Covert false data injection attack detection and security control method for quadrotor drones

Abstract

A method for detecting and safely controlling covert false data injection attacks on quadrotor drones belongs to the field of information security technology. The present invention solves the problem that existing attack detection methods are unable to detect covert false data injection attacks in quadrotor drone systems. The present invention makes the residual signal sensitive to attacks by introducing a watermark signal sequence and an auxiliary function, and proposes a residual signal calculation method based on linearized model observability and a parallel Kalman filter. The residual signal is further subjected to covert false data injection attack detection, and the control input is calculated based on the state estimation result of the parallel Kalman filter to achieve safe control of the quadrotor drone. The method of the present invention can be applied to the detection and safety control of covert false data injection attacks.

Description

Technical Field

[0001] The present invention belongs to the field of information security technology, and in particular relates to a covert false data injection attack detection and security control method for a quadrotor unmanned aerial vehicle (UAV). Background Art

[0002] Quadcopter drones (UAVs) are widely used in military and civilian applications due to their low price, excellent performance, convenient operation, and diverse functionality, such as aerial photography, pesticide spraying, environmental exploration, emergency rescue, and military strikes. As a typical secure cyber-physical system, the stable operation of UAVs relies on reliable controllers, precise sensors, efficient actuators, and real-time wireless communications. However, during wireless communications, UAVs are vulnerable to cyberattacks. In recent years, cyberattacks targeting quadcopters have become frequent, posing a threat to economic security, infrastructure safety, and public life and property. This has made ensuring the security of quadcopter UAV systems a critical issue that needs to be addressed. While research on quadcopter fault diagnosis has continued to make breakthroughs, physical UAV failures are fundamentally different from cyberattacks. Furthermore, since covert false data injection attacks barely alter the residual distribution of a quadcopter system, they can bypass attack detectors in the system. Therefore, designing detection and security control methods for covert false data injection attacks against quadcopters is of great significance for improving UAV security. Summary of the Invention

[0003] The purpose of the present invention is to solve the problem that existing attack detection methods cannot detect covert false data injection attacks in quadrotor drone systems, and propose a covert false data injection attack detection and security control method for quadrotor drones.

[0004] The technical solution adopted by the present invention to solve the above technical problems is: a covert false data injection attack detection and security control method for a quadrotor drone, the method specifically comprising the following steps:

[0005] Step 1: Linearize the dynamic model of the quadrotor drone at the hovering point to obtain a linearized quadrotor drone model; define the state space and input space based on the linearized quadrotor drone model, and then establish the linearized state equation of the quadrotor drone based on the state space and input space;

[0006] Step 2: The i-th subsystem of the quadrotor drone receives the control signal u sent by the controller i,k-1 After that, the state vector of the i-th subsystem is represented by x i,k-1 Update to x i,k , using sensors deployed on the quadrotor drone to measure the output vector y of the i-th subsystemi,k ;

[0007] Step 3: Subsystem i’s output vector y i,k With helper functions Multiply and add watermark sequence signal ξ to the multiplication result i,k , get the signal to be transmitted And the signal to be transmitted Send to the control center through the sensor communication network;

[0008] Step 4: The control center receives the signal transmitted from the sensor communication network Utilizing signals Subtracted watermark signal ξ i,k , and then divide the subtraction result by the auxiliary function After that, we get the signal y' i,k ;

[0009] Step 5: Deploy the parallel Kalman filter based on the observability of the quadrotor UAV system, and use the parallel Kalman filter and signal y' i,k Perform state estimation and then calculate the residual signal based on the state estimation result;

[0010] Step 6: Use χ 2 The detector performs covert false data injection attack detection on the residual signal;

[0011] Step 7: Calculate the control input u of each subsystem based on the detection results of the covert false data injection attack in step 6 i,k , and input the control of each subsystem into u i,k Send to quadrotor drone;

[0012] Step 8: Set k=k+1 and return to step 2.

[0013] Furthermore, the dynamic model of the quadrotor drone at the hovering point is:

[0014]

[0015] Among them, p i′ Indicates the position of the quadrotor drone in the inertial coordinate system, is a real number, the superscript T represents the transpose, x represents the x-axis position of the quadrotor drone in the inertial coordinate system, y represents the y-axis position of the quadrotor drone in the inertial coordinate system, and z represents the z-axis position of the quadrotor drone in the inertial coordinate system.

[0016] It is p i′ The second derivative of ; m is the mass of the quadrotor drone; Represents the propeller lift in the quadcopter body coordinate system; vector Used to describe the direction of gravity, g is the acceleration due to gravity; Indicates the angular velocity of the quadcopter body coordinate system relative to the inertial coordinate system, is the coordinate transformation matrix; represents the angular velocity of the quadrotor drone body coordinate system relative to the inertial coordinate system expressed in the quadrotor drone body coordinate system, and p, q and r are ω b The components of each coordinate axis direction in the quadrotor drone body coordinate system, Yes b The first derivative of ; W is the direction cosine matrix; I b =diag(I xx ,I yy ,I zz ) is the moment of inertia of the three main axes of the quadrotor drone; M b Represents the torque in the quadrotor drone body coordinate system, L, M and N are the rolling moment, pitching moment and yaw moment respectively.

