Methods, devices, equipment and storage media for watermark embedding and detection of GNSS observation data
By establishing a mapping relationship between the temporal and spatial characteristics of GNSS observation data and the watermark index, the problem that watermarking algorithms for GNSS observation data cannot be applied in existing technologies is solved, and the normal extraction of watermark information and maintenance of positioning accuracy are achieved under various attacks.
Patent Information
- Application Number
- CN202511212201.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-28
- Publication Date
- 2025-11-14
- Estimated Expiration
- 2045-08-28
AI Technical Summary
Existing geospatial data watermarking algorithms cannot be effectively applied to GNSS observation data, as they do not fully consider its spatiotemporal positioning characteristics, resulting in the inability to restore the correspondence between observation values and watermark indexes in common data processing operations.
By mining the temporal and spatial characteristics of GNSS observation data, a mapping relationship between the spatiotemporal characteristics of the original observations and the watermark index is established. A watermark embedding and detection scheme based on spatial mapping is designed so that the same watermark bit can be evenly embedded in multiple observations, thereby enhancing the resistance to attacks such as adding or deleting epochs.
In pseudorange single-point positioning applications, the embedding of watermark information does not impair the accuracy of the positioning results and has strong robustness, effectively resisting attacks such as data compression, version conversion, data segmentation and merging, satellite deletion, and epoch resampling.
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Figure CN120744888B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of digital watermarking technology, and in particular to a method, apparatus, device and storage medium for embedding and detecting watermarks in GNSS observation data. Background Technology
[0002] Global Navigation Satellite Systems (GNSS), as a core technology for airborne radio navigation and positioning, play an irreplaceable strategic role in aerospace, intelligent transportation, disaster monitoring, and other fields. However, with the continuous expansion of GNSS observation data applications, data security issues are becoming increasingly prominent. Digital watermarking technology is commonly used to address these security concerns. Currently, digital watermarking technology has made significant progress in the field of geospatial data protection. Geospatial data watermarking algorithms can generally be categorized into spatial domain-based and transform domain-based watermarking algorithms based on the different watermark embedding domains.
[0003] Spatial domain watermarking algorithms embed watermark information by directly manipulating spatial information such as location and coordinates of geographic data. LSB-based watermarking algorithms embed watermark information into the least significant bit of the carrier data; the embedding and extraction processes are fast and simple to implement. Coordinate mapping-based watermarking algorithms construct mapping functions to uniformly map map coordinates to the watermark index range. Feature point extraction-based watermarking algorithms use geospatial data compression techniques to extract feature points, further process them, and then embed the watermark; these algorithms exhibit good resistance to information compression. Normalization-based watermarking algorithms scale the data proportionally to a smaller, specific range, enhancing the algorithm's stability and ensuring that the watermark information is unaffected by geometric attacks such as translation and scaling. Spatial domain watermarking embeds the watermark directly into the data, offering greater flexibility.
[0004] Transform-domain-based digital watermarking algorithms transform carrier data from the spatial domain to the frequency domain using specific mathematical methods, and then embed watermark information using coefficients from a specific domain. This process is computationally complex. Existing transform-domain-based watermarking algorithms commonly use transform functions such as the Discrete Fourier Transform (DFT), Discrete Wavelet Transform (DWT), and Discrete Cosine Transform (DCT). In DFT-based watermarking algorithms, embedding the amplitude value provides good robustness against data translation and rotation; embedding the phase value provides strong robustness against data translation and scaling; however, embedding both amplitude and phase values results in slightly poorer watermark extraction due to the significant changes to the original data, but it can resist more types of geometric attacks. The DWT transform converts spatial domain data to the frequency domain through multi-scale decomposition, utilizing the complementary characteristics of low-frequency and high-frequency sub-bands to achieve watermark embedding. The low-frequency portion of the DWT transform retains the main features of the data, so embedding watermarks in the low-frequency coefficients can enhance anti-attack performance, but it can easily lead to data distortion. The high-frequency portion corresponds to detailed information, and embedding watermarks in the high-frequency portion provides stronger concealment, but it is more sensitive to common data processing operations such as compression and filtering. The choice of embedding position needs to be optimized in combination with data characteristics and application scenarios. DCT transform is an important method to improve the robustness of watermarking algorithms, especially against data compression attacks. Embedding watermark bits into the high-frequency coefficients of DCT causes less perceptual distortion, but requires error estimation models to control the accuracy of the watermarked data. Watermarking algorithms that embed watermarks into the mid-frequency coefficients of DCT embed watermark information by changing the non-feature vertices of the map, and are more robust to various attacks such as rotation, scaling, translation, and simplification. Since the essence of transform domain-based watermarking algorithms is to embed watermark information into the frequency domain using mathematical transformations, they have better concealment than spatial domain algorithms, but the control of data accuracy during the transformation process is poor.
[0005] As can be seen from existing technologies, significant progress has been made in the theoretical technology and research of geospatial data watermarking. However, watermark embedding and detection for GNSS observation data are still in their early stages. GNSS observation data possesses unique spatiotemporal positioning characteristics; each observation not only contains spatial location information but also exhibits temporal continuity and spatiotemporal feature correspondence. Existing vector geographic data spatial domain watermarking algorithms, due to insufficient consideration of the spatiotemporal positioning characteristics of GNSS observation data, cannot recover the correspondence between observation values and watermark indices in common data processing operations, and therefore cannot be directly applied to GNSS observation data. Summary of the Invention
[0006] This application provides a method, apparatus, device, and storage medium for embedding and detecting GNSS observation data watermarks. By fully exploiting the unique temporal and spatial characteristics of GNSS observation files, a mapping relationship between the spatiotemporal characteristics of the original observations and the watermark index is established. Based on this, a watermark embedding and detection scheme based on spatial mapping is designed, enabling the same watermark bit to be uniformly embedded in multiple observations, thereby enhancing resistance to attacks such as adding or deleting epochs.
