Multi-target Kalman security state estimation method under random spoofing attack

Abstract

The invention discloses a multi-target Kalman security state estimation method under random spoofing attack. The method comprises the following steps: acquiring a dynamic model of a multi-target system and related parameters of an attack; constructing a directed graph of information interaction between coupling states of the multi-target system, and designing a multi-target Kalman safety state observer according to the directed graph; inputting related parameters of attacks into the designed multi-target Kalman security state observers and updating related parameters of the observers; performing state estimation on the multi-target system based on the multi-target Kalman safety state observer after parameter updating, outputting the state estimation value of each target after the state estimation value of the multi-target observer designed for each target is updated, and completing safety state estimation under sensor attack; according to the invention, when the sensor is subjected to random spoofing attack, the system can still effectively estimate the states of a plurality of targets in real time, and the safe operation of the system is ensured.

Description

Technical Field

[0001] The present invention relates to a method for multi-target Kalman security state estimation under attacks, and belongs to the field of security control of cyber-physical systems. Background Art

[0002] In recent years, with the progress of computer and network communication technologies, cyber-physical systems have developed vigorously. Due to the advantage of collaborative work, such systems have been widely applied in industrial production, vehicle perception, smart home, and efficient data transmission in energy and power systems. Among them, multi-target state estimation is the core issue in fields such as target tracking, navigation, and monitoring. For example, in scenarios such as distributed positioning of multi-vehicle formations and collaborative tracking in sensor networks, it is necessary to obtain relative state information between targets (such as relative position, signal strength, etc.) through coupled measurements to achieve accurate estimation of the states of multiple targets. Therefore, for multi-target state estimation, it is necessary to derive new performance analysis conditions and consensus strategies. In addition, cyber-physical systems are also faced with many threats and uncertainties of attacks. Since the measurement data of sensors has a direct impact on the estimation of state observers. Therefore, attacks on sensors, as a common type of attack, greatly disrupt the normal operation of the system, bringing uncertainty and significant losses to actual production and life. Such as DoS (Denial of Service) attacks, FDI (False Data Injection), random attacks, etc. Therefore, multi-target security state estimation under cyber attacks is still a challenging problem. To ensure the safe operation of the system and the effectiveness of multi-target state estimation, it has important research value for multi-target security state estimation.

[0003] To achieve multi-target security state estimation under sensor attacks, scholars in this field have done a lot of work and proposed many effective methods. The Kalman consensus filter (KCF) is one of the earliest algorithms designed for distributed filtering of sensor node networks. It is designed based on the standard Kalman filter, where the consensus term is constructed by the difference between the local state estimate and the state estimates of its neighbors. Most existing research focuses on designing distributed Kalman filters for single-target tracking systems, that is, a single target is observed by a group of sensor nodes, and the distributed Kalman filter is used to handle the interaction between sensors, and the network topology is often described by an undirected graph. However, in multi-target tracking systems, the situation of relative state measurement or coupling of target measurement values may occur. Therefore, effective state estimation cannot be performed. Therefore, it is necessary to study the problem of multi-target Kalman security state estimation to ensure the safe and efficient operation of the system and promote the wide application of cyber-physical systems. Summary of the Invention

[0004] The purpose of the present invention is to provide a multi-target Kalman security state estimation method under random deception attacks, which solves the problems that the prior art cannot effectively estimate the system state when the sensor measurement values in a multi-target system contain the coupled state values of other targets, and the state observer cannot perform security state estimation when the sensor is under random deception attacks.

