Robust FDI Attack Detection Methods for Ship Navigation Systems

Abstract

This invention belongs to the field of information security technology, specifically relating to a robust FDI attack detection method for ship navigation systems. The invention constructs a linear discrete-time system model and designs an attack detector based on this model. The detector parameters are optimized using the linear matrix inequality method, and an adaptive detection threshold mechanism based on historical mean and standard deviation is designed. This mechanism can dynamically sense changes in system state, making the dynamic attack detection system asymptotically stable and meeting performance indicators.

Description

Technical Field

[0001] This invention belongs to the field of information security technology, specifically relating to a method based on A robust FDI attack detection method for ship navigation systems. Background Technology

[0002] With the rapid development of Cyber-Physical Systems (CPS) technology, the convergence of computing, communication, and control has driven the transformation of traditional industries towards intelligence and automation. CPS enables the modeling and scheduling of complex physical systems through perception, communication, and intelligent control, and is widely applied in fields such as intelligent manufacturing, smart transportation, and energy systems. In emerging scenarios such as marine environmental monitoring, surface patrol, and intelligent transportation, Unmanned Surface Vehicles (USVs), as typical CPS examples, demonstrate a high degree of intelligent perception, autonomous decision-making, and remote collaboration capabilities. USVs integrate multiple sensors, embedded control systems, and communication modules. Their operation relies on multi-source data fusion, real-time control, and task optimization under the CPS architecture, making them an important practical carrier of CPS theory in the field of marine intelligent equipment.

[0003] Due to the influence of the marine environment, USVs (Universal Vessels) rely heavily on wireless communication systems for remote control, data transmission, and mission coordination during maritime navigation. However, the complex and ever-changing marine environment poses significant challenges to the stability and security of these communication systems. On the one hand, extreme external environments and other natural factors can lead to unstable propagation paths, resulting in communication interruptions, data loss, and transmission delays. On the other hand, maritime communications often utilize open transmission channels, making them vulnerable to security threats such as cyberattacks, which could lead to data tampering, communication hijacking, or even USV loss of control or mission failure. Therefore, ensuring high reliability, low latency, and strong security in USV communications has become a key technical challenge in the design of USV systems for marine environments.

[0004] In unmanned vehicles (USVs), system safety and stability heavily rely on the accuracy of sensor data and the reliability of communication links. These systems commonly employ multi-source sensor fusion for environmental perception and state estimation. However, False Data Injection (FDI) attacks exploit this vulnerability by selectively altering or falsifying critical data in sensors or communication channels, leading the system to make incorrect perception and control decisions. Due to the high degree of concealment and wide-ranging impact of FDI attacks, a successful attack can result in serious consequences such as path deviation, obstacle avoidance failure, or even system loss of control. Therefore, in autonomous and unmanned systems, the detection and defense against FDI attacks has become a core issue in ensuring system robustness and operational safety.

[0005] Attack detection is crucial in USVs, enabling timely identification of potential network intrusions and sensor spoofing, effectively preventing interference or misdirection during navigation and control tasks. By enhancing the system's ability to identify false data, attack detection technology helps ensure the operational safety, mission reliability, and robustness of autonomous decision-making in USVs.

[0006] Currently, existing FDI attack detection and defense technologies targeting USVs mainly focus on anomaly detection based on statistical feature analysis and machine learning methods, as well as introducing redundancy mechanisms in the filtering and estimation stages to improve system security. These methods identify potential malicious injections by statistically modeling the residuals between sensor outputs and system models, or by using training data to build classifiers. However, these methods generally rely on large amounts of historical data or precise prior assumptions. When USVs operate in complex sea conditions or communication-restricted environments, their detection performance is easily affected by noise and environmental disturbances, resulting in high false alarm or false negative rates.

[0007] Meanwhile, some data-driven methods have limited generalization ability when facing unknown attack patterns, making it difficult to guarantee the reliability of detection. In contrast, Due to its excellent interference suppression capability, performance indicators have wide applications in dealing with external uncertainties and sensor noise. Therefore, this study proposes a method based on... The performance-constrained robust FDI attack detection method can effectively suppress the impact of noise interference on residuals and improve attack identification capabilities in dynamic ship navigation environments without relying on too much prior information. Summary of the Invention

[0008] The purpose of this invention is to address the problem of attack detection for USVs in environments where sensors are subjected to FDI attacks and communication is restricted. The method designed is based on... The performance-enhancing attack detector enables the attack detection dynamic system to be asymptotically stable and conforms to... The performance metrics validated its feasibility and effectiveness in a real-world USV system.