[0007] Firstly, this application provides a method for embedding and detecting watermarks in GNSS observation data, including:
[0008] Based on GNSS observation data, a set of observation values from different satellite systems was obtained. ,in For the first The set of observations from a satellite system to be embedded with watermark information The number of satellites in the satellite system. Indicates time information, Indicates the signal band. Indicates satellite Logo, Represents pseudorange observations. Represents the carrier phase observation value. epoch 1. epoch 1 and epoch m Let represent the sets of observations to be embedded with watermark information for the first, second, and m-th satellite systems, respectively;
[0009] The temporal and spatial features contained in the observation sets of the different satellite systems are quantized to obtain quantized values of temporal and spatial features; wherein, the temporal features include time information, and the spatial features include pseudorange observations and carrier phase observations;
[0010] Obtain a binary sequence based on the original watermark image;
[0011] A watermark index to be embedded is generated based on the time feature quantization value and the spatial feature quantization value, and the watermark bit to be embedded is obtained from the binary sequence based on the watermark index to be embedded.
[0012] Based on the watermark bits to be embedded and the set quantization step size, the pseudorange observations and carrier phase observations in the observation set are quantized to obtain observation data with embedded watermark information.
[0013] In one possible design, the temporal and spatial characteristics contained in the observation sets of the different satellite systems are quantized using the following formulas to obtain quantized values for the temporal and spatial characteristics:
[0014] ;
[0015] ;
[0016] ;
[0017] In the formula, Itime represents the quantized value of the time feature. Representing year, month, day, hour, minute, and second respectively. I obs1 This represents the quantized value of the pseudorange observation. I obs2 The quantization value represents the carrier phase observation. a This represents the key.
[0018] In one possible design, the watermark index to be embedded is generated based on the quantized values of the temporal and spatial features using the following formula:
[0019] ;
[0020] In the formula, index Indicates the watermark index to be embedded. Hash Represents a hash function. I obs Represents the quantized value of spatial features. I obs =( I obs1 , I obs2 ).
[0021] In one possible design, based on the watermark bits to be embedded and a set quantization step size, the pseudorange observations and carrier phase observations in the observation set are quantized, including:
[0022] When the watermark information bit in the watermark bit to be embedded is 1, the pseudorange observations and carrier phase observations in the observation set are quantized using the following formula:
[0023] ;
[0024] ;
[0025] In the formula, and These represent the values of the pseudorange observation and the carrier phase observation, respectively, to the third decimal place. S Indicates the quantization step size;
[0026] When the watermark information bit in the watermark bit to be embedded is 0, the pseudorange observations and carrier phase observations in the observation set are quantized using the following formula:
[0027] ;
[0028] .
[0029] Secondly, this application provides a method for detecting watermarks in GNSS observation data, including:
[0030] Determine the watermark index;
[0031] Based on the observation data with embedded watermark information obtained by the method described above and various possible designs of the first aspect, a detection value is obtained, wherein the detection value is the value of the pseudorange observation value and the carrier phase observation value after the third decimal place in the observation data with embedded watermark information.
[0032] Based on the set quantization step size and detection value, the embedded watermark bits are extracted;
[0033] Based on the watermark index and watermark bits, the extracted watermark sequence is obtained by majority voting, and the extracted watermark sequence is restored by inverse transformation to obtain the extracted watermark image.
[0034] The extracted watermark image is compared with the original watermark image to confirm whether the extracted watermark is consistent with the embedded watermark.
[0035] In one possible design, based on a set quantization step size and detection value, the embedded watermark bits are extracted using the following formula:
[0036] ;
[0037] In the formula, This represents the embedded watermark bits, and S represents the quantization step size. These are the third decimal place values of the pseudorange and carrier phase observations in the observation data containing embedded watermark information.
[0038] Thirdly, this application provides a GNSS observation data watermark embedding device, the device comprising:
[0039] The set determination module is configured to obtain the set of observations from different satellite systems based on GNSS observation data. ,in For the first The set of observations from a satellite system to be embedded with watermark information The number of satellites in the satellite system. Indicates time information, Indicates the signal band. Indicates satellite Logo, Represents pseudorange observations. Represents the carrier phase observation value. epoch 1. epoch 1 and epoch m Let represent the sets of observations to be embedded with watermark information for the first, second, and m-th satellite systems, respectively;
[0040] The first quantization module is configured to quantize the temporal and spatial features contained in the observation sets of the different satellite systems to obtain quantized values of temporal features and spatial features; wherein, the temporal features include time information, and the spatial features include pseudorange observations and carrier phase observations;
[0041] The watermark scanning module is configured to obtain a binary sequence based on the original watermark image;
[0042] The bit acquisition module is configured to generate a watermark index to be embedded based on the time feature quantization value and the spatial feature quantization value, and to acquire the watermark bit to be embedded from the binary sequence based on the watermark index to be embedded.
[0043] The second quantization module is configured to quantize the pseudorange observations and carrier phase observations in the observation set based on the watermark bits to be embedded and a set quantization step size, so as to obtain observation data with embedded watermark information.
[0044] Fourthly, this application provides a GNSS observation data watermark detection device, the device comprising:
[0045] The index determination module is configured to determine the watermark index;
[0046] The detection value acquisition module is configured to acquire a detection value from the observation data with embedded watermark information obtained by the device described in the third aspect above, wherein the detection value is the value of the third decimal place of the pseudorange observation value and the carrier phase observation value in the observation data with embedded watermark information.
[0047] The bit extraction module is configured to extract the embedded watermark bits based on a set quantization step size and detection value;
[0048] The image extraction module is configured to obtain the extracted watermark sequence according to the watermark index and watermark bits using a majority voting method, and to recover the extracted watermark sequence by inverse transformation to obtain the extracted watermark image.
