Track synthesis privacy protection method based on differential privacy

Abstract

The invention relates to a track synthesis privacy protection method based on differential privacy, and belongs to the technical field of data privacy protection. The method comprises the following steps: firstly, collecting original trajectory data, preprocessing the original trajectory data, extracting trajectory data in a certain longitude and latitude range as an original trajectory data set, performing geographic space discretization processing on the original trajectory data by adopting a gridding mode, and converting an original trajectory into a grid trajectory; extracting the characteristics of the grid track, obtaining a synthesized grid track according to the characteristics of the grid track, converting the synthesized grid track into a position track, and obtaining a final synthesized track; and the final synthetic trajectory is used to replace the original trajectory for publishing, and original trajectory protection is realized.

Description

Technical Field

[0001] The invention relates to a trajectory synthesis privacy protection method based on differential privacy, and belongs to the technical field of data privacy protection. Background Art

[0002] With the rapid development of mobile Internet technology, Internet of Things technology, and spatial positioning technology, location-based services (LBS) have been widely integrated into people's daily lives. If users need to use LBS, they must provide relevant information about their location to third-party service providers. In the road network environment, trajectory data reflects the user's movement trajectory in the road network. The trajectory data contains sensitive information such as the user's personal information, travel habits, and behavior patterns. If the original trajectory data is not protected and directly released, it is easy to cause the user's privacy to be leaked. Therefore, when users enjoy the services provided by LBS, the privacy of trajectory data is a very important security issue. In addition, when protecting user trajectory data, if the data distortion is serious, this will reduce the availability of trajectory data, and thus affect the service quality of location-based services. Therefore, how to select appropriate location points in trajectory data for user privacy protection and how to ensure the availability of trajectory data are very important research issues.

[0003] The technology of this invention is funded by the Yunnan Provincial Major Science and Technology Special Plan (202302AD080002); the Industrial Innovation Talent Project of the "Xingdian Talent Support Plan" (Yunnan Development and Reform Personnel

[2019] No. 1096); and the Yunnan Provincial Key Laboratory of Computer Technology Application Open Fund (CB22144S073A). Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a trajectory synthesis privacy protection method based on differential privacy, which synthesizes trajectory data by extracting the feature distribution of original trajectory data to achieve the purpose of privacy protection of the original trajectory while ensuring the availability of the synthesized trajectory data.

[0005] The technical solution of the present invention is: a trajectory synthesis privacy protection method (DPTS) based on differential privacy, the method comprising:

[0006] Step 1: Collect the original trajectory data, pre-process the original trajectory data, and extract the trajectory data within a certain longitude and latitude range as the original trajectory data set.

[0007] The preprocessing includes data deduplication, outlier cleaning, and deletion of tiny tracks.

[0008] Step 2: Use gridding to discretize the original trajectory data into geospatial space. Calculate the grid granularity N based on the noise error and non-uniformity error in the query. Use the grid granularity N to divide the entire geographic space into N×N grid cells of equal size. After geospatial discretization, convert the original trajectory into a grid trajectory.

[0009] Step 3: Use the first-order Markov model to build a mobility model, model the middle points of the grid trajectory as probability distribution, and perform normalization to obtain the normalized Markov state transition probability matrix.

[0010] The length distribution of the grid trajectory is extracted and the length distribution matrix is ​​obtained.

[0011] The travel distribution of the grid trajectory is extracted, the starting point transition state transfer probability matrix is ​​obtained, and the extraction of the grid trajectory feature distribution is completed.

[0012] The grid trajectory is thus modeled as three probability distributions, including a Markov state transition probability matrix, a length distribution matrix, and a starting point transition state transition probability matrix, which describe the key statistical characteristics of the motion in the original trajectory. Laplace noise is then added to the probability distributions to satisfy differential privacy.

[0013] Step 4: Use the Markov state transition probability matrix to sample the middle points of the grid trajectory.

[0014] Use the length distribution matrix to determine the length of the grid tracks.

