Four-rotor unmanned aerial vehicle concealed attack detection method based on innovation sequence

Abstract

The invention discloses a four-rotor unmanned aerial vehicle covert attack detection method based on an innovation sequence, and belongs to the technical field of information security. According to the invention, the problem that the existing four-rotor unmanned aerial vehicle system cannot detect the network attack of the information sequence is solved. According to the method, a four-rotor unmanned aerial vehicle dynamic equation is discretized through a forward Euler discretization method, a four-rotor unmanned aerial vehicle full-state system equation is obtained, and a system output equation is given. Then, a dynamic watermark function technology is utilized to enable distribution of an innovation sequence to be sensitive to attack signals, the innovation sequence is transmitted in a sensor communication network, then a network attack detection form based on the innovation sequence and residual errors is designed, and expansion Kalman filters are deployed at a four-rotor unmanned aerial vehicle end and a control center end respectively; and designing a remote state estimation method of the quad-rotor unmanned aerial vehicle, and continuing to control the quad-rotor unmanned aerial vehicle based on a state estimation result. The method can be applied to the four-rotor unmanned aerial vehicle hidden attack detection based on the innovation sequence.

Description

Technical Field

[0001] The present invention belongs to the field of information security technology, and in particular relates to a method for detecting covert attacks of a quad-rotor unmanned aerial vehicle based on an information sequence. Background Art

[0002] Quadcopter drones 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 other scenarios. As a typical security-oriented cyber-physical system, the stable operation of quadcopter drones depends on reliable controllers, precise sensors, efficient actuators and real-time wireless communication. However, drones are vulnerable to network attacks during wireless communication, which makes how to ensure the security of quadcopter drone systems a major problem that needs to be solved urgently. The method of transmitting new information sequences in the sensor communication network instead of directly transmitting sensor measurements to achieve remote state estimation can prevent attackers from obtaining the true state of the drone by eavesdropping on communication data, thereby greatly reducing the risk of the drone being captured by attackers. However, the existing quadcopter drone system lacks detection technology for network attacks based on new information sequences. Summary of the invention

[0003] The purpose of the present invention is to solve the problem that the existing quad-rotor UAV system cannot detect network attacks based on innovation sequences, and to propose a quad-rotor UAV covert attack detection method based on innovation sequences.

[0004] The technical solution adopted by the present invention to solve the above technical problems is: a method for detecting a concealed attack of a quad-rotor drone based on an innovation sequence, the method specifically comprising the following steps:

[0005] Step 1: discretize the dynamic equation of the quadrotor drone to obtain the full-state system equation of the quadrotor drone, and obtain the system output equation based on the full-state system equation of the quadrotor drone;

[0006] Step 2: The quadrotor drone receives the control signal U sent by the control center at time k-1 k-1 After that, the state vector of the quadrotor drone is X k-1 Update to X k , use the sensor deployed on the quadcopter to measure the state of the quadcopter, and record the sensor's measurement value as Y k ;

[0007] Step 3: The extended Kalman filter deployed locally on the quadrotor drone uses the sensor measurement value Y k Calculate the innovation sequence Z k ;

[0008] Step 4: Give the new information sequence Z k Add dynamic watermark function Get the new information sequence Z' k , and then the new information sequence Z' k Send to the control center via the communication network;

[0009] Step 5: The control center receives the new information sequence in the communication network After that, the new information sequence Subtract watermark function Get the new information sequence

[0010] Step 6: Use χ 2 The detector responds to the new information sequence Conduct attack detection;

[0011] If an attack is detected, the detector will sound an alarm and continue to step seven;

[0012] Otherwise, go directly to step 7;

[0013] Step 7: The extended Kalman filter deployed in the control center is used to analyze the new information sequence Processing to obtain the remote state estimate

[0014] Furthermore, the discretization of the dynamic equations of the quad-rotor drone adopts a forward Euler discretization method.

[0015] Furthermore, the dynamic equation of the quad-rotor drone is discretized to obtain the full-state system equation of the quad-rotor drone. The specific process is:

[0016] The dynamic equation of the quadrotor drone is:

[0017]

[0018] Where m is the mass of the quadcopter; x, y, and z represent the position of the quadcopter in the directions of the coordinate axes of the inertial reference system. is the second derivative of x, is the second derivative of y, is the second-order derivative of z; T is the total lift generated by the propeller of the quadrotor drone; φ, θ and ψ represent the roll, pitch and yaw attitude Euler angles of the quadrotor drone in the inertial reference frame respectively; g is the gravitational acceleration; I xx ,I yy and I zzThey represent the moments of inertia of the quadrotor drone around each main axis, L, M and N represent the rolling moment, pitching moment and yaw moment in the body reference system, respectively, and p, q and r are the angular velocities of the body reference system relative to the inertial reference system expressed in the directions of the coordinate axes of the body reference system;

