USV security state estimation method based on privacy protection under composite attack restriction

Abstract

The invention belongs to the technical field of information physical system control and network security, and particularly relates to a USV security state estimation method based on privacy protection under composite attack restriction. Firstly, a dynamic identity encryption algorithm is provided, and leakage of a real identity is avoided through transmission of anonymous identity information and a revocable key. Then, in order to more effectively resist spoofing attack and replay attack, an authentication detection mechanism is constructed based on an encryption algorithm, the two kinds of attacks can be effectively identified, the attacked sensor can be positioned at the same time, and comprehensive detection is realized. Secondly, the designed distributed state estimation system is combined with an encryption algorithm and a detection mechanism, only security measurement values are received, potential adverse effects are eliminated, and privacy security and stability of the state estimation system are ensured. Meanwhile, sufficient conditions for realizing performance indexes and ensuring the stability of an error estimation system are given, so that the safety performance of the system is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the technical field of information-physical system control and network security, and specifically relates to a USV (Unmanned Surface Vessel) security state estimation method based on privacy protection under the constraint of composite attacks. Background Art

[0002] With the rapid development of the Internet of Things, automation and intelligent systems, the application of Cyber-Physical Systems (CPS) and Wireless Sensor Networks (WSNs) in transportation, energy, medical and other fields has received widespread attention. As an important application of CPS, unmanned surface vessels (USVs) achieve real-time perception of the environment and intelligent decision-making by closely integrating physical systems with information systems, thereby improving operational efficiency. WSNs provide efficient data collection and transmission methods, enabling USVs to quickly obtain environmental information and respond in a timely manner, thereby adapting to the dynamically changing surrounding environment. Therefore, USVs have broad application prospects in the fields of marine environmental monitoring, maritime rescue, etc., and their role in these fields is becoming increasingly important.

[0003] However, due to the wireless characteristics of wireless sensor networks and the openness of cyber-physical systems, unmanned surface vessels face significant security threats during their maritime navigation. Malicious network attacks may lead to data leakage or system misoperation, thus affecting the efficiency of mission execution and the normal operation of the system. At the same time, USVs must ensure the stability and reliability of the system in complex and harsh environments, which requires accurate state estimation in the system. As a core component of CPS, malicious network attacks may destroy the authenticity of sensor data, which has a direct impact on the performance of the state estimation system and leads to a decrease in the accuracy of the state estimation results. Therefore, in the context of network attacks, studying the problem of secure state estimation of CPS has important theoretical and practical significance.

[0004] At present, the security issues in CPS mainly focus on types such as denial of service (DoS) attacks, spoofing attacks, and replay attacks. DoS attacks exhaust system resources through a large number of invalid requests, causing the system, service or network to fail to operate normally. Spoofing attacks forge identities or data, which may lead to data leakage, identity theft or system control; while replay attacks capture valid data packets and resend them, causing abuse of authority or information tampering. In contrast, if the CPS system does not take effective security protection measures, such as information encryption or privacy protection, spoofing attacks and replay attacks may carefully tamper with or replay the transmission of sensor data, leading to more serious security issues. In an open data environment, spoofing attacks and replay attacks can be carried out in conjunction. Ordinary detectors are not only difficult to effectively identify the existence of attacks, but may also cause significant deviations in the state of the USV system. Therefore, in this context, it is particularly important to study how to ensure the security of data transmission, especially in the case of spoofing attacks and replay attacks, to ensure the accuracy of the system's real data and state estimation results.

[0005] At present, the research on distributed state estimation and detection in the context of replay attacks and deception attacks in CPS is still in its infancy. Current methods mostly focus on a single attack type and do not fully consider data privacy issues. The present invention aims to propose a new secure state estimation method that can detect and prevent deception attacks and replay attacks in real time, so as to obtain the true value of the system through a secure state estimation method, thereby ensuring the privacy security and state estimation accuracy of the system, and improving the system performance and safety of unmanned surface vessels. Summary of the invention

[0006] In order to overcome the problems in the prior art, the present invention proposes a USV security state estimation method based on privacy protection under the constraint of composite attacks.

