A multi-objective Kalman secure state estimation method under random deception attacks

Abstract

The present invention discloses a multi-target Kalman safety state estimation method under random deception attacks. The method relates to the field of security control of cyber-physical systems and includes obtaining a dynamic model of the multi-target system and attack-related parameters; constructing a directed graph of information interaction between coupled states of the multi-target system and designing a multi-target Kalman safety state observer based on the graph; inputting attack-related parameters into the designed multi-target Kalman safety state observer and updating the relevant parameters of each observer; performing state estimation of the multi-target system based on the updated multi-target Kalman safety state observer, and outputting the state estimation value of each target after the state estimation value of the multi-target observer designed for each target is updated, thereby completing the safety state estimation under sensor attacks. The present invention can ensure that when a sensor is subjected to a random deception attack, the system can still effectively and real-timely estimate the states of multiple targets, thereby ensuring the safe operation of the system.

Description

Technical Field

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

[0002] In recent years, with advances in computer and network communication technologies, cyber-physical systems (CPSs) have flourished. Due to their collaborative advantages, these systems have been widely applied in fields such as industrial production, vehicle perception, smart homes, and efficient data transmission in energy and power systems. Multi-target state estimation is a core issue in target tracking, navigation, and monitoring. For example, scenarios such as distributed positioning of multi-vehicle platoons and cooperative tracking in sensor networks require coupled measurements to obtain relative state information (such as relative position and signal strength) between targets to accurately estimate their states. Therefore, new performance analysis conditions and consensus strategies are needed for multi-target state estimation. Furthermore, CPSs face numerous attack threats and uncertainties. Sensor measurement data directly influences the state observer's estimation. Therefore, attacks against sensors, a common type of attack, significantly disrupt the normal operation of the system, introducing uncertainty and significant losses to real-world production and life. Such as DoS (Denial of Service) attacks, FDI (False Data Injection), random attacks, etc. Therefore, multi-objective security state estimation under network attacks is still a challenging problem. In order to ensure the safe operation of the system and the effectiveness of multi-objective state estimation, multi-objective security state estimation has important research value.

[0003] To achieve secure multi-target state estimation under sensor attacks, researchers in this field have conducted extensive research and proposed many effective methods. The Kalman consensus filter (KCF) is one of the earliest algorithms designed for distributed filtering in sensor node networks. It is based on the standard Kalman filter design, where the consensus term is constructed by the difference between a local state estimate and its neighboring state estimates. Existing research has largely focused on designing distributed Kalman filters for single-target tracking systems, where a single target is observed by a group of sensor nodes. Distributed Kalman filters are used to handle interactions between sensors, and the network topology is often described as an undirected graph. However, in multi-target tracking systems, relative state measurements or coupled target measurements may occur, making effective state estimation impossible. Therefore, it is necessary to study the problem of secure multi-target Kalman state estimation to ensure the safe and efficient operation of the system and promote the widespread application of cyber-physical systems. Summary of the Invention

[0004] The purpose of the present invention is to provide a multi-target Kalman safe state estimation method under random deception attacks, so as to solve the problems in the prior art that in a multi-target system, when the sensor measurement values contain the coupled state values of other targets, the effective state estimation of the system state cannot be achieved, and the state observer cannot perform safe state estimation when the sensor is subjected to random deception attacks.

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

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

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

[0008] Construct a directed graph of information interaction between coupled states of a multi-objective system and design a multi-objective Kalman safety state observer based on it;

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

[0010] The state of the multi-objective system is estimated based on the multi-objective Kalman safety state observer with updated parameters. After the state estimation value of the multi-objective observer designed for each target is updated, the state estimation value of each target is output to complete the safety state estimation under sensor attack.