[0019] The angular velocity conversion relationship is expressed as:

[0020]

[0021] in, is the first derivative of φ, is the first-order derivative of θ, is the first derivative of ψ;

[0022] The position, velocity, Euler angle and body angular velocity of the quadrotor drone are taken as the system state, and the process noise is introduced to obtain the full state system equation of the quadrotor drone:

[0023]

[0024] Among them, x k ,y k and z k They represent the position of the quadrotor drone in the inertial reference system at time k, u k , v k and w k They represent the speed of the quadrotor drone in the inertial reference system at time k, δt represents the time interval between two adjacent moments, and φ k ,θ k and ψ k They represent the roll, pitch and yaw Euler angles of the quadrotor drone in the inertial reference frame at time k, respectively, and W k-1 represents the process noise matrix at time k-1; p k ,q k and r k are the angular velocities of the body reference system relative to the inertial reference system in the directions of the coordinate axes of the body reference system at time k; k-1 ,y k-1 and z k-1 They represent the position of the quadrotor drone in the inertial reference frame at time k-1, u k-1 , v k-1 and w k-1 They represent the speed of the quadrotor drone in the inertial reference frame at time k-1, φ k-1 ,θ k-1 and ψ k-1 They represent the roll, pitch and yaw Euler angles of the quadrotor drone in the inertial reference frame at time k-1 respectively; p k-1 ,q k-1and r k-1 are the angular velocities of the body reference system relative to the inertial reference system in the directions of the coordinate axes of the body reference system at time k-1;

[0025] Rewrite the full state system equation of the quadrotor drone into the following form:

[0026] X k =f(X k-1 ,U k-1 )+W k-1 ,

[0027] Among them, X k represents the state vector at time k, X k-1 represents the state vector at time k-1; f(X k-1 ,U k-1 ) represents the nonlinear system state equation; U k-1 is the vector composed of the four motor speeds of the quadcopter, U k-1 =[Ω 1,k-1 Ω 2,k-1 Ω 3,k-1 Ω 4,k-1 ] T ;

[0028] The total lift, rolling moment, pitch moment and yaw moment of the quadrotor drone are calculated by the motor speed:

[0029]

[0030] Among them, k T is the propeller lift coefficient, k D is the torque coefficient of the propeller, l is the distance from the motor to the center of the quadcopter, L k-1 、M k-1 and N k-1 are the rolling moment, pitching moment and yaw moment in the body reference system at time k-1, T k-1 It is the total lift generated by the propeller of the quadcopter at time k-1.

[0031] Furthermore, the system output equation is obtained according to the full-state system equation of the quadrotor drone, and the specific process is:

[0032] The system output equation taking into account the measurement noise is:

[0033] Y k =HX k +V k ,

[0034] Among them, Y kis the output vector at time k; H is the output matrix of the nonlinear system, V k represents the measurement noise matrix.

[0035] Furthermore, the specific process of step three is:

[0036]

[0037] in, is the estimated value of the state vector of the quadrotor drone at time k-1, is the one-step prediction of the quadrotor drone state vector at time k, P k-1 is the estimated value of the state estimation error covariance matrix at time k-1, is the one-step prediction of the state estimation error covariance matrix at time k, K k is the gain matrix at time k, F k-1 is the Jacobian matrix at time k-1, is the estimated value of the state vector of the quadrotor drone at time k, P k is the estimated value of the covariance matrix of the state estimation error at time k, I is the identity matrix, Q is the covariance matrix of the system process noise, and R is the covariance matrix of the system measurement noise;

[0038]

[0039] Among them, Z k is the new information sequence at time k.

[0040] Furthermore, the Jacobian matrix F at the k-1 moment k-1 Specifically:

[0041] Jacobian matrix F k-1 The submatrix F in 1:3,1:3 、F 4:6,4:6 、F 1:3,4:6 、F 4:6,7:9 、F 7:9,7:9 and F 10:12,10:12 satisfy:

[0042] F 1:3,1:3 =F 4:6,4:6 =I 3×3 ,

[0043]

[0044]

[0045] In the Jacobian matrix F k-1 In the divisor matrix F 1:3,1:3 、F 4:6,4:6 、F 1:3,4:6 、F4:6,7:9 、F 7:9,7:9 and F 10:12,10:12 Except for the position where , all other elements are 0.

[0046] Furthermore, the dynamic watermark function is a zero-mean one-dimensional Gaussian distribution random process, dynamic watermark function It is deployed on both the quadcopter and the remote control center.