[0007] The technical solution of the present invention to solve the above technical problems is as follows:

[0008] The present invention provides a USV security state estimation method based on privacy protection under the constraint of composite attack, comprising the following steps:

[0009] Step 100: Establish a privacy-protected cyber-physical system model and a state estimation system model according to the navigation posture of the unmanned surface vessel; and consider the way in which the attacker obtains the information of the privacy-protected cyber-physical system through deception and replay attacks, and its impact on the performance of the estimation system, and establish a composite attack model; modify the privacy-protected cyber-physical system model under the influence of the composite attack, modify the estimator under the composite attack, and establish a state estimation error system;

[0010] Step 200: Design an anonymous dynamic identity encryption algorithm and a detection and authentication mechanism; wherein the anonymous dynamic identity encryption algorithm is used to protect the privacy of the identity information of the unmanned surface vessel; and the authentication and detection mechanism is used to identify and prevent sensors that are subject to replay attacks and spoofing attacks from sending measurement data;

[0011] Step 300: Based on the detection mechanism, rewrite the state estimation error system, construct an augmented estimation error system, analyze the stability of the state estimation error system, and solve the gain matrix.

[0012] Furthermore, in step 100, the privacy-preserving cyber-physical system model is represented by the following state space equation:

[0013]

[0014] in, Indicates the system status. Represents x k Where n x dimensional real number space; x k+1 represents the system state at the next time k+1; i represents the sensor, k represents the time, and N represents a natural number; represents the measurement value obtained by the i-th sensor, Represents y i,k Where n y dimensional real number space; Indicates the interference to the system. Represents ω k The ω-dimensional real number space where it is located; ν i,k represents the interference to the i-th sensor; assuming ω k ,ν i,k ∈l2[0,∞),A k ,B k ,H i,k and D i,k is a real-valued time-varying matrix known to the system.

[0015] Furthermore, in the step 100, in the state estimation system model, the estimator uses the state estimation equation in the following form:

[0016]

[0017] in, L i,k and K i,k are the parameters of the estimator to be designed; Represents the system state x k An estimated value of Represents the system state x k The k+1 moment estimated value of Represents the state estimate of the neighbor estimator.

[0018] Furthermore, in step 100, the actual measured output of the privacy-preserving cyber-physical system model that is subjected to the composite attack is corrected under the influence of the composite attack.

[0019]

[0020] Among them, the replay attack strategy Represents the previous measurement value obtained by replaying; deception attack model s i,k ∈l2[0,∞), where l2 represents the norm; represents a replay attack, and the random variable μ i,k White sequence following Bernoulli distribution.

[0021] Furthermore, the estimator under the composite attack is:

[0022]

[0023] Furthermore, in step 100, a state estimation error system is established, including:

[0024] make Represents the estimation error, the estimation error system:

[0025]

[0026] Where P i,k represents the gain matrix of the design; Indicates the system status during T2-T1 obtained by replay; represents the measurement noise suffered during playback T2-T1; e j,k represents the neighbor estimation error, j represents the neighbor sensor; P i,k represents the gain matrix of the design.

[0027] Furthermore, in step 200, the anonymous dynamic identity encryption algorithm uses anonymous identity information and revocable key transmission to protect the privacy of the unmanned surface vessel identity information, including:

[0028] Before carrying out a mission, each unmanned surface vessel submits its unique identification to the key generation center to obtain an anonymous identity within a valid period;

[0029] After the key generation center verifies the unique identification of each unmanned surface vessel, it generates a unique public-private key pair for the unmanned surface vessel;

[0030] If the validity period of the anonymous identity expires or the key is found to be leaked, the key generation center immediately revokes its old key and anonymous identity, and records the anonymous identity and revocation time of the revoked unmanned surface vessel; at the same time, the key generation center sends a new key and anonymous identity to the unmanned surface vessel.