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

[0012] for The first target in a multi-target system goals, The dynamic model of the system at the moment is expressed as:

[0013]

[0014]

[0015] in, represents the true value of the state of target i in the linear system at time k+1, Indicates the target At the moment The true value of each state;

[0016] Indicates the target At the moment The state transfer matrix of each state is:

[0017] Indicates the target At the moment The noise driving matrix of each state is:

[0018] Indicates the target At the moment The inherent noise of each state is

[0019] Indicates the sensor's position on the target At the moment The measurement matrix of all states under

[0020] Indicates that the sensor is at time Next target The mapping matrix of the observation value of the true state;

[0021] is the target At the moment The sensor measurement noise below.

[0022] in:

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] in, arrive Indicates the target and goals Coupling goals arrive At the moment The true value of each state,

[0029] arrive Indicates the target and goals Coupling goals arrive At the moment The state transfer matrix of each state is:

[0030] arrive Indicates the target and goals Coupling goals arrive At the moment The noise driving matrix of each state is:

[0031] arrive Indicates the target and goals Coupling goals arrive At the moment The inherent noise of each state under

[0032] arrive Indicates sensor Towards the target and goals Coupling goals arrive At the moment The mapping matrix of the observation values of each state;

[0033] The superscript T indicates transposition;

[0034] 、 、 Bounded, The status is consistent and impressive.

[0035] Furthermore, for the state of a single target in a linear system , its dynamic equation is expressed as:

[0036]

[0037] in, is the target At the moment of dimensional system state vector, R n represents the dimension of the R space to which z belongs, It's time Next target The system matrix, Expressed as time Next target Gaussian noise with a mean of 0 and a variance of , Is a single target The input matrix is used to describe the process noise Status impact.

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

[0039]

[0040] in: Indicates the Sensors at the time The measured value of is the set of coupled measurement targets associated with the sensor, is the known measurement matrix, It is subject to the mean of 0 and the variance of Gaussian distributed noise random variable;

[0041] Align the sensor A random spoofing attack will change the sensor measurement value Tampered with , which is expressed as:

[0042]

[0043] in The probability of compliance is Bernoulli distribution (0 1), is the parameter of the Bernoulli distribution, , , is satisfied is a bounded random variable, and Pr{} represents the probability.

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

[0045] The information exchange between observers is through a directed graph describe,

[0046] in is a finite non-empty set of nodes in the graph, Indicates the first The observer node of the target, the edge set Used to describe the information flow between observer nodes,

[0047] node The incoming neighborhood set is expressed as ,

[0048] The in-degree ,node The out-neighborhood set is expressed as , out of degree ,

[0049] Set the filter to take information from its incoming neighborhood;

[0050] In order to describe the information transfer between the coupled states of the multi-objective system, the following augmented matrix is defined:

[0051]

[0052]

[0053] in, For the filter For the first an estimate of the target; , the top script ^ indicates an estimated value, arrive Indicates the target and goals Coupling goals arrive At the moment The estimated values for each state.

[0054] arrive Indicates the target and goals Coupling goals arrive The filter at time The state estimate sent to the outgoing neighborhood filter.

[0055] A directed graph of information interaction between coupled states of a multi-objective system is established as follows:

[0056] Opposite side , No. The estimator does not need to estimate the augmented state Send to its outbound neighborhood filter; Assume that for each target, there is only one state observer to estimate its state; target Observer Receive into neighborhood Target Observer Towards the target State estimation , in the generation Backward out of the neighborhood Target Observer Send Observer Towards the target State estimation , observer take over Generate state estimates Then send it to the target Out-of-neighborhood target Observer , until the last target The state observer generates and pass the state estimate to the out-of-neighborhood state observer .

[0057] Furthermore, the method for designing a multi-objective Kalman safety state observer based on the directed graph includes:

[0058] According to the established directed graph of information interaction between the coupled states of the multi-objective system, the multi-objective Kalman safety state observer is designed as follows:

[0059]

[0060] in, For the moment Next The gain in the Kalman safety state observer; For the moment Multi-objective state estimator under The gain of the interaction term with the adjacent nodes.

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

[0062] time Next Gains in a Kalman Safety State Observer Calculate as follows:

[0063]

[0064] in, For the moment Observer under The augmented error covariance matrix of the state estimate is . is Gaussian noise with a mean of 0 The covariance matrix of . The meaning of random variable The variance of .

