Hidden false data injection attack detection and safety control method for quad-rotor unmanned aerial vehicle

Abstract

The invention discloses a hidden false data injection attack detection and security control method for a quad-rotor unmanned aerial vehicle, and belongs to the technical field of information security. The problem that the hidden false data injection attack in the quad-rotor unmanned aerial vehicle system cannot be detected by the existing attack detection method is solved. According to the method, a watermark signal sequence and an auxiliary function are introduced to enable a residual signal to be sensitive to attacks, a residual signal calculation method based on linearization model observability and a parallel Kalman filter is provided, and hidden false data injection attack detection is further carried out on the residual signal. And control input is calculated based on a state estimation result of the parallel Kalman filter, so that safety control of the quad-rotor unmanned aerial vehicle is realized. The method can be applied to hidden false data injection attack detection and security control.

Description

Technical Field

[0001] The present invention belongs to the field of information security technology, and in particular relates to a concealed false data injection attack detection and security control method for a quad-rotor unmanned aerial vehicle. Background Art

[0002] Quadrotors are widely used in military and civilian fields due to their low price, excellent performance, convenient operation and diverse functions, such as aerial photography, pesticide spraying, environmental exploration, emergency rescue and military strikes. As a typical security-oriented cyber-physical system, the stable operation of quadrotors depends on reliable controllers, precise sensors, efficient actuators and real-time wireless communication. However, drones are vulnerable to network attacks during wireless communication. In recent years, network attacks on quadrotors have occurred frequently, posing a threat to economic security, infrastructure security, and people's lives and property. This makes how to ensure the safety of quadrotor drone systems a major problem that needs to be solved urgently. Although research related to quadrotor drone fault diagnosis has made continuous breakthroughs, drone physical failures are essentially different from network attacks. Moreover, since covert false data injection attacks hardly change the residual distribution of quadrotor drone systems and can bypass attack detectors in the system, designing detection methods and security control methods for covert false data injection attacks on quadrotors is of great significance to improving the safety of drones. Summary of the invention

[0003] The purpose of the present invention is to solve the problem that the existing attack detection method cannot detect the covert false data injection attack in the quad-rotor UAV system, and propose a covert false data injection attack detection and security control method for quad-rotor UAV.

[0004] The technical solution adopted by the present invention to solve the above technical problems is: a concealed false data injection attack detection and security control method for a quad-rotor 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 according to 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 x i,k-1 Update to x i,k , using the sensors deployed on the quadrotor drone to measure the output vector y of the i-th subsystemi,k ;

[0007] Step 3: Subsystem i output vector y i,k With helper functions Multiply and add the watermark sequence signal ξ to the multiplication result i,k , get the signal to be transmitted 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 Using signals Subtract 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 parallel Kalman filter based on the observability of the quadrotor drone 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 hidden false data injection attack detection results in step 6 i,k , and the control input of each subsystem is u i,k Send to a quadrotor drone;

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

[0013] Furthermore, the dynamic model of the quad-rotor drone at the hovering point is:

[0014]

[0015] Among them, p i′ represents the position of the quadrotor drone in the inertial coordinate system, is a real number, the superscript T represents transposition, 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] Yes 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; represents 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 quadcopter body coordinate system relative to the inertial coordinate system expressed in the quadcopter 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-order 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 drone 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 current state and the y-axis position of the quadrotor drone 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 quadcopter in the current state and the pitch attitude Euler angle when it is in equilibrium. 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 of the quadrotor drone 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 drone in the current state and the gravity in the equilibrium state, ΔL is the difference between the rolling moment of the quadrotor drone in the current state and the rolling moment in the equilibrium state, ΔM is the difference between the pitch moment of the quadrotor drone in the current state and the pitch moment in the equilibrium state, ΔN is the difference between the yaw moment of the quadrotor drone in the current state and the yaw moment in the equilibrium state, Δq, Δr and Δp are the differences between the angular velocity components of the quadrotor drone in the current state and the angular velocity components 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 according to 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 time, 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 time; u i,k-1 represents the control input vector of the ith 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 time, 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 51: From the output matrix C of the i-th subsystem i Select different rows to form a submatrix According to the matrix C i Total 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 watch;

[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, 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, 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, is the k-time submatrix The corresponding signal, is the k-time submatrix The corresponding covariance matrix of the state estimation error is, Representation and observable matrix The corresponding process noise covariance matrix, Representation and observable matrix The corresponding measurement noise covariance matrix;

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

[0042]

[0043] Residual 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 is If a concealed 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 hidden 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 hidden 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 attack that were attacked by covert false data injection.

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

[0052]

[0053] in, Yes 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 that are attacked by hidden false data injection, we get the matrix C i All row indices that have not been attacked by hidden false data injection are selected, and then any observable matrix pair corresponding to all row indices that have not been attacked by hidden false data injection is selected. Using the selected energy matrix And the observable matrix 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] Among them, X is the weight matrix.

