Unmanned aerial vehicle information physical system state observation method based on network attack detection and defense

Abstract

The invention discloses an unmanned aerial vehicle information physical system state observation method based on network attack detection and defense, and the method comprises the following steps: 1, monitoring an abnormal behavior in an unmanned aerial vehicle communication network in real time according to state information transmitted back by a sensor of an unmanned aerial vehicle, and judging whether a network attack exists or not; 2, collecting the attitude of the unmanned aerial vehicle sent by the signal receiver, and constructing a state information model of an unmanned aerial vehicle information physical system in combination with network attack, system noise and measurement noise for estimating an unmanned aerial vehicle attitude measurement value; step 3, analyzing the state observation model of the unmanned aerial vehicle based on Kalman filtering to obtain a posteriori estimation covariance of the unmanned aerial vehicle for estimating a measurement value of the pose of the unmanned aerial vehicle; 4, updating a system state, and calculating a control gain based on an unmanned aerial vehicle information physical system state equation; acting on the posterior estimation covariance of the state estimation of the unmanned aerial vehicle; and step 5, performing transmission encryption on the measurement value of the pose of the unmanned aerial vehicle, and outputting the measurement value through a signal transmitter.

Description

Technical Field

[0001] This invention relates to the field of security for unmanned aerial vehicle (UAV) cyber-physical systems (CPS), and in particular to a method for UAV system state observation and estimation in a cyberattack environment. Background Technology

[0002] With the rapid development of unmanned aerial vehicle (UAV) technology, UAVs are increasingly widely used in military, logistics, and agricultural monitoring fields. As a highly complex system integrating communication networks, intelligent control, data computing, and physical entities, the security of UAV cyber-physical systems (CPS) is paramount. CPS systems are complex systems integrating communication, control, and computing technologies, widely used in defense, healthcare, transportation, industrial production, and smart homes. CPS systems achieve efficient information transmission and intelligent device control through high integration. As a crucial component of CPS systems, UAVs' communication networks are typically open, making them vulnerable to various malicious network attacks, such as data injection attacks, denial-of-service (DoS) attacks, and replay attacks. These attacks can disrupt normal UAV operation and even lead to serious consequences. In UAV CPS systems, state observation is one of the key technologies for effective control. The design of state observers is crucial for the stable operation and safety of UAVs. In the context of network attacks, how to design robust state observers to ensure that UAV systems can maintain their performance during attacks has become an important research topic. The diversity and complexity of cyberattacks necessitate that the design of state observers for UAV cyber-physical systems (APIs) must consider various attack scenarios, including the combined effects of single and multiple attacks. Furthermore, the design of state observers must also take into account the impact of system and measurement noise, including state estimation based on Kalman filtering corrections, event triggering mechanisms, and detection and defense strategies against specific cyberattacks. Therefore, improving the accuracy of state estimation for UAV APIs under cyberattacks, achieving a certain degree of resistance to the impact of cyberattacks on UAV state observation, and ensuring the normal operation of UAVs are key technical challenges that need to be addressed. Summary of the Invention

[0003] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a method for accurately estimating the state information of a UAV in a network attack environment. Based on the Kalman filter principle, a state observer is designed to minimize the covariance of the state estimation to achieve effective observation of the state of the UAV cyber-physical system, ensuring control of the UAV and improving the security and robustness of the UAV cyber-physical system while ensuring that the system control performance indicators are met.

[0004] To address the aforementioned technical problems, the technical solution adopted by this invention is: a method for observing the state of a UAV cyber-physical system based on network attack detection and defense, comprising the following steps:

[0005] Step 1: Monitor abnormal behavior in the drone's communication network in real time based on the status information transmitted by the drone's sensors, and determine whether a network attack is occurring.

[0006] Step 2: Collect the UAV attitude transmitted by the signal receiver, and construct a state information model of the UAV cyber-physical system by combining network attack, system noise and measurement noise, in order to estimate the UAV attitude measurement value;

[0007] Step 3: Analyze the UAV state observation model based on Kalman filtering to obtain the UAV posterior estimated covariance, which is used to estimate the measured values ​​of UAV pose.

[0008] Step 4: Update the system state and calculate the control gain based on the UAV cyber-physical system state equation; and apply it to the posterior estimation covariance of the UAV state estimation.

[0009] Step 5: Encrypt the transmission of the UAV pose measurement values ​​and output them through the signal transmitter.