[0047] Furthermore, the specific process of step six is ​​as follows:

[0048]

[0049] Among them, g k is the detection statistic at time k, is the length of the detection window, is the covariance matrix, γ is the detection threshold, H1 indicates that an attack is detected, and H0 indicates that an attack is not detected. k ≥γ, the test result is H1. k When <γ, the test result is H0;

[0050]

[0051] where ‖·‖2 is the L2 norm.

[0052] Furthermore, the method further includes step eight, specifically:

[0053] Estimated value based on remote state Calculate the control input U at time k k , then set k=k+1 and return to step 2.

[0054] The beneficial effects of the present invention are:

[0055] The present invention discretizes the dynamic equation of the quadrotor drone by the forward Euler discretization method, obtains the full-state system equation of the quadrotor drone, and gives the system output equation. Then, the dynamic watermark function technology is used to make the distribution of the new information sequence sensitive to the attack signal, and the new information sequence is transmitted in the sensor communication network, and then a network attack detection form based on the new information sequence and the residual is designed. The extended Kalman filter is deployed at the quadrotor drone end and the control center end respectively, and the remote state estimation method of the quadrotor drone is designed, and the quadrotor drone control is continued based on the state estimation result. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a schematic diagram of the reference trajectory, long-range estimation and actual trajectory of a quadrotor drone in three-dimensional space;

[0057] Figure 2 is to use only χ 2 The detection result diagram of the detector;

[0058] Figure 3 It is a test result diagram of the method of the present invention;

[0059] Figure 4 It is a schematic diagram of the data relationship between the two EKFs during the remote state estimation process of a quadrotor drone;

[0060] Figure 5 It is a block diagram of a covert network attack detection and control system based on an information sequence of the present invention;

[0061] Figure 6 It is a flow chart of a method for detecting a concealed attack of a quad-rotor drone based on an information sequence of the present invention. DETAILED DESCRIPTION

[0062] Specific implementation method 1: Combination Figure 6 The present embodiment describes a method for detecting a concealed attack of a quad-rotor drone based on an innovation sequence, and the method specifically comprises the following steps:

[0063] Step 1: discretize the dynamic equation of the quadrotor drone to obtain the full-state system equation of the quadrotor drone, and obtain the system output equation based on the full-state system equation of the quadrotor drone;

[0064] Step 2: The quadrotor drone receives the control signal U sent by the control center at time k-1 k-1 After that, the state vector of the quadrotor drone is X k-1 Update to X k , use the sensor deployed on the quadcopter to measure the state of the quadcopter, and record the sensor's measurement value as Y k ;

[0065] Step 3: The extended Kalman filter deployed locally on the quadrotor drone uses the sensor measurement value Y k Calculate the innovation sequence Z k ;

[0066] Step 4: Give the new information sequence Z k Add dynamic watermark function Get the new information sequence Z' k , and then the new information sequence Z' k Send to the control center via the communication network;

[0067] Step 5: The control center receives the new information sequence in the communication network After that, the new information sequence Subtract watermark function Get the new information sequence

[0068] Step 6: Use χ 2 The detector responds to the new information sequence Perform attack detection (detect potential network attacks by analyzing the statistical properties of the received news sequence, including mean and covariance);

[0069] If an attack is detected, the detector will sound an alarm (prompting that an attack has been made and taking corresponding measures), and then proceed to step seven;

[0070] Otherwise, go directly to step 7;

[0071] Step 7: The extended Kalman filter deployed in the control center is used to analyze the new information sequence Processing to obtain the remote state estimate

[0072]

[0073] in, is the Jacobian matrix of the control center. In the absence of a cyber attack, the extended Kalman filter deployed locally on the quadcopter and the extended Kalman filter deployed by the remote control center have exactly the same form.

[0074] In order to remotely estimate the state of the quadrotor drone, an extended Kalman filter (EKF) is deployed on the drone side and the remote estimation center side. In the process of quadrotor drone state estimation, the relationship between the two extended Kalman filters is as follows: Figure 4 As shown in the figure. The UAV-side (local) EKF estimates the UAV state and sends the calculated new information sequence to the remote estimation center through the wireless sensor network. During the wireless transmission of the new information sequence, malicious attackers may attack the new information sequence. The remote estimation center uses the received new information sequence and calculates the remote estimated system state through another EKF.

[0075] Specific implementation method 2: This implementation method is different from specific implementation method 1 in that the forward Euler discretization method is used to discretize the dynamic equations of the quad-rotor drone.

[0076] The other steps and parameters are the same as those in the first embodiment.