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

[0062] The present invention designs an attack detection, attack positioning and safety control algorithm suitable for the false data injection attack situation of the sensor mechanism of a quad-rotor unmanned aerial vehicle system. By introducing a watermark signal sequence and an auxiliary function, the residual signal is made sensitive to the attack, and 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, thereby realizing the safety control of the quad-rotor 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 the safety controller is used under the covert false data injection attack;

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

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

[0070] Figure 4 It 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 concealed false data injection attack detection and security control method of the quadrotor drone of the present invention; DETAILED DESCRIPTION

[0072] Specific implementation method 1: Combination Figure 5 The present embodiment describes a method for detecting and safely controlling a concealed false data injection attack on a quad-rotor 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 according to 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 x i,k-1 Update to x i,k , using the sensors deployed on the quadrotor drone to measure the output vector y of the i-th subsystem i,k ;

[0075] Step 3: Subsystem i output vector y i,k With helper functions Multiply and add the watermark sequence signal ξ to the multiplication result i,k , get the signal to be transmitted 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 value is first multiplied by the auxiliary function, and then the multiplication result is added with the watermark signal. After the estimator receives the signal, it first subtracts the watermark signal from the received signal, and then divides the subtraction result by the auxiliary function.

[0078] Step 4: The control center receives the signal transmitted from the sensor communication network Using signals Subtract 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 parallel Kalman filter based on the observability of the quadrotor drone 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 hidden false data injection attack detection results in step 6 i,k , and the control input of each subsystem is u i,k Send to a quadrotor drone;

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

[0083] like Figure 4 As shown in the figure, the physical processes and state estimators in the quadrotor drone system are connected through a wireless network. The sensor-controller side and the controller-actuator side both exchange information through an open and shared communication network. Malicious attackers can obtain system knowledge by monitoring the quadrotor drone system, including a simple model of the physical system and the equipped attack detection mechanism. The attacker constructs a covert false data attack based on this knowledge and injects this malicious data into the sensor measurement signal, thereby destroying the system performance or manipulating and crashing the drone.

[0084] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the dynamic model of the quad-rotor 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′ represents the position of the quadrotor drone in the inertial coordinate system, is a real number, the superscript T represents transposition, 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. Yes 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; represents 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 quadcopter body coordinate system relative to the inertial coordinate system expressed in the quadcopter 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-order 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] The 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 drone in the inertial reference frame, respectively.

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

[0092] Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 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 current state and the y-axis position of the quadrotor drone 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 quadcopter in the current state and the pitch attitude Euler angle when it is in equilibrium. 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 of the quadrotor drone 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 drone in the current state and the gravity in the equilibrium state, ΔL is the difference between the rolling moment of the quadrotor drone in the current state and the rolling moment in the equilibrium state, ΔM is the difference between the pitch moment of the quadrotor drone in the current state and the pitch moment in the equilibrium state, ΔN is the difference between the yaw moment of the quadrotor drone in the current state and the yaw moment in the equilibrium state, Δq, Δr and Δp are the differences between the angular velocity components of the quadrotor drone in the current state and the angular velocity components 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 Specific Embodiments 1 to 3.

[0099] Specific implementation method five: This implementation method is different from the specific implementation methods one to four in that the linearized quadcopter drone model defines the state space and input space, and then establishes the linearized state equation of the quadcopter 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 drone 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 time, 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 time; u i,k-1 represents the control input vector of the ith 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 time, 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, respectively. 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 Specific Embodiments 1 to 4.

[0110] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that the specific process of step 5 is as follows:

[0111] Step 51: From the output matrix C of the i-th subsystem i Select different rows to form a submatrix According to the matrix C i Total 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 watch;

[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, 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, 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, is the k-time submatrix The corresponding signal, is the k-time submatrix The corresponding covariance matrix of the state estimation error is, Representation and observable matrix The corresponding process noise covariance matrix, Representation and observable matrix The corresponding measurement noise covariance matrix;

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

[0117]

[0118] Residual 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 Specific Implementation Methods 1 to 5.

[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 implementation method 7: This implementation method is different from one of the specific implementation methods 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 concealed 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 hidden 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 hidden 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 attack that were attacked by covert false data injection.

[0128] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[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, and the elements on the diagonal are all 0 or 1, which is used to describe which sensor data is attacked.

[0132] Specific implementation eight: This implementation differs from any one of specific implementations one to seven in that the threshold 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 Specific Embodiments 1 to 7.

