data; otherwise, they are not the same data.

[0035] This scheme is a dual zero-watermarking method for trajectory data that can resist both geometric and temporal attribute attacks. Compared with existing technologies, this invention constructs two different zero-watermarks based on the geometric features and temporal attributes of trajectory data, overcoming the problem of poor robustness of traditional methods when facing geometric and temporal attribute attacks. It improves the robustness of trajectory data digital watermarking algorithms against complex attacks and effectively protects the copyright of trajectory data.

[0036] The method provided in this invention is a dual zero-watermarking method for trajectory data that can resist both geometric and temporal attribute attacks. Compared with the prior art, this invention constructs two different zero-watermarks based on the geometric features and temporal attributes of trajectory data, respectively. This overcomes the problem of poor robustness of traditional methods when facing geometric and temporal attribute attacks, improves the robustness of trajectory data digital watermarking algorithms against complex attacks, and effectively protects the copyright of trajectory data.

[0037] In this application, unless otherwise expressly specified and limited, the terms "installation," "connection," "joining," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise expressly limited. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0038] In this application, unless otherwise expressly specified and limited, the use of descriptions such as "above" or "below" the second feature indicates that the first and second features are in direct contact or indirect contact via an intermediate medium. Furthermore, "above," "on top of," and "over" the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. Similarly, "below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0039] It should be noted that if an element is referred to as being "fixed to" or "set on" another element, it can be directly on the other element or there may be an intermediate element. If an element is considered to be "connected to" another element, it can be directly connected to the other element or there may be an intermediate element present. Where applicable, the terms "vertical," "horizontal," "upper," "lower," "left," "right," and similar expressions used in this application are for illustrative purposes only and do not represent the only possible implementations. The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described; however, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0040] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for adding a double-layer watermark to trajectory data, characterized in that, The method includes: Based on the relationship between the coordinate values ​​and timestamps of the previous trajectory data and the next trajectory data in the original trajectory data sequence, the target trajectory data sequence is extracted from the original trajectory data sequence; Based on the polar angle and connection order formed by the first target trajectory data and other trajectory data in space in the target trajectory data sequence, a convex hull vertex set is formed. From the set of convex hull vertices, determine the three vertices that form the largest triangle area, and determine the target edge from them; The first layer of zero watermark bit value is calculated based on the angles formed by the second target trajectory data in the target trajectory data sequence and the two vertices of the target edge. Based on the distances from the second target trajectory data to each side of the largest triangle, calculate the first index value of the first layer of zero watermark bit value; Based on the timestamp of the second target trajectory data, the second layer of zero watermark bit value is determined; Double-layer watermarking is added to the trajectory data sequentially based on the first index value, the first layer zero watermark bit value, and the second layer zero watermark bit value; the step of extracting the target trajectory data sequence from the original trajectory data sequence based on the relationship between the coordinate values ​​and timestamps of the previous and subsequent trajectory data in the original trajectory data sequence includes: Based on the relationship between the coordinate values ​​of the previous trajectory data and the next trajectory data and a preset threshold, intermediate trajectory data is determined from the original trajectory data sequence; Based on the difference between the current timestamp and the previous timestamp of the intermediate trajectory data, and the relationship with the preset timestamp, the target trajectory data is determined, and the target trajectory data sequence is obtained. Based on the distances from the second target trajectory data to each side of the largest triangle, the first index value of the first layer of zero watermark bits is calculated, including: The first index value is calculated according to the following formula (iii). : Formula (3); Where α, k, and r are preset keys, and >> indicates right shift. This indicates the length of the first layer of zero watermark bit values. The longest distance from the second target trajectory data to the three sides of the largest triangle is given by [reference to a specific location]. The shortest distance from the second target trajectory data to the three sides of the largest triangle.

2. The method as described in claim 1, characterized in that, The step of determining intermediate trajectory data from the original trajectory data sequence based on the relationship between the coordinate values ​​of the previous trajectory data and the subsequent trajectory data and a preset threshold includes: The intermediate trajectory data is determined from the original trajectory data sequence according to the following formula (I). : Formula (1); in, For the intermediate trajectory data Previous data, For point coordinates For point coordinates , This is a preset threshold.

3. The method as described in claim 1, characterized in that, The step of determining the target trajectory data and obtaining the target trajectory data sequence based on the relationship between the difference between the current timestamp and the previous timestamp of the intermediate trajectory data and a preset timestamp includes: The difference in timestamps is calculated using the following formula (II): Formula (II); in, To obtain the intermediate trajectory data The previous timestamp, To obtain the previous trajectory data of the intermediate trajectory data timestamp, Preset timestamp; The intermediate trajectory data that satisfies Formula (II) is taken as the target trajectory data, and at the same time deleted. and The target trajectory data sequence is obtained by analyzing the data between the points in between.

4. The method as described in claim 1, characterized in that, Based on the target trajectory data sequence, the polar angle formed by the first target trajectory data and the connection order of other trajectory data in space to form a convex hull vertex set includes: Using the first target trajectory data as the pole, other trajectory data are sequentially connected to the first target trajectory data to form polar angles. The data in the target trajectory data sequence are sorted in ascending order of the polar angles formed. If the polar angles are the same, the data closest to the first target trajectory data is sorted first. The target trajectory data that has completed the sorting operation is sequentially connected to the second vertex and the stack vertex in the pre-created empty stack. The target trajectory data that form counterclockwise or collinear connections are pushed onto the stack, and finally the convex hull vertex set is obtained.

5. The method as described in claim 1, characterized in that, The process of determining the three vertices forming the largest triangle area from the set of convex hull vertices, and determining the target edge from them, includes: Find the largest triangle formed by any three target trajectory data points from the set of convex hull vertices; Calculate the distance from the second target trajectory data in the target trajectory data sequence to the three sides of the largest triangle, and take the side with the second longest distance as the target side.

6. The method as described in claim 1, characterized in that, The step of calculating the first-layer zero-watermark bit value based on the angles formed by the second target trajectory data in the target trajectory data sequence and the two vertices of the target edge includes: When the formed angle is less than or equal to 45 degrees, the first layer of zero watermark bit value is 0; When the angle formed is greater than 45 degrees, the first layer of zero watermark bit value is 1.

7. The method as described in claim 1, characterized in that, The step of determining the second-layer zero-watermark bit value based on the timestamp of the second target trajectory data includes: The timestamps of the second target trajectory data are converted into Chinese character sequences, and the word vectors of each calculated Chinese character are summed to obtain an array. ; calculate With the pre-constructed projection matrix The product of the products is used to obtain the array according to the following formula (iv). : Formula (IV); When array If the value is greater than 0.5, assign a value of 1; otherwise, assign a value of 0. The value is then determined based on the assigned value. The second layer of zero watermark bit value is obtained.

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