Fusion Filtering Method for Unmanned Surface Vessels with Sensor Saturation under FDI Attacks

Abstract

The present invention belongs to the field of information security technology, and particularly relates to a fusion filtering method for unmanned surface vessels with sensor saturation under FDI attacks. A discrete-time multi-sensor network system model is constructed, and a real matrix inequality is constructed based on linear and non-linear functions to optimize the filter design, and the filter is made to exhibit exponential stability in the mean square sense; according to the local filter parameters, a distributed fusion filter is designed to resist FDI attacks. By using the optimized design and distributed strategy, the anti-interference ability and data fusion accuracy of unmanned surface vessels in harsh environments are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of information security, and particularly relates to a fusion filtering method for an unmanned surface vessel with sensor saturation under FDI attack. Background Art

[0002] With the deep integration of information technology and physical processes, the Cyber-Physical System (CPS) has become a frontier field in current control disciplines and artificial intelligence research, driving the development of intelligence, automation, and networking. Through the close combination of computing, communication, and physical processes, CPS is widely used in the intelligent decision-making and control of various complex systems, such as automatic control, intelligent manufacturing, and intelligent transportation. In the application of CPS, the real-time perception and control capabilities of sensors, actuators, and communication networks play a crucial role. Especially in the research of unmanned systems, CPS provides key support for the autonomy and intelligence of unmanned surface vessels (USVs).

[0003] A USV is an unmanned boat that sails on the water surface and can be controlled by remote control, autonomous navigation, or a hybrid method. Thanks to its excellent stability and reliability, USVs have been widely used in military patrols, maritime surveillance, intelligence collection, and other fields. By integrating sensors, real-time data processing, and intelligent decision-making algorithms, CPS technology endows USVs with powerful environmental perception and decision-making capabilities, enabling them to operate independently in complex tasks such as ocean monitoring and resource exploration.

[0004] However, with the continuous expansion of the application scope of USVs, especially in the execution of complex tasks in military and marine environments, USVs face severe challenges from harsh sea conditions and cybersecurity threats. In particular, cyberattacks, as a major risk of USV security hazards, may affect their normal operation and task execution. Cyberattacks mainly include Denial of Service (DoS) attacks and False Data Injection (FDI) attacks. DoS attacks can cause navigation failure, task interruption, or even loss of control of the USV by interrupting the communication between the USV and the control center or other devices. FDI attacks, on the other hand, mislead the decision-making process of the USV by tampering with or forging data, affecting its motion control, and may even lead to a complete loss of control of the ship in severe cases.

[0005] Existing network attack defense technologies for USVs mainly focus on anti-DoS attacks and data encryption. For FDI attacks, most current defense methods are based on anomaly detection or robust filtering, preventing malicious tampering through real-time monitoring of sensor data and data consistency checks. However, these traditional defense methods have certain limitations. For example, existing anomaly detection methods often rely on fixed rules or prior models and are difficult to adapt to a dynamically changing environment; while robust filtering-based solutions may not be able to identify attack behaviors in a timely and effective manner when facing high-frequency attacks or multi-path attacks.

[0006] In addition, although existing network security technologies can, to a certain extent, protect USVs from external attacks, these methods still face many problems in practical applications. Therefore, it is particularly important to develop a filtering method that can maintain stability and effectiveness under FDI attacks. Although existing technologies have proposed some filter design methods, there is a lack of a comprehensive processing solution for multi-sensor network systems in such attacks and sensor saturation situations. Therefore, the present invention aims to propose a new H∞ fusion filtering method, using optimized design and distributed strategies to enhance the anti-interference ability and data fusion accuracy of unmanned surface vessels in harsh environments. Summary of the Invention

[0007] The object of the present invention is to solve the FDI attack and sensor saturation problems, and a fusion filtering method for an unmanned surface vessel with sensor saturation under FDI attacks is proposed. This method studies the distributed H ∞ fusion filtering problem of the cyber-physical system constructed by an unmanned surface vessel (USV) under false data injection (FDI) attacks in the case of sensor saturation.

[0008] The technical solution of the present invention to solve the above technical problems is as follows:

[0009] The present invention provides a fusion filtering method for an unmanned surface vessel with sensor saturation under FDI attacks, including the following steps:

[0010] Step 100: Construct a sensor model: Considering the external interference and FDI attacks suffered by the USV, construct a discrete-time multi-sensor network model; use a non-linear function to describe the sensor saturation degree, and decompose the non-linear function into linear and non-linear parts; introduce a random variable to simulate the measurement data when the communication channel is attacked.

[0011] Step 200: Design the local filter structure: When designing the local filter of a single-sensor system, construct a local filtering error system and ensure its mean-square exponential stability to estimate the system state in real time and optimize the estimation performance and robustness.