[0010] The network attack in step 1 is a replay attack, as shown below:

[0011]

[0012] in This represents the status information transmitted back by the drone's sensors, y k This refers to the status information returned by the drone's sensors when it has not been subjected to a replay attack. s This indicates that the attacker stole historical data of the drone's state information from previous moments. q=1 indicates that the state information returned by the drone's sensors has been subjected to a replay attack, and q=0 indicates that the state information returned by the drone's sensors has not been subjected to a replay attack.

[0013] The state information model of the unmanned aerial vehicle cyber-physical system is as follows:

[0014]

[0015] Wherein, ΔU k Y represents the watermark signal at time K. s (k) represents the periodic state information compensation signal. w k and v k A represents the system noise and measurement noise during status information transmission. k B kand C k Represents a matrix of appropriate dimension. Represents the physical state of the system. Measurements representing the pose of the drone. This represents the system's control input.

[0016] Step 3, based on Kalman filter analysis of the UAV's state observation model, estimates the UAV's posterior covariance to estimate the measured values ​​of the UAV's pose, including:

[0017] Step 31) Define the prior estimate of the UAV. and posterior estimation It is expressed as follows:

[0018]

[0019] For the initial state estimate of the UAV Represented by the initial state value x0, that is

[0020]

[0021] The error in UAV state estimation is represented by covariance; where the prior estimate covariance of UAV state estimation is... and posterior estimate of covariance

[0022]

[0023] Step 32) The filtering for UAV state estimation is as follows:

[0024] Initial values ​​for posterior estimation in UAV state estimation filtering Initial values ​​of posterior covariance estimates Right now:

[0025]

[0026] Calculate the posterior estimate of the UAV state estimate:

[0027]

[0028] Calculate the posterior covariance of the UAV state estimate:

[0029]

[0030] Step 4 updates the system state by calculating the control gain based on the UAV cyber-physical system state equation; and the posterior estimation covariance applied to the UAV state estimation includes:

[0031] Calculate the prior estimate covariance of the UAV state using prior estimates:

[0032]

[0033] The gain feedback matrix for UAV state estimation is solved by prior estimation of the covariance:

[0034]

[0035] Prior estimate of covariance Control gain K k Substitute the values ​​into the posterior estimation covariance formulas (5) and (6) to solve.

[0036] The encrypted state information is as follows:

[0037]

[0038] Where, H = [H + H - ], The encryption coefficient matrix represents the drone's status information. The unencrypted coefficient matrix representing the drone's state information. Y represents + (k) is the new matrix obtained by multiplying by the coefficient matrix. Y represents - (k) is the new matrix obtained by multiplying by the coefficient matrix. This is the corresponding encryption key.

[0039] The advantages of this invention are:

[0040] 1. It can effectively and accurately estimate the state information of drones in a network attack environment;

[0041] 2. It can detect and defend against various cyberattacks in real time, improving the security of UAV cyber-physical systems;

[0042] 3. Encryption of communication protects data transmission, enhancing the confidentiality and integrity of the UAV system.

[0043] 4. It can effectively estimate the state of UAV cyber-physical systems in the event of various cyberattacks, and can also reduce the impact of noise on the state observation of UAV cyber-physical systems.

[0044] 5. Even if the status information transmitted by the drone is interrupted or replaced, the drone controller still has a status estimate available. Attached Figure Description

[0045] Figure 1 This is a system architecture diagram of the UAV cyber-physical system state observer of the present invention;

[0046] Figure 2 This is a flowchart of the UAV cyber-physical system state observation method of the present invention. Detailed Implementation

[0047] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0048] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0049] On one hand, the present invention provides a state observer for an unmanned aerial vehicle (UAV) cyber-physical system, including a state estimation module, a network attack detection module, a gain feedback module, a state correction module, and a communication encryption module.

[0050] The state estimation module is connected to the signal receiver and is used to receive the UAV information physical system state information sent by the signal receiver. Based on the UAV's dynamic model and the received state information, the state estimate is obtained by Kalman filtering correction.

[0051] The network attack detection module is used to monitor abnormal behavior in the UAV communication network in real time, determine whether a network attack exists, and identify and classify the types of network attacks.

[0052] The control gain feedback calculation module calculates the control gain based on the updated system state and system state equations, and according to the judgment results of the network attack detection module, while meeting the control performance index requirements.

