Four-rotor unmanned aerial vehicle GNSS spoofing attack detection method based on LSTM

Abstract

The invention discloses a quad-rotor unmanned aerial vehicle GNSS spoofing attack detection method based on LSTM, relates to the technical field of information security, and aims to solve the problem that an existing detection method is difficult to detect hidden GNSS spoofing attacks. And extracting time sequence characteristics of reliable measurement data by using an LSTM network, estimating a state estimation theoretical residual error of the quad-rotor unmanned aerial vehicle, and comparing the state estimation theoretical residual error with an actual residual error so as to judge whether the quad-rotor unmanned aerial vehicle is subjected to GNSS spoofing attack or not. According to the technical scheme, whether the quad-rotor unmanned aerial vehicle is subjected to the hidden GNSS spoofing attack or not can be effectively detected.

Description

Technical Field

[0001] This application relates to the field of information security technology, specifically to a method for detecting GNSS deception attacks on quadcopter UAVs based on LSTM. Background Technology

[0002] Quadrotor drones are widely used in civilian fields due to their low price, excellent performance, ease of operation, and diverse functions, such as aerial photography, pesticide spraying, environmental surveying, and disaster relief. As a typical secure cyber-physical system, the stable operation of a quadcopter drone relies on a reliable controller, sophisticated sensors, efficient actuators, and real-time wireless communication. However, because the Global Navigation Satellite System (GNSS) of quadcopter drones is often based on publicly available standards, attackers can perfectly replicate it, making deception extremely covert. Existing detection methods struggle to detect covert GNSS deception attacks. Summary of the Invention

[0003] The purpose of this invention is to provide an LSTM-based method for detecting GNSS spoofing attacks by quadcopter drones, addressing the problem that existing detection methods struggle to detect covert GNSS spoofing attacks.

[0004] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0005] A method for detecting GNSS spoofing attacks on quadrotor UAVs based on LSTM includes the following steps:

[0006] Step 1: Use an inertial measurement unit, magnetometer, and GNSS to obtain the position, velocity, Euler angles, and angular velocity of the quadcopter UAV;

[0007] Step 2: Input the position, velocity, Euler angle, and angular velocity of the quadcopter UAV into the extended Kalman filter to obtain the actual value of the state estimation residual norm of the quadcopter UAV. ;

[0008] Step 3: Input the speed, Euler angle, and body angular velocity of the quadcopter UAV into the trained LSTM network to obtain the estimated value of the state estimation residual norm of the quadcopter UAV. ;

[0009] Step 4: Obtain the actual value of the residual norm of the state estimation of the quadcopter UAV. Compared with the estimated value The absolute value of the difference between the two is used to determine whether the quadcopter UAV system is under GNSS spoofing attack. If the absolute value of the difference exceeds a preset threshold, the quadcopter UAV system is determined to be under GNSS spoofing attack. Otherwise, the quadcopter UAV system is determined not to be under GNSS spoofing attack.

[0010] Furthermore, the LSTM network includes a two-layer LSTM network and a three-layer FC layer. The two-layer LSTM network is used to extract temporal feature vectors. After the temporal feature vectors are processed by the three-layer FC layer, the estimated value of the residual norm of the quadcopter UAV state estimation is output. The first two fully connected (FC) layers both use the ReLU activation function.

[0011] Furthermore, the estimated value of the residual norm of the state estimation of the quadcopter UAV. Represented as:

[0012] ,

[0013] ,

[0014] ,

[0015] in, This represents the hidden state of the LSTM network. For network cell states, Represents the ReLU activation function. , This represents the weight matrix and bias of the FC layer. For reliable variable sequences, For the first The first layer of the LSTM network -1 output vector of LSTM units For the first The first layer of the LSTM network -1 hidden state vector of LSTM units, For sequence length, .