[0005] To achieve the above purpose, the present invention is implemented by the following technical solutions:

[0006] In the first aspect, the present invention provides a method for multi-target Kalman security state estimation under random deception attacks, including:

[0007] Obtain the dynamic model of the multi-target system and the relevant parameters of the attack;

[0008] Construct a directed graph for information interaction between the coupled states of the multi-target system, and design a multi-target Kalman security state observer accordingly;

[0009] Input the relevant parameters of the attack into the designed multi-target Kalman security state observer and update the relevant parameters of each observer;

[0010] Based on the multi-target Kalman security state observer with updated parameters, perform state estimation on the multi-target system. After the state estimation values of the multi-target observers designed for each target are updated, output the state estimation values of each target to complete the security state estimation under sensor attacks;

[0011] Furthermore, the method for obtaining the dynamic model of the multi-target system and the relevant parameters of the attack is as follows:

[0012] For the th target in a multi-target system composed of targets, the dynamic model of the system at time

[0013]

[0014]

[0015] where represents the true state value of target i in the linear system at time k + 1, represents the true state values of each state of target at time

[0016] at time is the state transition matrix of each state of target

[0017] Indicate the target At time The noise driving matrix of each state,

[0018] Indicate the target At time The inherent noise of each state,

[0019] Indicate the measurement value matrix of all states of the sensor for the target At time

[0020] Indicate that the sensor at time For the target The mapping matrix of the observed value of the true state;

[0021] Is the target At time The sensor measurement noise.

[0022] Where:

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] Among them, To Indicate the target And the target coupled with the target The coupled target To At time The true value of each state,

[0029] To Indicate the target And the target coupled with the target The coupled target To At time The state transition matrix of each state,

[0030] To Indicate the target And the target coupled with the target The coupled target​ to the noise-driven matrix of each state at the moment

[0031] to represent the target and the target coupled with the target to the inherent noise of each state at the moment

[0032] to represent the mapping matrix of the observed values of each state of the sensor to the target and the target coupled with the target to the moment

[0033] The superscript T in the upper right indicates the transpose;

[0034] , , bounded, the state is uniformly observable.

[0035] Furthermore, for the state of a single target in a linear system

[0036]

[0037] where is the dimensional system state vector of the target at the moment , R represents the dimension of the R space to which z belongs, n is the moment the system matrix of the target at is expressed as the moment the Gaussian noise of the target at with a mean of 0 and a variance of is the input matrix of the single target used to describe the influence of the process noise on the state

[0038] The sensor measurement value of the target is coupled with the measurement values of other targets, and the expression is as follows: ​​​​​​​​​

[0039]

[0040] wherein: represents the measurement value of the th sensor at time , is the set of coupled measurement targets associated with the sensor, is the known measurement matrix, is a noise random variable that follows a Gaussian distribution with a mean of 0 and a variance of ;

[0041] At time of the sensor, a random spoofing attack will change the sensor measurement value to , and its form is expressed as:

[0042]

[0043] where follows a Bernoulli distribution with a probability of (0 1), is the parameter of the Bernoulli distribution, , , is a bounded random variable that satisfies , and Pr{} represents probability.

[0044] Furthermore, a directed graph for information interaction between the coupled states of the multi-target system is constructed, including:

[0045] The information interaction between the observers is described by the directed graph ,

[0046] where is a finite non-empty node set of the graph, represents the observer node of the th target in the multi-target system, and the edge set is used to describe the information flow direction between the observer nodes,

[0047] The in-neighborhood set of the node is represented as ,

[0048] where the in-degree , and the out-neighborhood set of the node is represented as , and the out-degree ,

[0049] The filter is set to obtain information from its in-neighborhood;

[0050] To describe the information transfer between the coupling states of a multi-target system, the following augmented matrix is defined:

[0051]

[0052]

[0053] where represents the estimation of the th target for the filter , with the hat symbol ^ denoting the estimated value. to represent the estimated values of the states of target and the targets coupled with target to at time .

[0054] to represent the state estimation values sent by the filter of target and the targets coupled with target to to the neighboring filters at time .