[0077] Specific implementation method three: This implementation method is different from specific implementation method one or two in that the dynamic equation of the quad-rotor drone is discretized to obtain the full-state system equation of the quad-rotor drone. The specific process is:

[0078] The dynamic equation of the quadrotor drone is:

[0079]

[0080] Where m is the mass of the quadcopter; x, y, and z represent the position of the quadcopter in the directions of the coordinate axes of the inertial reference system. is the second derivative of x, is the second derivative of y, is the second-order derivative of z; T is the total lift generated by the propeller of the quadrotor drone; φ, θ and ψ represent the roll, pitch and yaw attitude Euler angles of the quadrotor drone in the inertial reference frame respectively; g is the gravitational acceleration; I xx ,I yy and I zz They represent the moments of inertia of the quadrotor drone around each main axis, L, M and N represent the rolling moment, pitching moment and yaw moment in the body reference system, respectively, and p, q and r are the angular velocities of the body reference system relative to the inertial reference system expressed in the directions of the coordinate axes of the body reference system;

[0081] The angular velocity conversion relationship is expressed as:

[0082]

[0083] in, is the first derivative of φ, is the first-order derivative of θ, is the first derivative of ψ;

[0084] The position, velocity, Euler angle and body angular velocity of the quadrotor drone are taken as the system state, and the process noise is introduced to obtain the full state system equation of the quadrotor drone:

[0085]

[0086] Among them, x k ,y k and z k They represent the position of the quadrotor drone in the inertial reference system at time k, u k , v k and w k They represent the speed of the quadrotor drone in the inertial reference system at time k, δt represents the time interval between two adjacent moments, and φ k ,θ k and ψ k They represent the roll, pitch and yaw Euler angles of the quadrotor drone in the inertial reference frame at time k, respectively, and W k-1 represents the process noise matrix at time k-1, p k ,qk and r k are the angular velocities of the body reference system relative to the inertial reference system in the directions of the coordinate axes of the body reference system at time k; k-1 ,y k-1 and z k-1 They represent the position of the quadrotor drone in the inertial reference frame at time k-1, u k-1 , v k-1 and w k-1 They represent the speed of the quadrotor drone in the inertial reference frame at time k-1, φ k-1 ,θ k-1 and ψ k-1 They represent the roll, pitch and yaw Euler angles of the quadrotor drone in the inertial reference frame at time k-1 respectively; p k-1 ,q k-1 and r k-1 are the angular velocities of the body reference system relative to the inertial reference system in the directions of the coordinate axes of the body reference system at time k-1;

[0087] Rewrite the full state system equation of the quadrotor drone into the following form:

[0088] X k =f(X k-1 ,U k-1 )+W k-1 ,

[0089] Among them, X k represents the state vector at time k, X k-1 represents the state vector at time k-1; f(X k-1 ,U k-1 ) represents the nonlinear system state equation (equivalent to the first term on the right side of the above equation); U k-1 is the vector composed of the four motor speeds of the quadcopter, U k-1 =[Ω 1,k-1 Ω 2,k-1 Ω 3,k-1 Ω 4,k-1 ] T ;

[0090] The total lift, rolling moment, pitch moment and yaw moment of the quadrotor drone are calculated by the motor speed:

[0091]

[0092] Among them, k T is the propeller lift coefficient, k D is the torque coefficient of the propeller, l is the distance from the motor to the center of the quadcopter, L k-1 、Mk-1 and N k-1 are the rolling moment, pitching moment and yaw moment in the body reference system at time k-1, T k-1 It is the total lift generated by the propeller of the quadcopter at time k-1.

[0093] The other steps and parameters are the same as those in the first or second embodiment.

[0094] Specific implementation method 4: This implementation method is different from one of the specific implementation methods 1 to 3 in that the system output equation is obtained according to the full-state system equation of the quad-rotor drone, and the specific process is:

[0095] Since the quadrotor drone is equipped with sensors including GPS, barometer, accelerometer, gyroscope, magnetometer, etc., all 12 state variables of the quadrotor drone can be measured by the sensors.

[0096] The system output equation taking into account the measurement noise is:

[0097] Y k =HX k +V k ,

[0098] Among them, Y k is the output vector at time k, H is the output matrix of the nonlinear system, V k represents the measurement noise matrix,

[0099] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0100] Specific implementation method 5: This implementation method is different from the specific implementation methods 1 to 4 in that the specific process of step 3 is as follows:

[0101]

[0102] in, is the estimated value of the state vector of the quadrotor drone at time k-1, is the one-step prediction of the quadrotor drone state vector at time k, P k-1 is the estimated value of the state estimation error covariance matrix at time k-1, P k - is the one-step prediction of the state estimation error covariance matrix at time k, K k is the gain matrix at time k, F k-1 is the Jacobian matrix at time k-1, is the estimated value of the state vector of the quadrotor drone at time k, P kis the estimated value of the covariance matrix of the state estimation error at time k, I is the identity matrix, Q is the covariance matrix of the system process noise, and R is the covariance matrix of the system measurement noise;

[0103]

[0104] Among them, Z k is the new information sequence at time k.

