Fusion filtering method for unmanned surface ship with sensor saturation under FDI attack

Abstract

The invention belongs to the technical field of information security, and particularly relates to an unmanned surface ship fusion filtering method with sensor saturation under FDI attack. Constructing a discrete time multi-sensor network system model, constructing a real number matrix inequality optimization filter design based on linear and nonlinear functions, and enabling filtering to show exponential stability under the mean square meaning; and according to local filter parameters, a distributed fusion filter is designed to resist FDI attacks. The anti-interference capability and the data fusion precision of the unmanned surface ship in a severe environment are improved by using an optimization design and a distributed strategy.

Description

Technical Field

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

[0002] With the deep integration of information technology and physical processes, Cyber-Physical System (CPS) has become the frontier of current control disciplines and artificial intelligence research, promoting the development of intelligence, automation and networking. Through the close integration of computing, communication and physical processes, CPS is widely used in intelligent decision-making and control of various complex systems, such as automated 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 vital role, especially in the research of unmanned systems. CPS provides key support for the autonomy and intelligence of unmanned surface vessels (USVs).

[0003] USV is an unmanned, surface-traveling vessel that can be controlled by remote control, autonomous navigation, or a combination of methods. Thanks to its excellent stability and reliability, USV has been widely used in military patrols, maritime surveillance, intelligence gathering, and other fields. Through integrated sensors, real-time data processing, and intelligent decision-making algorithms, CPS technology gives USV powerful environmental perception and decision-making capabilities, enabling it to operate independently in complex tasks such as ocean monitoring and resource exploration.

[0004] However, with the continuous expansion of the application scope of USV, especially the execution of complex tasks in military and marine environments, USV faces severe challenges from severe sea conditions and network security threats. In particular, cyber attacks, as a major risk of USV safety hazards, may affect its normal operation and mission execution. Cyber ​​attacks mainly include denial of service attacks (DoS) and false data injection attacks (FDI). DoS attacks may cause navigation failure, mission interruption, or even loss of control of USV by interrupting the communication between USV and the control center or other equipment. FDI attacks, on the other hand, mislead the decision-making process of USV by tampering with or falsifying data, affecting its motion control, and in severe cases, may lead to complete loss of control of the ship.

[0005] Existing cyber attack defense technologies for USVs mainly focus on anti-DoS attacks and data encryption. For FDI attacks, current defense methods are mostly based on anomaly detection or robust filtering, which prevent 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, which are difficult to adapt to dynamically changing environments; and 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 protect USVs from external attacks to a certain extent, 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 the prior art has proposed some filter design methods, it lacks a comprehensive processing solution for multi-sensor network systems under such attacks and sensor saturation. Therefore, the present invention aims to propose a new H∞ fusion filtering method, which uses optimization design and distributed strategy to improve the anti-interference ability and data fusion accuracy of unmanned surface ships in harsh environments. Summary of the invention

[0007] The purpose of this paper is to solve the problem of FDI attack and sensor saturation, and propose a fusion filtering method for unmanned surface vessels with sensor saturation under FDI attack. This method studies the distributed H-based filtering of a cyber-physical system constructed by an unmanned surface vessel (USV) under false data injection (FDI) attack under sensor saturation. ∞ Fusion filtering problem.

[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 ship with sensor saturation under FDI attack, comprising the following steps:

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

[0011] Step 200: Designing a local filter structure: When designing a local filter for a single sensor system, a local filter error system is constructed and its mean square exponential stability is ensured to estimate the system state in real time and optimize the estimation performance and robustness;

[0012] Step 300: Analyze local filtering performance: verify the exponential boundedness of the random process in the mean square sense, prove the exponential stability of the filter error system in the mean square sense; use the random process and constraints to derive the upper bound of the error change of the state variable of the filter; introduce performance indicators to evaluate the performance of the filter under FDI attack;

[0013] Step 400: designing local filter parameters: converting the nonlinear matrix inequality into a linear matrix inequality; introducing LMI constraints, decomposing the LMI matrix structure, and decomposing the LMI matrix structure into multiple sub-matrix blocks; designing the filter parameters according to the decomposed constraints to meet the stability requirements;

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

[0015] Furthermore, in step 100, a discrete-time multi-sensor network system model is established according to the external interference and FDI attack suffered by the USV:

[0016]

[0017] In the above formula, Indicates the system status of the USV navigation dynamics, represents the d-dimensional real space where x(k) is located; x(k+1) represents the system state at the next time k+1, which is obtained from the current state x(k) through the state transfer matrix A and the control input w(k); w(k) is the process noise belonging to l[0,∞), which is a q-dimensional vector, representing external interference or uncertainty to the system state; is the measurement value of sensor i, which represents 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) where m i dimensional real number space; is a state to be estimated, represents the l-dimensional real space where the state to be estimated z(k) 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).