[0055] A directed graph for information interaction between the coupling states of the multi-target system is established as described below:

[0056] For the edge , the th estimator does not have to send the augmented state estimation to the filters in its out-neighborhood ; it is assumed that for each target, there is exactly one state observer for state estimation; the observer of target receives the state estimation of target from the observer of target in its in-neighborhood . After generating , it sends the state estimation of target from the observer to the observer of target in its out-neighborhood . The observer receives and generates the state estimation , then sends it to target Out-neighborhood target Observer , until the last target The state observer generates And transmits the state estimate to the out-neighborhood state observer .

[0057] Furthermore, the method for designing a multi-target Kalman safety state observer according to the directed graph includes:

[0058] Design a multi-target Kalman safety state observer according to the directed graph established for information interaction between coupled states of the multi-target system as follows:

[0059]

[0060] Wherein, Is the gain in the th Kalman safety state observer at time Is the multi-target state estimator at time The gain of the interaction term between And adjacent nodes.

[0061] Furthermore, the method for updating the parameters related to each observer is:

[0062] At time The gain In the th Kalman safety state observer is calculated as follows:

[0063]

[0064] Wherein, Is the augmented error covariance matrix of the state estimate of the observer At time . Is the covariance matrix of Gaussian noise with mean 0 . Means the variance of the random variable .

[0065] At time The gain Of the interaction term between the multi-target state estimator And adjacent nodes is calculated as:

[0066]

[0067] Wherein, 0, Is the gain coefficient, and a suitable value needs to be selected according to the needs of the system;

[0068] Select the reference value according to the following formula:

[0069]

[0070] where is a constant;

[0071] time The calculation method of the observation matrix of the error covariance of the multi-target state estimator at is:

[0072]

[0073] where represents the augmented covariance matrix of the target at time; if it is the first calculation, its initial value is non-negative.

[0074] Furthermore, the method for outputting the state observation values of each target of the multi-target system is:

[0075] For the multi-target safety state estimation system, substitute all the updated parameters into the designed state observer to obtain the estimated value of the target state at the current time.

[0076] After each state observer is updated, check whether the multi-target observer designed for each target has been updated once. If the above state observer update is not completed, update the state estimation value of the above state observer at time in sequence according to the constructed directed graph of information interaction between state observer nodes;

[0077] After the estimated values of all state observers are updated once, output the state estimation values of each target at the current time.

[0078] In a second aspect, the present invention provides a multi-target Kalman safety state estimation device under random deception attacks, including a processor and a storage medium;

[0079] The storage medium is used to store instructions;

[0080] The processor is used to operate according to the instructions to execute the steps of the method according to the first aspect.

[0081] In a third aspect, the present invention provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the steps of the method according to the first aspect are implemented.

[0082] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0083] ​1. In view of the problem that the existing method cannot effectively estimate when the measured value of a single sensor contains the coupled state values of multiple targets, the present invention proposes a distributed Kalman iterative estimation, which can handle the coupling situation of the measured values and achieve an effective estimation of the system state.

[0084] 2. In view of the problem that the random spoofing attack faced by the sensor leads to a serious increase in the estimation error, the present invention considers the influence of the random attack on the error on the basis of the existing Kalman filter, ensuring that the state observer can still perform a safe state estimation under the influence of such attacks, and improving the reliability of the system under the threat of network attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 is a flowchart of the Kalman multi-target safe state estimation method under random spoofing attack provided by an embodiment of the present invention;

[0086] Figure 2 is a structure and transmission schematic diagram of a multi-target system under random spoofing attack provided by an embodiment of the present invention;

[0087] Figure 3 is a graph of the change of the average cumulative root mean square error of the position of the system when attacking target 1 provided by an embodiment of the present invention;

[0088] Figure 4 is a graph of the change of the average cumulative root mean square error of the speed of the system when attacking target 1 provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0089] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and cannot be used to limit the protection scope of the present invention.

[0090] Embodiment 1:

[0091] This embodiment provides a multi-target Kalman safe state estimation method under random spoofing attack, which can solve the problems that the existing technology cannot achieve an effective state estimation of the system state when the measured value of the sensor in a multi-target system contains the coupled state values of other targets and the state observer cannot perform a safe state estimation when the sensor is under a random spoofing attack.