[0031] Furthermore, in step 200, the authentication detection mechanism is used to identify and prevent sensors that are subject to replay attacks and spoofing attacks from sending measurement data, including:

[0032] The measurement value of each sensor is marked as n i , the received data of each estimator is labeled m i ,During the process of sending and receiving data packets, the sending and receiving status of the data packets is monitored and detected, and whether there is a replay attack is determined by comparing whether the received data packets have been received before;

[0033] If m i >n i , the received data packet has been received before, a replay attack has occurred, and an alarm is triggered; otherwise, there is no replay attack, and the validity of the information is verified; if the verification fails, it means that false data has been injected into the transmitted data, and an alarm is triggered; if the verification succeeds, secure transmission is performed.

[0034] Furthermore, in step 300, the state estimation error system is rewritten as:

[0035]

[0036] in, U i represents the safe neighbor set of node i;

[0037] set up θ i,k =[ω k ,ν i,k ] T , establish the following augmented estimation error system:

[0038]

[0039] in,

[0040] In the above formula, represents the augmented estimation error vector at time k; represents the augmented estimation error vector at the next moment k+1; θ i,k represents the interference signal vector; E i,k 、F i,k and G i,k Represent the system matrix of each part respectively.

[0041] Furthermore, in step 300, the gain matrix:

[0042]

[0043] In the above formula, Γ i,k and X i,k represents the matrix that makes LMI hold.

[0044] Compared with the prior art, the present invention has the following technical effects:

[0045] The present invention designs a dynamic identity encryption (DIE) algorithm, which effectively realizes the privacy protection of USV data information and significantly enhances the privacy and security of USV data transmission. Compared with the existing encryption algorithm, the present invention adopts the transmission method of anonymous identity information and revocable keys, avoids the exposure of the real identity, and allows the key and anonymous identity to be replaced at any time, thereby solving the problem of data leakage.

[0046] In addition, an authentication and verification mechanism (AVM) is proposed, which can effectively identify deception attacks and replay attacks, ensuring data privacy and the stability of the state estimation system. Compared with the existing attack detection methods, the detection algorithm of the present invention realizes comprehensive detection of two common attack types without affecting the system performance, significantly improving the response capabilities of USV and estimation systems when facing security threats.

[0047] Finally, combined with the detection mechanism, an estimator under composite attacks is designed to ensure that USV uses encryption algorithms to protect information privacy when transmitting data. At the same time, the impact of deception attacks and replay attacks on the system is eliminated through the authentication detection mechanism. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] 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.

[0049] Figure 1 It is a flow chart of a method for estimating the security state of a cyber-physical system with privacy protection under the constraints of compound attacks;

[0050] Figure 2 It is a flow chart for constructing system model and compound attack model;

[0051] Figure 3 It is to design anonymous dynamic identity encryption algorithm and detection and authentication mechanism flow chart;

[0052] Figure 4 It is the estimation system stability analysis flow chart;

[0053] Figure 5 It is the design flow chart of the estimated system gain matrix;

[0054] Figure 6 It is a structural diagram of the cyber-physical system under compound attack. DETAILED DESCRIPTION

[0055] 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.

[0056] The purpose of the present invention is to solve the problem of safe state estimation of unmanned surface vessels (USVs) with privacy protection under deception attacks and replay attacks. The present invention adopts a dynamic identity encryption (DIE) algorithm to ensure data security. First, the key generation center (KGC) uses forged identity information and revocable keys to resist attacks and ensure the authenticity of USV information transmission. Then, replay attacks and deception attacks are identified by detection algorithms in the certification and testing center. Finally, a distributed state estimation system combined with a detection mechanism is designed to ensure that the estimation system only receives secure measurement data, thereby ensuring the reliability and stability of the estimation system, thereby accurately estimating the true state of the USV.