[0136] Specific implementation method 9: This implementation method is different from the specific implementation methods 1 to 8 in that the specific process of step 7 is as follows:

[0137] According to all the row indices that are attacked by hidden false data injection, we get the matrix C i All row indices that have not been attacked by hidden false data injection are selected, and then any observable matrix pair corresponding to all row indices that have not been attacked by hidden false data injection is selected. (After determining all the row indexes that have not been attacked by hidden 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 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 implementation method ten: This implementation method is different from the specific implementation methods one to nine 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 Section

[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 A quadrotor drone with a time interval of Δt=0.005s between adjacent sampling moments is used to apply the attack detection and security control method proposed in the present invention, and then impose false data injection attacks on its different subsystems to verify the effectiveness of the method of 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 It represents the difference between the speed of the current state of the drone in the x-axis direction of the inertial coordinate system and the speed of the hovering point in the x-axis direction of the inertial coordinate system. 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 pitch angular velocity of the drone's current state and the pitch angular velocity of the hovering point state;

[0150] When k ≥ 100, the attacker launches a covert false data injection attack on the quadrotor drone in the form of The 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 prove that the attack detection method proposed in the present invention can effectively detect covert attacks. Using the attack location determination process, the output vector index corresponding to the Kalman filter that triggers the alarm is {1,2,3,4}, and the output vector index corresponding to the Kalman filter that does not trigger the alarm is {1,2,3}. The attacked sensor data is the fourth one. This result is completely consistent with the actual situation of the attack, proving the effectiveness of the attack location method proposed in the present invention. 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 the present invention can quickly eliminate the impact of hidden attacks and restore the system control performance, verifying its effectiveness.

[0152] like Figure 4 The figure shows the control system block diagram of the covert attack detection and security control method of the quadrotor drone. 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 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 calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for detecting and safely controlling covert false data injection attacks on quad-rotor 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 according to 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 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 output vector y i,k With helper functions Multiply and add the watermark sequence signal ξ to the multiplication result i,k , get the signal to be transmitted 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 Using signals Subtract 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 a parallel Kalman filter based on the observability of the quadrotor drone system. 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 hidden false data injection attack detection results in step 6 i,k , and the control input of each subsystem is u i,k Send to a 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 of a quad-rotor 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′ represents the position of the quadrotor drone in the inertial coordinate system, is a real number, the superscript T represents transposition, 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. Yes 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; represents 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 quadcopter body coordinate system relative to the inertial coordinate system expressed in the quadcopter 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-order 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 of a quad-rotor drone according to claim 2 is characterized in that: 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 drone in the inertial reference frame, respectively.

4. The method for detecting and safely controlling concealed false data injection attacks of a quad-rotor 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 current state and the y-axis position of the quadrotor drone 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 quadcopter in the current state and the pitch attitude Euler angle when it is in equilibrium. 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 of the quadrotor drone 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 drone in the current state and the gravity in the equilibrium state, ΔL is the difference between the rolling moment of the quadrotor drone in the current state and the rolling moment in the equilibrium state, ΔM is the difference between the pitch moment of the quadrotor drone in the current state and the pitch moment in the equilibrium state, ΔN is the difference between the yaw moment of the quadrotor drone in the current state and the yaw moment in the equilibrium state, Δq, Δr and Δp are the differences between the angular velocity components of the quadrotor drone in the current state and the angular velocity components 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 of a quad-rotor 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 time, 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 time; u i,k-1 represents the control input vector of the ith 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 time, 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 of a quad-rotor drone according to claim 5 is characterized in that: The specific process of step five is as follows: Step 51: From the output matrix C of the i-th subsystem i Select different rows to form a submatrix According to the matrix C i Total 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 watch; 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, 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, 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, is the k-time submatrix c ir The corresponding signal, is the k-time submatrix The corresponding covariance matrix of the state estimation error is, Representation and observable matrix The corresponding process noise covariance matrix, Representation and observable matrix The corresponding measurement noise covariance matrix; Step 53: Calculate the energy matrix pair 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 concealed false data injection attacks of a quad-rotor drone according to claim 6, characterized in that: 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 is If a concealed 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 hidden 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 hidden 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 attack that were attacked by covert false data injection.

8. The method for detecting and safely controlling concealed false data injection attacks of a quad-rotor drone according to claim 7, characterized in that: The threshold γ i The calculation method is: in, yes β is the false alarm rate.

9. The method for detecting and safely controlling concealed false data injection attacks of a quad-rotor drone according to claim 8, characterized in that: The specific process of step seven is as follows: According to all the row indices attacked by hidden false data injection, we get the matrix C i All row indices that have not been attacked by hidden false data injection are selected, and then any observable matrix pair corresponding to all row indices that have not been attacked by hidden false data injection is selected. Using the selected energy matrix And the observable matrix 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 concealed false data injection attacks of a quad-rotor drone according to claim 9, characterized in that: The calculation method of the intermediate variable S is: Among them, X is the weight matrix.

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