A method and system for detecting vulnerability of a multi-sensor network topology

Abstract

This application discloses a method and system for detecting the vulnerability of multi-sensor network topology, relating to the field of sensor technology. The method includes: calculating eigenvalues ​​of the state matrix. l i ( A Construct a weighted directed topological graph, establish the Laplace matrix, and obtain eigenvalues ​​through eigenvalue decomposition. m j ( L ); Calculate the state estimates of each sensor and stack them to obtain the overall system error; Establish the state matrix Φ of the unified consensus estimation error system and find the joint eigenvalues ​​of Φ; Construct the deviation system to form the reachability matrix. R If eigenvalues ​​exist m j ( L ) and eigenvalues l i ( A This allows for the simultaneous joint eigenvectors. v ij Belongs to reachable subspace span ( R If the current multi-sensor network topology and consensus gain configuration are vulnerable to Byzantine attacks, then the present application's method can determine the vulnerability of the topology without extensive time-domain simulations or physical attack experiments.

Description

Technical Field

[0001] This application relates to the field of sensor technology, and in particular to a method for detecting the vulnerability of nodes in a multi-sensor network topology to Byzantine measurement attacks. It can be used for topology security design and evaluation in multi-sensor network information fusion scenarios such as smart grids, industrial internet, and autonomous driving. Background Technology

[0002] With the widespread application of multi-sensor networks and distributed state estimation techniques, the communication topology and parameter configuration (such as edge weights and consensus gains) between multi-agent systems have a significant impact on system convergence performance and security. In existing technologies, multi-sensor networks often employ distributed Kalman consistent filters (KCFs) with unified consensus gains, which can significantly improve convergence speed and quickly bring sensor information to consensus when topological connectivity and edge weights are high. However, recent research has shown that in the presence of malicious sensor tampering (such as Byzantine attacks), such topology and gain configurations can cause errors to propagate rapidly in the network, leading to state estimation divergence. Traditional residual-based detection methods struggle to detect this in a timely manner, resulting in serious security risks.

[0003] Existing vulnerability analysis methods largely rely on time-domain simulations or attack injection experiments, lacking a rapid inspection method based on topology and system spectrum properties. Especially in practical engineering applications, topology and consensus gain often have some room for adjustment, requiring assessment of a configuration's susceptibility to Byzantine attacks during the design phase. Therefore, it is necessary to propose a topology vulnerability detection method to quantitatively evaluate the security margin of multi-sensor network topologies without extensive simulations. Summary of the Invention

[0004] This application provides a method and system for detecting the vulnerability of multi-sensor network topology, in order to solve the problem in the prior art of lacking vulnerability detection of the configuration of multi-sensor network topology and consensus gain during the design phase.

[0005] On the one hand, embodiments of this application provide a method for detecting the vulnerability of a multi-sensor network topology, including:

[0006] Read the state matrix from the system model of the multi-sensor network. A and the measurement matrix of each sensor C i For the state matrix A Find eigenvalues l i ( A and the corresponding feature vectors r i ;

[0007] Construct a weighted directed topology graph based on the topology of the multi-sensor network. G Based on weighted directed topology graph G Establish the Laplace matrix L For the Laplace matrix L Perform eigenvalue decomposition to obtain eigenvalues. m j ( L and the corresponding feature vectors q j ;

[0008] Multi-sensor networks employ a Kalman consensus filter with unified consensus gain, based on the system model and measurement matrix. C i Calculate the state estimates of each sensor The state estimates of each sensor Stacking yields the overall system error ;

[0009] Based on the state matrix A Laplace matrix L and consensus gain Establish the state matrix Φ of the unified consensus estimation error system, and find the joint eigenvalues ​​of the state matrix Φ. l ij joint eigenvalues l ij Represented as ;

[0010] Based on overall system error Construct a deviation system, and generate an reachability matrix based on the reachability analysis of the deviation system. R ;

[0011] Let the joint eigenvector v ij for If there are non-zero eigenvalues m j ( L ) and eigenvalues l i ( A ) makes Simultaneously, joint feature vectors v ij Belongs to reachable subspace span ( R If this is the case, then the current topology and consensus gain configuration of multi-sensor networks are vulnerable to Byzantine attacks.