[0049] The image comparison module is configured to compare the extracted watermark image with the original watermark image to confirm whether the extracted watermark is consistent with the embedded watermark.
[0050] Fifthly, this application provides an electronic device comprising: at least one processor and a memory; the memory storing computer-executable instructions; the at least one processor executing the computer-executable instructions stored in the memory, causing the at least one processor to perform the methods described in the first aspect, various possible designs of the first aspect, the second aspect, and various possible designs of the second aspect.
[0051] In a sixth aspect, this application provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the methods described in the first aspect, the various possible designs of the first aspect, the second aspect, and the various possible designs of the second aspect.
[0052] In a seventh aspect, this application provides a computer program product, including a computer program that, when executed by a processor, implements the methods described in the first aspect, various possible designs of the first aspect, the second aspect, and various possible designs of the second aspect.
[0053] The GNSS observation data watermark embedding and detection method, apparatus, equipment, and storage medium provided in this application have at least the following beneficial effects:
[0054] In pseudorange single-point positioning applications, this application controls the change in positioning results to the decimeter level, far exceeding the positioning accuracy of the positioning mode itself. Therefore, the watermark information embedded in this application will not damage the positioning performance of the original observation file. Experiments show that this application has a robustness to attacks such as data compression, version conversion, data segmentation, and merging (NC values) of over 0.95, and a robustness to attacks such as satellite deletion and epoch resampling (NC values) of over 0.85. Attached Figure Description
[0055] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.
[0056] Figure 1 This is a flowchart illustrating the overall process of a GNSS observation data watermark embedding method provided in an embodiment of this application.
[0057] Figure 2 This is a flowchart illustrating a specific implementation of a GNSS observation data watermark embedding method provided in an embodiment of this application.
[0058] Figure 3This is a flowchart illustrating a GNSS observation data watermark detection method provided in an embodiment of this application;
[0059] Figure 4 This is a diagram showing the experimental results of satellite deletion provided in an embodiment of this application;
[0060] Figure 5 This is a structural diagram of the GNSS observation data watermark embedding device provided in the embodiments of this application;
[0061] Figure 6 This is a structural diagram of the GNSS observation data watermark detection device provided in the embodiments of this application.
[0062] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation
[0063] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.
[0064] The collection, storage, use, processing, transmission, provision, and disclosure of GNSS data or user data and other information involved in the technical solution of this application all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.
[0065] It should be noted that in the embodiments of this application, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of this application. However, it does not mean that the applicant has used or necessarily used the solution.
[0066] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.
[0067] This application provides a method for embedding and detecting watermarks in GNSS observation data. Considering that operations such as version conversion, data segmentation, and epoch resampling are performed on the original observation files during data use, it is necessary to ensure the normal extraction of watermark information under various forms of attacks. Therefore, this watermarking method determines the watermark index based on the spatiotemporal characteristics of the original observations and establishes a many-to-one mapping relationship between the observations and the watermark index, resulting in good resistance to attacks under common GNSS data processing operations.
[0068] The following section will further explain the specific process of watermark embedding and watermark detection using GNSS observation data.
[0069] This application provides a method for embedding watermarks in GNSS observation data. Figure 1 This is a flowchart illustrating the overall process of a GNSS observation data watermark embedding method provided in an embodiment of this application. Figure 1 As shown, the GNSS observation data watermarking embedding method includes watermark embedding location selection and watermark information embedding. In the watermark embedding location selection stage, the watermark embedding domain is determined based on the structural characteristics of the GNSS observation data and the characteristics of various observation values to ensure the applicability and robustness of the watermarking method. The GNSS observation data structural characteristics include the file header and data records, which include time, pseudorange, carrier phase, Doppler, and signal parameters. In the watermark information embedding stage, hash operations are performed based on time and spatial characteristics to map the watermark index, and the watermark is embedded by combining spatial characteristics, ultimately obtaining the watermarked observation data. Specifically, during watermark information embedding, a quantization function is established to quantize the time and spatial characteristics contained in the set of observation values to be embedded. The quantization result is used as the input value of the hash function to generate the watermark index to be embedded for that observation value, thereby establishing a mapping relationship between the observation value and the watermark index. The establishment of a many-to-one mapping relationship can effectively resist various forms of attacks involving the addition or deletion of data records, and is also beneficial for the implementation of blind detection. Finally, watermark bits are embedded in specific decimal places of the observations based on quantization rules to ensure that the changes in the observations are minimal.
[0070] Figure 2 This is a flowchart illustrating a specific implementation of a GNSS observation data watermark embedding method provided in an embodiment of this application. Figure 2 As shown, the GNSS observation data watermark embedding method includes the following steps S210-S250.
[0071] S210: Based on GNSS observation data, obtain a set of observation values from different satellite systems.
[0072] In this embodiment, data parsing is performed based on the structural characteristics of GNSS observation data to obtain a set of observation values from different satellite systems to be embedded with watermark information.
[0073] Specifically, GNSS observation data, as an important foundation for navigation and positioning, has a series of unique characteristics that directly affect the embedding of watermarks. This embodiment analyzes the structural characteristics of GNSS observation data from the aspects of massive data volume, time and frequency characteristics, and data format uniformity, so as to lay the data foundation for subsequent steps. The structural characteristics of GNSS observation data include format characteristics, time characteristics, and spatial characteristics.
[0074] Regarding format characteristics, the storage formats for GNSS observation data are constantly evolving and standardizing. The widely adopted RINEX format is characterized by its uniformity and compatibility. However, RINEX is a plain text format, lacking typesetting and formatting settings, and does not include any styles. Therefore, although the observation file format is text, traditional text watermarking algorithms cannot be used. This characteristic necessitates the design of new watermark embedding methods specifically for GNSS observation data.