[0016] Furthermore, the reliable variable sequence It is obtained through the following steps:

[0017] Step 1: Constructing the dynamics of a quadcopter unmanned aerial vehicle system;

[0018] Step 2: Discretize the dynamics of the quadcopter UAV system using the forward Euler method to obtain the discrete-time state equation;

[0019] Step 3: Construct the measurement equations for the quadcopter UAV;

[0020] Step 4: Perform extended Kalman filtering using the quadcopter UAV's measurement equations and discrete-time state equations to obtain the quadcopter UAV's state estimate. ;

[0021] Step 5: Obtain the state measurement values ​​of the quadcopter UAV based on the measurement equations of the quadcopter UAV. And combined with the state estimation values ​​of the quadcopter UAV The state estimation residuals of the quadcopter UAV are obtained.

[0022] Step 6: The residuals of the quadcopter UAV state estimation have a zero-mean Gaussian distribution, and the covariance matrix is ​​obtained. ;

[0023] Step 7: Based on the covariance matrix The variables involved in the Jacobian matrix are identified, and a reliable variable sequence is then constructed. .

[0024] Furthermore, the quadcopter unmanned aerial vehicle system is dynamically represented as follows:

[0025] ,

[0026] ,

[0027] ,

[0028] ,

[0029] ,

[0030] ,

[0031] ,

[0032] ,

[0033] ,

[0034] in, For the quality of drones, Location of the drone. These are the Euler angles for the drone, namely roll, pitch, and yaw angles, respectively. The angular velocities of the UAV body are roll, pitch, and yaw angular velocities, respectively. For the total lift of the drone, , , These are the roll, pitch, and yaw moments of the drone, respectively. It is the acceleration due to gravity. Sampling time, For about Moment of inertia of the shaft For about Moment of inertia of the shaft For about Moment of inertia of the shaft for The second derivative, for The second derivative, for The second derivative, for The first derivative, for The first derivative, for The first derivative, for The first derivative, for The first derivative, for The first derivative.

[0035] Furthermore, the discrete-time state equation is expressed as:

[0036] ,

[0037] in, Sampling time, For Gaussian process noise, The Gaussian measurement noise covariance matrix, for Real-time drone location for The drone's position at time -1 , , Quadrone drone Time along Axial direction, Axial direction and Velocity in the axial direction, , , Quadrone drone +1 time along Axial direction, Axial direction and Velocity in the axial direction, for Euler angles of the drone for +1 moment, drone Euler angles, for The angular velocity of the drone body at all times. for The angular velocity of the drone at time +1 , , They are respectively The drone's roll, pitch, and yaw moments are constantly being monitored. for Total lift of the drone at all times.

[0038] Furthermore, the measurement equation for the quadcopter UAV is expressed as:

[0039] ,

[0040] in, For Gaussian noise measurement, The Gaussian measurement noise covariance matrix, This is the measurement matrix.

[0041] Furthermore, the extended Kalman filter is expressed as:

[0042] ,

[0043] ,

[0044] ,

[0045] ,

[0046] ,

[0047] in, for Jacobian matrix at time, These are the prior state estimates. The prior state estimation error covariance matrix is... To measure the transpose of the matrix, As a unit array, Here is the Kalman gain matrix. Let be the transpose of the state Jacobian matrix. For the system input vector, It is a nonlinear function.

[0048] Furthermore, the state estimation residual of the quadcopter UAV is expressed as:

[0049] ,

[0050] in, To estimate the residuals for the state.

[0051] Furthermore, the covariance matrix is ​​expressed as:

[0052] ,

[0053] in, This is the residual covariance matrix for state estimation.

[0054] The beneficial effects of this invention are:

[0055] This application uses sensors other than GNSS as reliable sensors, and uses the measurement data from these reliable sensors as input to an LSTM network. The LSTM network extracts the temporal characteristics of the reliable measurement data to estimate the theoretical residuals of the quadcopter UAV's state estimation. These theoretical residuals are then compared with the actual residuals to determine whether the quadcopter UAV is under GNSS spoofing attacks. The technical solution of this application can effectively detect whether a quadcopter UAV is under covert GNSS spoofing attacks. Attached Figure Description

[0056] Figure 1 This is the overall flowchart of this application;