[0012] On the other hand, embodiments of this application also provide a system for detecting the vulnerability of multi-sensor network topology, including:

[0013] The system information acquisition module is used to read the state matrix from the system model of the multi-sensor network. A and the measurement matrix of each sensor C i For the state matrix A Find eigenvalues l i ( A and the corresponding feature vectors r i ;

[0014] The matrix construction module is used to construct a weighted directed topology graph based on the topology of a multi-sensor network. G Based on weighted directed topology graph G Establish the Laplace matrix L For the Laplace matrix L Perform eigenvalue decomposition to obtain eigenvalues. m j ( L and the corresponding feature vectors q j ;

[0015] The error construction module is used in multi-sensor networks to employ a Kalman consensus filter with a unified consensus gain, based on the system model and measurement matrix. C i Calculate the state estimates of each sensor The state estimates of each sensor Stacking yields the overall system error ;

[0016] The joint eigenvalue calculation module is used for calculations based on the state matrix. A Laplace matrix L and consensus gain Establish the state matrix Φ of the unified consensus estimation error system, and find the joint eigenvalues ​​of the state matrix Φ. l ij joint eigenvalues l ij Represented as , To unify the consensus gain coefficient;

[0017] The reachability analysis module is used to analyze the overall system error. Construct a deviation system, and generate an reachability matrix based on the reachability analysis of the deviation system. R ;

[0018] The vulnerability determination module is used to make the joint feature vector v ij for If there are non-zero eigenvalues m j ( L ) and eigenvalues l i ( A ) makes Simultaneously, joint feature vectors v ij Belongs to reachable subspace span ( R If this is the case, then the current topology and consensus gain configuration of multi-sensor networks are vulnerable to Byzantine attacks.

[0019] On the other hand, embodiments of this application also provide an electronic device, including a memory and at least one processor;

[0020] This memory stores multiple computer instructions;

[0021] When the at least one processor executes the plurality of computer instructions, it causes the at least one processor to perform the method described above.

[0022] On the other hand, embodiments of this application also provide a computer storage medium storing a plurality of computer instructions for causing a computer to execute the above-described method.

[0023] The method and system for detecting the vulnerability of multi-sensor network topology in this application have the following advantages:

[0024] 1. Spectral detection process with low computational cost: Only eigenvalue operations are required on a finite-dimensional matrix, eliminating the need for extensive time-domain simulations or physical attack experiments to determine the vulnerability of the topology.

[0025] 2. It can reflect the joint effect of topology and system: It quantitatively reflects the mutual coupling between the Laplace spectrum of the topological structure, consensus gain and the spectrum of the observed system through the joint eigenvalue expression.

[0026] 3. Identification of critical nodes and security margins: The distribution of joint feature vectors on the topology graph is used to identify the nodes with the greatest vulnerability, and a stability margin index is constructed using the joint spectral radius to provide a quantitative basis for subsequent security protection and topology optimization. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 A flowchart illustrating a method for detecting the vulnerability of a multi-sensor network topology, provided in an embodiment of this application.

[0029] Figure 2 This is a schematic diagram of a six-sensor weighted directed topology provided in an embodiment of this application. Detailed Implementation

[0030] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0031] Figure 1 A flowchart illustrating a method for detecting the vulnerability of a multi-sensor network topology, provided in an embodiment of this application. This application provides a method for detecting the vulnerability of a multi-sensor network topology, including:

[0032] S100 reads the state matrix from the system model of the multi-sensor network. A and the measurement matrix of each sensor C i For the state matrix A Find eigenvalues l i ( A and the corresponding feature vectors r i .

[0033] For example, the observed multi-sensor network satisfies a discrete-time linear model, and the system model is expressed as:

[0034]

[0035] in, yes The state variable at time t, It is the first The measurement results of each sensor n It is the state dimension of the system. m It is the measurement dimension of a single sensor. Number of sensors. Process noise. and measuring noise It is an independent and identically distributed Gaussian signal with zero mean, in its initial state. It is a Gaussian random variable with zero mean.

[0036] Furthermore, the state matrix is ​​typically required.A It is the Schur stable matrix, meaning that all eigenvalues ​​lie inside the unit circle.