[0017] Furthermore, the coordinate transformation matrix And the direction cosine matrix W are:

[0018]

[0019] Among them, φ, θ, and ψ represent the roll, pitch, and yaw attitude Euler angles of the quadrotor UAV in the inertial reference frame, respectively.

[0020] Furthermore, the linearized quadrotor drone model is:

[0021] When the quadrotor drone is in a hovering state, the yaw attitude Euler angle is 0, then T = mg, L = M = N = 0, φ = θ = ψ = 0;

[0022] The linearized quadrotor drone model is:

[0023]

[0024] Among them, Δx is the difference between the x-axis position of the quadrotor drone in the inertial coordinate system when it is in the current state and the x-axis position of the quadrotor drone in the inertial coordinate system when it is in the equilibrium state. is the second-order derivative of Δx; Δy is the difference between the y-axis position of the quadrotor drone in the inertial coordinate system when it is in the current state and the y-axis position of the quadrotor drone in the inertial coordinate system when it is in the equilibrium state. is the second-order derivative of Δy; Δz is the difference between the z-axis position of the quadrotor drone in the current state and the z-axis position of the quadrotor drone in the equilibrium state. is the second-order derivative of Δz; Δθ is the difference between the pitch attitude Euler angle of the quadrotor drone when it is in the current state and the pitch attitude Euler angle when it is in the equilibrium state, is the first-order derivative of Δθ; Δφ is the difference between the Euler angle of the roll attitude of the quadrotor drone when it is in the current state and the Euler angle of the roll attitude when it is in the equilibrium state, is the first-order derivative of Δφ; Δψ is the difference between the yaw attitude Euler angle when the quadrotor drone is in the current state and the yaw attitude Euler angle when it is in the equilibrium state, is the first derivative of Δψ;

[0025] ΔT is the difference between the gravity of the quadrotor when it is in the current state and the gravity when it is in the equilibrium state, ΔL is the difference between the rolling moment of the quadrotor when it is in the current state and the rolling moment when it is in the equilibrium state, ΔM is the difference between the pitching moment of the quadrotor when it is in the current state and the pitching moment when it is in the equilibrium state, ΔN is the difference between the yaw moment of the quadrotor when it is in the current state and the yaw moment when it is in the equilibrium state, Δq, Δr and Δp are the differences between the angular velocity components of the quadrotor when it is in the current state and the angular velocity components when it is in the equilibrium state, is the first derivative of Δp; is the first derivative of Δq; is the first derivative of Δr.

[0026] Furthermore, the linearized quadrotor drone model defines a state space and an input space, and then establishes a linearized state equation of the quadrotor drone based on the state space and the input space; the specific process is:

[0027] Define the state space and input space:

[0028]

[0029]

[0030] Where x is the state space, u is the input space, u1=ΔT, u2=ΔL, u3=ΔM, u4=ΔN;

[0031] Then the linearized state equation of the quadrotor drone is:

[0032] x i,k =A i x i,k-1 +B i ui,k-1 +ω i,k ,

[0033] y i,k =C i x i,k +v i,k ,

[0034] Among them, x i,k represents the state vector of the i-th subsystem at the k-th moment, n x,i is the dimension of the system state vector; x i,k-1 represents the state vector of the i-th subsystem at the k-1th moment; u i,k-1 represents the control input vector of the i-th subsystem at the k-1th time, n u,i is the dimension of the system input vector; y i,k represents the output vector of the i-th subsystem at the k-th moment, n y,i is the dimension of the system measurement vector; ω i,k and v i,k Represent the independent Gaussian random process noise and measurement noise at the kth moment, A i is the system matrix of the ith subsystem, B i is the input matrix of the ith subsystem, C i is the output matrix of the ith subsystem.

[0035] Furthermore, the specific process of step five is as follows:

[0036] Step 5.1: From the output matrix C of the i-th subsystem i Select different rows to form a submatrix According to the matrix C i A total of sub-matrices, Judgment matrix pair Whether it meets: Among them, rank(·) represents the rank of the calculated matrix;

[0037] If it satisfies, then the matrix can be observed; if it is not satisfied, then the matrix Cannot observe;

[0038] Step 52: The observable matrix Recorded as For each observable matrix pair Deploy a Kalman filter respectively. The form of the Kalman filter is:

[0039]