[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 USV navigation dynamics of sensor i at time k, 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 of sensor i, A fi ,B fi ,C fi is the filter parameter matrix to be designed.

[0031] Furthermore, the local filtering error system is constructed in step 200, specifically including: defining the local error Construct the local filtering error system on sensor i:

[0032]

[0033] The symbols in the formula are as follows:

[0034]

[0035] C fi =[B fi B fi E], as well as

[0036] In the above formula, η i (k+1) represents the update of the local filter error system state at time k+1; Indicates the system status of 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 state transition matrix of the system, describing the process of system state update; represents the control input matrix, which describes how the control input affects the local filter error system; H i is a local error η i (k) Matrix mapped to sensor output; represents the measurement matrix, which converts the state of the system into the output of the sensor; d i (k) represents sensor error; a i (k) represents the attack or other uncertainties suffered by sensor i; represents the input noise of the system; Represents the gain matrix of the local filter, which is used to map the local filtering error state to the error estimate where L is a gain matrix and C fi is the matrix associated with the sensor model.

[0037] Furthermore, the local filtering error The following conditions are met:

[0038]

[0039] In the above formula, l i Represents the local error limit of sensor i and controls the upper limit of the local filtering error.

[0040] Furthermore, in step 400, the LMI constraint condition is introduced to decompose the LMI matrix structure, and the LMI matrix structure is decomposed into a plurality of sub-matrix blocks, including:

[0041] By introducing the matrix P i , R i And other correlation matrices to form the LMI constraints:

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

[0043] Yes ∞ Norm constraints make LMI valid, 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, the matrices Ξ1, Ξ2, Ξ3, Ξ4, Ξ5, Ξ6, and Ξ7 represent different parts of the system under LMI constraints, including state transition, input noise, disturbance, and sensor model constraints; the matrix P i ,R i ,Afi ,B fi ,C fi ,γ i ,ε i Etc. are the system dynamics, control and measurement parameters, and these matrices are used to describe the stability and performance of the system.

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

[0051]

[0052] Furthermore, in step 500, the output of each sensor is weighted by i Perform weighted summation to form a fused estimate

[0053]

[0054] In the above formula, l i represents the weighting factor of the i-th sensor, which measures the influence of the sensor or the signal quality; l j Represents the weighting factor of the i-th sensor, which is used to normalize 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 a real matrix inequality optimization filter design based on linear and nonlinear functions, and makes the filter show exponential stability in the mean square sense. The optimization design and distributed strategy are used to improve the anti-interference ability and data fusion accuracy of unmanned surface ships in harsh environments. 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 drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0058] Figure 1 It is a flow chart of a fusion filtering method of an unmanned surface ship with sensor saturation under FDI attack of the present invention;

[0059] Figure 2 It is a flow chart of the construction of the sensor model of the present invention;

[0060] Figure 3 It is a flow chart of the local filter structure of the present invention;

[0061] Figure 4 It is a flow chart of analyzing local filtering performance of the present invention;

[0062] Figure 5 It is a flow chart of designing a local filter according to the present invention;

[0063] Figure 6 The invention designs distributed H ∞ Fusion filter flow chart;

[0064] Figure 7 It is H established by the implementation of the present invention. ∞ Flowchart of the fusion filter application in USV. DETAILED DESCRIPTION

[0065] In order to further explain the technical means and effects taken by the present invention to achieve the predetermined invention purpose, the specific implementation methods, structures, features and effects of the technical solutions proposed by the present invention are described in detail below in conjunction with the accompanying drawings and preferred embodiments. The 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 those commonly understood by technicians in the technical field of the present invention.

[0066] The present invention discloses a fusion filtering method for unmanned surface ships with sensor saturation under FDI attack. Firstly, a discrete-time multi-sensor network system model is proposed, and the real matrix inequality optimization filter design is constructed based on linear and nonlinear functions, and the filter is made to show exponential stability in the mean square sense; secondly, a distributed H ∞ Fusion filter resists FDI attack.