[0065] time Multi-objective state estimator under Gains of interactions with adjacent nodes The calculation method is:

[0066]

[0067] in, 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] in is a constant;

[0071] time Multi-objective state estimator under The error covariance of the observation matrix is calculated as:

[0072]

[0073] in Indicates time Next target The augmented covariance matrix of ; if it is the first calculation, its initial value is non-negative.

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

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

[0076] After each state observer is updated, check whether the multi-objective observer designed for each target has completed an update. If the update of the above state observer is not completed, update the time in sequence according to the directed graph of information interaction between the constructed state observer nodes. The state estimate of the above state observer is:

[0077] After the estimated values of the state observer are updated once, the state estimated values of each target at the current moment are output.

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

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

[0080] The processor is configured 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 having a computer program stored thereon, which implements the steps of the method described in the first aspect when executed by a processor.

[0082] Compared with the prior art, the present invention has the following beneficial effects:

[0083] 1. To address the problem that existing methods cannot effectively estimate the state of a single sensor measurement value containing multiple target coupled state values, this paper proposes a distributed Kalman iterative estimation method that can handle the coupled measurement value situation and achieve effective estimation of the system state.

[0084] 2. This invention addresses the problem of random spoofing attacks on sensors, which can lead to severe increase in estimation errors. Based on the existing Kalman filter, this invention considers the impact of random attacks on errors, ensuring that the state observer can still perform safe state estimation under the influence of such attacks, thereby improving the reliability of the system under the threat of network attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 Flowchart of a Kalman multi-target security state estimation method under random deception attack provided by an embodiment of the present invention;

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

[0087] Figure 3 is a graph showing changes in the average cumulative root mean square error of the system's position when attacking target 1 according to an embodiment of the present invention;

[0088] Figure 4 3 is a graph showing changes in the average cumulative root mean square error of the system's speed when attacking target 1 provided by an embodiment of the present invention. DETAILED DESCRIPTION

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

[0090] Embodiment 1:

[0091] This embodiment provides a multi-target Kalman safe state estimation method under random deception attacks, which can solve the problems in the prior art that when the sensor measurement values in a multi-target system contain coupled state values of other targets, the effective state estimation of the system state cannot be achieved, and the state observer cannot perform safe state estimation when the sensor is subjected to random deception attacks.

[0092] In this embodiment, a scenario of tracking four targets is considered, and it is assumed that the sensor measurements are coupled (that is, only the difference in state can be measured). The system dynamic model of each target is assumed to be as follows:

[0093]

[0094] in:

[0095]

[0096]

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

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

[0099] Given an initial state , , , .

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

[0101]

[0102] in: Indicates the Sensors at the time The measured value of is the set of coupled measurement targets associated with the sensor (including targets itself), It is a sensor Towards the target Coupling target The mapping (measurement) matrix (here Can be equal to , It's the sensor Towards the target The measurement matrix of the sensor is consistent with the target number). Indicates the target Coupling target The status value (here Can be equal to , = Right now In itself, itself and itself is also a kind of coupling). It is subject to the mean of 0 and the variance of Gaussian distributed noise random variable;

[0103]

[0104]

[0105] in:

[0106]

[0107] Where H describes the mapping relationship between the sensor's observation value z and the true state x, v represents the noise introduced by the sensor during the measurement process; subscript i represents target i, subscript k represents time k; subscript represents the qth coupled to target i i targets; the subscript j belongs to the target of i entering the neighborhood, which can be understood as a coupled target;

[0108] Considering the diversity of noise in different states, the measurement noise The covariance matrix is =2i .