[0015] The starting and ending points of the grid trajectory are determined using the starting transition state transfer probability matrix.

[0016] According to the length of the trajectory, the starting point, the middle point and the end point are combined together to obtain a synthesized grid trajectory, which is converted into a position trajectory to obtain the final synthesized trajectory.

[0017] The Step 2 is specifically as follows:

[0018] Step 2.1: When executing a query, the error sources are mainly noise error and non-uniformity error. Given the noise error and non-uniformity error

[0019] Where r is the ratio of the query area to the entire area, N is the grid granularity, ε is the privacy budget, k is the scaling factor, and D L and D W are the domain length and width of the dataset D respectively.

[0020] Step 2.2: Minimize the noise error and non-uniformity error to obtain the grid size N:

[0021]

[0022] Then we get N as:

[0023]

[0024] Step 2.3: Use the grid granularity N to divide the entire geographic space into N×N grid cells of equal size. Each point in the original trajectory is mapped to the corresponding grid cell. For each grid, the grid coordinates are mapped to the state number, and C i Representation, and then convert the original trajectory into a grid trajectory.

[0025] The Step 3 is specifically as follows:

[0026] Step 3.1: After the geographic space is discretized, each area in the grid is regarded as a state in the Markov model. The first-order Markov model is used to construct the mobility model and calculate the grid C i to C j The Markov state transition probability is:

[0027]

[0028] In the formula, is a continuous point C in trajectory T i and C j is the count of the number of transitions, and |T| represents the number of points in trajectory T.

[0029] The Markov state transition probability matrix M is obtained by calculating the Markov state transition probability between every two grids, and the normalized Markov state transition probability matrix M' is obtained after M is normalized.

[0030] Step 3.2: Use Manhattan distance to calculate the length of each grid track. The track length refers to the number of grid cells that the track passes through. Retrieve and store the length of the track from the starting grid point forward, and calculate the proportion of the track length to the total length. The track T i The length distribution of is:

[0031]

[0032] In the formula, |T i | is the trajectory T i is the number of grid points in , and |D| is the number of trajectories contained in the dataset D.

[0033] When calculating the length distribution of each trajectory, create a zero matrix with the same size as the number of trajectories and a zero matrix size of 1×|D|, fill the length distribution into the matrix, and obtain the length distribution matrix L.

[0034] Step 3.3: Extract the travel distribution of the grid track. Use the starting point and end point of the grid track to define a trip. Extracting the travel distribution is to extract the distribution of the starting point and end point.

[0035] The distribution of the starting point is represented by the starting point transition state transfer probability matrix, and in order to maintain the correlation between the starting point and the end point, the corresponding end point is selected according to the selected starting point during the trajectory synthesis process, thereby determining the distribution of the end point.

[0036] Add virtual starting grid C to the grid track a and virtual end grid C b , calculate the starting transition state transfer probability based on the frequency estimate:

[0037]

[0038] In the formula, |C a →C i | for C a to C i The number of transitions, |D| is the total number of trajectories in the data set D, and the starting transition state transition probability is filled into a matrix to obtain the starting transition state transition probability matrix S.

[0039] Step 3.4: Set the total privacy budget to ε, which is used to control the amount of noise or randomness added to the original dataset. ε is divided into three sub-budgets, namely ε1, ε2, and ε3.

[0040] Assign a privacy budget of ε1 to the normalized Markov state transition probability matrix M', and use the logarithmic transformation method to add Laplace noise to obtain the noisy Markov transition probability matrix

[0041]

[0042] Where Lap(Δf / ε) is the noise added according to the Laplace distribution, lnM' is the logarithmic probability matrix obtained by logarithmic transformation of M', and x=lnM'+Lap(Δf / ε) means adding Laplace noise to the logarithmic probability matrix. The logarithmic probability matrix is ​​converted back to the probability space and normalized. The maximum value of x is subtracted here to ensure the stability of the value and avoid numerical accuracy problems caused by exponential function calculations.