[0012] Step 300: Analyze the local filtering performance: Verify the exponential boundedness of the stochastic process in the mean square sense, and prove the exponential stability of the filtering error system in the mean square sense; Derive the upper bound of the error variation of the state variables of the filter using the stochastic process and the constraint conditions; Introduce performance metrics to evaluate the performance of the filter under FDI attacks;

[0013] Step 400: Design the local filter parameters: Convert the non - linear matrix inequality into a linear matrix inequality; Introduce LMI constraint conditions, decompose the LMI matrix structure, and decompose the LMI matrix structure into multiple sub - matrix blocks; Design the filter parameters according to the decomposed constraint conditions to meet the stability requirements;

[0014] Step 500: Design the distributed fusion filter: Based on the local filter parameters, use the weighted fusion method to calculate the output of the multi - sensor system; Determine the weights of the local filters and prove the performance of the fusion filter.

[0015] Furthermore, in the said Step 100, based on the external interference and FDI attacks suffered by the USV, establish a discrete - time multi - sensor network system model:

[0016]

[0017] In the above formula, represents the system state of the USV navigation dynamics, represents the d - dimensional real number space where x(k) is located; x(k + 1) represents the system state at the next moment k + 1, which is obtained from the current state x(k) through the state - transition matrix A and the control input w(k); w(k) is a process noise belonging to l[0,∞), which is a q - dimensional vector representing the external interference or uncertainty of the system state; is the measurement value of sensor i, representing the measurement value generated by sensor i at time k, where m i is the measurement dimension of sensor i, represents the measurement result y i (k) in the m i dimensional real number space; is the state to be estimated, represents the l - dimensional real number space where the state z(k) to be estimated is located; is a measurement noise belonging to l[0,∞); A, B, C i and L are known constant matrices with appropriate dimensions, n represents the number of sensors; g(C i x(k)+v i (k)) represents the non - linear function of the sensor measurement value, where g(·) is a non - linear function, and C i x(k)+v i(k) is the ideal measurement value of the sensor plus the noise v i (k).

[0018] Further, the adopting of a nonlinear function to describe the sensor saturation includes:

[0019] Using the nonlinear function ψ(C i x(k)) describes the saturation of the sensor and sets the corresponding conditions:

[0020] (ψ(C i x(k))-M1C i x(k) T (ψ(C i x(k))-M2C i x(k))≤0;

[0021] In the above formula, M1 and M2 are known real matrices, and the relationship satisfies M2>M1≥0;

[0022] Rewrite the nonlinear function into a linear part and a nonlinear part:

[0023] ψ(C i x(k))=M1C i x(k))+ψ n (C i x(k));

[0024] In the above formula, the nonlinear part ψ n ={ψ n (C i x(k)):ψ n T (C i x(k))(ψ n (C i x(k))-MC i x(k))≤0}, M=M2-M1>0.

[0025] Furthermore, in step 100, random variables are introduced to simulate the measurement data when the communication channel is attacked.

[0026]

[0027] In the above formula, the random variable α i (k) means attack, E is a constant matrix, indicating that the system is attacked by FDI.

[0028] Furthermore, in step 200, H of a single sensor system is designed on sensor i. ∞ Local filter structure:

[0029]

[0030] In the above formula, is the estimated value of the system state of the USV navigation dynamics at time k for sensor i, is the estimated value of the system state of the USV navigation dynamics at time k, is the estimated value of the state to be estimated for sensor i, A fi , B fi , C fi are the filter parameter matrices to be designed.

[0031] Furthermore, constructing the local filtering error system in step 200 specifically includes: defining the local error Constructing the local filtering error system on sensor i:

[0032]

[0033] The representations of each symbol in the formula are as follows:

[0034]

[0035] C fi = [B fi B fi E], and

[0036] In the above formula, η i (k + 1) represents the update of the local filtering error system state at time k + 1; represents the system state of the USV navigation dynamics; x i (k) represents the estimated state of sensor i; η i (k) represents the local filtering error state vector; represents the system state transition matrix, describing the process of system state update; represents the control input matrix, describing how the control input affects the local filtering error system; H i is a matrix that maps the local error η i (k) to the sensor output; represents the measurement matrix, converting the system state to the sensor output; d i (k) represents the sensor error; a i (k) represents the attack or other uncertainties suffered by sensor i; represents the system input noise; represents the gain matrix of the local filter, used to map the local filtering error state to the error estimate above, where L is a gain matrix, C fi is a matrix related to the sensor model.

[0037] Furthermore, the local filtering error satisfies the following conditions:

[0038]

[0039] In the above formula, l i represents the local error bound of sensor i, controlling the upper limit of the local filtering error.

