GNSS anti-spoofing detection method and application based on damped accumulation and particle swarm optimization grey model

Abstract

The present invention discloses a GNSS anti-spoofing detection method based on a damped accumulation and particle swarm optimization gray model, comprising the following steps: obtaining vehicle-mounted IMU data and odometer data between any two frames of GPS signals, using the previous frame GPS data as a benchmark, using the above data to infer and record the vehicle's geographic coordinate position when each frame of IMU data arrives, that is, the longitude, latitude and altitude time series, as input to a gray model optimization algorithm based on damped accumulation and particle swarm optimization; using the optimization algorithm to predict the vehicle's geographic coordinate position when the next frame GPS signal arrives, as the algorithm output; after coordinate system conversion, using the Euler formula to calculate the distance between the predicted geographic coordinates and the geographic coordinates obtained by GPS; using the distance obtained in the previous step to compare with the range threshold to determine whether the vehicle has been deceived. The present invention improves the robustness of the vehicle's GPS and further enhances the vehicle's anti-spoofing capability for GPS deception signals by optimizing the prediction algorithm.

Description

Technical Field

[0001] The present invention belongs to the field of GNSS anti-spoofing technology security, and relates to an application of a GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model. Background Art

[0002] With the advent of the connected vehicle era, intelligent connected vehicle technology is playing an increasingly important strategic role in the nation's socioeconomic development and is permeating all sectors of society. While the automotive industry may appear relatively unchanged over its century-long history, the control systems within it have undergone significant changes over the past few decades, exemplified by the emergence of new energy vehicles.

[0003] It's well known that global navigation satellite signals can be spoofed by false signals, making detection of spoofing attacks a pressing global issue. Numerous cases of GNSS spoofing exist, such as the 2011 Iranian hijacking of a CIA drone, which was scheduled to land in Afghanistan, through Global Positioning System (GPS) spoofing. For automotive applications, spoofing detection typically utilizes in-vehicle sensors, namely the inertial measurement unit (IMU) and odometer.

[0004] Grey prediction models can effectively predict very small data series with low data integrity and reliability, but they are generally only suitable for short-term forecasts. Grey prediction identifies the degree of dissimilarity between the development trends of system factors, that is, conducts correlation analysis, and generates and processes the original data to find the laws of system changes. It generates a data series with strong regularity and then establishes a corresponding differential equation model to predict the future development trend of things. Summary of the Invention

[0005] In order to address the deficiencies in the prior art, the present invention proposes a GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model.

[0006] The gray model GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization proposed in this paper solves the problem that the prediction results are greatly affected by old data by using a damped accumulation gray model, so that the most recent data has a greater impact than the old data; using the particle swarm optimization algorithm, for time series prediction of data, the average relative error between the model prediction value and the true value is minimized, thereby improving the prediction accuracy.

[0007] Get any two frames of GPS signal i , signal i+1The geographic coordinates (about 9) calculated from the accelerometer and gyroscope data of the onboard IMU and the odometer data are used as the input of the algorithm proposed in this invention; the gray model optimization algorithm based on damped accumulation and particle swarm optimization proposed in this invention is used to predict the GPS signal frame signal i+1 The vehicle's geographic coordinates upon arrival are output by the algorithm. The predicted geographic coordinates are compared with the geographic coordinates in the received GPS signal using Euler's formula through coordinate system conversion to calculate the distance DS. The distance DS is compared with a predetermined range threshold (10m) to detect whether the vehicle has been spoofed, thus implementing GNSS anti-spoofing detection.

[0008] The geographic coordinates calculated by the onboard IMU and odometer data are obtained by the accelerometer and gyroscope of the onboard IMU and the odometer, and the geographic coordinates, i.e., longitude, latitude and altitude, are calculated and recorded by deriving formulas (1)-(9).

[0009] The IMU data and odometer data described in this method are as follows:

[0010]

[0011] in, Indicates the speed output by the odometer; Indicates the acceleration output by the odometer; and Indicates the acceleration in the x-axis and y-axis directions; Indicates the acceleration in the z-axis direction.