[0043] Next, a privacy budget of ε2 is allocated to the length distribution matrix L, and the Laplace noise is added to the matrix for perturbation and normalization using the logarithmic transformation method to obtain the noise length distribution matrix.

[0044] A privacy budget of ε3 is allocated to the starting transition state transfer probability matrix S, and the Laplace noise is added using the logarithmic transformation method to obtain the noisy starting transition state transfer probability matrix.

[0045] The Step 4 is specifically as follows:

[0046] Step 4.1: Use the starting point transition state transfer probability matrix to sample the starting point, and select a grid point C based on the noise starting point transition state transfer probability matrix start As the starting point, in order to maintain the correlation between the starting point and the end point, the starting point C is selected start Then, according to the grid point C start Select End Point C end .

[0047] Step 4.2: Use the length distribution to determine the length of the grid track. start , the length of the synthesized mesh trajectory is determined by sampling from the noise length distribution matrix.

[0048] Step 4.3: Use the first-order Markov model to sample the middle point of the grid trajectory. Sample the next grid point based on the noise Markov transition probability matrix until the trajectory length is reached or the virtual end point C is reached. b Stop sampling.

[0049] Step 4.4: Synthesize the grid trajectory according to Step 4.1-Step 4.3. Next, convert the grid form of the position in the trajectory into the position form by randomly sampling a position in each corresponding grid. The obtained position sequence constitutes the final synthesized trajectory. Use the final synthesized trajectory instead of the original trajectory for release, thereby protecting the original trajectory.

[0050] The beneficial effect of the present invention is that the method proposed by the present invention for calculating the Laplace noise probability matrix using logarithmic transformation can maintain the non-negativity of the probability when protecting the privacy of the probability matrix. The present invention can provide better protection for privacy information while maintaining data availability, so that users can enjoy higher service quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is an overview diagram of the architecture of the present invention;

[0052] Figure 2 : is a graph showing the influence of the grid granularity N on the result in an embodiment of the present invention;

[0053] Figure 3 is a diagram showing the impact of privacy budget allocation on error results in an embodiment of the present invention;

[0054] Figure 4 It is a comparison result diagram of the utility performance of the present invention. DETAILED DESCRIPTION

[0055] The present invention will be further described below in conjunction with the accompanying drawings and specific implementation methods.

[0056] Example 1: Figure 1 As shown in Figure 1, a privacy protection method for trajectory synthesis based on differential privacy is shown. The specific steps are as follows:

[0057] Step 1: Collect the original trajectory data, pre-process the original trajectory data, and extract the trajectory data within a certain longitude and latitude range as the original trajectory data set;

[0058] The preprocessing includes data deduplication, outlier cleaning and deletion of tiny tracks;

[0059] Step 2: Use gridding to discretize the original trajectory data into geospatial space, and discretize the geospatial space into grid cells. The grid granularity N is calculated based on the noise error and non-uniformity error in the query, and the entire geospatial space is divided into N×N grid cells of equal size using the grid granularity N. After geospatial discretization, the original trajectory is converted into a grid trajectory;

[0060] Step 3: Extract the characteristic distribution of the grid trajectory. Use the first-order Markov model to construct the mobility model, model the middle point of the grid trajectory as a probability distribution, and normalize it to obtain the normalized Markov state transition probability matrix; extract the length distribution of the grid trajectory to obtain the length distribution matrix; then extract the travel distribution of the grid trajectory to obtain the starting point transition state transfer probability matrix. In this way, the grid trajectory is modeled as three probability distributions, including the Markov state transition probability matrix, the length distribution matrix, and the starting point transition state transfer probability matrix. The probability distribution describes the key statistical characteristics of the movement in the original trajectory. Laplace noise is then added to the probability distribution to meet differential privacy;

[0061] Step 4: Perform grid trajectory synthesis. During the grid trajectory synthesis process, the travel distribution is used to determine the starting point and end point of the grid trajectory; the length distribution is used to determine the length of the grid trajectory; the first-order Markov model is used to sample the middle point of the grid trajectory to obtain a synthesized grid trajectory. The grid trajectory is then converted to a position trajectory to obtain the final synthesized trajectory, and finally the synthesized trajectory is used to replace the original trajectory for release, thereby protecting the original trajectory.