[0075] Regarding temporal characteristics, GNSS observation data exhibits significant temporal features. Each observation file records observations from multiple satellites at fixed time intervals, demonstrating temporal continuity and correlation among the data. These temporal characteristics can be utilized when designing digital watermarks to ensure the preservation of data temporal order and integrity during watermark embedding and extraction.
[0076] Regarding spatial characteristics, GNSS observation data also possesses significant spatial features. Its observations include information such as pseudorange and carrier phase between the receiver and each satellite. These data reflect the positional relationships of different satellites relative to the receiver. This spatial distribution characteristic gives the observation data a certain regularity in its geometric structure. When embedding digital watermarks, these spatial features can be fully utilized to ensure the rationality of the watermark embedding and reduce the impact on data accuracy.
[0077] A complete observation file can be divided into a header and a data record section. The header, as the metadata area of the GNSS observation file, contains configuration information such as receiver model, antenna parameters, and coordinate reference. Its data volume is limited and its tolerance range is small, thus it cannot meet the requirements for watermark embedding. In the data record section, the numerical changes in epoch time data directly affect the accuracy of satellite orbit calculation and clock bias. Embedding a watermark here could significantly impact data usability. The observations, as the main body of the data record, include four types of observations: pseudorange, carrier phase, Doppler, and signal strength. Pseudorange and carrier phase are core observations for GNSS positioning, directly participating in the least squares or Kalman filter solution process; Doppler and signal strength data, however, do not directly participate in common positioning solution models and are considered auxiliary observations, which may be lost during data processing. Furthermore, both have a large data volume, providing ample space for watermark embedding. Therefore, pseudorange and carrier phase observations are chosen as the watermark carrier.
[0078] Therefore, in this embodiment, the set of observations obtained from different satellite systems is represented as follows: ,in For the first The set of observations from a satellite system to be embedded with watermark information The number of satellites in the satellite system. Indicates time information, Indicates the signal band. Indicates satellite Logo, Represents pseudorange observations. Represents the carrier phase observation value. epoch 1. epoch 1 and epoch m Let represent the sets of observations to be embedded with watermark information for the first, second, and m-th satellite systems, respectively.
[0079] S220: Quantify the temporal and spatial features contained in the observation sets of the different satellite systems to obtain quantized values of temporal and spatial features; wherein, the temporal features include time information, and the spatial features include pseudorange observations and carrier phase observations.
[0080] In this embodiment, a quantization function can be established to... The temporal and spatial characteristics contained in the pseudorange and carrier phase observations are quantified. Pseudorange and carrier phase are used to represent the positional relationship between the receiver and the satellite at each epoch; therefore, the temporal and spatial characteristics represented by different pseudorange and carrier phase observations are unique. A mapping relationship between observations and watermark indexes can be established by quantifying the spatial and temporal characteristics contained in the pseudorange and carrier phase observations.
[0081] In some embodiments, three quantization functions are set, as shown in the following formulas (1)-(3):
[0082] (1)
[0083] (2)
[0084] (3)
[0085] In the formula, Represents the quantized value of time characteristics. Representing year, month, day, hour, minute, and second respectively. I obs1 This represents the quantized value of the pseudorange observation. I obs2 The quantization value represents the carrier phase observation. a This represents the key, and its value should be an integer greater than 1.
[0086] Formula (1) is used to represent the time information of each epoch as an integer, thereby realizing the quantization of time features. Formulas (2) and (3) obtain the quantization results of the original observation values by calculating the pseudorange observation value and the carrier phase observation value, that is, the two spatial feature quantization values are obtained.
[0087] S230: Obtain a binary sequence based on the original watermark image;
[0088] Step S230 is the step of generating watermark information. For example, let the original watermark image be... The size is The original watermark image is scanned to obtain a binary sequence. W ( i , j ), , The specific implementation of watermark information generation (i.e., the conversion from watermark image to binary sequence) can adopt existing technologies, such as the Arnold-Cat transform algorithm proposed in the paper "Zhang C, Wang J, Wang X. Digital Image Watermarking Algorithm with Double Encryption by ArnoldTransform and Logistic [J]. 2008 Fourth International Conference on NetworkedComputing and Advanced Information Management, 2008, 1: 329-334."
[0089] S240: Generate a watermark index to be embedded based on the time feature quantization value and the spatial feature quantization value, and obtain the watermark bit to be embedded from the binary sequence based on the watermark index to be embedded.
[0090] In some embodiments, according to formula (4), the quantized values of the temporal and spatial features in the set of observations to be embedded with the watermark are used as input values of the hash function to generate the watermark index of the observation to be embedded. According to formula (5), obtain the corresponding watermark bits to be embedded. .
[0091] (4)
[0092] (5)
[0093] In the formula, Hash Represents a hash function. I obs Represents the quantized value of spatial features. I obs =( I obs1 , I obs2 ), where W represents a binary sequence.
[0094] S250: Based on the watermark bit to be embedded and the set quantization step size, the pseudorange observation value and carrier phase observation value in the observation value set are quantized to obtain the observation data with embedded watermark information.
[0095] In some embodiments, the specific method for quantizing the pseudorange observations and carrier phase observations in the observation set is as follows:
[0096] Based on quantization rules in observation values and Embed watermark bits, set quantization step size to , , They are respectively , The value of the third decimal place. The specific quantization rules for the observations in the dataset containing the watermark information to be embedded are as follows.
[0097] When the watermark information is in place At that time, the quantization rules for the observed values are shown in formulas (6) and (7):
[0098] (6)
[0099] (7)
[0100] In the formula, and These represent the values of the pseudorange observation and the carrier phase observation, respectively, to the third decimal place.
[0101] When the watermark information is in place At that time, the quantization rules for the observed values are shown in formulas (8) and (9):
[0102] (8)
[0103] (9).
[0104] The maximum data error caused by watermark information embedding is the quantization step size. Therefore, during the process of embedding watermark bits into observations, the quantization step size is controlled to ensure that data changes always meet the accuracy requirements of the observations.