[0012] The entire state vector of the vehicle at time k is:

[0013]

[0014] in, Represents the position vector in the geodetic coordinate system, i.e., latitude, longitude, and altitude; are the velocities in the ENU coordinate system in the east, north and up directions respectively; {p k , r k , A k} represents the pitch, roll and heading angles of the vehicle.

[0015] Two frames of GPS signal i , signal i+1 Usually there are about 9 frames of IMU data imu k , k is the time when IMU data is obtained, k∈[i, i+1), and odometer data can be obtained in real time. Every time IMU data is obtained, the current vehicle state vector is updated, and the roll r, pitch p, and heading A of the vehicle state vector are updated using formulas (1)-(3).

[0016]

[0017]

[0018]

[0019] Where k represents time, g represents gravitational acceleration; ω e represents the angular velocity of the Earth's rotation; R N represents the radius of the earth's normal; Δt represents the interval between two frames of IMU data.

[0020] Update the eastward speed of the vehicle state vector using formulas (4)-(6) Northward speed and upward speed

[0021]

[0022]

[0023]

[0024] Where p and A are the pitch angle and heading angle obtained by formulas (1)-(3).

[0025] Latitude of the vehicle state vector Longitude λ and altitude h are obtained by formulas (7)-(9):

[0026]

[0027]

[0028]

[0029] Where, k represents time; R M Represents the normal radius of the earth; R N represents the meridian radius of the Earth; and The eastward velocity, northward velocity and upward velocity obtained by formulas (4)-(6) are shown in Table 1. The input of the algorithm, the longitude, latitude and altitude time series, are obtained through formulas (1)-(9).

[0030] Traditional grey models use first-order accumulation, requiring the construction of background values for prediction and subject to initial value constraints. The algorithm proposed in this paper uses damped accumulation, assigning smaller weights to past data and larger weights to recent data. Using a particle swarm optimization algorithm, prediction accuracy is independent of the value of λ (λ is a generation coefficient in traditional grey models, used to generate weighted neighbor values and affecting the grey model's prediction accuracy; λ∈[0,1]), resulting in more accurate predictions.

[0031] The grey model is improved based on damping accumulation and particle swarm optimization algorithm. In the traditional particle cluster optimization algorithm, each particle contains 1 position attribute, 1 speed attribute and 1 optimal position attribute, as well as the cluster optimal position attribute. In this method, each particle is defined as containing 3 position attributes a, b, s, 1 speed attribute and 1 optimal position attribute p id , and the cluster optimal location attribute g best .

[0032] The traditional grey model uses first-order accumulation, while this method uses damped accumulation, as shown in formula (10):

[0033]

[0034] Where i, k represent time; ζ represents the ζ-order cumulative generation operator, ζ∈(0,1]; x (ζ) (k) represents the element at time k of the damped cumulative sequence; x (0) (i) is the element at time i of the original time series, that is, the true value, i∈[1,k].

[0035] The traditional grey model usually calculates the optimal values of background condition parameters a and b (equivalent to the position attributes a and b of the particles) by optimizing the λ value in formula (11), where k represents time; λ represents the generation coefficient; Z (ζ) (k) represents the element at time k of the neighbor value generation sequence.

[0036] Z (ζ) (k) = λx (ζ) (k-1)+(1-λ)x (ζ) (k),λ∈[0,1] (11)

[0037] Based on the conclusion drawn from the formula, the adjacent value generation sequence Z (ζ) (k) can be expressed by formula (12):

[0038]

[0039] By comparing formulas (11) and (12), Z (ζ) The relationship between and λ can be expressed by formula (13):

[0040] ∫x (ζ) (t)dt=λx (ζ) (k-1)+(1-λ)x (ζ) (k) (13)