[0067] In one embodiment of the present invention, referring to Figure 1 - Figure 7, a fusion filtering method for unmanned surface vessels with sensor saturation under FDI attack is provided, comprising the following steps: Step 100: Constructing a sensor model: Considering the external interference and FDI attack suffered by the USV, a discrete-time multi-sensor network model is constructed; a nonlinear function is used to describe the sensor saturation, and it is decomposed into linear and nonlinear parts; random variables are introduced to simulate the measurement data when the communication channel is attacked; Step 200: Designing a local filter structure: When designing a local filter for a single sensor system, a local filter error system is constructed and its mean square exponential stability is ensured to estimate the system state in real time and optimize the estimation performance and robustness; Step 300: Analyzing the local filtering performance: Verifying that the exponential stability of the random process in the mean square sense is Boundedness, prove the exponential stability of the filter error system in the mean square sense; use random processes and constraints to derive the upper bound of the error change on the state variables of the filter; introduce performance indicators to evaluate the performance of the filter under FDI attack; Step 400: Design local filter parameters: convert nonlinear matrix inequalities into linear matrix inequalities; introduce LMI constraints, decompose the LMI matrix structure, and decompose the LMI matrix structure into multiple sub-matrix blocks; according to the decomposed constraints, design the filter parameters to meet the stability requirements; Step 500: Design distributed fusion filter: based on local filter parameters, use weighted fusion method to calculate the output of the multi-sensor system; determine the local filter weights and prove the performance of the fusion filter.

[0068] The following is a detailed explanation of each of the above steps:

[0069] Step 100: Build the Sensor Model:

[0070] Considering the external interference and FDI attack suffered by USV, a discrete-time multi-sensor network model is constructed; a nonlinear function is used to describe the saturation of the sensor, and the conditions it satisfies are set; the nonlinear function is decomposed into a linear part and a nonlinear part; when the communication channel is attacked, random variables are introduced and substituted to obtain the measurement data of the local filter when it is attacked by FDI.

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

[0072] Step 110: Based on the external interference and FDI attack suffered by the USV, a discrete time multi-sensor network system model is established:

[0073]

[0074] In the above formula, Indicates the system status of the USV navigation dynamics, represents the d-dimensional real space where x(k) is located; x(k+1) represents the system state at the next time k+1, which is obtained from the current state x(k) through the state transfer matrix A and the control input w(k); w(k) is the process noise belonging to l[0,∞), which is a q-dimensional vector, representing external interference or uncertainty to the system state; is the measurement value of sensor i, which represents 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) where m i dimensional real number space; is a state to be estimated, represents the l-dimensional real space where the state to be estimated z(k) 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 saturation and its conditions: When the signal or system reaches the maximum measurement or processing capability, use the nonlinear function ψ(C i x(k)) describes the saturation of the sensor and sets the corresponding satisfaction conditions.

[0076] The conditions to be met 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: Substitute the nonlinear function ψ(C i x(k)) is rewritten into a linear part and a nonlinear part.

[0080] In order to facilitate solving the subsequent matrix inequalities, the nonlinear function ψ(C ix(k)) is rewritten into two parts: the linear part and the nonlinear part, namely:

[0081] ψ(C i x(k))=M1C i x(k))+ψ n (C i x(k)) (3);

[0082] 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.

[0083] Step 140: Considering the situation where the communication channel is attacked, a parameter representing the attack is introduced and substituted to obtain the measurement data of the local filter when it is attacked by FDI.

[0084] When the communication channel is attacked, α is introduced i (k) represents the attack, and the measured data when the local filter is attacked by FDI is obtained.

[0085] When the communication channel is attacked, the local filter may receive false measurement data at a certain moment. In order to describe this phenomenon, a random variable α is introduced i (k), and substitute it into formula (4) to obtain the measured data when the local filter is attacked by FDI

[0086]

[0087] 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.

[0088] Step 200: Design local filter structure:

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

[0090]

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

[0092] When designing the local filter structure of a single sensor system on the sensor, the local filter error system on the sensor is constructed by defining the local error and combining the measurement data and the local filter structure; the mean square exponential stability of the filter error system is defined; when the USV system is running in real time, the local filter is designed to continuously estimate the USV system state; and it is ensured that the local filter error meets the predetermined conditions to optimize the state estimation performance and robustness of the USV system.

[0093] Step 210: Construct a local filter error system on the sensor by defining local errors and combining measurement data and local filter structures.