[0062] The Step 2 is specifically as follows:

[0063] Step 2.1: When executing a query, the main sources of error are noise error and non-uniformity error. Given the noise error and non-uniformity error:

[0064] The noise error is expressed as r is the ratio of the query area to the entire area, N is the grid granularity, and ε is the privacy budget. The non-uniformity error is expressed as k is the proportionality coefficient, D L and D W are the domain length and width of the dataset D respectively.

[0065] Step 2.2: Minimize the noise error and non-uniformity error to obtain the grid size N:

[0066]

[0067] Then we get N as:

[0068]

[0069] Step 2.3: Use the grid granularity N to divide the entire geographic space into N×N grid cells of equal size. Each point in the original trajectory is mapped to the corresponding grid cell, and the trajectory can be represented by grid coordinates. For the convenience of representation, the coordinates of each grid can be mapped to a unique state number, for example, the (0,0) coordinate is mapped to C0. Then traverse each trajectory, map each grid coordinate to a state number, and obtain a grid trajectory represented by a state sequence.

[0070] The Step 3 is specifically as follows:

[0071] Step 3.1: After the geographic space is discretized, each area in the grid is regarded as a state in the Markov model. The first-order Markov model is used to construct the mobility model and calculate the grid C i to C j The Markov state transition probability is:

[0072]

[0073] In the formula, is a continuous point C in trajectory T i and C j The count of the number of transitions. |T| represents the number of points in trajectory T.

[0074] The Markov state transition probability matrix M is obtained by calculating the Markov state transition probability between every two grids:

[0075]

[0076] Among them, the element P of the matrix M i,j It represents the probability of transitioning to state j at the next moment when the state is in state i at the current moment. Then M is normalized to obtain the normalized Markov state transition probability matrix M'.

[0077] Step 3.2: Use Manhattan distance to calculate the length of each grid track. The track length refers to the number of grid cells that the track passes through. Retrieve and store the length of the track from the starting grid point forward, and calculate the proportion of the track length to the total length. The track T i The length distribution of is:

[0078]

[0079] In the formula, |T i | is the trajectory T i is the number of grid points in , and |D| is the number of trajectories contained in the dataset D.

[0080] When calculating the length distribution of each trajectory, we create a zero matrix with the same size as the number of trajectories, the size of which is 1×|D|, and fill the length distribution into the matrix to obtain the length distribution matrix L.

[0081] Step 3.3: Extract the trip distribution of the grid trajectory. Use the starting point and end point of the grid trajectory to define a trip. Extracting the trip distribution is to extract the distribution of the starting point and the end point. The distribution of the starting point is represented by the starting point transition state transfer probability matrix, and in order to maintain the correlation between the starting point and the end point, the corresponding end point is selected according to the selected starting point during the trajectory synthesis process, thereby determining the distribution of the end point.

[0082] Add virtual starting grid C to the grid track a and virtual end grid C b . Calculate the starting transition state transition probability based on the frequency estimate:

[0083]

[0084] In the formula, |C a →C i | for C a to C i The number of transitions, |D| is the total number of trajectories in the data set D. Fill the starting transition state transition probability into a matrix to obtain the starting transition state transition probability matrix S.

[0085] Step 3.4: Set the total privacy budget to ε, which is used to control the amount of noise or randomness added to the original dataset. Divide ε into three sub-budgets, namely ε1, ε2, and ε3. There are:

[0086] Assign a privacy budget of ε1 to the normalized Markov state transition probability matrix M', and use the logarithmic transformation method to add Laplace noise to obtain the noisy Markov transition probability matrix

[0087]

[0088] Where Lap(Δf / ε) is the noise added according to the Laplace distribution. lnM' is the logarithmic probability matrix obtained by logarithmic transformation of M', and x=lnM'+Lap(Δf / ε) means adding Laplace noise to the logarithmic probability matrix. The logarithmic probability matrix is ​​converted back to the probability space and normalized. The maximum value of x is subtracted here to ensure the stability of the value and avoid numerical accuracy problems caused by exponential function calculations.