[0105] This application also provides a method for watermark detection in GNSS observation data. The watermark detection method is the reverse of the watermark embedding method; it mainly involves performing correlation detection between the extracted watermark information and the original watermark to determine whether the observation data contains user information.
[0106] like Figure 3 As shown, the method includes the following steps S310-S350.
[0107] S310: Determine the watermark index.
[0108] In this embodiment, the process for determining the watermark index is consistent with the method for determining the watermark index in the watermark embedding method. It is only used as an example, and the watermark index is determined through the following steps:
[0109] S311. Based on the structural characteristics of GNSS observation data, perform data parsing to obtain a set of observation values for different satellite systems to be embedded with watermark information;
[0110] S312. Based on the quantization functions of time and space characteristics, calculate according to formulas (2) and (3) respectively. Time quantization results for each observation and spatial quantization results ;
[0111] S313, Based on the quantification results and And calculate the watermark index corresponding to the observation based on formula (4).
[0112] S320: Based on the observation data with embedded watermark information, obtain a detection value, wherein the detection value is the value of the pseudorange observation value and the carrier phase observation value after the third decimal place in the observation data with embedded watermark information, and the observation data with embedded watermark information is obtained by the GNSS observation data watermark embedding method as described above.
[0113] S330: Extract the embedded watermark bits based on the set quantization step size and detection value.
[0114] In this embodiment, the observed values are taken. and The value of the third decimal place and The watermark position is extracted according to the watermark detection rules, and the watermark extraction rules are shown in formula (10).
[0115] (10)
[0116] In the formula, This represents the embedded watermark bits, and S represents the quantization step size. These are the third decimal place values of the pseudorange and carrier phase observations in the observation data containing embedded watermark information.
[0117] S340: Based on the watermark index and watermark bits, the extracted watermark sequence is obtained according to the majority voting method, and the extracted watermark sequence is restored by inverse transformation to obtain the extracted watermark image.
[0118] S350: Compare the extracted watermark image with the original watermark image to confirm whether the extracted watermark is consistent with the embedded watermark.
[0119] In this embodiment, the extracted watermark image can be compared with the original watermark image to confirm whether the extracted watermark is consistent with the embedded watermark. For example, common metrics used for similarity comparison include the Normalized Correlation Coefficient (NC) and the Bit Error Rate (BER). The NC measures overall similarity; the closer the value is to 1, the more similar the watermark. The BER measures the proportion of erroneous bits; the closer the value is to 0, the more accurate the BER. Threshold analysis is used to determine the effectiveness of the embedded watermark. As an example, if NC > 0.75 or BER < 5%, the watermark is considered effective.
[0120] The following will combine specific experiments and analyses to further demonstrate the feasibility and progressiveness of the method proposed in this application.
[0121] The GNSS observation data files selected in this embodiment mainly come from the IGS Center of Wuhan University (ftp: / / igs.gnsswhu.cn / pub / ) and the CDDIS official website (https: / / cddis.nasa.gov / ). Four datasets were selected for the experiment, and the detailed information of the experimental data is shown in Table 1. The watermark information to be embedded in the experiment is a meaningful binary image with a pixel size of 64*64, representing a certain meaning. In the experiment, the number of watermark scrambling times was set to 10, and the quantization step size was set to 5.
[0122] Table 1 Experimental Data Information
[0123]
[0124] To verify the usability and robustness of the watermark embedding method proposed in this embodiment for GNSS observation data in RINEX format, an experiment was conducted to perform applicability and robustness analysis on GNSS observation data containing watermark information.
[0125] In this embodiment, applicability refers to the degree to which watermark embedding affects the positioning solution results of GNSS observation data. GNSS positioning solution is based on observation files, navigation messages, clock error files, antenna correction files, etc., to calculate the coordinates of the satellite. Among them, observation files and navigation messages are necessary files for all positioning solutions. The applicability of the watermark embedding method will be analyzed from two aspects below.
[0126] (1) Data availability metrics
[0127] Understanding the availability of observational data is a prerequisite for any global navigation satellite system application, and the validity of the observational data is the foundation for subsequent positioning calculations. Availability Indicators R avai Defined as:
[0128] (11)
[0129] in, This indicates the expected number of time points used in the calculation with predefined data intervals and data sampling. This indicates the number of available time points supported by at least four satellites in each GNSS constellation that have dual-frequency data.
[0130] This embodiment calculates the expected time points for the observation files before and after watermark embedding. and available time points The data availability metric was obtained, and the final calculation result showed that the watermark embedding remained unchanged. Values were determined. Experimental results show that the watermark embedding process did not affect the usability index of GNSS observation data.
[0131] (2) Pseudorange single-point positioning
[0132] GNSS positioning methods are generally divided into absolute positioning and relative positioning, each with its own advantages and disadvantages. Absolute positioning mainly includes pseudorange single-point positioning (SPP) and precise single-point positioning (PPP), among others.
[35] Relative positioning mainly includes differential positioning and real-time kinematic positioning (RTK).
[0133] The positioning mode with the fewest observation restrictions is SPP. In order to further verify the applicability of the watermark embedding method to GNSS observation files, that is, to determine whether the method can meet the application scenarios of positioning solution, this embodiment will perform SPP solution on the RINEX files before and after watermark embedding, and statistically analyze the root mean square error (RMS) of the positioning results and its change, as well as the positioning results and their changes.
[0134] RMS is a commonly used indicator in GNSS positioning accuracy evaluation, used to quantify the deviation between the positioning result and the actual location. Its calculation formula is as follows:
[0135] (12)
[0136] in, The total number of observations. Indicates the first The deviation between the positioning result and the true coordinates for each epoch. The smaller the RMS value, the higher the consistency of the positioning result and the better the control of systematic and random errors.