[0053] The state correction module corrects the output of the state estimation module according to the defense strategy. It adjusts the gain feedback matrix during data injection attacks and performs weighted state estimation during denial-of-service attacks to eliminate the impact of network attacks on state estimation.

[0054] The communication encryption module is used to encrypt the data transmitted in the drone's communication network to prevent the data from being eavesdropped on or tampered with.

[0055] Furthermore, the network attack detection module detected a replay attack as the type of network attack.

[0056] A replay attack involves an attacker stealing historical data of the drone's state information from a previous moment, and then replaying the stolen state information back into the drone's communication network at a later moment to replace the current state information.

[0057]

[0058] in This represents the status information transmitted back by the drone's sensors, y k This refers to the status information returned by the drone's sensors when it has not been subjected to a replay attack. s This indicates that the attacker stole historical data of the drone's state information from previous moments. q=1 indicates that the state information returned by the drone's sensors has been subjected to a replay attack, and q=0 indicates that the state information returned by the drone's sensors has not been subjected to a replay attack.

[0059] In summary, the process of cyberattacks in UAV state observation refers to two aspects: analyzing the design rules of various aspects of the UAV's cyber-physical system and generating attack signals.

[0060] Furthermore, the state estimation module represents the physical state model of the UAV under different network attack conditions as a state vector. The physical state at the current moment depends on the physical state and control input at the previous moment. Based on the existing UAV physical state model, it is expressed as follows:

[0061] X(k+1)=AkX(k)+BkU(k)

[0062] Where X(k+1)∈Rn and X(k)∈Rn represent the physical states of the UAV at time k+1 and time k, respectively, and U(k)∈Rm represents the control input of the UAV system. Ak and Bk represent matrices of appropriate dimensions in the UAV system. Under noise-free and network attack-free conditions, the sensor measurements are represented as follows:

[0063] Y(k)=CkX(k)

[0064] Y(k) represents the measurement value of the UAV system at time k, X(k)∈Rn represents the physical state of the UAV at time k, and Ck represents the matrix of appropriate dimension in the UAV system.

[0065] In an unmanned aerial vehicle (UAV) system, the control input U(k) is designed based on the current state observations of the UAV, taking into account various factors such as motion requirements. Therefore, UAV state observation is fundamental to UAV control.

[0066] In the design of UAV state observers, errors caused by system modeling and sensor detection accuracy are typically considered. These errors can be categorized into system noise and measurement noise in UAV state observation. System noise is caused by inaccuracies in the system model, while measurement noise is caused by detection errors in the detection equipment. The model for UAV cyber-physical system state observation under the interference of system noise and measurement noise is as follows:

[0067]

[0068] in and This represents the physical state of the drone at time k+1 and time k. w represents the control input of the unmanned aerial vehicle (UAV) system. k This represents the system noise during the transmission of state information in the UAV cyber-physical system, v k Y(k) represents the measurement noise during the transmission of state information of the UAV cyber-physical system, and A represents the measurement value of the UAV system at time k. k B k and C k A matrix of appropriate dimension representing an unmanned aerial vehicle (UAV) system.

[0069] Considering the impact of cyberattacks on the state observation of UAV cyber-physical systems, and based on the above attack detection method, a binary variable {0, 1} is further used to determine whether the corresponding type of attack has been received.

[0070] To improve upon existing methods for determining the trigger of cyberattacks in unmanned aerial vehicle (UAV) cyber-physical systems (CPS) systems, we add a periodic watermark signal to the control signals of the physical system. Simultaneously, during state estimation, we calculate the value to counteract the periodic watermark signal. By analyzing whether the period of the received state information signal matches that of the added watermark signal, we determine whether the CPS system's state information has been subjected to a replay attack. The designed state information formula is shown below:

[0071]

[0072] Where ΔU k Y represents the watermark signal at time K. s (k) represents the periodic state information compensation signal. w k and v k A represents the system noise and measurement noise during status information transmission. k B k and C k Represents a matrix of appropriate dimension. Represents the physical state of the system. Represents the system's measured values. This represents the system's control input.

[0073] When dealing with the state observation problem of UAV cyber-physical systems containing system noise and measurement noise, filtering methods are mainly used to analyze the UAV state observation model. The main purpose is to filter out system noise and measurement noise, thereby obtaining more accurate UAV state information.