[0057] Figure 2 This diagram illustrates the impact and detection of periodic constant GNSS deception attacks during the autonomous path-tracking flight mode of a UAV. Figure 1 ;

[0058] Figure 3 This diagram illustrates the impact and detection of periodic constant GNSS deception attacks during the autonomous path-tracking flight mode of a UAV. Figure 2 ;

[0059] Figure 4 A diagram illustrating the impact and detection of continuous variable amplitude GNSS deception attacks in UAV remote control flight mode. Figure 1 ;

[0060] Figure 5 A diagram illustrating the impact and detection of continuous variable amplitude GNSS deception attacks in UAV remote control flight mode. Figure 2 ;

[0061] Figure 6 This is a diagram illustrating the principle of deception attack detection.

[0062] Figure 7 This is a diagram of the network structure for the theoretical state estimation residual estimation of a quadrotor UAV based on a long short-term memory network in this application.

[0063] Figure 8 This is a training algorithm for a theoretical residual norm generator for quadrotor UAVs based on LSTM networks. Detailed Implementation

[0064] It should be noted that, where there is no conflict, the various embodiments disclosed in this application can be combined with each other.

[0065] Specific Implementation Method 1: The LSTM-based GNSS spoofing attack detection method for quadcopter UAVs described in this implementation method includes the following steps:

[0066] Step 1: Use an inertial measurement unit, magnetometer, and GNSS to obtain the position, velocity, Euler angles, and angular velocity of the quadcopter UAV;

[0067] Step 2: Input the position, velocity, Euler angle, and angular velocity of the quadcopter UAV into the extended Kalman filter to obtain the actual value of the state estimation residual norm of the quadcopter UAV. ;

[0068] Step 3: Input the speed, Euler angle, and body angular velocity of the quadcopter UAV into the trained LSTM network to obtain the estimated value of the state estimation residual norm of the quadcopter UAV. ;

[0069] Step 4: Obtain the actual value of the residual norm of the state estimation of the quadcopter UAV. Compared with the estimated value The absolute value of the difference between the two is used to determine whether the quadcopter UAV system is under GNSS spoofing attack. If the absolute value of the difference exceeds a preset threshold, the quadcopter UAV system is determined to be under GNSS spoofing attack. Otherwise, the quadcopter UAV system is determined not to be under GNSS spoofing attack.

[0070] This application uses sensors other than GNSS as reliable sensors, uses the measurement data of reliable sensors as input to an LSTM network, uses the LSTM network to extract the temporal characteristics of the reliable measurement data, estimates the theoretical residual of the state estimation of the quadcopter UAV, and compares the theoretical residual of the state estimation with the actual residual to determine whether the quadcopter UAV is subjected to a GNSS spoofing attack.

[0071] Figure 6 This is a schematic diagram of the LSTM-based GNSS deception attack detection principle for quadrotor UAVs proposed in this application. The Extended Kalman Filter (EKF) utilizes data from the Inertial Measurement Unit (IMU), magnetometer, and GNSS measurements of the quadrotor UAV's position, velocity, Euler angles, and body angular velocity to perform state estimation, obtaining the actual state estimation residual norm. The LSTM network uses reliable sensor data from an IMU and a magnetometer to measure the velocity, Euler angles, and body angular velocity of a quadcopter drone, estimating the theoretical residual norm. Threshold-based detectors compare... and If the difference between the two exceeds a preset threshold, the quadcopter UAV system is determined to be under GNSS spoofing attack. The LSTM-based network structure for estimating the theoretical residual norm of a quadcopter UAV is as follows: Figure 7 As shown.

[0072] The details are as follows:

[0073] Quadrotor Unmanned Aerial Vehicle System Model

[0074] The dynamics of the quadcopter unmanned aerial vehicle system are as follows:

[0075] ,

[0076] ,

[0077] ,

[0078] ,

[0079] ,

[0080] ,

[0081] ,

[0082] ,

[0083] ,

[0084] in, For the quality of drones, Location of the drone. Euler angles for drones, The angular velocity of the drone body. For the total lift of the drone, , , These are the roll, pitch, and yaw moments of the drone, respectively. It is the acceleration due to gravity. Sampling time, For about Moment of inertia of the shaft For about Moment of inertia of the shaft For about Moment of inertia of the shaft.