[0094] By defining the local error Combined with formulas (1), (4) and (5), the local filtering error system on sensor i is constructed:

[0095]

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

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

[0098] C fi =[B fi B fi E], as well as

[0099] In the above formula, Indicates the system status of 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 state transition matrix of the system, describing the process of system state update; represents the control input matrix, which describes how the control input affects the local filter error system; H i is a local error η i (k) Matrix mapped to sensor output; represents the measurement matrix, which converts the state of the system into the output of the sensor; d i(k) represents sensor error; a i (k) represents the attack or other uncertainties suffered by sensor i; represents the input noise of the system; Represents the gain matrix of the local filter, which is used to map the local filtering error state to the error estimate where L is a gain matrix and C fi is the matrix associated with the sensor model.

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

[0101] The definition of filter error system mean square exponential stability means that when When , the variance of the filtering error will gradually decrease under the condition of exponential decay.

[0102] Specifically, if there are constants δ>0 and 0<τ<1, then the filter 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 initial filtering error of the system at time k = 0, that is, the difference between the initial estimated value and the true value. As time goes by, the filtering error will change according to τ k The exponential decay law of gradually decreases, and finally the system becomes 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, the local H ∞ The filter continuously adjusts its estimate based on the observed values ​​and control inputs to predict the future state of the USV system. In order to ensure the robustness and performance of the USV system, the filter needs to handle uncertainty and perform appropriate filter estimates.

[0108] Step 240: Ensure local filtering error The following conditions are met:

[0109]

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

[0111] Step 300: Analyze local filtering performance:

[0112] A lemma is introduced to verify the exponential boundedness of the random process in the mean square sense; a theorem is introduced to prove the exponential stability of the filtering error system in the mean square sense; the Lyapunov functional is defined and the error equation is derived, and the upper bound of the error variation with respect to η(k) is derived using random processes and constraints, and the stability of the system is further verified by matrix decomposition; performance indicators are introduced to evaluate the performance of the filter under FDI attacks; through derivation, it is proved 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: The lemma is introduced to verify the exponential boundedness of the random process in the mean square sense, and provide a theoretical basis for the subsequent optimization process.

[0115] The Lemma 1 is:

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

[0117]

[0118] The random process η(k) is exponentially bounded in the mean square sense, that is, assuming that η(k) is a random process, if there exists a Lyapunov functional U(η(k)) and a scalar And 0<ξ<1, so that:

[0119]

[0120] Among them, θ and λ are constants, η(k) is the state variable of the filter, V(η(k)) is the Lyapunov functional, and ξ is a constant that controls the decay rate of the control system state and affects the stability of the system.

[0121] Step 320: Introduce Theorem 1 to prove the exponential stability of the filter error system, describe the stability condition through matrix inequality, and prove that when the condition is met, the system is exponentially stable in the mean square sense.

[0122] Theorem 1: By giving the filtering parameter 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. If there exists a matrix P i =P i T > 0, and the scalar ε i >0, then H ∞ Norm constraints ensure the stability of the system:

[0123]

[0124] In the above formula, Δ i represents the matrix associated with the error or disturbance, ε i represents the disturbance attenuation coefficient, the robustness of the control system, Λ i A matrix representing the system dynamics and state related, affecting stability, represents the state matrix after perturbation, represents a symmetric positive definite matrix, describing 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 random process and constraints to derive the upper bound of the error change 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), defines the error change ΔV k ,

[0127]

[0128] Then the stability of the system is derived, and the upper bound of the error variation about η(k) is derived using random processes and constraints, and the stability of the system is further verified 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 of the Lyapunov functional, thereby ensuring that the performance index meets the expected constraints.

[0130] In order to further evaluate the performance of the filter under FDI attack, the performance index J(N) is defined:

[0131]

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

[0133] Step 350: Calculation results and stability assurance.

[0134]

[0135] Among them, suppose:

[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 of multiple terms involving various matrix parameters in the system; Π i represents a matrix, which is related to the filter gain or disturbance rejection part; Λ i A matrix representing the system dynamics and state related, affecting stability, represents the state matrix after perturbation.

[0138] We get J(N)<0, let N→∞, and we get:

[0139]

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

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

[0142] Step 400: Design local filter parameters:

[0143] The nonlinear matrix inequality is converted into a linear matrix inequality; LMI constraints are introduced to ensure that the filter is stable under specific conditions; the LMI matrix structure is decomposed into multiple sub-matrix blocks, each sub-matrix block represents a specific constraint; according to the decomposed constraints, the filter parameters are designed to ensure that the filter can meet the required stability requirements; by transforming and applying the inequality conditions, the required LMI form and filter parameter design formula are finally obtained.