[0041] in is x (ζ) (t) and the area between the x-axis (k-1≤t≤k), and λx (ζ) (k-1)+(1-λ)x (ζ) (k) is the sum of the areas of the two rectangles (k-1≤t≤k). Therefore, any value will affect the generated mean Z (ζ) The error caused by the sequence affects the prediction accuracy of the model. However, this problem can be solved by optimizing the background value based on the particle swarm optimization algorithm when calculating the parameters a and b. Therefore, the prediction accuracy of the model is not affected by the λ value. In order to minimize the relative error between the recovered value and the true value of the original sequence, the gray model can be converted into the following optimization model:

[0042]

[0043] Where k represents time; ζ represents the ζ-order cumulative generation operator; represents the recovery value at time k; x (0) (k) represents the true value at time k of the original sequence; a, b, s represent the position attributes of the current particle. In most practical applications, the value range of the position attribute a is set between [-0.5, 0.5]. The range of b can be obtained based on the range of a through formula (15), where x (0) (k) represents the true value of the original sequence at time k; Z (ζ) (k) Neighbor value generation sequence k-th element.

[0044] x (0) (k)+aZ (ζ) (k) = b (15)

[0045] Therefore, the range of b is derived as described in formula (16):

[0046] b∈[min(ax (ζ) (k-1)+x (0) (k)), max(ax (ζ) (k)+x (0) (k))], k=1, 2,..., n (16)

[0047] Where k is time; x (ζ) (k) represents the element at time k of the damped cumulative sequence; x (0) (k) represents the true value of the original sequence at time k;

[0048] In addition, the selection of initial values affects the prediction accuracy of the grey model. The traditional model selects the first value in the original data sequence as the initial value, which cannot be proved to be the optimal solution. Therefore, the initial value can be optimized to improve the prediction accuracy. (ζ) (k) related, the range of initial values is set to:

[0049] s∈[min(x (ζ) (k)), max(x (ζ) (k))], k=1, 2, ..., n (17)

[0050] Where k is time; x (ζ) (k) represents the element at time k of the damped cumulative sequence.

[0051] The specific algorithm steps of the grey model optimization algorithm based on damping accumulation and particle swarm optimization are as follows:

[0052] Step 1: Use n data points in the time series as the original data X (0) , that is, the true value, and then for the sequence X (0) Apply the damped cumulative generator to obtain the sequence X (ζ) .

[0053] Step 2: Randomly initialize the population and generate m particles, which can be used as candidate solutions to the problem of predicting the geographic coordinates at time i+1. The position attribute of each particle in the population is a i =(a i1 , a i2 , a i3 ,…,a im ), b i =(b i1 , b i2 , b i3 ,…,b im ) and s i =(s i1 , s i2 , s i3 ,...,s im ), the particle velocity attribute is V i =(v i1 , v i2 , v i3 ,...,v im ).

[0054] Step 3: Calculate the time response series based on the values of a, b, and s using formula (18)

[0055]

[0056] Among them, k represents time, and a, b, and s represent the position attributes of a particle in the cluster.

[0057] Step 4: Calculate the restored value of the original data using formula (19)

[0058]

[0059] Step 5: Use the defined fitness function to evaluate the individual best positions of all particles, minimizing the relative error between the restored value of the original sequence and the true value as the criterion for judging the quality of the particle position in the cluster. The smaller the error, the better the particle position value, and vice versa. The fitness function is defined as:

[0060]

[0061] Where k represents time; n represents the number of time series elements; ζ represents the ζ-order cumulative generation operator; represents the recovery value at time k; x (0) (k) represents the true value of the original sequence at time k;

[0062] Step 6: Compare the fitness value of each particle calculated by formula (20) with the individual best position p id If the particle fitness value is better than p id , then update p id .

[0063] Step 7: Compare the fitness value of each particle calculated by formula (20) with the optimal position g of the cluster best If the particle fitness is better than g best OK, update g best . Cluster optimal position g best is the individual optimal position p of m particles id The minimum value of .