[0085] The system dynamics are discretized using the forward Euler method, yielding the discrete-time state equations.

[0086] Taking the position, velocity, Euler angles, and Euler angular velocity of the quadcopter UAV as state variables, its discrete-time state equation is:

[0087] ,

[0088] in, , , For quadcopter drones The speed of time Sampling time, For Gaussian process noise, This is the Gaussian measurement noise covariance matrix.

[0089] To write the discrete state equations of a quadcopter UAV in a more concise form:

[0090] ,

[0091] in, ,

[0092] Quadrotor UAV State Observation and State Estimation

[0093] The measurement equations for a quadcopter UAV are as follows:

[0094] ,

[0095] in, For Gaussian noise measurement, The Gaussian measurement noise covariance matrix, For measurement matrix ( (Unit array).

[0096] Extended Kalman filtering is performed using discrete state equations and measurement equations.

[0097] The state of a quadcopter is estimated using EKF (Extended Kernel-Focused Function) based on sensor measurements. The EKF process is as follows:

[0098] ,

[0099] ,

[0100] ,

[0101] ,

[0102] ,

[0103] in, for The Jacobian matrix at time t is in the following form:

[0104] ,

[0105] ,

[0106] ,

[0107] , ,

[0108] ,

[0109] Apart from the Jacobian matrix submatrices given above, all other elements in the Jacobian matrix are 0.

[0110] The residual for state estimation of a quadcopter UAV is:

[0111] ,

[0112] The state estimation residuals of the quadrotor UAV are distributed with zero mean and a Gaussian distribution. Its covariance matrix is:

[0113] ,

[0114] GNSS spoofing attack description

[0115] Malicious attackers exploit vulnerabilities in GNSS to interfere with drones and prevent them from receiving correct signals, thus launching a deception attack by simulating satellite navigation signals. The position measurement equation under this deception attack is:

[0116] ,

[0117] in Sensor measurement vector The subvector represents the position measurement information of the quadrotor drone. This represents the GNSS spoofing attack vector. GNSS spoofing attack vectors can take various forms, such as constant vectors and time-varying vectors. GNSS spoofing attacks may occur continuously, periodically, or randomly. Based on the vector form and occurrence pattern of the GNSS spoofing attack, various types of GNSS spoofing attack combinations can be generated.

[0118] Theoretical Residual Norm Generator for Quadrotor UAVs Based on LSTM Network

[0119] Considering the residual covariance matrix of state estimation for a quadrotor UAV Format:

[0120] ,

[0121] according to In form, The evolution of the residual covariance matrix at time step 1 depends on the Jacobian matrix at several previous time steps. The Jacobian matrix involves only a few variables. , , , , , , There are a total of 7 variables. Of these 7 variables, The lift of the UAV can be calculated based on the rotational speed of the four propellers of the quadcopter. The remaining six variables are sensor measurements, which are not affected by GNSS spoofing attacks. In this application, the above seven variables are referred to as reliable variables.

[0122] State estimation residual norm With state estimation residual covariance matrix There is a correlation between them:

[0123] ,

[0124] That is, the residual norm of state estimation The expected value of the square is equal to the state estimate residual covariance matrix. The traces.

[0125] Therefore, there is a correlation between the reliable variable series and the state estimation residual norm. The state estimation residual norm can be estimated using the reliable variable series.

[0126] The seven reliable variables are combined to form a reliable vector:

[0127] ,

[0128] Further, a reliable sequence of variables is provided:

[0129] ,

[0130] in, The sequence length is given.