[0040] in, is the k-1 time submatrix The corresponding state vector estimate, is the one-step prediction result of the state vector, is the k-1 time submatrix The corresponding covariance matrix of the state estimation error, is the one-step prediction result of the covariance matrix of the state estimation error. The superscript -1 represents the inverse of the matrix. is the k-time submatrix The corresponding Kalman filter gain, is the k-time submatrix The corresponding state vector estimate, is the k-time submatrix The corresponding signal, is the k-time submatrix The corresponding covariance matrix of the state estimation error, Representation and observability matrix The corresponding process noise covariance matrix, Representation and observability matrix The corresponding measurement noise covariance matrix;

[0041] Step 53: Calculate the observable matrix The corresponding residual signal

[0042]

[0043] residuals is a zero-mean Gaussian random distribution variable;

[0044] Step 54: Calculate the residual signal The covariance matrix of

[0045]

[0046] Furthermore, the specific process of step six is ​​as follows:

[0047]

[0048] in, is the length of the detection window, is a statistic;

[0049] The statistics With threshold γ i For comparison, if The state estimation result If a covert false data injection attack is detected, the detector triggers an alarm, otherwise the detector does not trigger an alarm;

[0050] If the state estimation result If a covert false data injection attack is detected in The rows in the matrix C i The corresponding row index in is added to the set M. If the state estimation result If no covert false data injection attack is detected in The rows in the matrix C i The corresponding row index in is added to the set N; after traversing the state estimation results corresponding to the i-th subsystem, all elements in MN are the matrix C i The index of all rows in the that were attacked by covert false data injection.

[0051] Furthermore, the threshold γ i The calculation method is:

[0052]

[0053] in, It is g ir,k >γ i β is the false alarm rate.

[0054] Furthermore, the specific process of step seven is as follows:

[0055] According to all the row indices attacked by covert false data injection, we get the matrix C i All row indices that have not been attacked by covert false data injection are selected, and then any observable matrix pair corresponding to all row indices that have not been attacked by covert false data injection is selected. Using the selected observable matrix And the observable matrix pair The corresponding state vector estimate calculates the control input u of the i-th subsystem i,k :

[0056]

[0057] Among them, S is the intermediate variable and U is the weight matrix.

[0058] Furthermore, the calculation method of the intermediate variable S is:

[0059]

[0060] Where X is the weight matrix.

[0061] The beneficial effects of the present invention are:

[0062] The present invention designs an attack detection, attack location and safety control algorithm suitable for the false data injection attack scenario of the sensor mechanism of a quadrotor unmanned aerial vehicle system. By introducing a watermark signal sequence and an auxiliary function, the residual signal is made sensitive to the attack. A residual signal calculation method based on the observability of a linearized model and a parallel Kalman filter is proposed. The residual signal is further subjected to covert false data injection attack detection, and the control input is calculated based on the state estimation result of the parallel Kalman filter to achieve safe control of the quadrotor unmanned aerial vehicle. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is a parallel Kalman filter that does not trigger an alarm;

[0064] Taking g[1,2,3] as an example, g[1,2,3] represents the corresponding submatrix From C i The rows selected in are row 1, row 2 and row 3;

[0065] Figure 2 is the parallel Kalman filter that triggers the alarm;

[0066] Figure 3a It is the state trajectory of the first state of the third subsystem when using the security controller under the covert false data injection attack;

[0067] Figure 3b It is the state trajectory of the second state of the third subsystem when using the security controller under the covert false data injection attack;

[0068] Figure 3c It is the state trajectory of the third state of the third subsystem when using the security controller under the covert false data injection attack;

[0069] Figure 3d It is the state trajectory of the fourth state of the third subsystem when using the security controller under the covert false data injection attack;

[0070] Figure 4 This is a block diagram of the attack detection and safety control system for a quadrotor drone under covert attack;

[0071] Figure 5 It is a flow chart of the method for detecting and safely controlling covert false data injection attacks on a quadrotor drone of the present invention; DETAILED DESCRIPTION

[0072] Specific implementation method 1: Combination Figure 5 This embodiment describes a method for detecting and controlling covert false data injection attacks on a quadrotor drone, the method specifically comprising the following steps:

[0073] Step 1: Linearize the dynamic model of the quadrotor drone at the hovering point to obtain a linearized quadrotor drone model; define the state space and input space based on the linearized quadrotor drone model, and then establish the linearized state equation of the quadrotor drone based on the state space and input space;

[0074] Step 2: The i-th subsystem of the quadrotor drone receives the control signal u sent by the controller i,k-1 After that, the state vector of the i-th subsystem is represented by x i,k-1 Update to x i,k , using sensors deployed on the quadrotor drone to measure the output vector y of the i-th subsystem i,k ;

[0075] Step 3: Subsystem i’s output vector y i,k With helper functions Multiply and add watermark sequence signal ξ to the multiplication result i,k , get the signal to be transmitted And the signal to be transmitted Send to the control center through the sensor communication network;

[0076] The watermark sequence signal consists of two cryptographically protected pseudo-random number generators that share the same random number seed and are able to generate the same watermark sequence signal ζ on both sides. i,k , and the watermark sequence signal corresponding to each subsystem is the same.