[0009] A robust FDI attack detection method for ship navigation systems includes the following steps:

[0010] Step 1: Establish a discrete-time multi-sensor network system based on the external interference and FDI attacks suffered by the USV; and consider the case of the actuator being attacked by FDI, and reformulate the discrete-time multi-sensor network system under the attack in a form that is convenient for detector design and robust performance analysis.

[0011] Step 2: Based on the output of the discrete-time multi-sensor network system, construct a system based on... A robust attack detector is developed, which uses a gain matrix to generate residual signals and models the state of the discrete-time multi-sensor network system and the state of the robust attack detector in a unified manner to form a dynamic attack detection system. A Lyapunov function is introduced to establish performance constraints, and a robust attack detector is developed. The performance indicators limit the energy gain from the interference input to the residual signal output, resulting in a dynamic attack detection system that remains stable under external disturbances and attacks;

[0012] Step 3: Construct a residual evaluation function, define the residual mean and residual standard deviation of the residual evaluation function within the sliding window, and construct an adaptive threshold based on the residual mean and residual standard deviation; compare the residual evaluation function with the adaptive threshold, and when the detection result exceeds the adaptive threshold, determine that the attack detection dynamic system may be under FDI attack and trigger an alarm mechanism;

[0013] Step 4: Introduce a Lyapunov functional and, based on the linear matrix inequality, verify that the attack detection dynamic system is asymptotically stable and satisfies the following conditions. Performance metrics; optimize parameters for robust attack solution detector.

[0014] Furthermore, in step 1, a discrete-time multi-sensor network system is established based on the external interference and FDI attacks suffered by the USV, as detailed below:

[0015] ;

[0016] In the above formula, let , This indicates the ship's position and heading information in a plane coordinate system; Represents location coordinate information, where, The coordinates representing the ship's position in the lateral or eastward direction. The coordinates representing the ship's position in the longitudinal or northward direction. The heading angle represents the angle between the ship's direction of motion and a reference direction. It is the given initial state; Indicates time The system status; It is the first One sensor in The measurement output of time; It belongs to Process noise; It belongs to Measurement noise; It is a known constant matrix.

[0017] Furthermore, in step 1, the discrete-time multi-sensor network system under attack is reformulated into a form that facilitates detector design and robustness analysis:

[0018] ;

[0019] In the above formula, This represents the system state under an FDI attack. This is the system output under an FDI attack. This indicates that the system is under FDI attack. Indicates the system at time 10:00 The state under FDI attack. Further, in step 2, based on the output of the discrete-time multi-sensor network system, a system is constructed based on... Robust attack detector:

[0020] ;

[0021] In the above formula, This is the attack detector state vector; For a moment The attack detector state vector at that time; It is the first One sensor in The measurement output of time; The residual signal; matrix Gain for attack detectors;

[0022] Let augmented state The difference between residuals and attacks And to combine external disturbances and measurement noise into a composite disturbance vector. ,in, Indicates external disturbance. Indicates sensor noise; This is the residual signal.

[0023] Furthermore, the attack detection dynamic system in step 2 is expressed as follows:

[0024] ;

[0025] in, , ;

[0026] In the above formula, Represents the extended state vector; Indicates at time The extended state vector at that time; This is the residual signal; Represents the extended state transition matrix; This is the system state transition matrix; Indicates detector gain With observation matrix The combination; This represents the state transition matrix of the detector; Represents the extended perturbation input matrix; Represents the attack input matrix; Describe the attack signal Its effect on the system state; Indicates the extended output matrix; Indicates the detector output gain, which determines the auxiliary state. To residual Mapping; The direct channel matrix represents the attack signal. Enter the residual directly with the opposite sign; Represents the identity matrix.

[0027] Furthermore, in step 2, a Lyapunov function is introduced to establish performance constraints, and a method is adopted... Performance parameters limit the energy gain from interference input to residual signal output:

[0028] ;

[0029] In the above formula, This is the residual signal; It is a positive definite matrix; a positive scalar. Representing the system Performance metrics; This represents the upper bound of the energy gain, ensuring that the sensitivity of the residual output to disturbance inputs is constrained to an acceptable range. This represents the composite disturbance vector, including external disturbances. With sensor noise ; This represents the cumulative summation over time.