[0105] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0106] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that the Jacobian matrix F at the k-1 time k-1 Specifically:

[0107] Jacobian matrix F k-1 The submatrix F in 1:3,1:3 、F 4:6,4:6 、F 1:3,4:6 、F 4:6,7:9 、F 7:9,7:9 and F 10:12,10:12 satisfy:

[0108] F 1:3,1:3 =F 4:6,4:6 =I 3×3 ,

[0109]

[0110]

[0111] In the Jacobian matrix F k-1 In the divisor matrix F 1:3,1:3 、F 4:6,4:6 、F 1:3,4:6 、F 4:6,7:9 、F 7:9,7:9 and F 10:12,10:12 Except for the position where , all other elements are 0.

[0112] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0113] F 1:3,1:3 For example, F 1:3,1:3 represents the submatrix consisting of the elements located in rows 1 to 3 and columns 1 to 3, and the same applies to other submatrices.

[0114] Specific implementation method 7: This implementation method is different from any one of the specific implementation methods 1 to 6 in that the dynamic watermark function is a zero-mean one-dimensional Gaussian random process, whose distribution is Dynamic watermark function It is deployed on both the quadcopter and the remote control center, and the attacker cannot know its specific form.

[0115] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0116] After the network attack changes the sequence of new information, the form of the sequence of new information becomes

[0117]

[0118] Because Z k , b k , All are zero-mean Gaussian distributions and are independent of each other. The covariance matrix of the new information sequence after the attack is:

[0119]

[0120] Therefore, by choosing a suitable dynamic watermark function The distribution covariance matrix Λ of can easily cause the distribution of the new information sequence to change significantly in the case of an attack, that is,

[0121]

[0122] This indicates that the attack detection method of the present invention can ensure that the attack is detected by the detector.

[0123] The working process of the dynamic watermark function is as follows:

[0124] At time k, the new information calculated by the drone is annotated with a dynamic watermark function and transmitted to the control center through the communication network. After receiving the new information, the control center removes the dynamic watermark function and uses the obtained data for state estimation and attack detection.

[0125] Specific implementation eight: This implementation differs from one of specific implementations one to seven in that the specific process of step six is ​​as follows:

[0126] Based on the covariance matrix of the innovation sequence distribution The normalized residual sum of squares is used to determine whether an attack has occurred:

[0127]

[0128] Among them, g k is the detection statistic at time k, is the length of the detection window, is the covariance matrix, γ is the detection threshold, H1 indicates that an attack is detected, and H0 indicates that an attack is not detected. k ≥γ, the test result is H1. kWhen <γ, the test result is H0;

[0129]

[0130] where ‖·‖2 is the L2 norm.

[0131] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0132] Residual-based detectors are usually deployed in remote control centers to detect potential network attacks by analyzing the statistical properties of the received news sequence (including mean and covariance). The news sequence Z sent by the quadcopter to the remote control center k is zero mean, Σ k is its covariance matrix. Among them,

[0133] In the quad-rotor drone system, since the state of the quad-rotor drone changes during flight, F k The matrix is ​​time-varying. According to the form of the extended Kalman filter, However, since the inertia, Euler angles, and angular velocity of the quadcopter are limited during actual flight, the matrix The norm of has a supremum, and the following formula is defined:

[0134]

[0135] According to the Jacobian matrix F k In the form of ‖F k ‖2>‖I‖2, that is, F k The norm of has an infimum, and then the matrix The norm of has an infimum, which can be obtained by extending the Kalman filter formula by k Set it as the unit matrix, and the stable value obtained by iteration is The infimum of . Therefore,

[0136]

[0137] Among them, S 2 =Q 2 +4QR. Since the sampling time interval δt of the quadrotor drone is usually very small, according to the Jacobian matrix F k In the form of, within a certain error range, Σ k The upper and lower bounds of the norm of are very close. Therefore, within this margin range, Can be approximated by Σ k , and used as the covariance detection indicator of the attack detector.

[0138] Specific implementation method 9: This implementation method is different from any one of specific implementation methods 1 to 8 in that the method further includes step 8, which is specifically:

[0139] Estimated value based on remote state Calculate the control input U at time k k , then set k=k+1 and return to step 2.

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

[0141] The form of covert attack based on the new information sequence and its destructive effect on the system state estimation:

[0142] Consider the following linear attack form:

[0143]

[0144] in, is an arbitrarily chosen matrix, is a column matrix of dimension 12×1.

[0145] Obviously, the new information sequence under attack is a zero-mean Gaussian distribution, and its covariance matrix is According to χ 2 The properties of the detector, if the attack satisfies:

[0146]

[0147] The attack cannot be detected.