[0074] Kalman filtering is used to solve the state observation problem of unmanned aerial vehicles (UAVs). Specifically, it involves estimating the UAV's current state X(k) based on the known state equations and state information transmitted from the UAV's sensors. When using measurements from previous moments as the data basis for state estimation, the resulting UAV state estimate is called the prior estimate. When using both previous and current measurements as the data basis, the resulting UAV state estimate is called the posterior estimate.

[0075] Prior estimation of drones and posterior estimation It is expressed as follows:

[0076]

[0077] For the initial state estimate of the UAV Represented by the initial state value x0, that is

[0078]

[0079] This paper innovatively proposes that the error of UAV state estimation be represented by covariance, and the prior estimate covariance of UAV state estimation. and posterior estimate of covariance

[0080]

[0081] The basic filtering process for UAV state estimation is as follows:

[0082] (1) Assign initial values ​​to the posterior estimates in the UAV state estimation filter. Initial values ​​of posterior covariance estimates Right now:

[0083]

[0084] (2) Calculate the prior estimate of the UAV state:

[0085]

[0086] (3) Calculate the difference between the measured value and the prior estimate:

[0087]

[0088] (4) Due to the existence of network attacks, the feedback signal will contain network attack information.

[0089]

[0090] (5) Calculate the posterior estimate of the UAV state estimation when there is no network attack.

[0091]

[0092] (6) Calculate the posterior covariance of the UAV state estimation.

[0093]

[0094] This shows that Kalman filtering can effectively filter out system noise and measurement noise, but it cannot filter out the impact of network attacks on UAV state estimation.

[0095] Furthermore, the system correction module sends the UAV cyber-physical system state equation and system state estimate to the control gain feedback calculation module. Upon receiving the UAV cyber-physical system state equation and system state estimate from the system correction module, the gain feedback calculation module updates the system state and the system state equation, and calculates the control gain K based on the UAV cyber-physical system state equation. k ;

[0096] Calculate the prior estimate covariance of the UAV state using prior estimates:

[0097]

[0098] The gain feedback matrix for UAV state estimation is solved by prior estimation of the covariance:

[0099]

[0100] After the system correction module transmits the state equations and state estimates of the UAV cyber-physical system to the control gain feedback calculation module, the latter first uses the prior estimate covariance from the previous moment as a benchmark to characterize the uncertainty of the UAV state when no new observations are introduced; this covariance is then used to solve for the gain feedback matrix, thereby determining the correction weights of the observation information on the state estimate. Since K k The expression also includes the system noise covariance M. k Covariance of observation noise R k, any malicious tampering with these two items will directly distort the gain matrix, further amplifying the estimation error. Therefore, in scenarios with limited encrypted resources, the gain feedback module treats the above prior covariance and gain matrix as sensitive information and transmits them through a lightweight encryption strategy to ensure that even with limited encryption strength, attackers can be prevented from indirectly sabotaging \(K_k\) by stealing or tampering with \(P\), \(R\) k , \(M\) k and ultimately maintain the integrity and reliability of the UAV state estimate \(Y(k)\).

[0101] Furthermore, when the encrypted resources are limited during the information transmission of the observation data output by the gain feedback module, the UAV state information is encrypted for transmission to prevent the information from being stolen or tampered with by attackers during transmission. When the encrypted resources are limited during the transmission of the UAV state information, an analysis of the encryption of the information transmission is carried out. Assume that there are \(n\) column vectors in \(Y(k)\). Due to limited encrypted resources, the first \(r\) (\(r < n\)) column vectors among the \(n\) column vectors are encrypted, and the last \(n - r\) column vectors are not encrypted. The first \(r\) column vectors are denoted as \(Y^+(k)\), and the last \(n - r\) column vectors are denoted as \(Y^-(k)\). Based on the above two sets of situations of the UAV state information, the following two sets of coefficient matrices are designed:

[0102] \(H\) + = [b1, b2, b3 ··· b r

[0103] \(H\) - = [b r+1 , b r+2 , b r+3 ··· b n

[0104] \(H = [H\) + , \(H\) -

[0105] represents the encryption coefficient matrix of the UAV state information, which is related to the UAV pose measurement value, represents the unencrypted coefficient matrix of the UAV state information.