[0092] In this embodiment, a scenario of tracking 4 targets is considered, and it is assumed that the sensor measured values are coupled with each other (that is, only the difference in states can be measured). It is assumed that the system dynamic model of each target is as follows:

[0093]

[0094] Where:

[0095]

[0096]

[0097] State vector , where are the position vectors in the X and Y directions in the two-dimensional coordinate system respectively, are the velocity vectors in the X and Y directions in the two-dimensional coordinate system respectively. The sampling period T = 1, and the covariance matrix of the Gaussian noise is 0.01 .

[0098] In this embodiment, the initial conditions and parameter definitions involved are as follows:

[0099] Given the initial state , , , .

[0100] The sensor measures two targets simultaneously (but can only output the coupled measurement values), and its measurement values are generated according to the following equation:

[0101]

[0102] where: represents the measurement value of the th sensor at time , is the set of coupled measurement targets associated with the sensor (including the target itself), is the mapping (measurement) matrix of the sensor to the coupled target of the target (here can be equal to , is the measurement matrix of the sensor to the target , and the serial number plate of the sensor is the same as the serial number of the target), represents the state value of the coupled target of the target (here can be equal to , = i.e., itself, and itself and itself are also a kind of coupling). is a noise random variable that follows a Gaussian distribution with a mean of 0 and a variance of ;

[0103]

[0104]

[0105] Wherein:

[0106]

[0107] Where H describes the mapping relationship between the observed value z of the sensor for the true state x, and v represents the noise introduced by the sensor during the measurement process; the subscript i represents target i, and the subscript k represents time k; the subscript represents the qth i target coupled with target i; the subscript j belongs to the targets in the neighborhood of i, that is, it can be understood as the coupled targets;

[0108] Considering the diversity of different state noises, the measurement noise covariance matrix is = 2i .

[0109] As Figure 1 shown, the multi-target Kalman security state estimation method under random deception attack provided by the embodiment of the present invention includes the following steps:

[0110] S1. Obtain the dynamic model of the multi-target system and the relevant parameters of the attack;

[0111] The expression of the dynamic model is:

[0112]

[0113]

[0114] Wherein:

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123] The expression of the measurement equation is:

[0124]

[0125]

[0126] includes the target and the target coupled with the target ( to ) at time the true values of each state ( to ),

[0127] includes the target and the target coupled with the target ( to ) at time the state transition matrix of each state ( to ),

[0128] includes the target and the target coupled with the target ( to ) at time the noise drive matrix of each state ( to ), which describes how process noise affects the update of the target state,

[0129] includes the target and the target coupled with the target ( to ) at time the inherent noise of each state ( to ),

[0130] is the measurement value matrix of all states of the target and the target coupled with the target ( to ) at time by the sensor ,

[0131] is the sensor measurement noise of the target at time .

[0132] to Represents a sensor For the target And with the target Coupled target To At the moment The mapping matrix of the observed values of each state; (Here Theoretically, it can be represented only by , but it is better to use To represent, one is to keep consistent with the subscripts behind, and the other is that in practice, the measurement matrices of each sensor for the same target may be different, Can represent the sensor Target Measurement matrix, the number of the sensor is generally the same as the number of the target).

[0133] The superscript T in the upper right represents the transpose.

[0134] At the moment, for the sensor Of the random spoofing attack, will change the sensor measurement value To , and obtain its form as:

[0135]

[0136] Where Follows a Bernoulli distribution with probability , Is a bounded random variable that satisfies , that is , , Satisfies .