[0030] Furthermore, in step 3, a residual evaluation function is constructed:

[0031] ;

[0032] In the above formula, Represents the residual evaluation function; This represents the residual signal, which is the deviation between the system's observations and estimates.

[0033] Furthermore, in step 3, an adaptive threshold is constructed based on the residual mean and residual standard deviation, as follows:

[0034] ;

[0035] In the above formula, An adaptive residual threshold is used to determine whether an FDI attack exists. This is a sensitivity adjustment parameter used to balance detection accuracy and false alarm rate; Indicates the standard deviation of the residuals; This represents the mean of the residuals.

[0036] Furthermore, in step 4, the attack detection dynamic system is verified to be asymptotically stable and satisfy... Performance metrics, including:

[0037] If a positive scalar exists and symmetric matrix ,matrix ,satisfy:

[0038] ;

[0039] in, ;

[0040] ;

[0041] In the above formula, and Used respectively Performance definition and stability adjustment; It is a symmetric positive definite matrix; Solving linear matrix inequalities is used to calculate the detector gain matrix; ~ This represents the coupling and constraints in solving linear matrix inequalities. Energy constraints for residuals and disturbances;

[0042] The gain matrix is ​​obtained by solving the linear matrix inequalities. , .

[0043] Compared with the prior art, the present invention has the following technical effects:

[0044] This invention constructs a linear discrete-time system model and designs a method based on... The attack detector is solved by optimizing the detector parameters using the Linear Matrix Inequality (LMI) method. An adaptive detection threshold mechanism based on historical mean and standard deviation is designed, which can dynamically sense changes in system state, making the dynamic attack detection system asymptotically stable and conforming to... Performance metrics. Attached Figure Description

[0045] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This invention is based on A flowchart of a robust FDI attack detection method for ship navigation systems;

[0047] Figure 2 This is a flowchart of the sensor model construction process of the present invention;

[0048] Figure 3 This is a flowchart of the attack detector design of this invention;

[0049] Figure 4 This is a flowchart illustrating the construction of the residual evaluation function and threshold of the present invention;

[0050] Figure 5 This is a flowchart of the performance verification and parameter solving process of this invention. Detailed Implementation

[0051] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the specific implementation methods, structures, features, and effects of the technical solutions proposed according to the present invention are described in detail below with reference to the accompanying drawings and preferred embodiments. Specific features, structures, or characteristics in one or more embodiments may be combined in any suitable form. Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0052] This invention constructs a linear discrete-time system model and designs a method based on... The attack detector is solved by optimizing the detector parameters using the Linear Matrix Inequality (LMI) method. An adaptive detection threshold mechanism based on historical mean and standard deviation is designed, which can dynamically sense changes in system state, making the dynamic attack detection system asymptotically stable and conforming to... Performance metrics.

[0053] In one embodiment of the present invention, reference is made to... Figures 1-5 A robust FDI attack detection method for ship navigation systems is provided, including the following steps:

[0054] Step 1: Establish a discrete-time multi-sensor network system based on the external interference and FDI attacks suffered by the USV; and consider the case of the actuator being attacked by FDI, and reformulate the discrete-time multi-sensor network system under the attack in a form that is convenient for detector design and robust performance analysis.

[0055] Step 2: Based on the output of the discrete-time multi-sensor network system, construct a system based on... A robust attack detector is developed, which uses a gain matrix to generate residual signals and models the state of the discrete-time multi-sensor network system and the state of the robust attack detector in a unified manner to form a dynamic attack detection system. A Lyapunov function is introduced to establish performance constraints, and a robust attack detector is developed. By limiting the energy gain from the interference input to the residual signal output based on performance indicators, a dynamic attack detection system that remains stable under external disturbances and attacks is obtained.

[0056] Step 3: Construct a residual evaluation function, define the residual mean and residual standard deviation of the residual evaluation function within the sliding window, and construct an adaptive threshold based on the residual mean and residual standard deviation; compare the residual evaluation function with the adaptive threshold, and when the detection result exceeds the adaptive threshold, determine that the attack detection dynamic system may be under FDI attack and trigger an alarm mechanism;

[0057] Step 4: Introduce a Lyapunov functional and, based on the linear matrix inequality, verify that the attack detection dynamic system is asymptotically stable and satisfies the following conditions. Performance metrics; optimize parameters for robust attack solution detector.