[0089] Next, a privacy budget of ε2 is allocated to the length distribution matrix L. The Laplace noise is added to the matrix for perturbation and normalization using the logarithmic transformation method to obtain the noise length distribution matrix.

[0090] Afterwards, a privacy budget of ε3 is allocated to the starting transition state transfer probability matrix S, and the logarithmic transformation method is also used to add Laplace noise to obtain the noise starting transition state transfer probability matrix.

[0091] The Step 4 is specifically as follows:

[0092] Step 4.1: Use the travel distribution to determine the locations of the start and end points of the grid trajectory. Sample the start point and select a grid point C based on the transition state probability matrix of the noise start point start As the starting point. In order to maintain the correlation between the starting point and the end point, when selecting the starting point C start Afterwards, according to C start To select the end point C end , by building a dictionary to map all possible endpoints corresponding to each starting point, and giving priority to the endpoints that can make the synthetic trajectory more similar to the original trajectory when selecting the endpoints.

[0093] Step 4.2: Use the length distribution to determine the length of the grid track. start , the length of the synthesized mesh trajectory is determined by sampling from the noise length distribution matrix.

[0094] Step 4.3: Use the first-order Markov model to sample the middle point of the grid trajectory. Get the adjacent grids of the previous grid as candidates. The coordinates of the 8 adjacent grids around grid (i, j) are: [(i-1, j-1), (i-1, j), (i-1, j+1), (i, j+1), (i, j-1), (i+1, j+1), (i+1, j), (i+1, j-1)]. Then check whether the adjacent grid coordinates are valid (whether they are in the rows and columns of the grid map), and return the valid adjacent grid coordinates. For each candidate, select its probability given the previous grid according to the noise Markov transition probability matrix, normalize the candidate probability, sample based on the probability distribution of the candidate, select the next grid, reach the trajectory length or reach the virtual end point C b Stop sampling;

[0095] Step 4.4: Synthesize the grid trajectory according to Step 4.1-Step 4.3. Next, convert the grid form of the position in the trajectory into the position form by randomly sampling a position in each corresponding grid. The obtained position sequence constitutes the final synthetic trajectory. Use the synthetic trajectory instead of the original trajectory for release, thereby protecting the original trajectory.

[0096] Example 2: The present invention conducts experiments on the T-drive, Geolife and Taxi datasets based on the differential privacy trajectory synthesis privacy protection method in the present invention on the Python 3.10 platform. The details of the datasets are summarized in Table 1. The total privacy budget is denoted as ε, and ε is allocated to three sub-privacy budgets: the trajectory Markov transition probability matrix, the trajectory length distribution, and the trajectory travel distribution, which are denoted as ε1, ε2, and ε3 respectively. ε1 is set to 3 / 5ε, and ε2 and ε3 are both set to 1 / 5ε. The grid granularity parameter N of the T-drive, Geolife, and Taxi datasets is set to 6, 7, and 8, respectively. Experiments are conducted with total privacy budget ε of 0.1, 0.5, and 1.0, respectively. Figure 2 and Figure 3 It is confirmed that the parameter selection of the present invention is correct. Figure 2 As shown in Figure 2, the effect of different grid sizes on the results is shown. Figure 3 As shown, the impact of different privacy budget allocations on the error results is demonstrated. When the privacy budget ratio is 3:1:1, all errors are close to the minimum, so the present invention sets the privacy budget ratio to ε1:ε2:ε3=3:1:1.