[0148] because By collecting a large number of Σ k The obtained statistical value is very useful for attackers to obtain It is not easy to find the exact value of . Therefore, a reliable way to ensure the concealment of the attack is to avoid changing the distribution of the new information sequence after the attack. Specifically, the conditions for constructing a hidden attack sequence are:

[0149]

[0150] In addition, when T k =I,b k = 0, the new information sequence before and after the attack remains unchanged, and the attack is invalid. Therefore, the feasibility constraint of the attack is given:

[0151]

[0152] T k ≠I.

[0153] Next, we quantify the impact of attacks on remote estimates through mathematical derivation.

[0154] At time k, the remote prior estimates the state With the actual state X k The error covariance matrix between is:

[0155]

[0156] Remote A Posteriori State Estimation With the actual state X k The error covariance matrix between is:

[0157]

[0158] The last two terms in the above formula cannot be calculated directly. We need to recursively push them forward to the moment k=0. First, Recursively to time 0:

[0159]

[0160] When the attack does not occur, the local state estimate is exactly the same as the remote state estimate, so at time 0, we have Established. Since the new information sequence after the attack is a zero-mean Gaussian distribution, so at different times Independent of each other, that is, when i≠k,

[0161] In order to Recursively to time 0, we first need to Recursion to time 0

[0162]

[0163] Furthermore, Z can be obtained by the following formula k The form of recursion to time 0 is:

[0164]

[0165] Since the measurement noise matrix V and the attack offset matrix b are both zero-mean Gaussian distributions, it is not necessary to consider the items related to the measurement noise matrix V and the attack offset matrix b when calculating the covariance matrix.

[0166] According to the above recursive results, we can get

[0167]

[0168] The above calculation results are actually obtained through repeated iterations of two operations. In order to simplify the form of the calculation results, the following definition is used:

[0169] Mi (ζ)=(IK i H)ζ,

[0170]

[0171] The result can be written as:

[0172]

[0173] in, The symbol represents the composition of functions, such as represents g(h(x)). The “Ξ” symbol is used to represent nested functions.

[0174] Arranging the above formula, the remote estimation error covariance matrix is The iterative form is:

[0175]

[0176] In addition, in the attack constraint Solve the following optimization problem:

[0177]

[0178] The solution is T k =I,b k = 0. When T k =I,b k = 0, the iterative process of the remote estimation error covariance matrix under attack is exactly the same as that of the remote estimation error covariance matrix without attack. k Under the network attack with ≠I constraint, the system remote estimation error covariance matrix is The norm of is greater than the remote estimation error covariance matrix P when there is no attack k This indicates the destructiveness of the attack on the system state estimation.

[0179] The attack detection mechanism process proposed by the present invention is as follows: Figure 6 As shown in Figure 2, this attack detection mechanism can effectively detect covert attacks. Figure 4 , Figure 5 and Figure 6 The specific steps for detecting covert attacks based on the innovation sequence of a quadrotor drone are given as follows:

[0180] Step 1: The quadcopter receives the control signal U sent by the control center k-1 .

[0181] Step 2: The status of the quadcopter is determined by X k-1 Update to X k, the sensors deployed on the drone measure the drone state and output the sensor measurement value Y k .

[0182] Step 3: Locally extend the Kalman filter of the quadrotor drone using the sensor measurement value Y k Calculate the new information sequence Z k .

[0183] Step 4: New information sequence Z k Watermarking function Get Z' k Sent to the control center via the communication network.

[0184] Step 5: The control center receives the signal from the communication network Post-watermarking function get Used for attack detection.

[0185] Step 6: χ 2 The detector detects the new information sequence. If the detector alarms, it is determined that there is an attack in the system.

[0186] like Figure 4 As shown in the figure, the present invention proposes a covert network attack detection scheme based on the new information sequence. The quadrotor drone includes an actuator, a sensor, and a state estimator. The control center includes a state estimator, a controller, and an attack detector. The watermark function is used to assist in attack detection. The attacker launches a covert network attack during the transmission phase of the new information sequence. k-1 is the control input signal, Y k After executing the physical process, the system state X k The measured value, Z k The new information sequence calculated by the extended Kalman filter on the drone side, is the watermark function at time k, Z' k is the new information sequence signal after adding the watermark function, It is the signal that reaches the control center after being transmitted through the communication network. The new information sequence of the extended Kalman filter transmitted to the control center after the watermark function is subtracted. is the state estimation value calculated by the extended Kalman filter at the control center, U k To use Calculated control input.