[0037] S110, Construct a weighted directed topology graph based on the topology of the multi-sensor network. G Based on weighted directed topology graph G Establish the Laplace matrix L For the Laplace matrix L Perform eigenvalue decomposition to obtain eigenvalues. m j ( L and the corresponding feature vectors q j .

[0038] For example, based on weighted directed topology graph G Establish the Laplace matrix L The methods include:

[0039] Weighted directed topology G Represented as ,in Sensor assembly, N For the number of sensors, Let be the set of edges. Let be the edge weight matrix. w ij To connect the sensor i and j The weight of the edge;

[0040] For sensors i Calculate in-degree Construct a pair of angle matrices The Laplace matrix is ​​represented as .

[0041] Furthermore, in a strongly connected topology, L It has a single zero eigenvalue, and the real parts of the other eigenvalues ​​are positive.

[0042] The S120 multi-sensor network employs a Kalman consensus filter with unified consensus gain, based on the system model and measurement matrix. Calculate the state estimates of each sensor The state estimates of each sensor Stacking yields the overall system error .

[0043] For example, state estimator It can be represented as:

[0044]

[0045] All sensors use a unified consensus gain. ,available

[0046]

[0047] in, and Sensors The predicted state estimate and the filtered state estimate, For the first i Kalman gain of each sensor, For sensors consensus gain, For sensors j The predicted state estimate, To ensure a unified consensus gain coefficient, a value greater than zero is adopted. N i For sensors i The neighborhood group, for An identity matrix of order 1.

[0048] The overall system error is obtained by stacking the state estimates of each sensor. , can be represented as:

[0049]

[0050] in, for An identity matrix of order 1. for N An identity matrix of order 1. For Kronecker product, , , for k The overall systematic error at time -1 This is a deviation caused by a Byzantine sensor attack.

[0051] S130, based on the state matrix A Laplace matrix L And establish the state matrix Φ of the unified consensus estimation error system based on the consensus gain, and find the joint eigenvalues ​​of the state matrix Φ. l ij joint eigenvalues l ij Represented as .

[0052] For example, the state matrix Φ can be represented as Using the spectral properties of the Kronecker product, for By finding the eigenvalues, we can obtain .

[0053] When there is a certain sensor pair Make At that time, there exists an eigenvalue under a certain topological mode. With the eigenvalues ​​of the system mode The combination of these factors, under the influence of consensus gain, makes the joint eigenvalues... Entering or approaching the boundary of the unit circle.

[0054] S140, based on overall system error Construct a deviation system, and generate an reachability matrix based on the reachability analysis of the deviation system. R .

[0055] For example, the deviation system is shown below:

[0056]

[0057] in .

[0058] Based on the reachability analysis of systems theory, an reachability matrix is ​​formed:

[0059]

[0060] Furthermore, if there exists a vector with non-zero coefficients... α , so that the joint eigenvector v ij Represented as Rα A linear combination of these factors suggests that the current multi-sensor network topology and consensus gain configuration can be activated by a Byzantine sensor attack.

[0061] S150, let the joint eigenvector v ij for If there are non-zero eigenvalues m j ( L ) and eigenvalues l i ( A ) makes Simultaneously, joint feature vectors v ij Belongs to reachable subspace span ( R If this is the case, then the current topology and consensus gain configuration of multi-sensor networks are vulnerable to Byzantine attacks.

[0062] For example, if neither of the above two conditions is met, the configuration of the current multi-sensor network topology and consensus gain is considered non-fragile.

[0063] Furthermore, the joint eigenvalues ​​between all sensor pairs l ij The maximum value is taken as the joint spectral radius. r max Based on joint spectral radius r max Determine stability margin d According to stability margin d Assess the vulnerability of the current multi-sensor network topology and consensus gain configuration.

[0064] Specifically, stability margin d Represented as stability margin d The closer a value is to 0, the more fragile the current multi-sensor network's topology and consensus gain configuration are. At that time, it can be or As a vulnerability index, i.e. The larger the value, the greater the corresponding stability margin. The smaller the value, the more fragile the topology and consensus gain configuration of the multi-sensor network become.

[0065] Furthermore, after determining the vulnerability of the current multi-sensor network's topology and consensus gain configuration, the feature vectors are... q j After normalization, sensors with absolute component values ​​higher than a threshold are selected as the set of critical nodes. These critical nodes represent the main energy concentration locations of hazardous joint modes in the network and should be given priority protection in physical security and anomaly detection strategies.