[0137] In this embodiment, the change is the difference in RMS positioning error before and after watermark embedding, used to represent the degree to which watermark embedding affects the performance of data positioning calculation. Generally, when the change is on the same order of magnitude as or lower than the RMS of the original data, watermark embedding is considered not to compromise the fidelity of the data positioning calculation result; conversely, when the change is on a higher order of magnitude than the RMS of the original data, watermark embedding is considered to affect the performance of the data positioning calculation. Tables 2 and 4 show the RMS and changes of four sets of data for two SPPs. The error indices are divided into three directions: E, N, and U, representing the east, north, and celestial directions, respectively. Tables 3 and 5 show the positioning results of the two SPPs and their changes.
[0138] Table 2 shows the pseudorange single-point positioning error before and after watermark embedding.
[0139]
[0140] Table 3 Data A: Pseudorange Single-Point Localization Results Before and After Watermark Embedding
[0141]
[0142] Table 4. Pseudorange single-point positioning error before and after watermark embedding in Data B
[0143]
[0144] Table 5. Pseudorange single-point localization results before and after watermark embedding in Data B
[0145]
[0146] The positioning accuracy of SPP is typically in the range of a few meters to tens of meters. In practical applications, the accuracy may decrease due to environmental factors and technical limitations. Under optimized conditions, modern global positioning systems (such as GPS, GLONASS, Galileo, etc.) can achieve an accuracy of a few meters, while the magnitude of the RMS change shown in Tables 2 to 5 is less than or equal to the RMS magnitude of the original data, and the change in the positioning result is controlled at the decimeter level, which is far greater than the positioning accuracy of SPP itself. Therefore, the watermark embedded by the embedding method proposed in this application will not damage the SPP positioning performance of the original observation file.
[0147] Robustness analysis.
[0148] (1) Data compression and version conversion
[0149] The compression attack converts the watermarked data into CRX compressed format using the rnx2crx program, and then uses the crx2rnx program to convert the compressed file back to the original format. Since the algorithm only processes the observations in the data, and the file structure remains unchanged, the data compression and decompression operations do not affect watermark extraction. The watermark information extracted after the original observation file is compressed and decompressed is complete, and calculations show that... The value is 1.
[0150] The version conversion attack experiment converted data A, B, and C to versions 2.10, 2.11, 2.12, 3.00, 3.01, 3.02, 3.03, and 3.05 respectively before watermark extraction. The experimental results are shown in Table 6.
[0151] Table 6. Results of Version Switching Attack Experiment
[0152]
[0153] The experimental results in Table 6 show that the watermark extraction efficiency improved after the data was converted to various versions. All values are 1. When data is converted from a higher version to a lower version, the number of supported satellite systems and bands will decrease, resulting in the loss of some data. Even if the original version is restored, the missing data cannot be recovered. However, the loss of watermark information caused here is small relative to the total amount of watermark embedded, so it will not affect watermark extraction.
[0154] (2) Data splitting and merging
[0155] In the data segmentation experiment, since data A and B are relatively short in duration, further segmentation is less valuable. Therefore, data C and D with longer observation periods were selected for segmentation, with the number of segments set to 2, 4, and 6. Watermarks were extracted from each segment. The experimental results are shown in Table 7.
[0156] Table 7 Results of the Data Segmentation Attack Experiment
[0157]
[0158] The data merging experiment involves merging several observation files with consecutive time periods into a single complete observation file before extracting the watermark information. In this embodiment, watermark extraction was performed on observation files with consecutive time periods of 2, 4, and 6, respectively. The experimental results are shown in Table 8.
[0159] Table 8 Results of the Data Merging Attack Experiment
[0160]
[0161] As shown in Table 8, the experimental results demonstrate that this embodiment can completely resist data merging attacks involving 2 to 6 copies.
[0162] (3) Deleting satellites
[0163] In GNSS observation files, due to limitations in observation conditions, some satellite observations may have low quality. In such cases, it is necessary to remove the data of those satellites before proceeding with further research. Therefore, in the satellite deletion experiment, satellites will be randomly deleted from the observation files before watermark extraction.
[0164] For observation files A and B with relatively small data volumes, a satellite from a different satellite system was randomly deleted. The experimental results are shown in Table 9.
[0165] Table 9 Results of the satellite deletion attack experiment
[0166]
[0167] As shown in Table 9, the watermarked data is resistant to attacks that randomly delete satellites. Due to the establishment of the spatiotemporal mapping relationship, the watermark bits corresponding to different indices are distributed relatively evenly throughout the observation file. Therefore, the deletion of a single satellite will not affect the overall watermark extraction result.
[0168] For observation files C and D, which have large amounts of data, the number of deleted satellites was set to 10% to 80% for watermark extraction. Experimental results are shown below. Figure 4 .
[0169] Depend on Figure 4 It can be seen that as the proportion of deleted satellites increases, the similarity of the watermark extraction results will decrease. When the proportion of deleted satellites reaches 80%, the NC value of watermark extraction for data C is 0.89, which is still greater than the threshold. In summary, it can be considered that the watermark embedding method proposed in this application can effectively resist satellite deletion attacks.
[0170] (4) Epoch Resampling
[0171] Epoch resampling involves changing the sampling interval of GNSS observation files before extracting watermarks. The sampling interval of data B was changed from 1s to 2s, 5s, and 10s, respectively, and the sampling interval of data C was changed from 30s to 60s to 150s. The experimental results are shown in Tables 10 and 11.
[0172] Table 10 Results of the Data B Epoch Resampling Attack Experiment
[0173]
[0174] Table 11 Results of the C-epoch Resampling Attack Experiment
[0175]
[0176] As shown in Tables 10 and 11, the NC value of the watermark extraction decreases with the increase of the epoch sampling interval. However, when the sampling interval is increased by 5 to 10 times, the NC value of the watermark extraction can still be greater than the threshold. In practical applications, it is rare to expand the sampling interval to a larger multiple. Therefore, it can be considered that the watermark is robust to epoch resampling attacks.