[0097]

[0098] Table 1: Experimental dataset information

[0099] The following parameters are selected as evaluation parameters:

[0100] Trip Error=JSD(Trip(D),Trip(D′))

[0101] Length Error=JSD(Len(D),Len(D′))

[0102] Diameter Error=JSD(Dia(D),Dia(D′))

[0103] Density Error=JSD(Den(D),Den(D′))

[0104]

[0105] Trip error uses Jensen-Shannon Divergence (JSD) to measure the difference in probability distribution of the start / end points of the trajectories in the original trajectory dataset D and the synthetic trajectory dataset D'. Length error uses the JSD between the length distribution of the original trajectory and the synthetic trajectory as a measure of length error. Diameter error uses the JSD between the diameter distribution of the original trajectory and the synthetic trajectory as a measure of diameter error (the diameter of a trajectory refers to the maximum distance between any pair of points). Density error is used to evaluate the difference between the density distribution of the synthetic trajectory and the original trajectory. QueryAvRE refers to comparing the results of the original database and the synthetic database when executing a set of queries and calculating the average value of their errors. In the formula, q is the soundness constraint, q = 1% × |D|, generates the average result of 200 random queries, and returns the average relative error of the query. FPAvRE is used to evaluate the similarity of frequent patterns between two datasets and calculate the average relative error of frequent patterns between datasets. In the formula, pattern P is defined as an ordered sequence of units, and the pattern support sup(D,P) is defined as the number of times P appears in D. Defined as the first k patterns in D, with k value set to 100.

[0106] In Table 2 and Figure 4 In the paper, the utility performance of the DPTS mentioned in this invention is compared with three methods under three data sets and three privacy budgets ε.

[0107]

[0108]

[0109] Table 2: Utility performance comparison results

[0110] It can be seen that DPTS performs better in the experimental dataset and the utility metric of the experiment. In most cases, DPTS provides superior performance at the same privacy level. In general, the present invention can ensure the privacy security of user trajectories and the availability of trajectories, so that users can enjoy a higher quality of service.

[0111] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A privacy protection method for trajectory synthesis based on differential privacy, characterized in that: The method comprises: Step 1: Collect the original trajectory data, pre-process the original trajectory data, and extract the trajectory data within a certain longitude and latitude range as the original trajectory data set; The preprocessing includes data deduplication, outlier cleaning and deletion of tiny tracks; Step 2: Use gridding to discretize the original trajectory data into geospatial space. Calculate the grid granularity N based on the noise error and non-uniformity error in the query. Use the grid granularity N to divide the entire geographic space into N×N grid cells of equal size. After geospatial discretization, convert the original trajectory into a grid trajectory. Step 3: Use the first-order Markov model to build a mobility model, model the middle points of the grid trajectory as probability distribution, and perform normalization to obtain a normalized Markov state transition probability matrix; Extract the length distribution of the grid trajectory and obtain the length distribution matrix; Extract the travel distribution of the grid trajectory, obtain the starting point transition state transfer probability matrix, and complete the extraction of the grid trajectory feature distribution; Step 4: Use the Markov state transition probability matrix to sample the middle points of the grid trajectory; Use the length distribution matrix to determine the length of the grid tracks; Use the starting transition state transfer probability matrix to determine the starting and ending points of the grid trajectory; According to the length of the trajectory, the starting point, the middle point and the end point are combined together to obtain a synthesized grid trajectory, and the synthesized grid trajectory is converted into a position trajectory to obtain the final synthesized trajectory; The final synthetic trajectory is used instead of the original trajectory for publication to protect the original trajectory.

2. The privacy protection method for trajectory synthesis based on differential privacy according to claim 1, characterized in that: The Step 2 is specifically as follows: Step 2.1: Given the noise error and non-uniformity error Where r is the ratio of the query area to the entire area, N is the grid granularity, ε is the privacy budget, k is the scaling factor, and D L and D W are the domain length and width of the data set D respectively; Step 2.2: Minimize the noise error and non-uniformity error to obtain the grid size N: Then we get N as: Step 2.3: Use the grid granularity N to divide the entire geographic space into N×N grid cells of equal size. Each point in the original trajectory is mapped to the corresponding grid cell. For each grid, the grid coordinates are mapped to the state number, and C i Representation, and then convert the original trajectory into a grid trajectory.