[0064] g best =min{p i1 , p i2 ,…,p im} (twenty one)

[0065] Step 8: Update the velocity and position of each particle, i.e., a, b, s, v attributes, based on formulas (22) and (23).

[0066]

[0067]

[0068] Where d is a particle in the cluster; c1 and c2 are factors that control the particle's velocity and acceleration; r1 and r2 are two random numbers generated independently in the range [0, 1]; w is the inertia weight factor; a, b, and s are the position attributes of a particle; is the velocity property of a particle; p id is the optimal position of the individual particle; g best is the optimal position of the cluster. In each iteration, each particle tracks two “extreme values” (p id , g best ) to update itself. The first part of formula (22) wv id It is called the memory term, which represents the influence of the last speed magnitude and direction; the second part of formula (22) c1r1(g best -a id ) is called the self-cognition term, which is a vector pointing from the current point to the particle's own best point, indicating that the particle's action comes from its own experience; the third part of formula (22) c2γ2(p id -a id ) is called the group cognition term. It is a vector pointing from the current point to the optimal point in the population, reflecting the collaboration and knowledge sharing among particles. Particles use their own experience and the best experience of their peers to determine their next movement. Formula (23) shows how particles update their position attributes using their velocity attributes.

[0069] Step 9: Use the number of iterations or standard error accuracy to determine whether to terminate the iteration process to avoid infinite loops. If the number of iterations exceeds the maximum value or reaches the standard error, output the solution; otherwise, return to step 3.

[0070] In step 1, the damping accumulation generation operator is implemented as follows:

[0071] Assume that the sequence X (ζ) ={x (ζ) (1), x (ζ) (2), ..., x (ζ) (n)} is X (0) The ζ-order damped cumulative sequence and the ζ-order damped cumulative generating operator (ζ-DAGO) are:

[0072]

[0073] Where i, k represent time; ζ represents the ζ-order cumulative generation operator, ζ∈(0,1]; x (ζ) (k) represents the element at time k of the damped cumulative sequence; x (0)(i) is the element at time i of the original time series, i∈[1,k]. When the damped accumulation generator is 1, ζ-DAGO is equivalent to the traditional first-order accumulation (1-AGO). The calculation process of ζ-DAGO can be converted into matrix form:

[0074]

[0075] ζ-DAGO is an optimized form of traditional 1-AGO. It is well known that in the gray prediction model, the gray generation operator is a necessary operation to reduce the random fluctuations of the original sequence. In the cumulative calculation process, it is unreasonable to assign equal weight to all available data. Therefore, the present invention assigns different weights to distinguish the impact of new and old data. Based on the principle of new information priority, recent data is given greater weight than historical data. As a result, the newly generated sequence will be more consistent with the trend of exponential growth.

[0076] In step 2, the grey model is optimized using the particle swarm optimization algorithm, which is widely used in parameter optimization of various continuous and discrete problems. The particle swarm consisting of n particles is defined as X=(X1, X2, ..., X n ), the position of a particle in the particle swarm is defined as x i =(x i1 , x i2 ,...,x in ); the particle's velocity is defined as v i =(v i1 , v i2 ,...,v in ); the calculated optimal position of the i-th particle is defined as p id (Step 6); The calculated optimal position of the particle swarm is g best (Step 7). During the iterative search process, each particle updates its velocity and position based on the individual and global extrema (Step 8).

[0077] In step 2, a, b, and s represent the position of the particle in the group, and v represents the velocity of the particle. The ranges of a, b, and s are as follows:

[0078] -0.5≤a ik ≤0.5,

[0079] b∈[min(x (0) (k)-0.5x (1) (k-1)), max(x (0) (k)+0.5x (1) (k))], k=1, 2,..., n (26)

[0080] s∈[min(x (1) (k)), max(x(1) (k))], k = 1, 2, ..., n

[0081] In step 9, in order to prevent the problem of infinite iteration of the algorithm, the present invention sets an iteration maximum value or a standard error threshold, and ends the algorithm when the iteration maximum value is reached or is less than the standard error threshold.