[0106] Multiplying the above two sets of vectors of the UAV state information by the corresponding coefficient matrices gives:

[0107]

[0108] where represents the new matrix obtained by multiplying \(Y\) + (k) by the coefficient matrix, represents the new matrix obtained by multiplying \(Y\) - (k) by the coefficient matrix. The following encryption is performed on the UAV state information:

[0109]

[0110] Where ∝ is the encryption function used in the transmission of UAV status information. For the corresponding encryption key, Θ k This represents the ciphertext of the encrypted state information at time k. Decrypting and recombine the encrypted UAV state information yields:

[0111]

[0112] The encrypted UAV status information is transmitted linearly to signal receivers 1 to n via signal transmitters, and then to observers 1 to n; ultimately ensuring the real-time and accurate transmission of the unmanned cyber-physical system.

[0113] On the other hand, the present invention also provides a method for observing the state of an unmanned aerial vehicle (UAV) cyber-physical system, which employs the aforementioned UAV cyber-physical system state observer to implement the following steps:

[0114] Step 1: System Initialization

[0115] Initialize the physical state model of the UAV and set the initial state estimates. For the initial state estimates of the UAV... Represented by the initial state value x0, that is

[0116] Step 2: Network Attack Detection and Classification

[0117] It receives real-time status information from drone sensors and detects whether replay network attacks are present.

[0118] Step 3: Model building for the state observer

[0119] The physical state model of the UAV under different network attack conditions is represented as a state vector. The physical state at the current moment depends on the physical state and control input at the previous moment. The physical state model of the UAV is represented as follows:

[0120] X(k+1)=A k X(k)+B k U(k)

[0121] Where X(k+1)∈Rn and X(k)∈Rn represent the physical states of the UAV at time k+1 and time k, respectively, and U(k)∈Rm represents the control input of the UAV system. A k and B k A matrix of appropriate dimension representing an unmanned aerial vehicle (UAV) system.

[0122] Step 4: State Vector System Correction

[0123] Based on the UAV's state vectors under different network attack conditions, the system is corrected to obtain updated system states and system state equations. The sensor measurements under noise-free and network attack-free conditions are represented as follows:

[0124] Y(k)=C k X(k)

[0125] Y(k) represents the measurement value of the UAV system at time k, X(k)∈Rn represents the physical state of the UAV at time k, and C k A matrix of appropriate dimension representing an unmanned aerial vehicle (UAV) system.

[0126] Step 5: Application of Kalman Filtering Principle

[0127] When an unmanned aerial vehicle (UAV) cyber-physical system is subjected to independent or related process noise and measurement noise interference, the Kalman filtering process is analyzed, and the system model is as follows:

[0128]

[0129] Where w k The system noise during the transmission of state information in the UAV cyber-physical system is represented by Q, and its covariance matrix is ​​Q. k v k The covariance matrix of the measurement noise during the transmission of state information in an unmanned aerial vehicle (UAV) cyber-physical system is R. k And w k With v k The covariance between the two related factors is M. k .

[0130]

[0131] Where ΔU k Y represents the watermark signal at time K. s (k) represents the periodic state information compensation signal. w k and v k A represents the system noise and measurement noise during status information transmission. k B k and C k Represents a matrix of appropriate dimension. Represents the physical state of the system. Represents the system's measured values. This represents the system's control input.

[0132] Step 6: Control Gain Calculation

[0133] If a network injection attack is detected, the state estimation is adjusted according to the gain feedback matrix based on the updated system state and system state equations, while meeting the control performance requirements.

[0134] The specific method involves calculating the estimated covariance of the UAV state using the estimated values, and then solving for the gain feedback matrix of the UAV state estimation using the prior estimated covariance: K is the gain feedback matrix of the UAV state estimation obtained by solving for the prior estimated covariance. k The formula is as follows:

[0135]

[0136] It is a fixed formula, and it is a transpose of a matrix.

[0137] Step 7: Linear Encryption of Information Transmission

[0138] Based on the calculated control gain and system state estimate, the observed state is calculated and transmitted to the observer via a wireless communication network. The data in the UAV communication network is encrypted using a communication encryption module. Decrypting and recombining the encrypted UAV state information yields:

[0139]

[0140] Where H is a matrix satisfying the following equation:

[0141] H = [H] + H - -] represents the encryption coefficient matrix of the UAV status information. An unencrypted coefficient matrix representing the drone's status information.