[0066] The following is based on Figure 2 The method of this application will be further explained using the six-sensor weighted directed topology graph shown as an example.

[0067] Step S1: System information acquisition and spectrum calculation.

[0068] The object of observation is a discrete-time linear model:

[0069]

[0070] The state matrix is:

[0071]

[0072] right Find the feature values l i ( A The set of these eigenvalues ​​is Therefore If so, the system is stable in the Schur sense.

[0073] Step S2: Construct the topological edge weight matrix.

[0074] in accordance with Figure 2 Construct the edge weight matrix for the given topology. This example uses the sensor's in-neighbor nodes, and the corresponding edge weight matrix can be obtained as follows:

[0075]

[0076] Step S3: In-degree calculation and Laplacian matrix construction.

[0077] Defined by in-degree Calculate the in-degree of each node and construct a pairwise angle matrix. Calculate the Laplace matrix .

[0078] Step S4: Calculation of topological spectrum and determination of topological modes.

[0079] Laplace matrix Find the eigenvalues ​​and eigenvectors. The eigenvalues ​​are obtained through calculation. m j ( L The maximum value of ) .

[0080] Step S5: Construct joint feature values ​​and calculate detection index.

[0081] Set a unified consensus gain coefficient And construct the state matrix of the error system:

[0082]

[0083] Using the spectral properties of the Kronecker product, we can obtain The joint eigenvalues ​​are .

[0084] Define the joint spectral radius as an indicator of topological vulnerability: .when , indicating existence and The combination of these conditions crosses the unit circle boundary, triggering vulnerability conditions at the spectral level; when This indicates that the vulnerability condition was not triggered at the spectral level.

[0085] Step S6: Detect and output the two sets of gain configurations.

[0086] To illustrate the output format of the detection method in this application, this example provides two sets of... Configurations for comparison:

[0087] (1) Configuration 1: .

[0088] The calculation yielded:

[0089]

[0090] Stability margin can be further provided:

[0091]

[0092] Therefore, the topology and gain configuration are nonfragile at the spectral level.

[0093] (2) Configuration 2: .

[0094] consider and ,have:

[0095]

[0096] Therefore, we can conclude that:

[0097]

[0098] Therefore, this topology and gain configuration are fragile.

[0099] Step S7, Key Node Identification.

[0100] For dangerous modes q j maximum value Sorting by amplitude:

[0101]

[0102] If a threshold is taken Then the set of key nodes is That is, when Byzantine sensor attacks are carried out on nodes 1 and 2, the state estimation is most likely to diverge, meaning that multi-sensor network systems are vulnerable under this condition.

[0103] It can be seen that, given the system matrix and network topology, the method of this application does not require attack injection or extensive time-domain simulation, but constructs... By calculating the joint spectral radius, it is possible to output whether the topology triggers the vulnerability condition, thus providing a vulnerability detection method for multi-sensor networks based on topology.

[0104] This application also provides a system for detecting the vulnerability of multi-sensor network topology, including:

[0105] The system information acquisition module is used to read the state matrix from the system model of the multi-sensor network. A and the measurement matrix of each sensor For the state matrix A Find eigenvalues l i ( A and the corresponding feature vectors r i ;

[0106] The matrix construction module is used to construct a weighted directed topology graph based on the topology of a multi-sensor network. G Based on weighted directed topology graph G Establish the Laplace matrix L For the Laplace matrix L Perform eigenvalue decomposition to obtain eigenvalues. m j ( L and the corresponding feature vectors q j ;

[0107] The error construction module is used in multi-sensor networks to employ a Kalman consensus filter with a unified consensus gain, based on the system model and measurement matrix. Calculate the state estimates of each sensor. The state estimates of each sensor Stacking yields the overall system error ;

[0108] The joint eigenvalue calculation module is used for calculations based on the state matrix. A Laplace matrix L And establish the state matrix Φ of the unified consensus estimation error system based on the consensus gain, and find the joint eigenvalues ​​of the state matrix Φ. l ij joint eigenvalues l ij Represented as ;

[0109] The reachability analysis module is used to analyze the overall system error. Construct a deviation system, and generate an reachability matrix based on the reachability analysis of the deviation system. R ;

[0110] The vulnerability determination module is used to make the joint feature vector v ij for If there are non-zero eigenvalues m j ( L ) and eigenvalues l i (A ) makes Simultaneously, joint feature vectors v ij Belongs to reachable subspace span ( R If this is the case, then the current topology and consensus gain configuration of multi-sensor networks are vulnerable to Byzantine attacks.