[0137] S2. Construct a directed graph for information interaction between the coupled states of the multi-target system, and design a multi-target Kalman safety state observer accordingly;

[0138] The information interaction between the observers is described by the directed graph , where Is a finite non-empty node set of the graph, Represents the observer node of the th target in the multi-target system, and the edge set Is used to describe the information flow direction between the observer nodes. The in-neighborhood set of the node Is expressed as: , where the in-degree , and the out-neighborhood set of the node Is expressed as , and the out-degree . It is assumed that the filter can obtain information from its in-neighborhood.

[0139] To further describe the information transfer between the coupled states of the multi-target system, the following augmented matrix is defined:

[0140]

[0141]

[0142] where, denotes the estimation of the th target by the filter at time .

[0143] A directed graph for information interaction between the coupled states of the multi-target system is established as follows:

[0144] For the edge , the th estimator does not need to send the augmented state estimate to the filters in its out-neighborhood . And it is assumed that for each target, there is exactly one state observer for state estimation. The observer receives the state estimate of the observer in its in-neighborhood for the target . After generating , it sends the state estimate of the observer for the target to the observer in its out-neighborhood , and so on, until the last state observer generates and transfers the state estimate to the out-neighborhood state observer. .

[0145] A multi-target Kalman safety state observer is designed according to the established directed graph for information interaction between the coupled states of the multi-target system as follows:

[0146]

[0147] where, is the gain in the th Kalman safety state observer at time ; is the gain of the interaction term between the multi-target state estimator at time and its adjacent nodes.

[0148] Establish as Figure 2Directed graph of information interaction among the four state observers shown:

[0149] According to the assumption, if each target has only one state observer, the number of the observer is the same as that of the target (at least the quantity is the same). For example, observer 1 observes the first target, and observer 2 observes the second target. Figure 2 A Kalman safety state observer is designed for each target. The th observer receives the state estimation of the target from the incoming neighborhood observers, and inputs the state estimation of the target to the outgoing neighborhood state observer after generating until the last state observer generates to complete a cycle. Generate

[0150] S-3. Input the relevant parameters of the attack into the multi-target Kalman safety state observer and update the relevant parameters of each observer.

[0151] S3-1. Update the augmented Kalman gain of the multi-target state observer at time .

[0152]

[0153] Among them, is the augmented error covariance matrix of the state estimation of the observer at time . is the covariance matrix of the Gaussian noise with a mean of 0.

[0154] S3-2. Update the gain of the interaction term between the multi-target state estimator at time and the adjacent nodes.

[0155]

[0156] Among them, 0, and a suitable value needs to be selected according to the needs of the system. The following formula is provided here for reference in selecting the reference value:

[0157]

[0158] Among them is a relatively small constant, and usually a value such as 0.01 can be selected.

[0159] Set​ , , 。

[0160] S3-3, Update Time Multi-target State Estimator under Observation matrix of the error covariance.

[0161]

[0162] Where represents the time under the target Augmented covariance matrix. If it is the first calculation, ensure that its initial value is non-negative.

[0163] Where , 。

[0164] S4. Perform state estimation on the multi-target system using the multi-target Kalman safety state observer after updating the parameters, and update the state estimation values of each target of the multi-target at the update time 。

[0165] For the multi-target safety state estimation system, substitute all the updated parameters in S3 into the state observer designed in S2 to obtain the estimated value of the target state at the current time. After updating each state observer, it should be detected whether the multi-target observer designed for each target has completed an update. If the above state observer update is not completed, the state estimation values of the above state observer at the time should be updated in sequence according to the constructed directed graph of information interaction between state observer nodes. After the estimated values of the above state observers have all been updated once, output the state estimation values of each target at the current time.

[0166] According to the analysis and parameter setting requirements described above, when a random spoofing attack is carried out on Target 1 within 60 time steps, it can be set to reduce the random interference of noise, and the number of Monte Carlo experiments 。

[0167] Define The calculation methods for the cumulative root mean square error of the position and the cumulative root mean square error of the velocity in the jth Monte Carlo experiment at the time

[0168]

[0169]

[0170] Where , , , The sequential state observer for the target The position estimate value and velocity estimate value in the X direction, and the state observer for the target The position estimate value and velocity estimate value in the Y direction.