[0040] Furthermore, in step 400, LMI constraint conditions are introduced to decompose the LMI matrix structure into multiple sub - matrix blocks, including:

[0041] By introducing matrix P i , R i and other related matrices, an LMI constraint is formed:

[0042] A fi , B fi , C fi and γ i > 0, ε i > 0, then when time,

[0043] there is an H ∞ norm constraint, making the LMI hold, that is:

[0044]

[0045] Ξ2 = [Ξ 21 Ξ 22 Ξ 23 ,

[0046]

[0047] Ξ4 = [ε i MH i 0 0],

[0048] Ξ5 = - ε i I, Ξ7 = - I.

[0049] In the above formula, matrices Ξ1, Ξ2, Ξ3, Ξ4, Ξ5, Ξ6, Ξ7 represent different parts of the system under LMI constraint conditions, including state transition, input noise, disturbance, and constraints of the sensor model; matrices P i , R i , Afi , B fi , C fi , γ i , ε i , etc. are parameters for system dynamics, control, and measurement, and the stability and performance of the system are described through these matrices.

[0050] In the said step 400, the filter parameters are designed through the following formula:

[0051]

[0052] Furthermore, in the said step 500, the output of each sensor is weighted and summed according to the weight σ i to form a fused estimated value

[0053]

[0054] In the above formula, l i represents the weighting factor of the i-th sensor, measuring the influence or signal quality of the sensor; l j represents the weighting factor of the i-th sensor, used for normalizing the weight.

[0055] Compared with the prior art, the present invention has the following technical effects:

[0056] The present invention constructs a discrete-time multi-sensor network system model, constructs real matrix inequalities to optimize filter design based on linear and non-linear functions, and makes the filter exhibit exponential stability in the mean square sense. Using the optimized design and distributed strategy, the anti-interference ability and data fusion accuracy of the unmanned surface vessel in a harsh environment are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0058] Figure 1 is a flowchart of a fusion filtering method for an unmanned surface vessel with sensor saturation under FDI attack of the present invention;

[0059] Figure 2 is a flowchart of the sensor model construction of the present invention;

[0060] Figure 3 is a flowchart of the local filter structure of the present invention;

[0061] Figure 4 It is the flowchart for analyzing the local filtering performance of the present invention;

[0062] Figure 5 It is the flowchart for designing the local filter of the present invention;

[0063] Figure 6 It is for designing the distributed H ∞ fusion filter flowchart of the present invention;

[0064] Figure 7 It is the flowchart for the application of the H ∞ fusion filter established in the implementation of the present invention in the USV. Specific implementation manners

[0065] In order to further elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the specific implementation manners, structures, features and their 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 the present invention have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs.

[0066] The present invention discloses a fusion filtering method for an unmanned surface vessel with sensor saturation under FDI attacks. First, a discrete-time multi-sensor network system model is proposed, and a real matrix inequality is constructed based on linear and non-linear functions to optimize the filter design, and the filtering shows exponential stability in the mean square sense; secondly, according to the local filter parameters, a distributed H ∞ fusion filter is designed to resist FDI attacks.

[0067] In one embodiment of the present invention, with reference to Figure 1 - Figure 7, a fusion filtering method for unmanned surface vessels with sensor saturation under FDI attacks is provided, including the following steps: Step 100: Build a sensor model: Considering the external disturbances and FDI attacks suffered by the USV, build a discrete-time multi-sensor network model; Use a non-linear function to describe the sensor saturation and decompose it into linear and non-linear parts; Introduce a random variable to simulate the measurement data when the communication channel is attacked; Step 200: Design the local filter structure: When designing the local filter of a single-sensor system, build a local filtering error system and ensure its mean-square exponential stability to estimate the system state in real time and optimize the estimation performance and robustness; Step 300: Analyze the local filtering performance: Verify the exponential boundedness of the stochastic process in the mean-square sense and prove the exponential stability of the filtering error system in the mean-square sense; Use the stochastic process and constraint conditions to derive the upper bound of the error variation of the state variable of the filter; Introduce a performance index to evaluate the performance of the filter under FDI attacks; Step 400: Design the local filter parameters: Convert the non-linear matrix inequality into a linear matrix inequality; Introduce LMI constraint conditions, decompose the LMI matrix structure, and decompose the LMI matrix structure into multiple sub-matrix blocks; According to the decomposed constraint conditions, design the filter parameters to meet the stability requirements; Step 500: Design a distributed fusion filter: Based on the local filter parameters, use a weighted fusion method to calculate the output of the multi-sensor system; Determine the weights of the local filters and prove the performance of the fusion filter.