[0057] To achieve the above object, the present invention adopts the following technical solution:

[0058] Reference Figure 1 The present invention relates to a USV security state estimation method based on privacy protection under composite attack constraints, comprising the following steps:

[0059] Step 100: Establish a privacy-protected cyber-physical system model and a state estimation system model according to the navigation posture of the unmanned surface vessel; and consider the way in which the attacker obtains the information of the privacy-protected cyber-physical system through deception and replay attacks, and its impact on the performance of the estimation system, and establish a composite attack model; modify the privacy-protected cyber-physical system model under the influence of the composite attack, design an estimator under the composite attack, and establish a state estimation error system;

[0060] Step 200: Design an anonymous dynamic identity encryption algorithm and a detection and authentication mechanism; wherein the anonymous dynamic identity encryption algorithm is used to protect the privacy of the identity information of the unmanned surface vessel; and the authentication and detection mechanism is used to identify and prevent sensors that are subject to replay attacks and spoofing attacks from sending measurement data;

[0061] Step 300: Based on the detection mechanism, rewrite the state estimation error system, construct an augmented estimation error system, analyze the stability of the state estimation error system, and solve the gain matrix.

[0062] The following is a detailed explanation of each of the above steps:

[0063] Step 100: Establish a privacy-protected cyber-physical system model and a state estimation system model according to the navigation posture of the unmanned surface vessel; and consider the way in which the attacker obtains the information of the privacy-protected cyber-physical system through deception and replay attacks, as well as its impact on the performance of the estimation system, to establish a composite attack model; modify the privacy-protected cyber-physical system model under the influence of the composite attack, design an estimator under the composite attack, and establish a state estimation error system.

[0064] As an example, see Figure 2 , this step may include the following steps:

[0065] Step 110: Construct a privacy-preserving cyber-physical system model and a state estimation system model.

[0066] According to the navigation posture of unmanned surface vessel (USV), a cyber-physical system model with privacy protection is constructed, and a state estimation system model is designed.

[0067] The privacy-preserving cyber-physical system model can be expressed as the following state-space equation:

[0068]

[0069] in, Indicates the system status. Represents x k Where n x dimensional real number space; x k+1 represents the system state at the next time k+1; i represents the sensor, k represents the time, and N represents a natural number; represents the measurement value obtained by the i-th sensor, Represents y i,k Where n y dimensional real number space; Indicates the interference to the system. Represents ω kThe ω-dimensional real number space where it is located; ν i,k represents the interference to the i-th sensor; assuming ω k ,ν i,k ∈l2[0,∞),A k ,B k ,H i,k and D i,k is a real-valued time-varying matrix known to the system.

[0070] In the state estimation system model, the estimator uses the state estimation equation of the following form:

[0071]

[0072] in, L i,k and K i,k are the parameters of the estimator to be designed; Represents the system state x k An estimated value of Represents the system state x k The k+1 moment estimated value of Represents the estimated value of the neighbor estimator at time k.

[0073] Step 120: construct a composite attack model, wherein the composite attack model includes a replay attack strategy and a deception attack model.

[0074] Consider the ways in which attackers can obtain system information through spoofing and replay attacks, as well as the potential impact on estimated system performance, and establish a replay attack strategy based on the attacker's capabilities and the specific methods of implementing the attack. and deception attack models i,k ∈l2[0,∞).

[0075] Replay attack strategy:

[0076] (1) The attacker records the sensor measurements in the time interval [T1, T2] during the entire time k, where T2-T1 is the effective time for the attacker to replay the measurements for a long period of time in the future.

[0077] (2) From time T2+1 to time k, the adversary modifies the measured value to Where r = 1, 2, ... represents the number of replay attacks; Replay measurement value representing the replay attack.

[0078] Deception Attack Model: Definitions i,k∈l2[0,∞) is the deception attack vector, where l2 represents the norm. The attacker randomly launches a deception attack in the k time period, and injects some deception attack signals into the measurement value during the data transmission process, thereby affecting the estimation performance of the estimation system.

[0079] Step 130: Under the influence of the composite attack, correct the sensor measurement values ​​in the privacy-preserving cyber-physical system model.