[0131] Develop a deep neural network based on LSTM to establish a reliable correlation between variable sequences and residual norms. The network structure is as follows: Figure 7 As shown, the network consists of a two-layer LSTM network, three FC layers, and two ReLU activation functions. The two-layer LSTM network is used to extract reliable variable sequences. The temporal information in the data is processed by a two-layer LSTM network. The temporal feature vector output by the two-layer FC layer undergoes feature transformation, and after the ReLU activation function introduces nonlinearity, it finally passes through a single FC network to output an estimate of the residual norm of the quadcopter UAV state estimation. This process can be expressed as a formula:

[0132] ,

[0133] ,

[0134] ,

[0135] in, This represents the hidden state of the LSTM network. For network cell states, Represents the ReLU activation function. , This represents the weight matrix and bias of the FC layer. For reliable variable sequences, For the first The first layer of the LSTM network -1 output vector of LSTM units For the first The first layer of the LSTM network The hidden state vector of -1 LSTM unit. The LSTM network has 128 hidden units, and the number of input and output nodes in the three FC layers are as follows: 128 inputs, 64 outputs; 64 inputs, 32 outputs; 32 inputs, 1 output.

[0136] The loss function of this network is used for backpropagation to adjust the network parameters, and its form is:

[0137] ,

[0138] in, A positive loss coefficient. .

[0139] Estimates of the residual norm of state estimation for quadcopter UAVs in the absence of GNSS attacks. With respect to the actual residual norm It is close to the theoretical residual norm, which is referred to in this application.

[0140] Based on the above, a training algorithm for a theoretical residual norm generator for quadrotor UAVs based on LSTM networks is presented, such as... Figure 8 As shown, this algorithm can be used to train a theoretical residual norm generator for quadrotor UAVs based on an LSTM network.

[0141] Design of a GNSS spoofing attack detector based on a theoretical residual norm generator

[0142] The theoretical residual norm estimated by the LSTM-based quadcopter theoretical residual norm generator after training remains within a certain threshold difference from the actual residual norm in the absence of attack. If the difference between the theoretical residual norm estimated by the residual norm generator and the actual residual norm exceeds this threshold, it is determined that the actual residual norm of the system has been affected by a GNSS spoofing attack, that is, the quadcopter has been subjected to a GNSS spoofing attack.

[0143] The difference between the theoretical residual norm and the actual residual norm is expressed as:

[0144] ,

[0145] The detection threshold is set as follows:

[0146] ,

[0147] in, and These represent sequences under no-attack conditions. The mean and variance, The length of the test dataset.

[0148] The attack detection logic is as follows:

[0149] ,

[0150] That is: if Exceeding the threshold If the condition is met, the quadcopter UAV system is determined to be under GNSS deception attack; otherwise, the quadcopter UAV system is determined not to be under GNSS deception attack.

[0151] To demonstrate the effectiveness of this application in detecting GNSS spoofing attacks, a quadcopter UAV system was used for verification. The parameters of the quadcopter UAV are shown in Table 1. The training parameters for the theoretical residual norm generator of the quadcopter UAV based on the LSTM network are shown in Table 2.

[0152] Table 1. Quadrotor UAV Parameters in GNSS Spoofing Attack Detection Scenarios

[0153]

[0154] Table 2. Hyperparameters related to the training of the LSTM-based quadrotor UAV theoretical residual norm generator proposed in this application.

[0155]

[0156] To verify the effectiveness of the proposed LSTM network-based GNSS spoofing attack detection method for quadcopter UAVs, attack detection was conducted under different UAV operating conditions and different attack scenarios.

[0157] First, consider periodic GNSS spoofing attacks during the autonomous path-following flight mode of a UAV, the form of which is as follows:

[0158] ,

[0159] in, This attack pattern indicates that the quadcopter drone is subjected to a constant GNSS spoofing attack every 150 moments for a period of 5 moments. Figure 2 and Figure 3 This paper demonstrates the impact of such GNSS spoofing attacks on the state estimation of quadrotor UAVs and the detection effect of the proposed LSTM network-based GNSS spoofing attack detection method for quadrotor UAVs.

[0160] Next, we consider continuous GNSS deception attacks in the remote-controlled flight mode of a drone, which take the following form:

[0161] ,

[0162] in, , Indicating a uniform distribution, this attack pattern means that the quadcopter drone is subjected to a continuous variable-amplitude GNSS spoofing attack between time 1500 and time 1800. Figure 4 and Figure 5 This paper demonstrates the impact of such GNSS spoofing attacks on the state estimation of quadrotor UAVs and the detection effect of the proposed LSTM network-based GNSS spoofing attack detection method for quadrotor UAVs.