[0077] Helper Functions is the system control input u i,k-1 A nonlinear function of e is the base of the natural logarithm, and ‖·‖2 is the L2 norm. Before being sent to the estimator, the sensor measurement is first multiplied by the auxiliary function, and the result is then watermarked. After receiving the signal, the estimator subtracts the watermark signal from the received signal and divides the result by the auxiliary function.

[0078] Step 4: The control center receives the signal transmitted from the sensor communication network Utilizing signals Subtracted watermark signal ξ i,k , and then divide the subtraction result by the auxiliary function After that, we get the signal y' i,k ;

[0079] Step 5: Deploy the parallel Kalman filter based on the observability of the quadrotor UAV system, and use the parallel Kalman filter and signal y' i,k Perform state estimation and then calculate the residual signal based on the state estimation result;

[0080] Step 6: Use χ 2 The detector performs covert false data injection attack detection on the residual signal;

[0081] Step 7: Calculate the control input u of each subsystem based on the detection results of the covert false data injection attack in step 6 i,k , and input the control of each subsystem into u i,k Send to quadrotor drone;

[0082] Step 8: Set k=k+1 and return to step 2.

[0083] like Figure 4 As shown, the physical processes and state estimators within the quadrotor drone system are connected via a wireless network. Information exchange between the sensor-controller and controller-actuator interfaces takes place over an open and shared communication network. By monitoring the quadrotor drone system, malicious attackers can gain system knowledge, including a simplified model of the physical system and the attack detection mechanisms employed. Using this knowledge, attackers can construct covert false data attacks and inject this malicious data into sensor measurement signals, potentially disrupting system performance or manipulating or crashing the drone.

[0084] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that the dynamic model of the quadrotor drone at the hovering point is:

[0085]

[0086] Among them, the subscript i′ represents the inertial coordinate system; the subscript b represents the quadrotor drone body coordinate system; p i′ Indicates the position of the quadrotor drone in the inertial coordinate system, is a real number, the superscript T represents the transpose, x represents the x-axis position of the quadrotor drone in the inertial coordinate system, y represents the y-axis position of the quadrotor drone in the inertial coordinate system, and z represents the z-axis position of the quadrotor drone in the inertial coordinate system. It is p i′ The second derivative of ; m is the mass of the quadrotor drone; Represents the propeller lift in the quadcopter body coordinate system; vector Used to describe the direction of gravity, g is the acceleration due to gravity; Indicates the angular velocity of the quadcopter body coordinate system relative to the inertial coordinate system, is the coordinate transformation matrix; represents the angular velocity of the quadrotor drone body coordinate system relative to the inertial coordinate system expressed in the quadrotor drone body coordinate system, and p, q and r are ω bThe components of each coordinate axis direction in the quadrotor drone body coordinate system, Yes b The first derivative of ; W is the direction cosine matrix; I b =diag(I xx ,I yy ,I zz ) is the moment of inertia of the three main axes of the quadrotor drone; M b Represents the torque in the quadrotor drone body coordinate system, L, M and N are the rolling moment, pitching moment and yaw moment respectively.

[0087] Other steps and parameters are the same as those in the first embodiment.

[0088] Specific implementation method three: This implementation method is different from specific implementation methods one or two in that the coordinate transformation matrix And the direction cosine matrix W are:

[0089]

[0090] Among them, φ, θ, and ψ represent the roll, pitch, and yaw attitude Euler angles of the quadrotor UAV in the inertial reference frame, respectively.

[0091] Other steps and parameters are the same as those in the first or second embodiment.

[0092] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that the linearized quadrotor drone model is:

[0093] When the quadrotor drone is in a hovering state, the yaw attitude Euler angle is 0, then T = mg, L = M = N = 0, φ = θ = ψ = 0;

[0094] The linearized quadrotor drone model is:

[0095]

[0096] Among them, Δx is the difference between the x-axis position of the quadrotor drone in the inertial coordinate system when it is in the current state and the x-axis position of the quadrotor drone in the inertial coordinate system when it is in the equilibrium state. is the second-order derivative of Δx; Δy is the difference between the y-axis position of the quadrotor drone in the inertial coordinate system when it is in the current state and the y-axis position of the quadrotor drone in the inertial coordinate system when it is in the equilibrium state. is the second-order derivative of Δy; Δz is the difference between the z-axis position of the quadrotor drone in the current state and the z-axis position of the quadrotor drone in the equilibrium state. is the second-order derivative of Δz; Δθ is the difference between the pitch attitude Euler angle of the quadrotor drone when it is in the current state and the pitch attitude Euler angle when it is in the equilibrium state, is the first-order derivative of Δθ; Δφ is the difference between the Euler angle of the roll attitude of the quadrotor drone when it is in the current state and the Euler angle of the roll attitude when it is in the equilibrium state, is the first-order derivative of Δφ; Δψ is the difference between the yaw attitude Euler angle when the quadrotor drone is in the current state and the yaw attitude Euler angle when it is in the equilibrium state, is the first derivative of Δψ;