[0080] Actual measured output under composite attack It is given by the following formula (3):

[0081]

[0082] in, represents a replay attack, and the random variable μ i,k The white sequence obeys the Bernoulli distribution and takes the value 0 or 1 with the following probabilities:

[0083]

[0084] in, is a known constant, given The value represents the success rate of the attack; if Then the deception attack can arbitrarily manipulate the system to inject false data.

[0085] Step 140: Design an estimator under composite attack and establish a state estimation error system.

[0086] In an open network environment, the designed estimator under composite attack can be written as:

[0087]

[0088] make Represents the estimation error, and the estimation error system is expressed by formula (6):

[0089]

[0090] Where P i,k represents the gain matrix of the design; Indicates the system status during T2-T1 obtained by replay; represents the measurement noise suffered during playback T2-T1; e j,k represents the neighbor estimation error, and j represents the neighbor sensor.

[0091] Step 200: Design an anonymous dynamic identity encryption algorithm and a detection and authentication mechanism; wherein the anonymous dynamic identity encryption algorithm is used to protect the privacy of the unmanned surface vessel identity information; and the authentication and detection mechanism is used to identify and prevent sensors that are subject to replay attacks and spoofing attacks from sending measurement data.

[0092] As an example, see Figure 3 , this step may include the following steps:

[0093] Step 210: Before executing a mission, each unmanned surface vessel submits its unique identification to the key generation center to obtain an anonymous identity within a validity period; and in each mission, each unmanned surface vessel updates this identity and sends it to the state estimation system.

[0094] Referring to Table 1, an anonymous identity AID (Anonymous Identity) is generated for each unmanned surface vessel USV. Before performing a mission, each unmanned surface vessel USV (US j ) needs to submit its unique identifier to the Key Generation Center (KGC) To obtain an anonymous identity Where T j The anonymous identity is valid for a certain period of time. Each unmanned surface vessel (USV) will obtain a new anonymous identity each time it performs a mission. And send it to the state estimation system ES k for storage.

[0095] Table 1 Anonymous identity generation algorithm

[0096]

[0097] Step 220: After the key generation center verifies the unique identification of each unmanned surface vessel, it will generate a unique public-private key pair for it to ensure the security of communication and the privacy of data.

[0098] Referring to Table 2, the secure channel interacts with the key generation center to generate and verify the public-private key pair for the unmanned surface vessel to ensure communication security.

[0099] Unmanned surface vehicle selects a random number as a secret value, using which the public key is calculated The public key and the chosen fake identity Send to the key generation center to obtain the key;

[0100] The key generation center will generate some private keys Sent to US j ,in, Represents a partial private key, Indicates a partial public key; if the unmanned surface vessel US j After receiving the above partial private key message, the hash value is calculated Verify the hash value to confirm the validity of the received information, where H0 represents the hash function; confirm the validity and integrity of the partial private key by comparing the results of the verification process. The verification is successful, confirming that some private keys are valid, where k pub Represents the system public key, Represents a hash value;

[0101] The key generation center will use the other part of the public and private key Sent to US j ,in, Represents a partial private key, represents part of the public key, t is the system initialization time; if the unmanned surface vessel US j Received message Unmanned Surface Vehicle US j Calculating the hash value like The verification is successful, confirming that some private keys are valid; return and and Represents public and private keys.

[0102] Table 2 Key generation algorithm

[0103]

[0104]

[0105] Step 230: If the validity period of the anonymous identity expires or the key is found to be leaked, the key generation center will revoke its old key and anonymous identity information. The key generation center will record the identity information and revocation time of the revoked unmanned surface vessel; at the same time, the key generation center will send a new key and anonymous identity information to the unmanned surface vessel to ensure the security of its subsequent communications.

[0106] Refer to Table 3, if T j =0 or US j The key is leaked, and the key generation center KGC revokes US j of US records revoked j anonymous identity information and revocation time; key generation center KGC and unmanned surface vessel US j New keys are exchanged through a secure channel. If the detection mechanism detects that the transmission process is attacked by FDI, an alarm is triggered and the default key is leaked.