[0058] The following is a detailed explanation of each of the above steps:

[0059] Step 1: Establish a discrete-time multi-sensor network system based on the external interference and FDI attacks suffered by the USV; and consider the case of the actuator being attacked by FDI, and reformulate the discrete-time multi-sensor network system under the attack in a form that is convenient for detector design and robust performance analysis.

[0060] As an example, step 1 includes the following steps:

[0061] Step 1.1: Establish a discrete-time multi-sensor network system based on the external interference and FDI attacks suffered by the USV.

[0062] Considering that ships are easily affected by unpredictable external environmental factors such as wind, waves, and currents during navigation, resulting in uncertain interference noise, a discrete-time multi-sensor network system is established based on external interference and FDI attacks suffered by the USV, as detailed below:

[0063] (1);

[0064] In the above formula, let , This indicates the ship's position and heading information in a plane coordinate system; Represents location coordinate information, where, The coordinates representing the ship's position in the lateral or eastward direction. The coordinates representing the ship's position in the longitudinal or northward direction. The heading angle represents the angle between the ship's direction of motion and a reference direction. It is the given initial state; Indicates time The system status; It is the first One sensor in The measurement output of time; It belongs to Process noise; It belongs to Measurement noise; It is a known constant matrix.

[0065] Step 1.2: Considering the case where the actuator is attacked by FDI, the discrete-time multi-sensor network system under the attack is reformulated into a form that facilitates detector design and robust performance analysis.

[0066] Specifically, a discrete-time multi-sensor network system can be redescribed as follows:

[0067] (2);

[0068] In the above formula, This represents the system state under an FDI attack. This is the system output under an FDI attack. This indicates that the system is under FDI attack. Indicates the system at time 10:00 The state when under FDI attack.

[0069] Step 2: Construct a robust attack detector: Based on the output of the discrete-time multi-sensor network system, construct a robust attack detector. A robust attack detector is developed, which uses a gain matrix to generate residual signals and models the state of the discrete-time multi-sensor network system and the state of the robust attack detector in a unified manner to form a dynamic attack detection system. A Lyapunov function is introduced to establish performance constraints, and a robust attack detector is developed. By limiting the energy gain from the interference input to the residual signal output, a dynamic attack detection system that remains stable under external disturbances and attacks is obtained.

[0070] As an example, step 2 includes the following steps:

[0071] Step 2.1: Construct a system based on the output of a discrete-time multi-sensor network system. Robust attack detector:

[0072] (3);

[0073] In the above formula, This is the attack detector state vector; For at any time The attack detector state vector at that time; The residual signal; matrix Gain for attack detectors.

[0074] Let augmented state The difference between residuals and attacks And to combine external disturbances and measurement noise into a composite disturbance vector. ,in, Indicates external disturbance. Indicates sensor noise; This is the residual signal.

[0075] Step 2.2: Unify the state of the discrete-time multi-sensor network system with the state of the robust attack detector to form a dynamic attack detection system.

[0076] By combining a discrete-time multi-sensor network system with a robust attack detector, a dynamic attack detection system is constructed, expressed as follows:

[0077] (4);

[0078] in, ,

[0079] In the above formula, Represents the extended state vector; Indicates at time The extended state vector at that time; The residual signal represents the observed output. With attack signals The differences between them are the criteria for attack detection; Represents the extended state transition matrix; This is the system state transition matrix; Indicates detector gain With observation matrix The combination; This represents the state transition matrix of the detector; Represents the extended perturbation input matrix; Represents the attack input matrix; Describe the attack signal Its effect on the system state; Indicates the extended output matrix; Indicates the detector output gain, which determines the auxiliary state. To residual Mapping; The direct channel matrix represents the attack signal. Enter the residual directly with the opposite sign; Represents the identity matrix.

[0080] Step 2.3: Introduce Lyapunov functions to establish performance constraints, and adopt... The performance indicators limit the energy gain from the interference input to the residual signal output. The resulting attack detection dynamic system remains stable under external disturbances and attacks, and achieves attack detection with a low false alarm rate.