[0068] The above steps are detailed as follows:

[0069] Step 100: Build a sensor model:

[0070] Considering the external disturbances and FDI attacks suffered by the USV, build a discrete-time multi-sensor network model; Use a non-linear function to describe the saturation of the sensor and set the conditions it satisfies; Decompose the non-linear function into a linear part and a non-linear part; When the communication channel is attacked, introduce a random variable and substitute it to obtain the measurement data of the local filter when suffering from FDI attacks.

[0071] As an example, this step may include the following steps:

[0072] Step 110: Based on the external disturbances and FDI attacks suffered by the USV, establish a discrete-time multi-sensor network system model:

[0073]

[0074] In the above formula, represents the system state of the USV's navigation dynamics, Denote the d-dimensional real space where x(k) is located; x(k + 1) represents the system state at the next moment k + 1, which is obtained from the current state x(k) through the state transition matrix A and the control input w(k); w(k) is a process noise belonging to l[0, ∞), which is a q-dimensional vector representing the external interference or uncertainty of the system state; is the measurement value of sensor i, representing the measurement value generated by sensor i at time k, where m i is the measurement dimension of sensor i, represents the measurement result y of sensor i i (k) in the m i -dimensional real space; is the state to be estimated, represents the l-dimensional real space where the state z(k) to be estimated is located; is the measurement noise belonging to l[0, ∞); A, B, C i and L are known constant matrices with appropriate dimensions, n represents the number of sensors; g(C i x(k) + v i (k)) represents the nonlinear function of the sensor measurement value, where g(·) is a nonlinear function, and C i x(k) + v i (k) is the ideal measurement value of the sensor plus the noise v i (k).

[0075] Step 120: Set the saturation degree and its conditions: When the signal or system reaches the maximum measurement or processing capacity, use the nonlinear function ψ(C i x(k)) to describe the saturation of the sensor and set the corresponding satisfied conditions.

[0076] The set conditions to be satisfied are:

[0077] (ψ(C i x(k)) - M1C i x(k)) T (ψ(C i x(k)) - M2C i x(k)) ≤ 0 (2);

[0078] In the above formula, M1 and M2 are known real matrices, and the relationship satisfies M2 > M1 ≥ 0.

[0079] Step 130: Rewrite the nonlinear function ψ(C i x(k)) into a linear part and a nonlinear part.

[0080] To make it convenient to solve the subsequent matrix inequalities, rewrite the nonlinear function ψ(C iRewrite \(x(k)\) as the sum of a linear part and a non - linear part, i.e.:

[0081] \(\psi(C\) i \(x(k)) = M_1C\) i \(x(k))+\psi\) n (C i \(x(k))\ (3)\);

[0082] In the above formula, the non - linear part \(\psi\) n \(=\{\psi\) n (C i \(x(k)):\psi\) n T (C i \(x(k))(\psi\) n (C i \(x(k)) - M C\) i \(x(k))\leq0\}, M = M_2 - M_1>0\).

[0083] Step 140: Consider the case where the communication channel is attacked, introduce parameters representing the attack, and substitute to obtain the measurement data of the local filter when suffering from FDI attack.

[0084] When the communication channel is attacked, introduce \(\alpha\) i (k) to represent the attack, and substitute to obtain the measurement data of the local filter when suffering from FDI attack

[0085] When the communication channel is attacked, the local filter may receive false measurement data at a certain moment To describe this phenomenon, a random variable \(\alpha\) i (k) is introduced, and substituting into Equation (4) gives the measurement data of the local filter when suffering from FDI attack

[0086]

[0087] In the above formula, the random variable \(\alpha\) i (k) represents the attack, E is a constant matrix, indicating that the system suffers from FDI attack.

[0088] Step 200: Design the local filter structure:

[0089] Design the H of the single - sensor system on sensor i ∞ Local filter structure:

[0090]

[0091] In the above formula, is the estimated value of the system state of the USV navigation dynamics of sensor i at time k, is the estimated value of the system state of the USV's navigation dynamics at time k, is the estimated value of the state to be estimated by sensor i, A fi , B fi , C fi are the filter parameter matrices to be designed.

[0092] When designing the local filter structure of the single-sensor system on the sensor, by defining the local error and combining the measurement data and the local filter structure, construct the local filtering error system on the sensor; define the mean-square exponential stability of the filtering error system; when the USV system is running in real time, design the local filter to continuously estimate the state of the USV system; ensure that the local filtering error meets the predetermined conditions to optimize the state estimation performance and robustness of the USV system.

[0093] Step 210: By defining the local error and combining the measurement data and the local filter structure, construct the local filtering error system on the sensor.