[0187] Experimental Section

[0188] In order to demonstrate that the present invention can effectively detect the covert network attack of the quadrotor drone based on the new information sequence, the mass is 3.5 kg, and the three-axis rotation inertia is I xx =Iyy =0.05kg·m 2 , I zz =0.1kg·m 2 , the lift parameter is k T =2×10 -5 N·s 2 / rad 2 , the torque parameter is k T =1×10 -6 N·s 2 / rad 2 , the arm length is l = 0.5m, the sampling time interval is δt = 0.01s, and the quadrotor drone equipped with PID controller is used in the covert network attack T k =-I,b k =0, the detection method for covert attack of a quad-rotor drone based on an innovation sequence proposed in the present invention is applied to verify the effect of the present invention.

[0189] The reference trajectory of the quadcopter is generated by the segmented acceleration trajectory planning method. At 0 seconds, the drone takes off. At 93 seconds, the network attack occur. Figure 1 The trajectory tracking effect before and after the drone attack is shown. In the figure, "×" indicates the starting position of the drone, "five-pointed star" indicates the end point of the reference trajectory, "solid dot" indicates the end point of the drone's actual trajectory, "hollow circle" indicates the remote estimation and end point of the drone's trajectory, and "triangle" indicates that the attack occurred at that moment. Figure 1 As shown in the figure, after the attack, there is a huge error between the remote estimated trajectory of the drone and the actual trajectory. Affected by the estimation error, the actual trajectory of the drone deviates from the reference trajectory, which shows the impact of the attack on the performance of the drone.

[0190] In order to verify the effect of the attack detection scheme proposed in the present invention, 2 The detection result of the detector is consistent with the present invention (watermark function + χ 2 Under the attack detection scheme proposed by the present invention, the deployed dynamic watermark function is Figure 2 This indicates that the attack is covert. k It rises after the attack because the control performance deteriorates after the attack. The distribution matrix norm of the residual ||Σ k || gets larger, but it is still smaller than the threshold and therefore cannot trigger an alert. Figure 3 Middle, after attack g k The threshold is exceeded immediately, which verifies the effectiveness of the attack detection scheme proposed in the present invention.

[0191] 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 a concealed attack of a quadrotor drone based on an innovation sequence, characterized in that: The method specifically comprises the following steps: Step 1: discretize the dynamic equation of the quadrotor drone to obtain the full-state system equation of the quadrotor drone, and obtain the system output equation based on the full-state system equation of the quadrotor drone; Step 2: The quadrotor drone receives the control signal U sent by the control center at time k-1 k-1 After that, the state vector of the quadrotor drone is X k-1 Update to X k , use the sensor deployed on the quadcopter to measure the state of the quadcopter, and record the sensor's measurement value as Y k ; Step 3: The extended Kalman filter deployed locally on the quadrotor drone uses the sensor measurement value Y k Calculate the innovation sequence Z k ; Step 4: Give the new information sequence Z k Add dynamic watermark function Get the new information sequence Z' k , and then the new information sequence Z' k Send to the control center via the communication network; Step 5: The control center receives the new information sequence in the communication network After that, the new information sequence Subtract watermark function Get the new information sequence Step 6: Use χ 2 The detector responds to the new information sequence Conduct attack detection; If an attack is detected, the detector will sound an alarm and continue to step seven; Otherwise, go directly to step 7; Step 7: The extended Kalman filter deployed in the control center is used to analyze the new information sequence Processing to obtain the remote state estimate 2. According to the method for detecting a concealed attack of a quadrotor drone based on an innovation sequence according to claim 1, it is characterized in that: The forward Euler discretization method is used to discretize the dynamic equations of the quad-rotor drone.