[0142] In this invention, the UAV cyber-physical system state observer can be integrated into the UAV's ground control station or as part of the UAV's flight control system. The state estimation module can employ Kalman filtering, extended Kalman filtering, or other advanced state estimation algorithms. The network attack detection module can detect abnormal behavior based on different triggering conditions and judgment threshold algorithms. The state correction module can perform a weighted average of the estimation results or employ other correction algorithms. The communication encryption module can encrypt data using encryption algorithms such as AES and RSA.

[0143] The embodiments of the present invention are for reference only and do not constitute a limitation on the scope of protection of the present invention. Any modifications, substitutions, or variations made to the present invention by those skilled in the art without departing from the concept of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for state observation of unmanned aerial vehicle (UAV) cyber-physical systems based on network attack detection and defense, characterized in that, Includes the following steps: Step 1: Monitor abnormal behavior in the drone's communication network in real time based on the status information transmitted by the drone's sensors, and determine whether a network attack is occurring. Step 2: Collect the UAV attitude transmitted by the signal receiver, and construct a state information model of the UAV cyber-physical system by combining network attack, system noise and measurement noise, in order to estimate the UAV attitude measurement value; Step 3: Analyze the UAV state observation model based on Kalman filtering to obtain the UAV posterior estimated covariance, which is used to estimate the measured values ​​of UAV pose. Step 4: Update the system state and calculate the control gain based on the UAV cyber-physical system state equation; and apply it to the posterior estimation covariance of the UAV state estimation. Step 5: Encrypt the transmission of the UAV pose measurement values ​​and output them through the signal transmitter.

2. The method for state observation of unmanned aerial vehicle (UAV) cyber-physical systems based on network attack detection and defense according to claim 1, characterized in that, The network attack in step 1 is a replay attack, as shown below: in This represents the status information transmitted back by the drone's sensors, y k This refers to the status information returned by the drone's sensors when it has not been subjected to a replay attack. s This indicates that the attacker stole historical data of the drone's state information from previous moments. q=1 indicates that the state information returned by the drone's sensors has been subjected to a replay attack, and q=0 indicates that the state information returned by the drone's sensors has not been subjected to a replay attack.

3. The method for state observation of unmanned aerial vehicle (UAV) cyber-physical systems based on network attack detection and defense according to claim 1, characterized in that, The state information model of the unmanned aerial vehicle cyber-physical system is as follows: Wherein, ΔU k Y represents the watermark signal at time K. s (k) represents the periodic state information compensation signal. w k and v k A represents the system noise and measurement noise during status information transmission. k B k and C k Represents a matrix of appropriate dimension. Represents the physical state of the system. Measurements representing the pose of the drone. This represents the system's control input.

4. The method for state observation of unmanned aerial vehicle (UAV) cyber-physical systems based on network attack detection and defense according to claim 1, characterized in that, Step 3, based on Kalman filter analysis of the UAV's state observation model, estimates the UAV's posterior covariance to estimate the measured values ​​of the UAV's pose, including: Step 31) Define the prior estimate of the UAV. and posterior estimation It is expressed as follows: For the initial state estimate of the UAV Represented by the initial state value x0, that is The error in UAV state estimation is represented by covariance; where the prior estimate covariance of UAV state estimation is... and posterior estimate of covariance Step 32) The filtering for UAV state estimation is as follows: Initial values ​​for posterior estimation in UAV state estimation filtering Initial values ​​of posterior covariance estimation Right now: Calculate the posterior estimate of the UAV state estimate: Calculate the posterior covariance of the UAV state estimate:

5. The method for state observation of unmanned aerial vehicle (UAV) cyber-physical systems based on network attack detection and defense according to claim 4, characterized in that, Step 4 updates the system state by calculating the control gain based on the UAV cyber-physical system state equation; and the posterior estimation covariance applied to the UAV state estimation includes: Calculate the prior estimate covariance of the UAV state using prior estimates: The gain feedback matrix for UAV state estimation is solved by prior estimation of the covariance: Prior estimate of covariance Control gain K k Substitute the values ​​into the posterior estimation covariance formulas (5) and (6) to solve.

6. The method for state observation of unmanned aerial vehicle (UAV) cyber-physical systems based on network attack detection and defense according to claim 1, characterized in that, The encrypted state information is as follows: Where, H = [H + H - ], The encryption coefficient matrix represents the drone's status information. The unencrypted coefficient matrix representing the drone's state information. Y represents + (k) is the new matrix obtained by multiplying by the coefficient matrix. Y represents - (k) is the new matrix obtained by multiplying by the coefficient matrix. This is the corresponding encryption key.

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