[0094] By defining the local error and combining formulas (1), (4) and (5), construct the local filtering error system on sensor i:

[0095]

[0096] The representations of the symbols in the formula are as follows:

[0097] H i = [C i 0],

[0098] C fi = [B fi B fi E], and

[0099] In the above formula, represents the system state of the USV's navigation dynamics; x i (k) represents the estimated state of sensor i; η i (k) represents the local filtering error state vector; represents the state transition matrix of the system, describing the process of system state update; represents the control input matrix, describing how the control input affects the local filtering error system; H i is a matrix that maps the local error η i (k) to the sensor output; represents the measurement matrix, converting the state of the system into the output of the sensor; d i(k) represents the sensor error; a i (k) represents the attack on or other uncertainties of sensor i; represents the input noise of the system; represents the gain matrix of the local filter, used to map the local filtering error state to the error estimate thereon, where L is a gain matrix, C fi is a matrix related to the sensor model.

[0100] Step 220: Define the mean-square exponential stability of the filtering error system.

[0101] Defining the mean-square exponential stability of the filtering error system means that when holds, the variance of the filtering error will gradually decrease under the condition of exponential decay.

[0102] Specifically, there exist constants δ > 0 and 0 < τ < 1, then the filtering error variance satisfies the condition:

[0103] E{||η i (k)|| 2} ≤ δτ k E{||η i (0)|| 2} (7);

[0104] Then the filtering error of the system will decay over time, making the system more stable;

[0105] In the above formula, η i (0) represents the filtering error at the initial time of the system when k = 0, that is, the difference between the initial estimate value and the true value. As time goes by, the filtering error will gradually decrease according to the exponential decay law of τ k and finally make the system stable, and the error approaches zero.

[0106] Step 230: When the system is running in real time, a local filter is designed to continuously estimate the system state.

[0107] When the USV system is running in real time, a local H ∞ filter is designed to continuously adjust its estimate according to the observed values and control inputs, and predict the future state of the USV system. To ensure the robustness and performance of the USV system, the filter needs to handle uncertainties and perform appropriate filtering estimates.

[0108] Step 240: Ensure that the local filtering error satisfies the following conditions:

[0109]

[0110] By adjusting the parameters of the filter, such as the disturbance attenuation level l i , the state estimation performance and robustness of the system are optimized, enabling the local filtering error system to provide accurate and robust estimation results through continuous state estimation and disturbance suppression.

[0111] Step 300: Analyze the local filtering performance:

[0112] Introduce a lemma to verify the exponential boundedness of the stochastic process in the mean square sense; introduce a theorem to prove the exponential stability of the filtering error system in the mean square sense; define a Lyapunov functional and derive the error equation, use the stochastic process and constraint conditions to derive the upper bound of the error variation of η(k), and further verify the stability of the system through matrix decomposition; introduce a performance index to evaluate the performance of the filter under FDI attacks; through derivation, prove that the system can effectively resist disturbances and has exponential stability in long-term operation.

[0113] As an example, this step may include the following steps:

[0114] Step 310: Introduce a lemma to verify the exponential boundedness of the stochastic process in the mean square sense and provide a theoretical basis for the subsequent optimization process.

[0115] The lemma 1 is as follows:

[0116] θ||η(k)|| 2 ≤V(η(k))≤λ||η(k)|| 2 (9);

[0117]

[0118] The stochastic process η(k) is exponentially bounded in the mean square sense, that is, assume η(k) is a stochastic process. If there exists a Lyapunov functional U(η(k)) and a scalar and 0 < ξ < 1 such that:

[0119]

[0120] where θ and λ are constants, η(k) is the state variable of the filter, V(η(k)) is the Lyapunov function, and ξ is a constant affecting the state attenuation rate of the control system and affects the stability of the system.

[0121] Step 320: Introduce Theorem 1 to prove the exponential stability of the filtering error system, describe the stability conditions through matrix inequalities, and prove that when the conditions are satisfied, the system is exponentially stable in the mean square sense.

[0122] Theorem 1: By given filtering parameters A fi ,Bfi , C fi , and the scalar γ i > 0, which proves the exponential stability of the filtering error system in the mean square sense. When , if there exists a matrix P i = P i T > 0, and the scalar ε i > 0, then the stability of the system can be guaranteed by the H ∞ -norm constraint:

[0123]

[0124] In the above formula, Δ i represents a matrix related to the error or disturbance, ε i represents the disturbance attenuation coefficient, which controls the robustness of the control system, Λ i represents a matrix related to the system dynamics and states, which affects the stability, represents the state matrix after the disturbance, represents a symmetric positive definite matrix, which describes the filter state or error, and I is the identity matrix.

[0125] Step 330: Define the Lyapunov functional and derive the error equation. Use the stochastic process and constraint conditions to derive the upper bound of the error variation of the state variable η(k) of the filter, and further verify the stability of the system through matrix decomposition.