[0081] In terms of disturbance suppression, the following methods are adopted: Performance metrics are as follows:

[0082] (5);

[0083] In the above formula, The residual signal represents the difference between the output of the discrete-time multi-sensor network system and the estimation of the robust attack detector, and is the core criterion for attack detection. It is a positive definite matrix that assigns different weights to different directions of the output energy; a positive scalar. Representing the system The performance metric is the maximum allowable energy amplification factor for a discrete-time multi-sensor network system, used to measure the performance under worst-case perturbation input conditions. For detecting residual signals The intensity of the impact reflects the robustness of the attack detection dynamic system to external interference; This represents the upper bound of the energy gain, ensuring that the sensitivity of the residual output to disturbance inputs is constrained to an acceptable range. This represents the composite disturbance vector, including external disturbances. With sensor noise ; This represents the cumulative sum over time, representing the total time over the entire operation (from...). Energy transfer relationships (to infinity).

[0084] Step 3: Construct an adaptive threshold: Construct a residual evaluation function, define the residual mean and residual standard deviation of the residual evaluation function within the sliding window, and construct an adaptive threshold based on the residual mean and residual standard deviation; compare the residual evaluation function with the adaptive threshold, and when the detection result exceeds the adaptive threshold, determine that the attack detection dynamic system may be under FDI attack and trigger an alarm mechanism to achieve accurate identification and real-time response to attack behavior.

[0085] This step proposes an adaptive detection threshold adjustment mechanism based on historical mean and standard deviation. This mechanism dynamically senses changes in the operating state of the attack detection system, enabling the robust attack detector to adaptively increase or decrease sensitivity according to the current operating state of the attack detection system, thus balancing detection speed and false alarm rate.

[0086] As an example, step 3 may include the following steps:

[0087] Step 3.1: Construct the residual evaluation function:

[0088] To detect FDI attacks, a robust attack detector is proposed, which constructs a residual evaluation function:

[0089] (6);

[0090] In the above formula, This represents the residual evaluation function, used to quantify the system at time t. The cumulative residual strength before; This represents the residual signal, which is the deviation between the system's observations and estimates.

[0091] Step 3.2: Define the mean and standard deviation of the residuals for the residual evaluation function within the sliding window:

[0092] Mean residual: ;

[0093] In the above formula, This represents the mean residual of the residual evaluation function within the sliding window, indicating the average performance of the attack detection dynamic system at the current stage. If there is no attack, this value should remain stable; once an anomaly occurs, A significant shift will occur. This indicates the length of the sliding window, which determines the range of historical data used in the calculation of the mean and standard deviation. Indicates at time The residual evaluation function value.

[0094] Residual standard deviation: ;

[0095] In the above formula, This indicates the degree of fluctuation in the residual. Among them, The standard deviation represents the squared difference between the residual evaluation function value and the mean. The introduction of the standard deviation helps to improve the detection method's adaptability to noise changes, thereby reducing the false alarm probability while maintaining sensitivity.

[0096] Step 3.3: Construct an adaptive residual threshold as follows:

[0097] (7);

[0098] In the above formula, This is an adaptive residual threshold used to determine the presence of an FDI attack. This is a sensitivity adjustment parameter used to balance detection accuracy and false alarm rate. When the attack detection dynamic system is in normal operation, residual fluctuations mainly originate from modeling errors and noise. It can adaptively adjust to reflect normal fluctuation range; once the system is attacked, the residual evaluation function It will quickly exceed that threshold, that is, satisfy the condition. This enables accurate identification of attack behaviors and triggers an alarm mechanism, i.e.

[0099] (8);

[0100] By designing the relevant parameters of the observer, the result of the residual calculation function can be made to exceed the threshold when an FDI attack exists in the attack detection dynamic system, thus enabling the detection of FDI attacks.

[0101] Step 4: Performance Analysis: Introducing a Lyapunov functional, based on linear matrix inequalities, we verify that the attack detection dynamic system is asymptotically stable and satisfies... The performance metrics are used to find the optimal parameters of the robust attack solution detector, and the gain matrix of the robust attack detector meets the conditions, thereby ensuring that the robust attack detector achieves an effective balance between robustness and sensitivity. The constructed linear matrix inequality calculation method reduces the complexity and improves the detection efficiency in complex dynamic environments.