[0082] After the conversion between the geodetic coordinate system and the ENU coordinate system (East-North-Up), the distance between the predicted geographic coordinate position and the geographic coordinate position obtained by GPS is calculated using the Euler formula (27), which is defined as follows:

[0083]

[0084] in, Indicates the geographic coordinates obtained by GPS. Represents the geographic coordinates of the prediction.

[0085] The calculated distance is compared to a predetermined range threshold to detect if the vehicle has been spoofed.

[0086] If the Euler distance is greater than the set range threshold, it means that the vehicle has been deceived; otherwise, the vehicle has not been deceived.

[0087] The present invention also provides an application of the above method in vehicle GNSS spoofing detection.

[0088] The present invention provides a GNSS anti-spoofing detection method that improves the robustness and stability of vehicle GPS. The proposed gray model optimization algorithm, based on damped accumulation and particle swarm optimization, optimizes the original gray model by replacing the first-order accumulation of the original grayscale model with damped accumulation. This solves the problem of prediction results being affected by old data, resulting in more recent data having a greater impact than old data. The particle swarm optimization algorithm also reduces the impact of the model's prediction accuracy on the lambda value, utilizing the characteristics of the particle swarm to improve the algorithm's prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 This is a flowchart of the GNSS anti-spoofing detection based on the grey model optimization algorithm of the present invention.

[0090] Figure 2 This is a flow chart of the grey model optimization algorithm for damping accumulation and particle swarm optimization of the present invention. DETAILED DESCRIPTION

[0091] The invention is further described in detail with reference to the following specific examples and accompanying drawings. The processes, conditions, experimental methods, etc. for implementing the present invention, except for those specifically mentioned below, are common knowledge and common common sense in the art and are not particularly limited by the present invention.

[0092] The present invention provides a GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model. The specific implementation steps are as follows:

[0093] Step 1: Get any two frames of GPS signal i , signal i+1 The vehicle-mounted IMU and odometer data are combined. The vehicle-mounted IMU frame is an East-North-Up (ENU) frame, with the vehicle's center of gravity as the origin, and the three axes extending along the east (y-axis), north (x-axis), and vertical upward (z-axis). The vehicle-mounted IMU contains an accelerometer and a gyroscope (angular velocity meter), which provide acceleration and angular velocity in the three-axis direction. Two frames of GPS signal i , signal i+1 Usually there are about 9 frames of IMU data imu k , k is the time when IMU data is obtained, k∈[i, i+1). The longitude, latitude and altitude time series are obtained according to the derived formulas (1)-(9).

[0094] Record each frame imu k The longitude time series of the data at time k is [λ k ,λ k+Δt ,…,λ k+8Δt ], the latitude time series is [h k , h k+Δt ,...,h k+8Δt ] and the height time series is As input to the grayscale model algorithm based on damped accumulation and particle swarm optimization.

[0095] Step 2: Use the grayscale model algorithm based on damped accumulation and particle swarm optimization to predict the signal i+1 The predicted geographic coordinates are used as the algorithm output when the real GPS signal arrives. i , signal i+1 The longitude, latitude and altitude time series between are used as input to the algorithm;

[0096] The step 2 specifically includes the following steps:

[0097] Step 2.1: Apply the damped accumulation generation operator to the longitude, latitude and altitude time series to obtain the damped accumulation sequence; taking the longitude time series as an example, the obtained longitude time series damped accumulation sequence x (ζ) (k), where the ζ-order cumulative generation operator is used, and the value of ζ is 0.94 during the implementation.

[0098] Step 2.2: Use the particle swarm optimization algorithm to randomly generate 5 particles as candidate solutions for predicting the longitude in the geographic coordinates at time i+1; the position attribute of the 5 particles in the swarm is a i =(a i1 , a i2 ,...,a i5 ), b i =(b i1 , b i2 ,...,b i5 ) and s i =(s i1 , s i2 ,...,s i5 ), the speed attribute is V i =(v i1 , v i2 ,...,v i5 ).