[0107] Table 3 Key dynamic update algorithm

[0108]

[0109]

[0110] Step 240: Design and implement an authentication detection mechanism that identifies and prevents sensors that are subject to replay attacks and spoofing attacks from sending data to the state estimation system ES. k Send measurement data. Through this mechanism, it can ensure that the state estimation system ES k The data received is reliable and secure.

[0111] In order to prevent replay attacks and spoofing attacks, the sensor sends the measurement data to the state estimation system ES k , design an authentication detection mechanism to identify the attacked sensor. Referring to Table 4, first initialize the alarm factor η = 0, two counters n i and m i , cycle factor k and termination time T end During the loop execution phase, the measured value of each sensor is marked as n i , the received data of each estimator is labeled m i , during the sending and receiving process of data packets, monitor and detect the sending and receiving status of data packets, and determine whether there is a replay attack by comparing whether the received data packets have been received before. i >n i , the received data packet has been received before, a replay attack has occurred, and an alarm is triggered; otherwise, there is no replay attack, ES k The validity of information is verified through mutual authentication of identity and judging the integrity of the message. If the session key sk is negotiated, the verification is successful, otherwise it fails. Failure of verification indicates that false data has been injected into the transmitted information, and an alarm is triggered; if the verification is successful, the information has not been attacked and can be transmitted safely. The entire algorithm is designed to ensure the security and integrity of data during transmission, and effectively resist compound attacks such as replay attacks and spoofing attacks.

[0112] Table 4 Authentication detection mechanism algorithm based on compound attack

[0113]

[0114]

[0115] Step 300: Based on the detection mechanism, rewrite the state estimation error system, construct an augmented estimation error system, analyze the stability of the state estimation system, and solve the gain matrix.

[0116] As an example, see Figure 4-Figure 5 , this step may include the following steps:

[0117] Step 310: construct an augmented estimation error system.

[0118] The distributed safety estimation system (i.e., the state estimation system) only receives the measurement data of the certified safety sensors. By rewriting the state estimation error system, an augmented estimation error system is constructed. The augmented estimation error system is established to ensure the stability of the distributed safety estimation system, in order to analyze the stability and solve the gain matrix of the estimator.

[0119] The state estimation error system can be rewritten as:

[0120]

[0121] in, U i Represents the set of safe neighbors of node i.

[0122] Then, set θ i,k =[ω k ,ν i,k ] T , combined with equations (1)-(7), the following augmented estimation error system is established:

[0123]

[0124] in,

[0125] In the above formula, represents the augmented estimation error vector at time k; represents the augmented estimation error vector at the next moment k+1; θ i,k represents the interference signal vector; E i,k 、F i,k and G i,k Represent the system matrix of each part respectively.

[0126] Step 320: Performance analysis and cost function design.

[0127] In order to ensure that the state estimation system meets the specified H ∞ Performance, introduce a cost function, the cost function represents the interference signal vector θ i,k This causes inconsistencies between adjacent estimators.

[0128]

[0129] In the above formula, C represents the cost function; N represents a natural number; represents the state estimate of the neighbor estimator; e j,k represents the neighbor state estimation error; represents the neighbor augmentation estimation error vector.

[0130] Step 330: Distributed safety estimation system (state estimation system) stability analysis and proof.

[0131] The Lyapunov function is used to analyze the stability of the system under composite attacks. Theorem 1 is introduced and it is proved that when the system is not subjected to composite attacks and θ i,k ≡0, the state estimation error system is stable. Through the dynamic anonymous identity encryption algorithm and authentication detection mechanism, the state estimation error system can still maintain θ under the action of compound attacks. i,k ≡0, thus ensuring the stability of the system.

[0132] Question 1: How to design the state estimation system gain matrix P i,k and L i,k So that the state estimation error system (7) satisfies:

[0133] (1) When the system is not subjected to composite attacks and θ i,k ≡0, the state estimation error system (7) is stable. Relying on the encryption algorithm and authentication detection mechanism, the state estimation error system can also maintain θ under the action of compound attacks. i,k ≡0.