[0102] As an example, step 4 may include the following steps:

[0103] Step 4.1: Performance Verification and Parameter Solving: Verify that the attack detection dynamic system is asymptotically stable and satisfies... Performance metrics are introduced, and a stability and performance analysis framework for a dynamic attack detection system is established.

[0104] Set positive scalar and symmetric matrix and matrix The corresponding linear matrix inequality conditions are satisfied as follows:

[0105] (9);

[0106] in, .

[0107] In the above formula, scalar and Indicates used for Performance indicators define the maximum allowable energy gain of the system. This represents the adjustment parameters used in stability analysis; The matrix is ​​a symmetric positive definite matrix used to construct the Lyapunov function, ensuring the asymptotic stability of the attack detection dynamic system; The gain matrix for calculating the robust attack detector is obtained by solving the linear matrix inequality (LMI). ~ This represents the various coupling and constraint relationships in LMI conditions, used to characterize the system state, disturbance input, and Lyapunov matrix. stability and Energy constraints; weight matrix Energy constraints are used between the residual and the perturbation. The robust attack detector gain matrix can be obtained by solving the LMI. These are used for state updates, perturbation weighting, and residual output generation, respectively, to achieve effective detection of FDI attacks.

[0108] If the above matrix inequality holds, it can be proven that the attack detection dynamic system remains asymptotically stable under external disturbances and attacks, and satisfies the following conditions: Performance metrics are used to ensure the system has good robustness.

[0109] Step 4.2: Prove the stability of the attack detection dynamic system:

[0110] In the attack detection dynamic system (4), to verify the system stability, a Lyapunov function is first constructed. Where the symmetric matrix P>0,

[0111] Calculate its difference form Substituting the system state update equation into the equation, we obtain...

[0112] (10);

[0113] In the above formula, This can be expressed as a representation of the system state. Disturbance input and attack signals The quadratic expansion of the system's energy change shows the relationship between the system's energy change and the state matrix. Perturbation matrix Attack Matrix It is directly related to the detector gain matrix.

[0114] Step 4.3: Further define the performance index function:

[0115] definition ,in It is a positive definite matrix. for Performance metrics. When there is no attack signal ( When combining Lyapunov function differences can Transform into inclusion and The quadratic form matrix inequality expression:

[0116] (11);

[0117] In the above formula,

[0118] , .

[0119] If the matrix This indicates that the system satisfies the condition under disturbance. Performance constraints effectively suppress residual energy.

[0120] Step 4.4: Using Schur's lemma, the above matrix inequality can be equivalently transformed into a linear matrix inequality (LMI) form:

[0121] (12);

[0122] The introduction of a block matrix ,definition , .

[0123] Perform a congruential transformation on the above equation and define an auxiliary matrix. To achieve optimized design of system gain, the following is a detailed explanation:

[0124] (13);

[0125] Equation (9) holds true.

[0126] Finally, by solving for the LMI, the gain matrix of the robust attack detector is obtained:

[0127]

[0128] therefore, Substituting into the system equations, we get:

[0129] (14);

[0130] The proof is complete.

[0131] Finally, by solving this optimization problem, the gain matrix of the robust attack detector is obtained, specifically as follows: This enables effective detection and suppression of system attacks. This demonstrates that the dynamic attack detection system satisfies... While maintaining asymptotic stability while adhering to performance constraints, the detector parameter design is complete.