[0177] In an open network environment and with the sharing of satellite navigation and positioning reference station information, the illegal use of GNSS observation data during the sharing process is more likely to occur. Therefore, how to trace illegal activities afterward during data sharing has become a critical issue that urgently needs to be addressed. The method proposed in this application can safeguard the shared application of GNSS observation data based on digital watermarking technology.
[0178] This application addresses the limited research on GNSS observation data watermarking algorithms. Taking into full account the unique spatiotemporal positioning characteristics of GNSS observation data, it proposes a GNSS observation data watermark embedding and detection method based on spatiotemporal mapping. The watermark embedding position is selected based on the structure of GNSS observation data and the essential characteristics of the observation values. A mapping relationship between the original observation values and the watermark index is established, and the same watermark bit is uniformly embedded into multiple observation values through hash mapping, enhancing resistance to common attacks. Experimental results show that, in terms of applicability, in pseudorange single-point positioning applications, the change in positioning results is controlled at the decimeter level, far exceeding the positioning accuracy of the positioning mode itself. Therefore, this application does not damage the positioning performance of the original observation file. Regarding robustness, the NC value of this application is above 0.95 against data compression, version conversion, data segmentation, and merging attacks, and above 0.85 against satellite deletion and epoch resampling attacks.
[0179] This application also provides a GNSS observation data watermark embedding device, such as... Figure 5 As shown, the GNSS observation data watermark embedding device includes:
[0180] The set determination module 501 is configured to obtain the set of observations from different satellite systems based on GNSS observation data. ,in For the first The set of observations from a satellite system to be embedded with watermark information The number of satellites in the satellite system. Indicates time information, Indicates the signal band. Indicates satellite Logo, Represents pseudorange observations. Represents the carrier phase observation value. epoch 1. epoch 1 and epoch m Let represent the sets of observations to be embedded with watermark information for the first, second, and m-th satellite systems, respectively;
[0181] The first quantization module 502 is configured to quantize the time and spatial features contained in the observation sets of the different satellite systems to obtain quantized time feature values and quantized spatial feature values; wherein, the time features include time information, and the spatial features include pseudorange observations and carrier phase observations;
[0182] The watermark scanning module 503 is configured to acquire a binary sequence based on the original watermark image;
[0183] The bit acquisition module 504 is configured to generate a watermark index to be embedded based on the time feature quantization value and the spatial feature quantization value, and to acquire the watermark bit to be embedded from the binary sequence based on the watermark index to be embedded.
[0184] The second quantization module 505 is configured to quantize the pseudorange observations and carrier phase observations in the observation set based on the watermark bits to be embedded and a set quantization step size, so as to obtain observation data with embedded watermark information.
[0185] This application also provides a GNSS observation data watermark detection device, such as... Figure 6 As shown, the GNSS observation data watermark detection device includes:
[0186] The index determination module 601 is configured to determine the watermark index;
[0187] The detection value acquisition module 602 is configured to acquire a detection value from the observation data with embedded watermark information obtained by the GNSS observation data watermark embedding device as described above, wherein the detection value is the third decimal place value of the pseudorange observation value and the carrier phase observation value in the observation data with embedded watermark information.
[0188] The bit extraction module 603 is configured to extract the embedded watermark bits based on a set quantization step size and detection value;
[0189] The image extraction module 604 is configured to obtain the extracted watermark sequence according to the watermark index and watermark bits using the majority voting method, and to recover the extracted watermark sequence by inverse transformation to obtain the extracted watermark image.
[0190] The image comparison module 605 is configured to compare the extracted watermark image with the original watermark image to confirm whether the extracted watermark is consistent with the embedded watermark.
[0191] This application provides an electronic device. The electronic device may include a processor and a memory, wherein the processor and the memory can communicate; exemplarily, the processor and the memory communicate via a communication bus.
[0192] The processor executes computer execution instructions stored in memory, causing the processor to perform the scheme in the above embodiments. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.
[0193] The communication bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The system bus can be divided into address bus, data bus, control bus, etc. Transceivers are used to enable communication between database access devices and other computers (e.g., clients, read-write libraries, and read-only libraries). Memory may include random access memory (RAM) and may also include non-volatile memory.
[0194] The electronic device provided in this application embodiment can be the terminal device described in the above embodiments.
[0195] This application also provides a computer-readable storage medium storing computer instructions. When the computer instructions are executed on a computer, the computer performs the technical solution of the GNSS observation data watermark embedding and detection method described in the above embodiment.
[0196] This application also provides a computer program product, which includes a computer program stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium. When the at least one processor executes the computer program, it can implement the technical solution of the GNSS observation data watermark embedding and detection method in the above embodiments.
[0197] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or modules, and may be electrical, mechanical, or other forms.
[0198] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.
[0199] Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit composed of the above modules can be implemented in hardware or in the form of hardware plus software functional units.
[0200] The integrated modules described above, implemented as software functional modules, can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods of the various embodiments of this application.
[0201] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as execution by a hardware processor, or execution by a combination of hardware and software modules within the processor.
[0202] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage device, and may also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.
[0203] Buses can be Industry Standard Architecture (ISA) buses, Peripheral Component Interconnect (PCI) buses, or Extended Industry Standard Architecture (EISA) buses, etc. Buses can be categorized into address buses, data buses, control buses, etc.
[0204] The aforementioned storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer.
[0205] An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor. The processor and storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and storage medium can exist as discrete components in an electronic control unit or main control device.
[0206] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.
[0207] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.