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

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

[0146] Step 420: By introducing the matrix P i , R i and other related matrices to 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 hour,

[0148] Yes ∞ Norm constraints make the following LMI hold, namely:

[0149]

[0150] In the above formula, the matrices Ξ1, Ξ2, Ξ3, Ξ4, Ξ5, Ξ6, and Ξ7 represent different parts of the system under LMI constraints, including state transition, input noise, disturbance, and sensor model constraints; the matrix P i ,R i ,γ i ,ε i etc. are system dynamic, control and measurement parameters, A fi ,B fi ,C fi These matrices are used to describe the stability and performance of the system.

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

[0152] These matrices are defined by state equations 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 associated with sensor i in the system, The measurement matrix of sensor i.

[0159] Step 440: Design filter parameters according to the decomposed constraints to ensure that the filter can meet the required stability requirements.

[0160] According to the LMI condition, the filter parameter A fi ,B fi ,C fi 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 using Schur's complement lemma, the formula can be rewritten as:

[0163]

[0164] Perform a congruence transformation on it and use the relation -R i P i -1 R i T ≤P i -R i -R i T Transformation yields (P i -R i ) i -1 (P i -R i ) T ≥0, we can get the following inequality:

[0165]

[0166] Step 450: By transforming and applying the inequality conditions, the required LMI form and filter parameter design formula are finally obtained, thereby completing the filter design.

[0167] definition It can be deduced that (17) holds, and therefore (18) holds, and the filter design is complete.

[0168] Step 500: Design distributed H ∞ Fusion Filters:

[0169] Based on the designed local filter parameters, a weighted fusion method is used to calculate the output of the multi-sensor system; the local filter weights are determined, and the weights are determined by the local filter errors; according to the design of the fusion filter, the fusion error is defined; the performance of the fusion filter is proved to ensure that the fused filter is equivalent to or better than the average level of each local filter in terms of performance indicators.

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

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

[0172] Through the local filter parameters designed previously, the weighted fusion method is used to calculate the output of the multi-sensor system. The output of each sensor is weighted by σ i Perform weighted summation to form a fused estimate

[0173]

[0174] In the above formula, l i represents the weighting factor of the i-th sensor, which measures the influence of the sensor or the signal quality; l j Represents the weighting factor of the i-th sensor, which is used to normalize the weight.

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

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

[0177] Weight σ i The error l of the local filter i Determine, specifically, the weights and It is proportional to the error, which means that the filter with smaller error is given a higher weight, thus playing a greater role in fusion.

[0178] Step 530: Define the fusion error according to the design of the fusion filter.

[0179] make

[0180]

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

[0182] From the above derivation, we can see that the fusion error satisfies H ∞ Performance indicators.

[0183] Explain that the fused H ∞ The estimated performance of the filter is not less than the average value of the information of all local filters. This means that the performance index of the fused filter is equivalent to or better than the average level of each local filter. 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 the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention.

Claims

1. A fusion filtering method for unmanned surface ships with sensor saturation under FDI attack, characterized in that: The following steps are involved: Step 100: Construct sensor model: Consider the external interference and FDI attack suffered by USV, and construct a discrete time multi-sensor network model; use nonlinear function to describe sensor saturation, and decompose the nonlinear function into linear and nonlinear parts; introduce random variables to simulate the measurement data when the communication channel is attacked; Step 200: Design a local filter structure: design a local filter for a single sensor system, construct a local filter error system and ensure its mean square exponential stability, so as to estimate the USV track information status in real time and optimize the estimation performance and robustness; Step 300: Analyze local filtering performance: verify the exponential boundedness of the random process in the mean square sense, and prove the exponential stability of the filtering error system in the mean square sense; The upper bound of the error variation of the state variables of the filter is derived using random processes and constraints; performance indicators are introduced to evaluate the performance of the filter under FDI attacks; Step 400: designing local filter parameters: converting the nonlinear matrix inequality into a linear matrix inequality; introducing LMI constraints, decomposing the LMI matrix structure, and decomposing the LMI matrix structure into multiple sub-matrix blocks; designing the filter parameters according to the decomposed constraints to meet the stability requirements; Step 500: Design a distributed fusion filter: Based on local filter parameters, use a weighted fusion method to calculate the multi-sensor system output; determine local filter weights and prove the fusion filter performance.