[0126] By setting the Lyapunov functional V k (η i (k)) = η i T (k)P i η i (k), define the change in error ΔV k ,

[0127]

[0128] Then derive the stability of the system. Use the stochastic process and constraint conditions to derive the upper bound of the error variation of η(k), and further verify the stability of the system through matrix decomposition.

[0129] Step 340: Introduce the performance index J(N), and derive the optimal performance of the system by calculating the expectation of the error and the change in the Lyapunov functional, thus ensuring that the performance index meets the desired constraints.

[0130] To further evaluate the performance of the filter under FDI attacks, the performance index J(N) is defined:

[0131]

[0132] wherein, is the output of the filter, is the disturbance term, and γ i is the gain parameter of the filter.

[0133] Step 350: Calculation result and stability guarantee.

[0134]

[0135] wherein, let:

[0136]

[0137] In the above formula, β i (k) is a combined column vector containing system state variables and disturbance terms; ξ i T (k) represents the transpose of the filter state; represents a matrix, which is a weighted sum composed of multiple terms and involves various matrix parameters in the system; Π i represents a matrix related to the filter gain or disturbance suppression part; Λ i represents a matrix related to system dynamics and state, which affects stability, represents the state matrix after disturbance.

[0138] Obtain J(N) < 0, let N → ∞, and obtain:

[0139]

[0140] The proof is completed. Therefore, the system can effectively resist disturbances and has exponential stability during long-term operation.

[0141] Through derivation, it is proved that the desired loss metric J(N) is negative, that is, the system can effectively resist disturbances and has exponential stability during long-term operation.

[0142] Step 400: Design local filter parameters:

[0143] Convert the nonlinear matrix inequality into a linear matrix inequality; introduce LMI constraint conditions to ensure the stability of the filter under specific conditions; decompose the LMI matrix structure into multiple sub-matrix blocks, and each sub-matrix block represents a specific constraint condition; design the filter parameters according to the decomposed constraint conditions to ensure that the filter can meet the required stability requirements; finally, obtain the required LMI form and filter parameter design formula through transformation and application of inequality conditions.

[0144] As an example, this step may include the following steps:

[0145] Step 410: Process the non - linear matrix inequality (12) and convert the non - linear matrix inequality into a linear matrix inequality (LMI).

[0146] Step 420: By introducing matrices P i , R i and other related matrices, form LMI constraints to ensure that the filter is stable under specific conditions;

[0147] A fi , B fi , C fi and γ i > 0, ε i > 0, then when time,

[0148] there is an H ∞ norm constraint such that the following LMI holds, that is:

[0149]

[0150] In the above formula, matrices Ξ1, Ξ2, Ξ3, Ξ4, Ξ5, Ξ6, Ξ7 represent different parts of the system under LMI constraint conditions, including constraints on state transition, input noise, disturbance, and sensor model; matrices P i , R i , γ i , ε i etc. are parameters of system dynamics, control, and measurement, and A fi , B fi , C fi are filter parameters to be designed, and the stability and performance of the system are described by these matrices.

[0151] Step 430: The LMI matrix structure is decomposed into multiple sub - matrix blocks, and each sub - matrix block represents a specific constraint condition.

[0152] These matrices are defined by the state equation and filter parameters to ensure the stability of the filter;

[0153]

[0154] Ξ2 = [Ξ 21 Ξ 22 Ξ 23 ,

[0155]

[0156] Ξ4 = [ε i MH i0 0],

[0157] Ξ5 = -ε i I, Ξ7 = -I。

[0158] In the above formula, is the state matrix related to sensor i in the system dynamic model, the input matrix related to sensor i in the system, the measurement matrix of sensor i.

[0159] Step 440: According to the decomposed constraint conditions, design the filter parameters to ensure that the filter can meet the required stability requirements.

[0160] According to the LMI condition, the filter parameters A fi , B fi , C fi are designed in a specific form to ensure that the filter can meet the required stability requirements. The filter parameters can be designed by the following formula:

[0161]

[0162] By the Schur complement lemma, the formula can be rewritten as:

[0163]

[0164] Perform a congruence transformation on it, using the relationship -R i P i -1 R i T ≤ P i -R i -R i T Transform to get (P i -R i )P i -1 (P i -R i ) T ≥ 0, and the following inequality can be obtained:

[0165]

[0166] Step 450: Through transformation and application of the inequality conditions, finally obtain the required LMI form and the filter parameter design formula, thus completing the design of the filter.

[0167] Define Then it can be deduced that (17) holds, so (18) holds and the filter design is completed.