[0163] According to the simulation results in the figure above, both representative GNSS spoofing attacks affect the system state estimation, leading to state estimation bias. The LSTM network-based GNSS spoofing attack detection method for quadrotor UAVs proposed in this application can effectively detect both representative GNSS spoofing attacks, thus verifying the effectiveness of the proposed LSTM network-based GNSS spoofing attack detection method for quadrotor UAVs.

[0164] like Figure 6 The diagram shows the principle of LSTM-based quadrotor UAV GNSS deception attack detection proposed in this application. Specifically, the EKF utilizes data from the IMU, magnetometer, and GNSS measurements of the quadrotor UAV's position, velocity, Euler angles, and body angular velocity to perform state estimation and obtain the actual state estimation residual norm. The LSTM network uses reliable sensor data from an IMU and a magnetometer to measure the velocity, Euler angles, and body angular velocity of a quadcopter drone, estimating the theoretical residual norm. Threshold-based detectors compare... and If the difference between the two exceeds a preset threshold, the quadcopter drone system is determined to be under GNSS deception attack.

[0165] like Figure 7 The diagram shows the network structure of the LSTM-based residual estimation network for the theoretical state estimation of a quadrotor UAV designed in this application. The network consists of a two-layer LSTM network, three FC layers, and two ReLU activation functions. The two-layer LSTM network extracts temporal information from the reliable variable sequence. The temporal feature vector output by the two-layer LSTM network undergoes feature transformation through two FC layers. After introducing nonlinearity through the ReLU activation function, it finally passes through one FC layer to output the estimated value of the residual norm for the theoretical state estimation of the quadrotor UAV. .

[0166] It should be noted that the specific embodiments are merely explanations and illustrations of the technical solution of the present invention and should not be used to limit the scope of protection. Any modifications made in accordance with the claims and specification of the present invention that are only partial should still fall within the protection scope of the present invention.

Claims

1. A method for detecting GNSS spoofing attacks on quadrotor UAVs based on LSTM, characterized in that... Includes the following steps: Step 1: Use an inertial measurement unit, magnetometer, and GNSS to obtain the position, velocity, Euler angles, and angular velocity of the quadcopter UAV; Step 2: Input the position, velocity, Euler angle, and angular velocity of the quadcopter UAV into the extended Kalman filter to obtain the actual value of the state estimation residual norm of the quadcopter UAV. ; Step 3: Input the speed, Euler angle, and body angular velocity of the quadcopter UAV into the trained LSTM network to obtain the estimated value of the state estimation residual norm of the quadcopter UAV. ; Step 4: Obtain the actual value of the residual norm of the state estimation of the quadcopter UAV. Compared with the estimated value The absolute value of the difference between the two is used to determine whether the quadcopter UAV system is under GNSS spoofing attack. If the absolute value of the difference exceeds a preset threshold, the quadcopter UAV system is determined to be under GNSS spoofing attack. Otherwise, the quadcopter UAV system is determined not to be under GNSS spoofing attack.

2. The method for detecting GNSS spoofing attacks on quadrotor UAVs based on LSTM according to claim 1, characterized in that... The LSTM network comprises a two-layer LSTM network and a three-layer FC layer. The two-layer LSTM network is used to extract temporal feature vectors. After the temporal feature vectors are passed through the three-layer FC layer, the estimated value of the residual norm of the quadcopter UAV state estimation is output. The first two fully connected (FC) layers both use the ReLU activation function.

3. The LSTM-based GNSS spoofing attack detection method for quadrotor UAVs according to claim 2, characterized in that... The estimated value of the residual norm of the state estimation of the quadrotor UAV Represented as: ， ， ， in, This represents the hidden state of the LSTM network. For network cell states, Represents the ReLU activation function. , This represents the weight matrix and bias of the FC layer. For reliable variable sequences, For the first The first layer of the LSTM network -1 output vector of LSTM units For the first The first layer of the LSTM network -1 hidden state vector of LSTM units, For sequence length, .