3. According to claim 2, a method for detecting a concealed attack of a quadrotor drone based on an innovation sequence is characterized in that: The dynamic equation of the quad-rotor drone is discretized to obtain the full-state system equation of the quad-rotor drone. The specific process is: The dynamic equation of the quadrotor drone is: Where m is the mass of the quadcopter; x, y, and z represent the position of the quadcopter in the directions of the coordinate axes of the inertial reference system. is the second derivative of x, is the second derivative of y, is the second-order derivative of z; T is the total lift generated by the propeller of the quadrotor drone; φ, θ and ψ represent the roll, pitch and yaw attitude Euler angles of the quadrotor drone in the inertial reference frame respectively; g is the gravitational acceleration; I xx ,I yy and I zz They represent the moments of inertia of the quadrotor drone around each main axis, L, M and N represent the rolling moment, pitching moment and yaw moment in the body reference system, respectively, and p, q and r are the angular velocities of the body reference system relative to the inertial reference system expressed in the directions of the coordinate axes of the body reference system; The angular velocity conversion relationship is expressed as: in, is the first derivative of φ, is the first-order derivative of θ, is the first derivative of ψ; The position, velocity, Euler angle and body angular velocity of the quadrotor drone are taken as the system state, and the process noise is introduced to obtain the full state system equation of the quadrotor drone: Among them, x k ,y k and z k They represent the position of the quadrotor drone in the inertial reference system at time k, u k , v k and w k They represent the speed of the quadrotor drone in the inertial reference system at time k, δt represents the time interval between two adjacent moments, and φ k ,θ k and ψ k They represent the roll, pitch and yaw Euler angles of the quadrotor drone in the inertial reference frame at time k, respectively, and W k-1 represents the process noise matrix at time k-1; p k ,q k and r k are the angular velocities of the body reference system relative to the inertial reference system in the directions of the coordinate axes of the body reference system at time k; k-1 ,y k-1 and z k-1 They represent the position of the quadrotor drone in the inertial reference frame at time k-1, u k-1 , v k-1 and w k-1 They represent the speed of the quadrotor drone in the inertial reference frame at time k-1, φ k-1 ,θ k-1 and ψ k-1 They represent the roll, pitch and yaw Euler angles of the quadrotor drone in the inertial reference frame at time k-1 respectively; p k-1 ,q k-1 and r k-1 are the angular velocities of the body reference system relative to the inertial reference system in the directions of the coordinate axes of the body reference system at time k-1; Rewrite the full state system equation of the quadrotor drone into the following form: X k =f(X k-1 ,U k-1 )+W k-1 , Among them, X k represents the state vector at time k, X k-1 represents the state vector at time k-1; f(X k-1 ,U k-1 ) represents the nonlinear system state equation; U k-1 It is a vector composed of the four motor speeds of the quadcopter drone. The total lift, rolling moment, pitch moment and yaw moment of the quadrotor drone are calculated by the motor speed: Among them, k T is the propeller lift coefficient, k D is the torque coefficient of the propeller, l is the distance from the motor to the center of the quadcopter, L k-1 、M k-1 and N k-1 are the rolling moment, pitching moment and yaw moment in the body reference system at time k-1, T k-1 It is the total lift generated by the propeller of the quadcopter at time k-1.

4. According to claim 3, a method for detecting a concealed attack of a quadrotor drone based on an innovation sequence is characterized in that: The system output equation is obtained according to the full-state system equation of the quadrotor drone, and the specific process is: The system output equation taking into account the measurement noise is: Y k =HX k +V k , Among them, Y k is the output vector at time k; H is the output matrix of the nonlinear system, V k represents the measurement noise matrix.

5. The method for detecting a concealed attack of a quad-rotor drone based on an innovation sequence according to claim 4 is characterized in that: The specific process of step three is: in, is the estimated value of the state vector of the quadrotor drone at time k-1, is the one-step prediction of the quadrotor drone state vector at time k, P k-1 is the estimated value of the state estimation error covariance matrix at time k-1, is the one-step prediction of the state estimation error covariance matrix at time k, K k is the gain matrix at time k, F k-1 is the Jacobian matrix at time k-1, is the estimated value of the state vector of the quadrotor drone at time k, P k is the estimated value of the covariance matrix of the state estimation error at time k, I is the identity matrix, Q is the covariance matrix of the system process noise, and R is the covariance matrix of the system measurement noise; Among them, Z k is the new information sequence at time k.

6. The method for detecting a concealed attack of a quadrotor drone based on an innovation sequence according to claim 5 is characterized in that: The Jacobian matrix F at the k-1 moment k-1 Specifically: Jacobian matrix F k-1 The submatrix F in 1:3,1:3 、F 4:6,4:6 、F 1:3,4:6 、F 4:6,7:9 、F 7:9,7:9 and F 10:12,10:12 satisfy: F 1:3,1:3 =F 4:6,4:6 =I 3×3 , In the Jacobian matrix F k-1 In the divisor matrix F 1:3,1:3 、F 4:6,4:6 、F 1:3,4:6 、F 4:6,7:9 、F 7:9,7:9 and F 10:12,10:12 Except for the position where , all other elements are 0.

7. The method for detecting a concealed attack of a quadrotor drone based on an innovation sequence according to claim 6 is characterized in that: The dynamic watermark function is a zero-mean one-dimensional Gaussian distribution random process, dynamic watermark function It is deployed on both the quadcopter and the remote control center.

8. The method for detecting a concealed attack of a quadrotor drone based on an innovation sequence according to claim 7, characterized in that: The specific process of step six is ​​as follows: Among them, g k is the detection statistic at time k, is the length of the detection window, is the covariance matrix, γ is the detection threshold, H1 indicates that an attack is detected, and H0 indicates that an attack is not detected. k ≥γ, the test result is H1. k When <γ, the test result is H0; where ‖·‖2 is the L2 norm.

9. The method for detecting a concealed attack of a quadrotor drone based on an innovation sequence according to claim 8, characterized in that: The method further comprises step eight, specifically: Estimated value based on remote state Calculate the control input U at time k k , then set k=k+1 and return to step 2.

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