Claims
1. A method for embedding watermarks into GNSS observation data, characterized in that, The method includes: Based on GNSS observation data, a set of observation values from different satellite systems was obtained. ,in For the first The set of observations from a satellite system to be embedded with watermark information The number of satellites in the satellite system. Indicates time information, Indicates the signal band. Indicates satellite Logo, Represents pseudorange observations. Represents the carrier phase observation value. epoch 1. epoch 1 and epoch m Let represent the sets of observations to be embedded with watermark information for the first, second, and m-th satellite systems, respectively; The temporal and spatial features contained in the observation sets of the different satellite systems are quantized to obtain quantized values of temporal and spatial features; wherein, the temporal features include time information, and the spatial features include pseudorange observations and carrier phase observations; Obtain a binary sequence based on the original watermark image; A watermark index to be embedded is generated based on the time feature quantization value and the spatial feature quantization value, and the watermark bit to be embedded is obtained from the binary sequence based on the watermark index to be embedded. Based on the watermark bit to be embedded and the set quantization step size, the pseudorange observation value and carrier phase observation value in the observation value set are quantized to obtain the observation data with embedded watermark information. Based on the watermark bits to be embedded and the set quantization step size, the pseudorange observations and carrier phase observations in the observation set are quantized, including: When the watermark information bit in the watermark bit to be embedded is 1, the pseudorange observations and carrier phase observations in the observation set are quantized using the following formula: ; In the formula, and These represent the values of the pseudorange observation and the carrier phase observation, respectively, to the third decimal place. S Indicates the quantization step size; When the watermark information bit in the watermark bit to be embedded is 0, the pseudorange observations and carrier phase observations in the observation set are quantized using the following formula: 。 2. The GNSS observation data watermark embedding method according to claim 1, characterized in that, The temporal and spatial features contained in the observation sets of the different satellite systems are quantized using the following formulas to obtain quantized values for the temporal and spatial features: ; ; ; In the formula, Itime represents the quantized value of the time feature. Representing year, month, day, hour, minute, and second respectively. I obs1 This represents the quantized value of the pseudorange observation. I obs2 The quantized value representing the carrier phase observation. a This represents the key.
3. The GNSS observation data watermark embedding method according to claim 2, characterized in that, Based on the quantized values of the temporal and spatial features, the watermark index to be embedded is generated using the following formula: ; In the formula, index Indicates the watermark index to be embedded. Hash Represents a hash function. I obs Represents the quantized value of spatial features. I obs =( I obs1 , I obs2 ).
4. A method for detecting watermarks in GNSS observation data, characterized in that, include: Determine the watermark index; Based on the observation data with embedded watermark information obtained by the method of any one of claims 1 to 3, a detection value is obtained, wherein the detection value is the value of the pseudorange observation value and the carrier phase observation value after the third decimal place in the observation data with embedded watermark information; Based on the set quantization step size and detection value, the embedded watermark bits are extracted; Based on the watermark index and watermark bits, the extracted watermark sequence is obtained by majority voting, and the extracted watermark sequence is restored by inverse transformation to obtain the extracted watermark image. The extracted watermark image is compared with the original watermark image to confirm whether the extracted watermark is consistent with the embedded watermark.
5. The GNSS observation data watermark detection method according to claim 4, characterized in that, Based on the set quantization step size and detection value, the embedded watermark bits are extracted using the following formula: ; In the formula, This represents the embedded watermark bits, and S represents the quantization step size. These are the third decimal place values of the pseudorange and carrier phase observations in the observation data containing embedded watermark information.
6. A GNSS observation data watermark embedding device, characterized in that, The watermark embedding device includes: The set determination module is configured to obtain the set of observations from different satellite systems based on GNSS observation data. ,in For the first The set of observations from a satellite system to be embedded with watermark information The number of satellites in the satellite system. Indicates time information, Indicates the signal band. Indicates satellite Logo, Represents pseudorange observations. Represents the carrier phase observation value. epoch 1. epoch 1 and epoch m Let represent the sets of observations to be embedded with watermark information for the first, second, and m-th satellite systems, respectively; The first quantization module is configured to quantize the temporal and spatial features contained in the observation sets of the different satellite systems to obtain quantized values of temporal features and spatial features; wherein, the temporal features include time information, and the spatial features include pseudorange observations and carrier phase observations; The watermark scanning module is configured to obtain a binary sequence based on the original watermark image; The bit acquisition module is configured to generate a watermark index to be embedded based on the time feature quantization value and the spatial feature quantization value, and to acquire the watermark bit to be embedded from the binary sequence based on the watermark index to be embedded. The second quantization module is configured to quantize the pseudorange observations and carrier phase observations in the observation set based on the watermark bits to be embedded and a set quantization step size, to obtain observation data with embedded watermark information, including: When the watermark information bit in the watermark bit to be embedded is 1, the pseudorange observations and carrier phase observations in the observation set are quantized using the following formula: ; In the formula, and These represent the values of the pseudorange observation and the carrier phase observation, respectively, to the third decimal place. S Indicates the quantization step size; When the watermark information bit in the watermark bit to be embedded is 0, the pseudorange observations and carrier phase observations in the observation set are quantized using the following formula: 。 7. A GNSS observation data watermark detection device, characterized in that, The watermark detection device includes: The index determination module is configured to determine the watermark index; The detection value acquisition module is configured to acquire a detection value based on the observation data with embedded watermark information obtained by the device of claim 6, wherein the detection value is the value of the third decimal place of the pseudorange observation value and the carrier phase observation value in the observation data with embedded watermark information. The bit extraction module is configured to extract the embedded watermark bits based on a set quantization step size and detection value; The image extraction module is configured to obtain the extracted watermark sequence according to the watermark index and watermark bits using a majority voting method, and to recover the extracted watermark sequence by inverse transformation to obtain the extracted watermark image. The image comparison module is configured to compare the extracted watermark image with the original watermark image to confirm whether the extracted watermark is consistent with the embedded watermark.
8. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory to implement the method as described in any one of claims 1-3 or 4-5.
9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method as described in any one of claims 1-3 or 4-5.
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