[0097] ΔT is the difference between the gravity of the quadrotor when it is in the current state and the gravity when it is in the equilibrium state, ΔL is the difference between the rolling moment of the quadrotor when it is in the current state and the rolling moment when it is in the equilibrium state, ΔM is the difference between the pitching moment of the quadrotor when it is in the current state and the pitching moment when it is in the equilibrium state, ΔN is the difference between the yaw moment of the quadrotor when it is in the current state and the yaw moment when it is in the equilibrium state, Δq, Δr and Δp are the differences between the angular velocity components of the quadrotor when it is in the current state and the angular velocity components when it is in the equilibrium state, is the first derivative of Δp; is the first derivative of Δq; is the first derivative of Δr.

[0098] The other steps and parameters are the same as those in the first to third embodiments.

[0099] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the linearized quadrotor drone model defines the state space and input space, and then establishes the linearized state equation of the quadrotor drone based on the state space and input space; the specific process is:

[0100] Define the state space and input space:

[0101]

[0102]

[0103] Where x is the state space, u is the input space, u1=ΔT, u2=ΔL, u3=ΔM, u4=ΔN;

[0104] The state space and output space are divided into four independent parts, each of which can generate a state equation as a subsystem.

[0105] Considering the influence of system noise and measurement noise during sensor measurement, the linearized state equation of the quadrotor UAV is:

[0106] x i,k =A i x i,k-1 +B i u i,k-1 +ω i,k ,

[0107] y i,k =C i x i,k +v i,k ,

[0108] Among them, x i,k represents the state vector of the i-th subsystem at the k-th moment, n x,i is the dimension of the system state vector; x i,k-1 represents the state vector of the i-th subsystem at the k-1th moment; u i,k-1 represents the control input vector of the i-th subsystem at the k-1th time, n u,i is the dimension of the system input vector; y i,k represents the output vector of the i-th subsystem at the k-th moment, n y,i is the dimension of the system measurement vector; ω i,k and v i,k represent the independent Gaussian random process noise and measurement noise at the kth moment, A i is the system matrix of the ith subsystem, B i is the input matrix of the ith subsystem, C i is the output matrix of the ith subsystem.

[0109] The other steps and parameters are the same as those in the first to fourth embodiments.

[0110] Specific embodiment 6: This embodiment differs from any one of specific embodiments 1 to 5 in that the specific process of step 5 is as follows:

[0111] Step 5.1: From the output matrix C of the i-th subsystem i Select different rows to form a submatrix According to the matrix C i A total of sub-matrices (including matrix C i itself), Judgment matrix pair Whether it meets: Among them, rank(·) represents the rank of the calculated matrix;

[0112] If it satisfies, then the matrix can be observed; if it is not satisfied, then the matrix Cannot observe;

[0113] Step 52: The observable matrix Recorded as For each observable matrix pair Deploy a Kalman filter respectively. The form of the Kalman filter is:

[0114]

[0115] in, is the k-1 time submatrix The corresponding state vector estimate, is the one-step prediction result of the state vector, is the k-1 time submatrix The corresponding covariance matrix of the state estimation error, is the one-step prediction result of the covariance matrix of the state estimation error. The superscript -1 represents the inverse of the matrix. is the k-time submatrix The corresponding Kalman filter gain, is the k-time submatrix The corresponding state vector estimate, is the k-time submatrix The corresponding signal, is the k-time submatrix The corresponding covariance matrix of the state estimation error, Representation and observability matrix The corresponding process noise covariance matrix, Representation and observability matrix The corresponding measurement noise covariance matrix;

[0116] Step 53: Calculate the observable matrix The corresponding residual signal

[0117]

[0118] residuals is a zero-mean Gaussian random distribution variable,

[0119] Step 54: Calculate the residual signal The covariance matrix of

[0120]

[0121] The other steps and parameters are the same as those in the first to fifth embodiments.

[0122] After determining the attacked sensor measurements, only the unattacked sensor measurements are used for state estimation to obtain an accurate system state estimate.

[0123] Specific embodiment 7: This embodiment differs from any one of specific embodiments 1 to 6 in that the specific process of step 6 is as follows:

[0124]

[0125] in, is the length of the detection window, g ir,k is a statistic;

[0126] The statistic g ir,k With threshold γ i For comparison, if g ir,k >γ i , then the state estimation result If a covert false data injection attack is detected, the detector triggers an alarm, otherwise the detector does not trigger an alarm;

[0127] If the state estimation result If a covert false data injection attack is detected in The rows in the matrix C i The corresponding row index in is added to the set M. If the state estimation result If no covert false data injection attack is detected in The rows in the matrix C i The corresponding row index in is added to the set N; after traversing the state estimation results corresponding to the i-th subsystem, all elements in MN are the matrix C i The index of all rows in the that were attacked by covert false data injection.