[0111] This application also provides an electronic device, including a memory and at least one processor;

[0112] This memory stores multiple computer instructions;

[0113] When the at least one processor executes the plurality of computer instructions, it causes the at least one processor to perform the method described above.

[0114] This application also provides a computer storage medium storing a plurality of computer instructions for causing a computer to execute the above-described method.

[0115] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0116] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for detecting the vulnerability of a multi-sensor network topology, characterized in that, include: Read the state matrix from the system model of the multi-sensor network. A and the measurement matrix of each sensor C i For the state matrix A Find eigenvalues λ i ( A and the corresponding feature vectors r i ; Construct a weighted directed topology graph based on the topology of the multi-sensor network. G Based on the weighted directed topology graph G Establish the Laplace matrix L For the Laplace matrix L Perform eigenvalue decomposition to obtain eigenvalues. μ j ( L and the corresponding feature vectors q j ; The multi-sensor network employs a Kalman consensus filter with unified consensus gain, based on the system model and the measurement matrix. C i Calculate the state estimates of each sensor The state estimates of each sensor Stacking yields the overall system error ; Based on the state matrix A The Laplace matrix L and consensus gain Establish the state matrix Φ of the unified consensus estimation error system, and find the joint eigenvalues ​​of the state matrix Φ. λ ij The joint eigenvalues λ ij Represented as , To unify the consensus gain coefficient; Based on the overall system error Construct a deviation system, and form an reachability matrix based on the reachability analysis of the deviation system. R ; Let the joint eigenvector v ij for If there exists a non-zero eigenvalue. μ j ( L ) and the eigenvalues λ i ( A ) makes Meanwhile, the joint feature vector v ij Belongs to reachable subspace span ( R If the current multi-sensor network topology and the configuration of the consensus gain are vulnerable to Byzantine attacks, then the current multi-sensor network topology and the consensus gain configuration are vulnerable to Byzantine attacks. Among them, based on the weighted directed topology graph G Establish the Laplace matrix L The methods include: The weighted directed topology graph G Represented as ,in Sensor assembly, N For the number of sensors, Let be the set of edges. Let be the edge weight matrix. w ij To connect the sensor i and j The weight of the edge; For sensors i Calculate in-degree Construct a pair of angle matrices The Laplace matrix is ​​represented as ; The state estimate Represented as: All sensors use a unified consensus gain. ,get: in, and Sensors The predicted state estimate and the filtered state estimate, For the first i Kalman gain of each sensor, It is the first The measurement results of each sensor For sensors consensus gain, For sensors j The predicted state estimate, To ensure a unified consensus gain coefficient, a value greater than zero is adopted. N i For sensors i The neighborhood group, for An identity matrix of order 1. n It is the state dimension of the system; The overall system error is obtained by stacking the state estimates of each sensor. , is represented as: in, for An identity matrix of order 1. N For the number of sensors, for N An identity matrix of order 1. For Kronecker product, , , for k The overall systematic error at time -1 This is a deviation caused by a Byzantine sensor attack; The state matrix Φ is represented as Using the spectral properties of the Kronecker product, for Find the feature value ; The deviation system is: in ; Based on the reachability analysis of systems theory, the reachability matrix is ​​formed as follows: 。 2. The method for detecting the vulnerability of a multi-sensor network topology according to claim 1, characterized in that, The joint feature values ​​between all sensor pairs λ ij The maximum value is taken as the joint spectral radius. ρ max Based on the joint spectral radius ρ max Determine stability margin δ According to the stability margin δ Assess the vulnerability of the current multi-sensor network topology and the configuration of the consensus gain.

3. The method for detecting the vulnerability of a multi-sensor network topology according to claim 2, characterized in that, stability margin δ Represented as The stability margin δ The closer the value is to 0, the more fragile the current multi-sensor network topology and the configuration of the consensus gain are.