4. The LSTM-based GNSS spoofing attack detection method for quadrotor UAVs according to claim 3, characterized in that... The reliable variable sequence It is obtained through the following steps: Step 1: Constructing the dynamics of a quadcopter unmanned aerial vehicle system; Step 2: Discretize the dynamics of the quadcopter UAV system using the forward Euler method to obtain the discrete-time state equation; Step 3: Construct the measurement equations for the quadcopter UAV; Step 4: Perform extended Kalman filtering using the quadcopter UAV's measurement equations and discrete-time state equations to obtain the quadcopter UAV's state estimate. ; Step 5: Obtain the state measurement values ​​of the quadcopter UAV based on the measurement equations of the quadcopter UAV. And combined with the state estimation values ​​of the quadcopter UAV The state estimation residuals of the quadcopter UAV are obtained. Step 6: The residuals of the quadcopter UAV state estimation have a zero-mean Gaussian distribution, and the covariance matrix is ​​obtained. ; Step 7: Based on the covariance matrix The variables involved in the Jacobian matrix are identified, and a reliable variable sequence is then constructed. .

5. The LSTM-based GNSS spoofing attack detection method for quadrotor UAVs according to claim 4, characterized in that... The dynamic representation of the quadcopter unmanned aerial vehicle system is as follows: ， ， ， ， ， ， ， ， ， in, For the quality of drones, Location of the drone. These are the Euler angles for the drone, namely roll, pitch, and yaw angles, respectively. The angular velocities of the UAV body are roll, pitch, and yaw angular velocities, respectively. For the total lift of the drone, , , These are the roll, pitch, and yaw moments of the drone, respectively. It is the acceleration due to gravity. Sampling time, For about Moment of inertia of the shaft For about Moment of inertia of the shaft For about Moment of inertia of the shaft for The second derivative, for The second derivative, for The second derivative, for The first derivative, for The first derivative, for The first derivative, for The first derivative, for The first derivative, for The first derivative.

6. The method for detecting GNSS spoofing attacks on quadrotor UAVs based on LSTM according to claim 5, characterized in that... The discrete-time state equation is expressed as: ， in, Sampling time, For Gaussian process noise, The Gaussian measurement noise covariance matrix, for Real-time drone location for The drone's position at time -1 , , Quadrone drone Time along Axial direction, Axial direction and Velocity in the axial direction, , , Quadrone drone +1 time along Axial direction, Axial direction and Velocity in the axial direction, for Euler angles of the drone for +1 moment, drone Euler angles, for The angular velocity of the drone body at all times. for The angular velocity of the drone at time +1 , , They are respectively The drone's roll, pitch, and yaw moments are constantly being monitored. for Total lift of the drone at all times.

7. A method for detecting GNSS spoofing attacks on quadrotor UAVs based on LSTM according to claim 6, characterized in that... The measurement equation for the quadcopter UAV is expressed as follows: ， in, For Gaussian noise measurement, The Gaussian measurement noise covariance matrix, This is the measurement matrix.

8. The LSTM-based GNSS spoofing attack detection method for quadrotor UAVs according to claim 7, characterized in that... The extended Kalman filter is expressed as: ， ， ， ， ， in, for Jacobian matrix at time, These are the prior state estimates. The prior state estimation error covariance matrix is... To measure the transpose of the matrix, As a unit array, Here is the Kalman gain matrix. Let be the transpose of the state Jacobian matrix. For the system input vector, It is a nonlinear function.

9. A method for detecting GNSS spoofing attacks on quadrotor UAVs based on LSTM according to claim 8, characterized in that... The state estimation residual of the quadcopter UAV is expressed as follows: ， in, To estimate the residuals for the state.

10. A method for detecting GNSS spoofing attacks on quadrotor UAVs based on LSTM according to claim 9, characterized in that... The covariance matrix is ​​expressed as follows: ， in, This is the residual covariance matrix for state estimation.

Images