[0128] The other steps and parameters are the same as those in the first to sixth embodiments.

[0129] Under the covert False Data Injection (FDI) attack, the system sensor measurements are tampered with to:

[0130]

[0131] in, Represents the attack vector, Γ is a diagonal matrix with all diagonal elements being 0 or 1, which is used to describe which sensor data is attacked.

[0132] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the threshold value γ i The calculation method is:

[0133]

[0134] in, yes β is the false alarm rate.

[0135] The other steps and parameters are the same as those in the first to seventh embodiments.

[0136] Specific embodiment 9: This embodiment differs from any one of specific embodiments 1 to 8 in that the specific process of step 7 is as follows:

[0137] According to all the row indices attacked by covert false data injection, we get the matrix C i All row indices that have not been attacked by covert false data injection are selected, and then any observable matrix pair corresponding to all row indices that have not been attacked by covert false data injection is selected. (After determining all the row indices that have not been attacked by covert false data injection, there may be more than one observable matrix pair corresponding to these rows, and any one can be selected here). And the observable matrix pair The corresponding state vector estimate calculates the control input u of the i-th subsystem i,k :

[0138]

[0139] Among them, S is the intermediate variable, U is the weight matrix, and U>0.

[0140] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0141] Specific embodiment 10: This embodiment differs from any one of specific embodiments 1 to 9 in that the calculation method of the intermediate variable S is:

[0142]

[0143] Where X is the weight matrix, X≥0.

[0144] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0145] Experimental part

[0146] In order to demonstrate the attack detection, attack location and security control effects of the present invention under the covert false data injection attack, the mass is selected to be 1.5 kg, and the three-axis rotation inertia is Ixx =I yy =0.05kg·m 2 , I zz =0.1kg·m 2 The attack detection and security control method proposed in the present invention is applied to a quadrotor drone with a time interval of Δt=0.005s between adjacent sampling moments, and false data injection attacks are then applied to its different subsystems to verify the effectiveness of the method proposed in the present invention.

[0147] Consider the third subsystem in the linearized model of the quadrotor drone:

[0148]

[0149] in, u k =ΔL,x 1,k Indicates the difference between the current position of the drone in the x-axis direction of the inertial coordinate system and the hovering point position in the x-axis direction of the inertial coordinate system, x 2,k Indicates the difference between the current state of the drone in the x-axis direction of the inertial coordinate system and the hovering point state in the x-axis direction of the inertial coordinate system, x 3,k Indicates the difference between the pitch angle of the current state of the drone and the pitch angle of the hovering point state, x 4,k Indicates the difference between the current pitch velocity of the drone and the pitch velocity of the hovering point;

[0150] When k ≥ 100, the attacker launches a covert false data injection attack on the quadrotor drone in the form of Attack detector results are as follows Figure 1 and Figure 2 The safety controller results are as follows. Figure 3a 、 Figure 3b 、 Figure 3c and Figure 3d shown.

[0151] Figure 1 and Figure 2 The attack detection results demonstrate that the proposed attack detection method is effective in detecting covert attacks. Using the attack localization process, the Kalman filter output vector indexes corresponding to the triggering alarm are {1, 2, 3, 4}, while the Kalman filter output vector indexes corresponding to the non-alarming Kalman filter are {1, 2, 3}. Therefore, the attacked sensor data is the fourth one. This result fully aligns with the actual attack scenario, demonstrating the effectiveness of the proposed attack localization method. Figure 3a 、 Figure 3b 、 Figure 3c and Figure 3dThe security control results show that based on the attack positioning, the security control method proposed in this invention can quickly eliminate the impact of covert attacks and restore system control performance, verifying its effectiveness.

[0152] like Figure 4 The following is a block diagram of the control system for the covert attack detection and security control method of the quadrotor UAV. It includes auxiliary functions for covert attack detection, watermark sequence signal generation module and χ 2 Attack detector module, parallel Kalman filter module for state estimation and attack localization, and safety controller module for safety control and the physical process of quadrotor drone. The attacker launches a covert false data injection attack during the sensor data transmission stage, where u is the control input and y is the sensor measurement value. is the auxiliary function, ξ is the watermark signal, The sensor measurement value is multiplied by the auxiliary function and the watermark signal is added to the signal sent to the communication network, y a is the attack vector, is the signal after network transmission, y' is the signal used for state estimation after subtracting the watermark signal and dividing by the auxiliary function, z r is the parallel residual sequence generated by the parallel Kalman filter, is the state estimate used to calculate the control input.