[0134] (2) For a given scalar γ>0 and Q>0, the state estimation system satisfies the specified H ∞ performance:

[0135]

[0136] in,

[0137] Theorem 1: For a given scalar 0 < σ i <1, 0<λ i <((1-σ i ) / q i ) and the state estimation system gain matrix P i,k and L i,k , if there exists a matrix Q i >0,i=1,2,…,N, so that inequality (11) holds, then problem 1 is effectively solved for the estimation error system (7).

[0138]

[0139] Where, ΔV i (k) = Vi (k+1)-σ i V i (k); ΔV i (k) represents the change; V i (k+1) represents the Lyapunov function at time k+1; γ represents a given constant, a scalar.

[0140] Step 340: Solve the LMI conditions.

[0141] Through the Kronecker operator and the neighbor information of each observer, Theorem 2 is introduced to transform the conditions for Theorem 1 into solvable linear matrix inequality (LMI) conditions, thus providing an operational mathematical basis for system design.

[0142] Theorem 2: For a given scalar 0 < σ i <1, 0<λ i <((1-σ i ) / q i ), γ>0 and the state estimation system gain matrix P i,k and L i,k , if there exists a matrix Q i >0,M i ,K i ,R i , i=1,2,…,N so that the following LMI holds

[0143]

[0144] In the above formula, i,k represents the matrix that satisfies LMI; represents the matrix associated with the augmented estimation error vector; and represents any compatibility matrix; Represents 1×p i The unit vector of ; I represents the identity matrix.

[0145] Step 350: Design the gain matrix P i,k and L i,k With any compatible matrix M i ,K i ,R i Coupling,Theorem 3 is introduced to provide a decoupling scheme for the design of the gain matrix of the state estimation system.

[0146] Theorem 3: For a given constant γ>0,0<σ i <1,0<λ i <((1-σ i ) / q i ), if there exists a matrix Qi >0,M i ,|M i |≠0,Γ i,k ,X i,k So that the following LMI holds:

[0147]

[0148] Among them, i,k represents the matrix that satisfies the decoupling scheme; Ψ i,k Each part in it represents the correlation matrix of the augmented estimation error vector in order to satisfy the LMI under the decoupling scheme;

[0149] Then the gain matrix of the state estimation system is obtained by equation (14):

[0150]

[0151] In the above formula, Γ i,k and X i,k represents the matrix that makes LMI hold.

[0152] 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 privacy-preserving USV security state estimation method under composite attack constraints, characterized in that: The following steps are involved: Step 100: Establish a privacy-protected cyber-physical system model and a state estimation system model according to the navigation posture of the unmanned surface vessel; and consider the way in which the attacker obtains the information of the privacy-protected cyber-physical system through deception and replay attacks, and its impact on the performance of the estimation system, and establish a composite attack model; modify the privacy-protected cyber-physical system model under the influence of the composite attack, modify the estimator under the composite attack, and establish a state estimation error system; Step 200: Designing an anonymous dynamic identity encryption algorithm and a detection and authentication mechanism; wherein the anonymous dynamic identity encryption algorithm is used to protect the privacy of the identity information of the unmanned surface vessel; The authentication detection mechanism is used to identify and prevent sensors that are subject to replay attacks and spoofing attacks from sending measurement data; Step 300: Based on the detection mechanism, rewrite the state estimation error system, construct an augmented estimation error system, analyze the stability of the state estimation error system, and solve the gain matrix.

2. According to claim 1, a privacy-preserving USV security state estimation method under composite attack constraints is characterized in that: In step 100, the privacy-preserving cyber-physical system model is represented by the following state-space equation: in, Indicates the system status. Represents x k Where n x dimensional real number space; x k+1 represents the system state at the next time k+1; i represents the sensor, k represents the time, and N represents a natural number; represents the measurement value obtained by the i-th sensor, Represents y i,k Where n y dimensional real number space; Indicates the interference to the system. Represents ω k The ω-dimensional real number space where it is located; ν i,k represents the interference to the i-th sensor; assuming ω k ,ν i,k ∈l2[0,∞),A k ,B k ,H i,k and D i,k is a real-valued time-varying matrix known to the system.