[0171] Then at time The calculation method of the average cumulative root mean square error of position and velocity is as follows:

[0172]

[0173]

[0174] Combining the above parameters, a change diagram of the average total error of position and the average total error value of velocity within 60 time steps (i.e., 60 s) of this embodiment is obtained. According to Figures 3 - 4 It can be seen that when suffering from random deception attacks of sensors, the average cumulative root mean square error of the position and velocity of the multi-target system converges rapidly, and the designed multi-target Kalman safety state estimation method can realize the safety state estimation of the multi-target system.

[0175] Embodiment 2:

[0176] This embodiment provides a multi-target Kalman safety state estimation device under random deception attacks, including a processor and a storage medium;

[0177] The storage medium is used to store instructions;

[0178] The processor is used to operate according to the instructions to execute the steps of the method according to Embodiment 1.

[0179] Embodiment 3:

[0180] This embodiment provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the steps of the method according to Embodiment 1 are implemented.

[0181] Those skilled in the art should understand that the embodiments of the present application take the method as the core innovation, and can be specifically embodied in the form of a method executed by pure hardware, a method implemented by pure software, or a form of implementation combining software and hardware.

[0182] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program codes.

[0183] This application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0184] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0185] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0186] The above is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A multi-target Kalman security state estimation method under random spoofing attacks, characterized in that Including: Obtain the dynamic model of the multi-target system and the relevant parameters of the attack; Construct a directed graph for information interaction between the coupled states of the multi-target system, and design a multi-target Kalman safety state observer according to the directed graph; Input the relevant parameters of the attack into the designed multi-target Kalman safety state observer and update the relevant parameters of each observer; Perform state estimation on the multi-target system based on the multi-target Kalman safety state observer with updated parameters, and output the state estimation values of each target after the state estimation value of the multi-target observer designed for each target is updated once, completing the safety state estimation under sensor attack.

2. The multi-target Kalman security state estimation method under random spoofing attack according to claim 1, characterized in that The method for obtaining the dynamic model of the multi-target system and the relevant parameters of the attack is: For the th target in a multi-target system composed of targets, the dynamic model of the system at time ； ； wherein, represents the true state value of target i in the linear system at time k + 1, represents the target at time the true values of each state; Indicate the target At the moment The state transition matrix of each state below represent the target at the moment the noise-driven matrix of each state below Indicates the target At the moment The inherent noise of each state below Indicates the measurement matrix of all states of the sensor for the target At the moment underneath, Denote the mapping matrix of the observed value of the true state of the target by the sensor at time of the target ; is the target at the moment the sensor measurement noise below; , , bounded, and the state is uniformly observable; Where: ； ； ； ； ； Among them, to represent the true values of the target and the target coupled with the target at each state at the moment to at the moment and the true values of each state to represent the target and the target coupled with the coupled target to at the moment the state transition matrix of each state below, to represent the target and the target coupled with the coupled target to at the moment the noise-driven matrix of each state, to represent the target and the target coupled with the coupled target to at the moment the inherent noise of each state below; to represent the sensor for the target and the target coupled with the coupled target to at the moment the mapping matrix of the observed values of each state; The superscript T in the upper right represents the transpose.

3. The multi-target Kalman security state estimation method under random deception attack according to claim 2, wherein, For the state of a single target in a linear system , its dynamic equation is expressed as: ； Among them, is the target at time system state vector, is the time under the target system matrix, denoted as the time under the target Gaussian noise, with a mean of 0, is the single-target input matrix, used to describe the process noise on the state impact; Target The sensor measurement value of is coupled with other target measurement values, and the expression is as follows: ； Wherein: represents the measurement value of the th sensor at time is the set of coupled measurement targets associated with the sensor is at time the mapping matrix of the coupled target of the target by the sensor ; is the system state vector of the coupled target of the target at time ; is a noise random variable that follows a Gaussian distribution with a mean of 0 and a variance of ; At a certain moment, for the sensor a random spoofing attack will change the sensor measurement value to the sensor tampered value , which is expressed in the form of: ； where obeys a Bernoulli distribution with a probability of , 0 1, is the parameter of the Bernoulli distribution, , , is a bounded random variable satisfying , and Pr{} represents probability.