[0153] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A method for detecting and controlling covert false data injection attacks on quadrotor drones, characterized in that: The method specifically comprises the following steps: Step 1: Linearize the dynamic model of the quadrotor drone at the hovering point to obtain a linearized quadrotor drone model; define the state space and input space based on the linearized quadrotor drone model, and then establish the linearized state equation of the quadrotor drone based on the state space and input space; Step 2: The i-th subsystem of the quadrotor drone receives the control signal u sent by the controller i,k-1 After that, the state vector of the i-th subsystem is represented by x i,k-1 Update to x i,k , using sensors deployed on the quadrotor drone to measure the output vector y of the i-th subsystem i,k ; Step 3: Subsystem i’s output vector y i,k With helper functions Multiply and add watermark sequence signal ξ to the multiplication result i,k , get the signal to be transmitted And the signal to be transmitted Send to the control center through the sensor communication network; Step 4: The control center receives the signal transmitted from the sensor communication network Utilizing signals Subtracted watermark signal ξ i,k , and then divide the subtraction result by the auxiliary function After that, we get the signal y′ i,k ; Step 5: Deploy the parallel Kalman filter based on the observability of the quadrotor UAV system, and use the parallel Kalman filter and signal y i ' ,k Perform state estimation and then calculate the residual signal based on the state estimation result; Step 6: Use χ 2 The detector performs covert false data injection attack detection on the residual signal; Step 7: Calculate the control input u of each subsystem based on the detection results of the covert false data injection attack in step 6 i,k , and input the control of each subsystem into u i,k Send to quadrotor drone; Step 8: Set k=k+1 and return to step 2.

2. The method for detecting and safely controlling covert false data injection attacks on a quadrotor drone according to claim 1 is characterized in that: The dynamic model of the quadrotor drone at the hovering point is: Among them, p i′ Indicates the position of the quadrotor drone in the inertial coordinate system, is a real number, the superscript T represents the transpose, x represents the x-axis position of the quadrotor drone in the inertial coordinate system, y represents the y-axis position of the quadrotor drone in the inertial coordinate system, and z represents the z-axis position of the quadrotor drone in the inertial coordinate system. It is p i′ The second derivative of ; m is the mass of the quadrotor drone; Represents the propeller lift in the quadcopter body coordinate system; vector Used to describe the direction of gravity, g is the acceleration due to gravity; Indicates the angular velocity of the quadcopter body coordinate system relative to the inertial coordinate system, is the coordinate transformation matrix; represents the angular velocity of the quadrotor drone body coordinate system relative to the inertial coordinate system expressed in the quadrotor drone body coordinate system, and p, q and r are ω b The components of each coordinate axis direction in the quadrotor drone body coordinate system, Yes b The first derivative of ; W is the direction cosine matrix; I b =diag(I xx ,I yy ,I zz ) is the moment of inertia of the three main axes of the quadrotor drone; M b Represents the torque in the quadrotor drone body coordinate system, L, M and N are the rolling moment, pitching moment and yaw moment respectively.

3. The method for detecting and safely controlling covert false data injection attacks on a quadrotor drone according to claim 2, wherein: The coordinate transformation matrix And the direction cosine matrix W are: Among them, φ, θ, and ψ represent the roll, pitch, and yaw attitude Euler angles of the quadrotor UAV in the inertial reference frame, respectively.

4. The method for detecting and safely controlling covert false data injection attacks on a quadrotor drone according to claim 3 is characterized in that: The linearized quadrotor drone model is: When the quadrotor drone is in a hovering state, the yaw attitude Euler angle is 0, then T = mg, L = M = N = 0, φ = θ = ψ = 0; The linearized quadrotor drone model is: Among them, Δx is the difference between the x-axis position of the quadrotor drone in the inertial coordinate system when it is in the current state and the x-axis position of the quadrotor drone in the inertial coordinate system when it is in the equilibrium state. is the second-order derivative of Δx; Δy is the difference between the y-axis position of the quadrotor drone in the inertial coordinate system when it is in the current state and the y-axis position of the quadrotor drone in the inertial coordinate system when it is in the equilibrium state. is the second-order derivative of Δy; Δz is the difference between the z-axis position of the quadrotor drone in the inertial coordinate system when it is in the current state and the z-axis position of the quadrotor drone in the inertial coordinate system when it is in the equilibrium state. is the second-order derivative of Δz; Δθ is the difference between the pitch attitude Euler angle of the quadrotor drone when it is in the current state and the pitch attitude Euler angle when it is in the equilibrium state, is the first-order derivative of Δθ; Δφ is the difference between the Euler angle of the roll attitude of the quadrotor drone when it is in the current state and the Euler angle of the roll attitude when it is in the equilibrium state, is the first-order derivative of Δφ; Δψ is the difference between the yaw attitude Euler angle when the quadrotor drone is in the current state and the yaw attitude Euler angle when it is in the equilibrium state, is the first derivative of Δψ; ΔT is the difference between the gravity of the quadrotor when it is in the current state and the gravity when it is in the equilibrium state, ΔL is the difference between the rolling moment of the quadrotor when it is in the current state and the rolling moment when it is in the equilibrium state, ΔM is the difference between the pitching moment of the quadrotor when it is in the current state and the pitching moment when it is in the equilibrium state, ΔN is the difference between the yaw moment of the quadrotor when it is in the current state and the yaw moment when it is in the equilibrium state, Δq, Δr and Δp are the differences between the angular velocity components of the quadrotor when it is in the current state and the angular velocity components when it is in the equilibrium state, is the first derivative of Δp; is the first derivative of Δq; is the first derivative of Δr.