2. The fusion filtering method for unmanned surface ships with sensor saturation under FDI attack according to claim 1 is characterized in that: In step 100, a discrete-time multi-sensor network system model is established according to the external interference and FDI attack suffered by the USV: In the above formula, Indicates the system status of the USV navigation dynamics, represents the d-dimensional real space where x(k) is located; x(k+1) represents the system state at the next time k+1, which is obtained from the current state x(k) through the state transfer matrix A and the control input w(k); w(k) is the process noise belonging to l[0,∞), which is a q-dimensional vector, representing external interference or uncertainty to the system state; is the measurement value of sensor i, which represents 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) where m i dimensional real number space; is a state to be estimated, represents the l-dimensional real space where the state to be estimated z(k) 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).

3. The fusion filtering method for unmanned surface ships with sensor saturation under FDI attack according to claim 2 is characterized in that: In step 100, a nonlinear function is used to describe the sensor saturation, and the nonlinear function is decomposed into linear and nonlinear parts, including: Using the nonlinear function ψ(C i x(k)) describes the saturation of the sensor and sets the corresponding conditions: (ψ(C i x(k))-M1C i x(k)) T (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; Rewrite the nonlinear function into a linear part and a nonlinear part: ψ(C i x(k))=M1C i x(k))+ψ n (C i x(k)); 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.

4. The fusion filtering method for unmanned surface ships with sensor saturation under FDI attack according to claim 3 is characterized in that: In step 100, random variables are introduced to simulate the measurement data when the communication channel is attacked. 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.

5. The fusion filtering method for unmanned surface ships with sensor saturation under FDI attack according to claim 4 is characterized in that: In step 200, a local filter structure of a single sensor system is designed on sensor i: In the above formula, is the estimated value of the system state of USV navigation dynamics of sensor i at time k, 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 of sensor i, A fi ,B fi ,C fi is the filter parameter matrix to be designed.

6. The method for fusion filtering of unmanned surface vessels with sensor saturation under FDI attack according to claim 5 is characterized in that: In step 200, a local filtering error system is constructed, specifically including: defining a local error Construct the local filtering error system on sensor i: The symbols in the formula are as follows: H i [C i 0], C fi =[B fi B fi E], as well as In the above formula, η i (k+1) represents the update of the local filter error system state at time k+1; Indicates the system status of 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 state transition matrix of the system, describing the process of system state update; represents the control input matrix, which describes how the control input affects the local filter error system; H i is a local error η i (k) Matrix mapped to sensor output; represents the measurement matrix, which converts the state of the system into the output of the sensor; d i (k) represents sensor error; a i (k) represents the attack or other uncertainties suffered by sensor i; represents the input noise of the system; Represents the gain matrix of the local filter, which is used to map the local filtering error state to the error estimate where L is a gain matrix and C fi is the matrix associated with the sensor model.

7. The method for fusion filtering of unmanned surface vessels with sensor saturation under FDI attack according to claim 6 is characterized in that: Local filtering error The following conditions are met: In the above formula, l i Represents the local error limit of sensor i and controls the upper limit of the local filtering error.

8. The method for fusion filtering of unmanned surface vessels with sensor saturation under FDI attack according to claim 7 is characterized in that: In step 400, the LMI constraint condition is introduced to decompose the LMI matrix structure, and the LMI matrix structure is decomposed into multiple sub-matrix blocks, including: By introducing the matrix P i , R i And other correlation matrices to form the LMI constraints: A fi ,B fi ,C fi and γ i >0,ε i >0, then when hour, H ∞ Norm constraint makes LMI hold, that is: In the above formula, the matrices Ξ1, Ξ2, Ξ3, Ξ4, Ξ5, Ξ6, and Ξ7 represent different parts of the system under LMI constraints, including state transition, input noise, disturbance, and sensor model constraints; the matrix P i ,R i ,A fi ,B fi ,C fi ,γ i ,ε i It is a parameter of system dynamics, control and measurement.

9. The method for fusion filtering of unmanned surface vessels with sensor saturation under FDI attack according to claim 8, characterized in that: In step 400, the filter parameters are designed by the following formula:

10. The method for fusion filtering of unmanned surface vessels with sensor saturation under FDI attack according to claim 1, characterized in that: In step 500, the output of each sensor is weighted by σ i Perform weighted summation to form a fused estimate In the above formula, l j represents the weighting factor of the i-th sensor, which measures the influence of the sensor or the signal quality; l j Represents the weighting factor of the i-th sensor, which is used to normalize the weight.

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