[0132] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A robust FDI attack detection method for a ship navigation system, characterized in that, Includes the following steps: Step 1: Establish a discrete-time multi-sensor network system based on the external interference and FDI attacks suffered by the USV; Furthermore, considering the scenario where the actuator is subjected to an FDI attack, the discrete-time multi-sensor network system under attack is reformulated into a form that facilitates detector design and robust performance analysis. Step 2: Based on the output of the discrete-time multi-sensor network system, construct a system based on... A robust attack detector is developed, which uses a gain matrix to generate residual signals and models the state of the discrete-time multi-sensor network system and the state of the robust attack detector in a unified manner to form a dynamic attack detection system. A Lyapunov function is introduced to establish performance constraints, and a robust attack detector is developed. By limiting the energy gain from the interference input to the residual signal output based on performance indicators, a dynamic attack detection system that remains stable under external disturbances and attacks is obtained. In step 2, a system is constructed based on the output of the discrete-time multi-sensor network system. Robust attack detector: ； In the above formula, This is the attack detector state vector; For a moment The attack detector state vector at that time; It is the first One sensor in The measurement output of time; The residual signal; matrix Let the attack detector gain be defined; let the augmented state be defined. The difference between residuals and attacks And to combine external disturbances and measurement noise into a composite disturbance vector. ,in, Indicates external disturbance. Indicates sensor noise; This is the residual signal; The dynamic attack detection system in step 2 is expressed as follows: ； in, , ; In the above formula, Represents the extended state vector; Indicates at time The extended state vector at that time; This is the residual signal; Represents the extended state transition matrix; This is the system state transition matrix; Indicates detector gain With observation matrix The combination; This represents the state transition matrix of the detector; Represents the extended perturbation input matrix; Represents the attack input matrix; Describe the attack signal Its effect on the system state; Indicates the extended output matrix; Indicates the detector output gain, which determines the auxiliary state. To residual Mapping; The direct channel matrix represents the attack signal. Enter the residual directly with the opposite sign; Represents the identity matrix; Step 3: Construct a residual evaluation function, define the residual mean and residual standard deviation of the residual evaluation function within the sliding window, and construct an adaptive threshold based on the residual mean and residual standard deviation; compare the residual evaluation function with the adaptive threshold, and when the detection result exceeds the adaptive threshold, determine that the attack detection dynamic system may be under FDI attack and trigger an alarm mechanism; Step 4: Introduce a Lyapunov functional and, based on the linear matrix inequality, verify that the attack detection dynamic system is asymptotically stable and satisfies the following conditions. Performance metrics, and optimization parameters for a robust attack detector, including: If a positive scalar exists and symmetric matrix ,matrix ,satisfy: ； in, ; ； In the above formula, and Used respectively Performance definition and stability adjustment; It is a symmetric positive definite matrix; Solving linear matrix inequalities is used to calculate the detector gain matrix; ~ This represents the coupling and constraints in solving linear matrix inequalities. Energy constraints for residuals and disturbances; The gain matrix is ​​obtained by solving the linear matrix inequalities. , .

2. The robust FDI attack detection method for a ship navigation system according to claim 1, characterized in that, In step 1, a discrete-time multi-sensor network system is established based on the external interference and FDI attacks suffered by the USV, as detailed below: ； In the above formula, let , This indicates the ship's position and heading information in a plane coordinate system; Represents location coordinate information, where, The coordinates representing the ship's position in the lateral or eastward direction. The coordinates representing the ship's position in the longitudinal or northward direction. The heading angle represents the angle between the ship's direction of motion and a reference direction. It is the given initial state; Indicates time The system status; It is the first One sensor in The measurement output of time; It belongs to Process noise; It belongs to Measurement noise; It is a known constant matrix.

3. The robust FDI attack detection method for a ship navigation system according to claim 2, characterized in that, In step 1, the discrete-time multi-sensor network system under attack is reformulated in a form that facilitates detector design and robustness analysis: ； In the above formula, This represents the system state under an FDI attack. This is the system output under an FDI attack. This indicates that the system is under FDI attack. Indicates the system at time 10:00 The state when under FDI attack.

4. The robust FDI attack detection method for a ship navigation system according to claim 1, characterized in that, In step 2, a Lyapunov function is introduced to establish performance constraints, and the following is adopted: Performance parameters limit the energy gain from interference input to residual signal output: ； In the above formula, This is the residual signal; It is a positive definite matrix; a positive scalar. Representing the system Performance metrics; This represents the upper bound of the energy gain, ensuring that the sensitivity of the residual output to disturbance inputs is constrained to an acceptable range. This represents the composite disturbance vector, including external disturbances. With sensor noise ; This represents the cumulative summation over time.

5. A robust FDI attack detection method for a ship navigation system according to claim 1, characterized in that, In step 3, the residual evaluation function is constructed: ； In the above formula, Represents the residual evaluation function; This represents the residual signal, which is the deviation between the system's observations and estimates.

6. A robust FDI attack detection method for a ship navigation system according to claim 5, characterized in that, In step 3, an adaptive threshold is constructed based on the residual mean and residual standard deviation, as follows: ； In the above formula, An adaptive residual threshold is used to determine whether an FDI attack exists. This is a sensitivity adjustment parameter used to balance detection accuracy and false alarm rate; Indicates the standard deviation of the residuals; This represents the mean of the residuals.

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