3. The privacy protection method for trajectory synthesis based on differential privacy according to claim 1, characterized in that: The Step 3 is specifically as follows: Step 3.1: Use the first-order Markov model to build a mobile model and calculate the grid C i to C j The Markov state transition probability is: In the formula, is a continuous point C in trajectory T i and C j The count of the number of transitions, |T| represents the number of points in the trajectory T; The Markov state transition probability matrix M is obtained by calculating the Markov state transition probability between every two grids, and the normalized Markov state transition probability matrix M' is obtained after normalizing M; Step 3.2: Use Manhattan distance to calculate the length of each grid track. The track length refers to the number of grid cells that the track passes through. Retrieve and store the length of the track from the starting grid point forward, and calculate the proportion of the track length to the total length. The track T i The length distribution of is: In the formula, |T i | is the trajectory T i The number of grid points in , |D| is the number of trajectories contained in the dataset D; When calculating the length distribution of each trajectory, create a zero matrix with the same size as the number of trajectories, the size of the zero matrix is ​​1×|D|, fill the length distribution into the matrix, and obtain the length distribution matrix L; Step 3.3: Extract the trip distribution of the grid track. Use the starting point and end point of the grid track to define a trip. Extracting the trip distribution is to extract the distribution of the starting point and end point. The distribution of the starting point is represented by the starting point transition state transfer probability matrix. In the trajectory synthesis process, the corresponding end point is selected according to the selected starting point, thereby determining the distribution of the end point; Add virtual starting grid C to the grid track a and virtual end grid C b , calculate the starting transition state transfer probability based on the frequency estimate: In the formula, |C a →C i | for C a to C i The number of transitions, |D| is the total number of trajectories in the data set D, and the starting transition state transition probability is filled into a matrix to obtain the starting transition state transition probability matrix S; Step 3.4: Set the total privacy budget to ε, which is used to control the amount of noise or randomness added to the original dataset. ε is divided into three sub-budgets, namely ε1, ε2, and ε3. Assign a privacy budget of ε1 to the normalized Markov state transition probability matrix M', and use the logarithmic transformation method to add Laplace noise to obtain the noisy Markov transition probability matrix Where Lap(Δf / ε) is the noise added according to the Laplace distribution, lnM' is the logarithmic probability matrix obtained by logarithmic transformation of M', and x=lnM'+Lap(Δf / ε) means adding Laplace noise to the logarithmic probability matrix. The log probability matrix is ​​converted back to the probability space and normalized; Assign a privacy budget of ε2 to the length distribution matrix L, use the logarithmic transformation method to add Laplace noise to the matrix for perturbation and normalization, and obtain the noise length distribution matrix; A privacy budget of ε3 is allocated to the starting transition state transfer probability matrix S, and the Laplace noise is added using the logarithmic transformation method to obtain the noisy starting transition state transfer probability matrix.

4. The privacy protection method for trajectory synthesis based on differential privacy according to claim 1, characterized in that: The Step 4 is specifically as follows: Step 4.1: Use the starting point transition state transfer probability matrix to sample the starting point, and select a grid point C based on the noise starting point transition state transfer probability matrix start As a starting point, according to the grid point C start Select End Point C end ; Step 4.2: Based on starting point C start , sampling from the noise length distribution matrix to determine the length of the synthesized grid trajectory; Step 4.3: Sample the next grid point based on the noise Markov transition probability matrix until the trajectory length is reached or the virtual end point C is reached b Stop sampling; Step 4.4: Synthesize the grid trajectory according to Step 4.1-Step 4.

3. By randomly sampling a position in each corresponding grid, the grid form of the position in the trajectory is converted into a position form. The obtained position sequence constitutes the final synthetic trajectory. The final synthetic trajectory is used instead of the original trajectory for release, thereby protecting the original trajectory.

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