[0109] like Figure 1 As 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 relevant attack parameters;

[0111] The expression of the dynamic model is:

[0112]

[0113]

[0114] in:

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123] The expression of the measurement equation is:

[0124]

[0125]

[0126] Contains the target and goals Coupling target ( arrive ) at the moment The true value of each state ( arrive ),

[0127] Contains the target and goals Coupling target ( arrive ) at the moment The state transfer matrix of each state ( arrive ),

[0128] Contains the target and goals Coupling target ( arrive ) at the moment The noise driving matrix of each state is arrive ), which characterizes how process noise affects the update of the target state,

[0129] Included Target and goals Coupling target ( arrive ) at the moment The inherent noise of each state under arrive ),

[0130] It contains sensor to target and goals Coupling target ( arrive ) at the moment Next target The measurement matrix of all states,

[0131] is the target At the moment The sensor measurement noise below.

[0132] arrive Indicates sensor Towards the target and goals Coupling goals arrive At the moment The mapping matrix of the observation values of each state under Theoretically, you can only use Indicates, but it is best to use Indicates that, firstly, it is to keep consistent with the following subscript, and secondly, in practice, the measurement matrix of each sensor for the same target may be different. Can represent sensor Target Measurement matrix, the sensor number is generally consistent with the target number).

[0133] The superscript T indicates transpose.

[0134] Align the sensor A random spoofing attack will change the sensor measurement value Tampered with , and obtain its form as:

[0135]

[0136] in The probability of compliance is The Bernoulli distribution of is satisfied A bounded random variable, that is , , satisfy .

[0137] S2. Construct a directed graph of information interaction between coupled states of a multi-objective system and design a multi-objective Kalman safety state observer based on it;

[0138] The information exchange between observers is through a directed graph Description, where is a finite non-empty set of nodes in the graph, Indicates the first The observer node of the target, the edge set Used to describe the information flow between observer nodes. The incoming neighborhood set is expressed as: , where indegree ,node The out-neighborhood set is expressed as , out of degree , assuming that the filter can obtain information from its incoming neighborhood.

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

[0140]

[0141]

[0142] in, Indicates that ,filter For the first An estimate of the target.

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

[0144] Opposite side , No. The estimator does not need to estimate the augmented state Send to its outbound neighborhood And assume that for each target, there is only one state observer to estimate its state. Receive into neighborhood Observer in Towards the target State estimation , in the generation Backward out of the neighborhood Observer in Send Observer Towards the target State estimation , and so on, until the last state observer generate and pass the state estimate to the out-of-neighborhood state observer .

[0145] According to the established directed graph of information interaction between the coupled states of the multi-objective system, the multi-objective Kalman safety state observer is designed as follows:

[0146]

[0147] in, For the moment Next The gain in the Kalman safety state observer; For the moment Multi-objective state estimator under The gain of the interaction term with the adjacent nodes.

[0148] Establish as Figure 2The directed graph of information interaction between the four state observers shown is:

[0149] Assuming that there is only one state observer for each target, the observer number is the same as the target number (at least the number 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 observer receives the neighborhood observer Towards the target State estimation , in the generation Backward out-of-neighborhood state observer input observer Towards the target State estimation , until the last state observer generate , completing a cycle.

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

[0151] S3-1. Update time The augmented Kalman gain of the multi-objective state observer under .

[0152]

[0153] in, For the moment Observer under The augmented error covariance matrix of the state estimate is . is Gaussian noise with a mean of 0 The covariance matrix of .

[0154] S3-2, Update time Multi-objective state estimator under The gain of the interaction term with the adjacent nodes.

[0155]

[0156] in, 0, you need to select an appropriate value according to the needs of the system. Here is the following formula for selecting a reference value:

[0157]

[0158] in It is a relatively small constant, usually a value such as 0.01 can be selected.

[0159] set up , , .

[0160] S3-3. Update time Multi-objective state estimator under The observation matrix of the error covariance.

[0161]

[0162] in Indicates time Next target If you are calculating it for the first time, you should make sure that its initial value is non-negative.

[0163] in , .

[0164] S4, based on the multi-objective Kalman safety state observer with updated parameters, the state of the multi-objective system is estimated, and the update time The state estimation value of each target under multiple targets.