5. The method for detecting and safely controlling covert false data injection attacks on a quadrotor drone according to claim 4 is characterized in that: The linearized quadrotor drone model defines the state space and input space, and then establishes the linearized state equation of the quadrotor drone based on the state space and input space; the specific process is: Define the state space and input space: Where x is the state space, u is the input space, u1=ΔT, u2=ΔL, u3=ΔM, u4=ΔN; Then the linearized state equation of the quadrotor drone is: x i,k =A i x i,k-1 +B i u i,k-1 +ω i,k , y i,k =C i x i,k +v i,k , Among them, x i,k represents the state vector of the i-th subsystem at the k-th moment, n x,i is the dimension of the system state vector; x i,k-1 represents the state vector of the i-th subsystem at the k-1th moment; u i,k-1 represents the control input vector of the i-th subsystem at the k-1th time, n u,i is the dimension of the system input vector; y i,k represents the output vector of the i-th subsystem at the k-th moment, n y,i is the dimension of the system measurement vector; ω i,k and v i,k Represent the independent Gaussian random process noise and measurement noise at the kth moment, A i is the system matrix of the ith subsystem, B i is the input matrix of the ith subsystem, C i is the output matrix of the ith subsystem.

6. The method for detecting and safely controlling covert false data injection attacks on a quadrotor drone according to claim 5, wherein: The specific process of step five is: Step 5.1: From the output matrix C of the i-th subsystem i Select different rows to form a submatrix According to the matrix C i A total of sub-matrices, Judgment matrix pair Whether it meets: Among them, rank(·) represents the rank of the calculated matrix; If it satisfies, then the matrix can be observed; if it is not satisfied, then the matrix Cannot observe; Step 52: The observable matrix Recorded as For each observable matrix pair Deploy a Kalman filter respectively. The form of the Kalman filter is: in, is the k-1 time submatrix The corresponding state vector estimate, is the one-step prediction result of the state vector, is the k-1 time submatrix The corresponding covariance matrix of the state estimation error, is the one-step prediction result of the covariance matrix of the state estimation error. The superscript -1 represents the inverse of the matrix. is the k-time submatrix The corresponding Kalman filter gain, is the k-time submatrix The corresponding state vector estimate, is the k-time submatrix c ir The corresponding signal, is the k-time submatrix The corresponding covariance matrix of the state estimation error, Representation and observability matrix The corresponding process noise covariance matrix, Representation and observability matrix The corresponding measurement noise covariance matrix; Step 53: Calculate the observable matrix The corresponding residual signal residual is a zero-mean Gaussian random distribution variable; Step 54: Calculate the residual signal The covariance matrix of 7. The method for detecting and safely controlling covert false data injection attacks on a quadrotor drone according to claim 6, wherein: The specific process of step six is ​​as follows: in, is the length of the detection window, is a statistic; The statistics With threshold γ i For comparison, if The state estimation result If a covert false data injection attack is detected, the detector triggers an alarm, otherwise the detector does not trigger an alarm; If the state estimation result If a covert false data injection attack is detected in The rows in the matrix C i The corresponding row index in is added to the set M. If the state estimation result If no covert false data injection attack is detected in The rows in the matrix C i The corresponding row index in is added to the set N; after traversing the state estimation results corresponding to the i-th subsystem, all elements in MN are the matrix C i The index of all rows in the that were attacked by covert false data injection.

8. The method for detecting and safely controlling covert false data injection attacks on a quadrotor drone according to claim 7, wherein: The threshold γ i The calculation method is: in, yes β is the false alarm rate.

9. The method for detecting and safely controlling covert false data injection attacks on a quadrotor drone according to claim 8, wherein: The specific process of step seven is as follows: According to all the row indices attacked by covert false data injection, we get the matrix C i All row indices that have not been attacked by covert false data injection are selected, and then any observable matrix pair corresponding to all row indices that have not been attacked by covert false data injection is selected. Using the selected observable matrix And the observable matrix pair The corresponding state vector estimate calculates the control input u of the i-th subsystem i,k : Among them, S is the intermediate variable and U is the weight matrix.

10. The method for detecting and safely controlling covert false data injection attacks on a quadrotor drone according to claim 9, wherein: The calculation method of the intermediate variable S is: Where X is the weight matrix.

Images