[0099] Step 2.3: Calculate the time response sequence of 5 particles

[0100] Step 2.4: Calculate the recovery value of 5 particles

[0101] Step 2.5: Use the fitness function Evaluate the individual optimal positions p of the 5 particles id . Where k represents time; x (0) (k) represents the longitude time series (true value); represents the longitude recovery value; ζ is the same as the value of ζ in step 2.1. The fitness function f uses minimizing the relative error between the recovery value and the true value as the criterion for judging the quality of the particle's position in the cluster. A smaller error indicates a better particle position, and vice versa.

[0102] Step 2.6: Similarly, use the fitness function to calculate the optimal position g of the particle cluster best ; Cluster optimal position g best is the individual optimal position p of the five particles id The minimum value of

[0103] Step 2.7: Update the properties of the five particles; the properties include a, b, s, and v, where a, b, and s represent the position properties of the particles, and v represents the velocity property of the particles;

[0104] Taking the position attribute a of the first particle as an example, Where c1, c2 are the control particle speed and acceleration factors c1 = c2 = 2; r1, r2 are two random numbers generated independently in the range [0, 1]; w is the inertia weight factor with a value of w = 0.9; v i1 Represents the velocity attribute of the first particle.

[0105] Step 2.8: Determine whether the number of iterations exceeds the given threshold of 20 times, or is less than the given standard error of 0.09. If so, output the predicted value generated by the corresponding time response sequence; otherwise, return to step 2.3.

[0106] Step 3: Compare the geodetic coordinate system (including longitude, latitude and altitude) at time i+1 predicted by the algorithm and the GPS frame signal obtained at time i+1 i+1 The geodetic coordinate system in the is converted to the coordinates in the ENU coordinate system (East-North-Up). Then, the Euler formula is used: Calculate the distance between the predicted geographic coordinates and the geographic coordinates obtained by GPS; where, Indicates the geographic coordinates obtained by GPS. Represents the geographic coordinates of the prediction.

[0107] Step 4: Use the distance calculated in step 3 to compare with the range threshold of 10m to determine whether the vehicle is deceived. In step 4, if the Euler distance is greater than the set range threshold, it means that the vehicle is deceived; otherwise, the vehicle is not deceived.

[0108] The protection content of the present invention is not limited to the above embodiments. Without departing from the spirit and scope of the inventive concept, changes and advantages that can be thought of by those skilled in the art are included in the present invention and are protected by the appended claims.

Claims

1. A GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model, characterized in that: The following steps are involved: Step 1: Get any two frames of GPS signal i , signal i+1 The geographic coordinates calculated by the onboard IMU and odometer data are used as the algorithm input, signal i represents the GPS signal at the i-th moment; Step 2: Use the grayscale model algorithm based on damped accumulation and particle swarm optimization to predict the signal i+1 The geographical coordinates when the frame GPS true value signal arrives are used as the algorithm output; Step 3: Use Euler's formula to calculate the distance between the predicted geographic coordinates and the geographic coordinates obtained by GPS; Step 4: Use the distance obtained in the previous step to compare with the range threshold to determine whether the vehicle is being deceived.

2. The GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model according to claim 1, characterized in that: In step 1, the geographic coordinates calculated by the onboard IMU and odometer data are obtained by the accelerometer and gyroscope of the onboard IMU, and the odometer, and the geographic coordinates, i.e., longitude, latitude and altitude, are calculated and recorded by a derivation formula.