[0168] Step 500: Design a distributed H ∞ fusion filter:

[0169] Based on the designed local filter parameters, use the weighted fusion method to calculate the output of the multi-sensor system; determine the local filter weights, which are determined by the errors of the local filters; according to the design of the fusion filter, define the fusion error; prove the performance of the fusion filter to ensure that the fused filter is comparable to or better than the average level of each local filter in terms of performance metrics.

[0170] As an example, this step may include the following steps:

[0171] Step 510: Based on the design of a single-sensor system, expand it into a multi-sensor system and propose a distributed H ∞ fusion filtering system to improve the filtering performance of the multi-sensor system.

[0172] Using the previously designed local filter parameters, use the weighted fusion method to calculate the output of the multi-sensor system. The output of each sensor is weighted and summed according to the weight σ i to form the fused estimated value

[0173]

[0174] In the above formula, l i represents the weighting factor of the i-th sensor, measuring the influence or signal quality of the sensor; l j represents the weighting factor of the i-th sensor, used to normalize the weights.

[0175] Step 520: Determine the weights of the local filters.

[0176] Ensure that the weights of each local filter are related to its performance (error or uncertainty), and filters with better performance should be given higher weights;

[0177] The weight σ i is determined by the error l i of the local filter. Specifically, the weight is proportional to which means that filters with smaller errors are given higher weights and thus play a greater role in the fusion.

[0178] Step 530: According to the design of the fusion filter, define the fusion error.

[0179] Let

[0180]

[0181] Step 540: Prove the performance of the fusion filter.

[0182] From the above derivation, it can be seen that the fusion error satisfies H ∞ Performance metrics.

[0183] It shows that the estimated performance of the fused H ∞ The filter is not less than the average of the information amounts of all local filters. This means that the fused filter is equivalent to or better than the average level of each local filter in terms of performance metrics. Therefore, the fusion process can effectively integrate the information of each local filter and improve the overall filtering performance.

[0184] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements 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 in the protection scope of the present invention.

Claims

1. A fusion filtering method for an unmanned surface vehicle with sensor saturation under FDI attacks, characterized in that It includes the following steps: Step 100: Construct a sensor model: Considering the external interference and FDI attacks suffered by the USV, construct a discrete-time multi-sensor network model; Use a non-linear function to describe sensor saturation and decompose the non-linear function into linear and non-linear parts; Introduce random variables to simulate the measurement data when the communication channel is attacked; Using a non-linear function to describe sensor saturation and decomposing the non-linear function into linear and non-linear parts includes: Use the non-linear function ψ(C i x(k)) to describe the saturation of the sensor and set the corresponding satisfaction conditions: (ψ(C i x(k)) - M1C i x(k)) T (ψ(C i x(k)) - M2C i (ψ(C i x(k)) - M2C i x(k)) ≤ 0; In the above formula, M1 and M2 are known real matrices, and the relationship satisfies M2 > M1 ≥ 0; C i is a known constant matrix with appropriate dimensions; x(k) represents the system state of the USV's navigation dynamics; Rewrite the non-linear function into a linear part and a non-linear part: ψ(C i x(k)) = M1C i x(k)) + ψ n (C i x(k)); In the above formula, the non-linear part ψ n ={ψ n (C i x(k)):ψ n T (C i x(k))(ψ n (C i x(k)) - MC i x(k)) ≤ 0}, M = M2 - M1 > 0; Step 200: Design the local filter structure: Design the local filter for a single-sensor system, construct the local filtering error system and ensure its mean-square exponential stability to estimate the USV trajectory information state in real time and optimize the estimation performance and robustness; Step 300: Analyze the local filtering performance: Verify the exponential boundedness of the stochastic process in the mean-square sense and prove the exponential stability of the filtering error system in the mean-square sense; Derive the upper bound of the error change of the state variables of the filter using the stochastic process and constraint conditions; Introduce performance metrics to evaluate the performance of the filter under FDI attacks; Step 400: Design the local filter parameters: Convert the non-linear matrix inequality into a linear matrix inequality; Introduce LMI constraint conditions, decompose the LMI matrix structure, and decompose the LMI matrix structure into multiple sub-matrix blocks; According to the decomposed constraint conditions, design the filter parameters to meet the stability requirements; Step 500: Design a distributed fusion filter: Based on the local filter parameters, use a weighted fusion method to calculate the output of the multi-sensor system; Determine the weights of the local filters and prove the performance of the fusion filter.