3. According to claim 2, a USV security state estimation method based on privacy protection under composite attack constraints is characterized in that: In step 100, in the state estimation system model, the estimator uses the state estimation equation in the following form: in, L i,k and K i,k is the parameter of the estimator to be designed, i.e., the solution gain matrix; Represents the system state x k An estimated value of Represents the system state x k The k+1 moment estimated value of represents the state estimate of the neighbor estimator, indicates that j is An element of a collection.

4. According to claim 3, a privacy-preserving USV security state estimation method under composite attack constraints is characterized in that: In step 100, the actual measured output of the privacy-preserving cyber-physical system model that is subjected to the composite attack is corrected under the influence of the composite attack. Among them, the replay attack strategy Represents the previous measurement value obtained by replaying; deception attack model s i,k ∈l2[0,∞), l2 represents the norm; represents a replay attack, and the random variable μ i,k White sequence following Bernoulli distribution.

5. According to claim 4, a privacy-preserving USV security state estimation method under composite attack constraints is characterized in that: The estimator under the composite attack is:

6. The method for estimating the safety status of a USV based on privacy protection under the constraints of a composite attack according to claim 5 is characterized in that: In step 100, a state estimation error system is established, including: make Represents the estimation error, the estimation error system: In the formula, Indicates the system status during T2-T1 obtained by replay; represents the measurement noise suffered during playback T2-T1; e j,k represents the neighbor estimation error; P i,k represents the gain matrix of the design.

7. The method for estimating the safety status of a USV based on privacy protection under the constraints of a composite attack according to claim 1 is characterized in that: In step 200, the anonymous dynamic identity encryption algorithm uses anonymous identity information and revocable key transmission to protect the privacy of the unmanned surface vessel identity information, including: Before carrying out a mission, each unmanned surface vessel submits its unique identification to the key generation center to obtain an anonymous identity within a valid period; After the key generation center verifies the unique identification of each unmanned surface vessel, it generates a unique public-private key pair for the unmanned surface vessel; If the validity period of the anonymous identity expires or the key is found to be leaked, the key generation center immediately revokes its old key and anonymous identity, and records the revoked anonymous identity and revocation time of the unmanned surface vessel; at the same time, the key generation center sends a new key and anonymous identity to the unmanned surface vessel.

8. The method for estimating the safety status of a USV based on privacy protection under the constraints of a composite attack according to claim 7 is characterized in that: In step 200, the authentication detection mechanism is used to identify and prevent sensors that are subject to replay attacks and spoofing attacks from sending measurement data, including: The measured value of each sensor is marked as n i , the received data of each estimator is labeled m i ,During the process of sending and receiving data packets, the sending and receiving status of the data packets is monitored and detected, and whether there is a replay attack is determined by comparing whether the received data packets have been received before; If m i >n i , the received data packet has been received before, a replay attack has occurred, and an alarm is triggered; otherwise, there is no replay attack, and the validity of the information is verified; if the verification fails, it means that false data has been injected into the transmitted data, and an alarm is triggered; if the verification succeeds, secure transmission is performed.

9. The method for estimating the safety status of a USV based on privacy protection under the constraints of a composite attack according to claim 6 is characterized in that: In step 300, the state estimation error system is rewritten as: in, U i represents the safe neighbor set of node i; set up θ i,k =[ω k ,ν i,k ] T , establish the following augmented estimation error system: in, In the above formula, represents the augmented estimation error vector at time k; represents the augmented estimation error vector at the next moment k+1; θ i,k represents the interference signal vector; E i,k 、F i,k and G i,k Represent the system matrix of each part respectively.

10. The method for estimating the safety status of a USV based on privacy protection under the constraints of a composite attack according to claim 9 is characterized in that: In step 300, the gain matrix: In the above formula, Γ i,k and X i,k represents the matrix that makes LMI hold.

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