4. The method for detecting the vulnerability of a multi-sensor network topology according to claim 1, characterized in that, After determining the current multi-sensor network topology and the vulnerability of the consensus gain configuration, the feature vector is... q j After normalization, sensors with absolute component values ​​higher than the threshold are selected as the set of key nodes.

5. The method for detecting the vulnerability of a multi-sensor network topology according to claim 1, characterized in that, The state matrix A This is the Schur stability matrix.

6. The method for detecting the vulnerability of a multi-sensor network topology according to claim 1, characterized in that, If there exists a vector with non-zero coefficients α , so that the joint feature vector v ij Represented as Rα A linear combination of these elements would allow the current multi-sensor network topology and the configuration of the consensus gain to be activated via a Byzantine sensor attack.

7. A system applying the method for detecting the vulnerability of multi-sensor network topology according to any one of claims 1-6, characterized in that, include: The system information acquisition module is used to read the state matrix from the system model of the multi-sensor network. A and the measurement matrix of each sensor C i For the state matrix A Find eigenvalues λ i ( A and the corresponding feature vectors r i ; The matrix construction module is used to construct a weighted directed topology graph based on the topology of a multi-sensor network. G Based on the weighted directed topology graph G Establish the Laplace matrix L For the Laplace matrix L Perform eigenvalue decomposition to obtain eigenvalues. μ j ( L and the corresponding feature vectors q j ; The error construction module is used in multi-sensor networks to employ a Kalman consensus filter with a unified consensus gain, based on the system model and the measurement matrix. C i Calculate the state estimates of each sensor The state estimates of each sensor Stacking yields the overall system error ; The joint eigenvalue calculation module is used to calculate the eigenvalues ​​based on the state matrix. A The Laplace matrix L And establish the state matrix Φ of the unified consensus estimation error system based on the consensus gain, and calculate the joint eigenvalues ​​of the state matrix Φ. λ ij The joint eigenvalues λ ij Represented as , To unify the consensus gain coefficient; The reachability analysis module is used to analyze the overall system error. Construct a deviation system, and form an reachability matrix based on the reachability analysis of the deviation system. R ; The vulnerability determination module is used to make the joint feature vector v ij for If there exists a non-zero eigenvalue. μ j ( L ) and the eigenvalues λ i ( A ) makes Meanwhile, the joint feature vector v ij Belongs to reachable subspace span ( R If the current multi-sensor network topology and the configuration of the consensus gain are vulnerable to Byzantine attacks, then the current multi-sensor network topology and the consensus gain configuration are vulnerable to Byzantine attacks. Among them, based on the weighted directed topology graph G Establish the Laplace matrix L The methods include: The weighted directed topology graph G Represented as ,in Sensor assembly, N For the number of sensors, Let be the set of edges. Let be the edge weight matrix. w ij To connect the sensor i and j The weight of the edge; For sensors i Calculate in-degree Construct a pair of angle matrices The Laplace matrix is ​​represented as ; The state estimate Represented as: All sensors use a unified consensus gain. ,get: in, and Sensors The predicted state estimate and the filtered state estimate, For the first i Kalman gain of each sensor, It is the first The measurement results of each sensor For sensors consensus gain, For sensors j The predicted state estimate, To ensure a unified consensus gain coefficient, a value greater than zero is adopted. N i For sensors i The neighborhood group, for An identity matrix of order 1. n It is the state dimension of the system; The overall system error is obtained by stacking the state estimates of each sensor. , is represented as: in, for An identity matrix of order 1. N For the number of sensors, for N An identity matrix of order 1. For Kronecker product, , , for k The overall systematic error at time -1 This is a deviation caused by a Byzantine sensor attack; The state matrix Φ is represented as Using the spectral properties of the Kronecker product, for Find the feature value ; The deviation system is: in ; Based on the reachability analysis of systems theory, the reachability matrix is ​​formed as follows: 。 8. An electronic device, characterized in that, Includes memory and at least one processor; The memory stores multiple computer instructions; When the at least one processor executes the plurality of computer instructions, it causes the at least one processor to perform the method according to any one of claims 1-6.

9. A computer storage medium, characterized in that, The computer storage medium stores a plurality of computer instructions, which are used to cause the computer to perform the method described in any one of claims 1-6.

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