2. A fusion filtering method for an unmanned surface vessel with sensor saturation under FDI attack according to claim 1, characterized in that In the said Step 100, based on the external interference and FDI attacks suffered by the USV, establish a discrete-time multi-sensor network system model: In the above formula, represents the system state of the USV's navigation dynamics, represents the d-dimensional real space where x(k) is located; x(k + 1) represents the system state at the next moment k + 1, which is obtained from the current state x(k) through the state transition matrix A and the control input w(k); w(k) is a process noise belonging to l[0, ∞), which is a q-dimensional vector representing the external interference or uncertainty of the system state; is the measurement value of sensor i, representing the measurement value generated by sensor i at moment k, where m i is the measurement dimension of sensor i, represents the measurement result y of sensor i i (k) in the m i dimensional real space; is the state to be estimated, represents the l-dimensional real space where the state to be estimated z(k) is located; is a measurement noise belonging to l[0, ∞); A, B, C i and L are known constant matrices with appropriate dimensions, n represents the number of sensors; g(C i x(k) + v i (k)) represents the non-linear function of the sensor measurement value, where g(·) is a non-linear function, and C i x(k) + v i (k) is the ideal measurement value of the sensor plus the noise v i (k).

3. A fusion filtering method for an unmanned surface vessel with sensor saturation under FDI attack according to claim 2, characterized in that In the said step 100, a random variable is introduced to simulate the measurement data when the communication channel is attacked. In the above formula, the random variable α i (k) represents an attack, E is a constant matrix, indicating that the system is subject to an FDI attack.

4. A fusion filtering method for an unmanned surface vessel with sensor saturation under FDI attack according to claim 3, characterized in that, In the said Step 200, design the local filter structure of the single-sensor system on sensor i: In the above formula, is the estimated value of the system state of the USV navigation dynamics at time k for sensor i, is the estimated value of the system state of the USV navigation dynamics at time k, is the estimated value of the state to be estimated for sensor i, A fi , B fi , C fi are the filter parameter matrices to be designed.

5. A fusion filtering method for an unmanned surface vessel with sensor saturation under FDI attack according to claim 4, characterized in that In the step 200, a local filtering error system is constructed, which specifically includes: defining a local error Construct the local filtering error system on sensor i: The representations of each symbol in the formula are as follows: H i = [C i 0], C fi = [B fi B fi E], and In the above formula, η i (k + 1) represents the update of the local filtering error system state at time k + 1; represents the system state of the USV's navigation dynamics; x i (k) represents the estimated state of sensor i; η i (k) represents the local filtering error state vector; represents the system's state transition matrix, which describes the process of system state update; represents the control input matrix, which describes how the control input affects the local filtering error system; H i is a matrix that maps the local error η i (k) to the sensor output; represents the measurement matrix, which converts the system's state into the sensor's output; d i (k) represents the sensor error; a i (k) represents the attack or other uncertainties suffered by sensor i; represents the system's input noise; represents the gain matrix of the local filter, which is used to map the local filtering error state to the error estimate above, where L is a gain matrix, C fi is a matrix related to the sensor model.

6. A fusion filtering method for an unmanned surface vessel with sensor saturation under FDI attack according to claim 5, characterized in that Local filtering error Satisfies the following conditions: In the above formula, represents the local error bound of sensor i, which controls the upper limit of the local filtering error.

7. A fusion filtering method for an unmanned surface vessel with sensor saturation under FDI attack according to claim 6, characterized in that, In the said Step 400, introducing LMI constraint conditions to decompose the LMI matrix structure and decomposing the LMI matrix structure into multiple sub-matrix blocks includes: By introducing matrix P i , R i and other relevant matrices, an LMI constraint is formed: A fi ,B fi ,C fi and γ i >0, ε i >0, then when at that time There is H ∞ norm constraint, making the LMI hold, that is: Ξ2 = [Ξ 21 Ξ 22 Ξ 23 , Ξ4 = [ε i MH i 0 0], Ξ5 = -ε i I, Ξ7 = -I。 In the above formula, the matrices Ξ1, Ξ2, Ξ3, Ξ4, Ξ5, Ξ6, Ξ7 represent different parts of the system under the LMI constraint conditions, including the constraints of state transition, input noise, disturbance, and sensor model; the matrix P i , R i , A fi , B fi , C fi , γ i , ε i are the parameters of system dynamics, control, and measurement.

8. A fusion filtering method for an unmanned surface vessel with sensor saturation under FDI attack according to claim 7, characterized in that In the said Step 400, the filter parameters are designed through the following formula:

9. A fusion filtering method for an unmanned surface vessel with sensor saturation under FDI attack according to claim 1, characterized in that In the said step 500, the output of each sensor is weighted and summed according to the weight σ i to form a fused estimated value In the above formula, represents the weighting factor of the i-th sensor, which measures the influence or signal quality of the sensor; represents the weighting factor of the i-th sensor, which is used for normalizing the weights; is the estimated value of the state to be estimated by sensor i.

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