3. The GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model according to claim 1, characterized in that: The step 2 specifically includes the following steps: Step 2.1: Select the latest n data points from the original data as the original data sequence, and apply the damped accumulation generation operator to the original data sequence to obtain the damped accumulation sequence; Step 2.2: Use the particle swarm optimization algorithm to randomly generate m particles as candidate solutions to the problem of predicting the geographic coordinates at time i+1; Step 2.3: Calculate the time response sequence for each particle Step 2.4: Calculate the recovery value of each particle Step 2.5: Use the fitness function to evaluate the individual best position p of each particle id ; Step 2.6: Use the fitness function to calculate the optimal cluster position g best ; Step 2.7: Update the properties of the particle; the properties include a, b, s, v; a, b, s each represent the position of the particle in the cluster, and v represents the velocity of the particle; Step 2.8: Determine whether the number of iterations exceeds a given threshold or is less than the standard error. If so, output the predicted value generated by the corresponding time response sequence; otherwise, return to step 2.

3.

4. The GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model according to claim 3, characterized in that: In step 2.1, a damped accumulation operator is used to adjust the weight of each data in the time series to solve the degree to which the prediction result is affected by old data. The generation formula of the operator is: Where i, k represent time; ζ represents the ζ-order cumulative generation operator, ζ∈(0,1]; x (ζ) (k) represents the element at time k of the damped cumulative sequence; x (0) (i) is the element at time i of the original time series, that is, the true value, i∈[1,k].

5. The GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model according to claim 3, characterized in that: In step 2.2, the particle swarm optimization algorithm is used to generate m particles to form a cluster. Each particle has its own position attributes a, b, s, velocity attribute v and optimal position attribute p in the cluster. id , and for the entire particle cluster containing the cluster's optimal location attribute g best .

6. The GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model according to claim 3, characterized in that: In step 2.3, the time response sequence is solved based on the values of a, b, and s of each particle. The solution formula of the time response sequence is: Among them, k represents time, and a, b, and s represent the position attributes of a particle in the cluster.

7. The GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model according to claim 3, characterized in that: In step 2.4, the time response sequence in step 2.3 is used to obtain the recovery value of the original sequence of each particle. The calculation formula of the recovery value is:

8. The GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model according to claim 3, characterized in that: In step 2.5, the individual optimal positions of all particles are evaluated based on the fitness function, and the fitness function is: That is, calculate the relative error between the restored value and the true value; k represents time; n represents the number of time series elements; ζ represents the ζ-order cumulative generation operator; represents the recovery value at time k; x (0) (k) represents the true value of the original sequence at time k.

9. The GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model according to claim 3, characterized in that: In step 2.6, the fitness function is used to calculate the optimal position of the cluster g best , the optimal location of the cluster g best is the minimum value among the best positions of all individual particles, that is, g best =min{p i1 , p i2 ,…,p im }.

10. The GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model according to claim 3, characterized in that: In step 2.7, the a, b, s, and v attributes of each particle are updated using the following formula: Where d is a particle, c1 and c2 represent the factors that control the particle speed and acceleration; r1 and r2 represent two random numbers generated independently in the range [0, 1]; w is the inertia weight factor; a, b, s are the position attributes of a particle; v is the velocity attribute of a particle; p id is the optimal position of the individual particle, g best is the optimal position of the cluster; update the velocity attribute of each particle and position attributes a, b, s, each particle has its own optimal position p id and the optimal location of the cluster g best To update the speed attribute, and update the position attribute according to the speed attribute.

11. The GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model according to claim 3, characterized in that: In step 2.8, whether to terminate the iteration process is determined by the number of iterations or the standard error precision to avoid the occurrence of an infinite loop.

12. The GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model according to claim 3, characterized in that: In step 3, the Euler formula is used to calculate the distance between the predicted geographic coordinates and the geographic coordinates obtained by GPS. The distance formula is defined as: in Indicates the geographic coordinates obtained by GPS. Represents the geographic coordinates of the prediction.

13. The GNSS anti-spoofing detection method based on damped accumulation and particle swarm optimization grey model according to claim 3, characterized in that: In step 4, the distance obtained in step 3 is compared with a given range threshold, and the comparison result is used to determine whether the vehicle is subject to GPS spoofing; the range threshold is 10m.

14. Application of the method according to any one of claims 1 to 13 in vehicle GNSS spoofing detection.

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