4. The multi-objective Kalman security state estimation method under random spoofing attack according to claim 3, wherein Constructing a directed graph for information interaction between the coupled states of the multi-target system includes: The information interaction between the observers is described by a directed graph description Among them is a finite non-empty set of nodes of the graph, represents the observer node of the th target in the multi-target system, and the edge set is used to describe the information flow between observer nodes. Node The in-neighborhood set of is denoted as , the in-degree Node The out-neighborhood set of is denoted as , the out-degree Set the filter to obtain information from its in-neighborhood; To describe the transmission of information between the coupled states of the multi-target system, define the following augmented matrix: Augmented state matrix of target i at time k ; Consensus state matrix of target i at time k ; Among them, the top label ^ represents the estimated value, to represent the target and the target coupled with the coupled target to at the moment the estimated values of each state; to represent the target and the target coupled with the coupled target to at the moment of the filter sends the state estimate value of the neighborhood filter; Establish a directed graph for information interaction between the coupled states of the multi-target system as described below: Assume that for each target, there is exactly one state observer for state estimation; the target 's observer receives the target in its neighborhood 's observer for the target 's state estimation and, after generating the backward out - neighborhood target 's observer sends the observer for the target 's state estimation to the observer which receives the generated state estimation and then sends it to the out - neighborhood target 's observer until the state observer of the last target generates and passes the state estimation to the out - neighborhood state observer .

5. The multi-target Kalman security state estimation method under random spoofing attack according to claim 4, characterized in that The method for designing a multi-target Kalman safety state observer according to the directed graph includes: Design a multi-target Kalman safety state observer according to the established directed graph for information interaction between the coupled states of the multi-target system as follows: ； Among them, is the gain in the -th Kalman safety state observer at time ; is the gain of the interaction term between the multi-target state estimator at time and adjacent nodes.

6. The multi-target Kalman security state estimation method under random spoofing attack according to claim 5, characterized in that, The method for updating the relevant parameters of each observer is: Moment the gain in the th Kalman safety state observer is calculated according to the following formula: ； Among them, is the observer at time augmented error covariance matrix of the state estimate; is the covariance matrix of Gaussian noise with a mean of 0; means the variance of the random variable ; Moment Multi-target state estimator Gain of interaction term with adjacent nodes The calculation method is as follows: ； Among them, 0, is the gain coefficient; Select a reference value according to the following formula: ； wherein is a constant; Moment Multi-target state estimator The calculation method of the observation matrix of the error covariance is as follows: ； wherein represents a moment next target augmented covariance matrix; if it is the first calculation, its initial value is non - negative.

7. The multi-object Kalman security state estimation method under random spoofing attacks according to claim 6, characterized in that The method for outputting the state observation values of each target of the multi-target system is: For the multi-target safety state estimation system, substitute all the updated parameters into the designed state observer to obtain the estimated value of the state of this target at the current moment, After updating each state observer, check whether the multi-target observer designed for each target has completed an update. If the update of the above state observer has not been completed, update the time in sequence according to the directed graph of information interaction between the constructed state observer nodes the state estimation value of the above state observer; After the estimated values of the state observer are all updated once, output the state estimation values of each target at the current moment.

8. A multi-target Kalman security state estimation device under random deception attack, characterized in that, Including a processor and a storage medium; The storage medium is used to store instructions; The processor is used to operate according to the instructions to execute the steps of the method according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, the steps of the method according to any one of claims 1-7 are implemented.

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