[0165] For the multi-objective safety state estimation system, all the parameters updated by S3 are substituted into the state observer designed in S2 to obtain the estimated value of the target state at the current moment. After each state observer is updated, it should be checked whether the multi-objective observer designed for each target has completed an update. If the update of the above state observer is not completed, the time should be updated 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 is updated once, and the state estimation value of each target at the current moment is output after the estimation value of the above state observer is updated once.

[0166] According to the analysis and parameter setting requirements mentioned above, when a random deception attack is carried out on target 1 within 60 time steps, the random interference of the noise can be reduced, and the number of Monte Carlo experiments is .

[0167] definition The calculation method of the cumulative root mean square error of the j-th Monte Carlo experiment position and the cumulative root mean square error of the j-th Monte Carlo experiment velocity at time is:

[0168]

[0169]

[0170] in 、 、 、 Sequential state observers The estimated position and velocity in the X direction, as well as the state observer's response to the target Position estimate and velocity estimate in the Y direction.

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

[0172]

[0173]

[0174] Combining the above parameters, we can obtain the change diagram of the average total position error and the average total speed error within 60 time steps (i.e. 60s) of this embodiment. Figure 3-Figure 4 It can be seen that when the multi-target system is subjected to random deception attacks by sensors, the average cumulative root mean square error of the position and velocity converges rapidly. The designed multi-target Kalman security state estimation method can realize the security state estimation of the multi-target system.

[0175] Example 2:

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

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

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

[0179] Example 3:

[0180] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps of the method described in Embodiment 1 are implemented.

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

[0182] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0183] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes 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 a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0184] These computer program instructions may 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, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0185] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0186] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A multi-target Kalman security state estimation method under random deception attack, characterized in that: include: Obtain the dynamic model of the multi-target system and relevant attack parameters; Construct a directed graph of information interaction between coupled states of a multi-objective system, and design a multi-objective Kalman safety state observer based on the directed graph; Input the relevant parameters of the attack into the designed multi-objective Kalman security state observer and update the relevant parameters of each observer; The state of the multi-objective system is estimated based on the multi-objective Kalman safety state observer with updated parameters. After the state estimation value of the multi-objective observer designed for each target is updated once, the state estimation value of each target is output to complete the safety state estimation under sensor attack. Construct a directed graph of information interaction between coupled states of a multi-objective system, including: The information exchange between observers is through a directed graph describe, in is a finite non-empty set of nodes in the graph, v i It represents the observer node of the i-th target in the multi-target system, and the edge set ε={(v i ,v j ):i,j∈N} is used to describe the information flow between observer nodes, The incoming neighborhood set of node i is expressed as The in-degree The out-neighborhood set of node i is expressed as out degree Set the filter to take information from its incoming neighborhood; In order to describe the information transfer between the coupled states of the multi-objective system, the following augmented matrix is defined: in, For filter i j For the i l an estimate of the target; A directed graph of information interaction between coupled states of a multi-objective system is established as follows: Opposite side (v j ,v i ), the j-th estimator does not need to estimate the augmented state Send to its outbound neighborhood filter; Assume that for each target, there is only one state observer to estimate its state; Observer i receives the neighborhood Observer i in l For target i l State estimation In the generation Backward out of the neighborhood Observer i in m Send observer i j For target i j State estimation Observer i m take over Generate state estimates Then send it to observer i m+1 , until the last state observer n generates and pass the state estimate to the out-of-neighborhood state observer 2. The multi-objective Kalman security state estimation method under random deception attack according to claim 1 is 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 i-th target in a multi-target system consisting of n targets, the dynamic model of the system at time k is expressed as: in, represents the true value of the state of target i in the linear system at time k+1, Represents the true value of each state of target i at time k; Represents the state transfer matrix of each state of target i at time k, represents the noise driving matrix of each state of target i at time k, represents the inherent noise of each state of target i at time k, z i,k Represents the measurement value matrix of the sensor for all states of target i at time k, Represents the mapping matrix of the sensor's observation value of the true state of target i at time k; v i,k is the sensor measurement noise of target i at time k; Bounded, The status is consistent and impressive; in: Among them, x i,k arrive Represents target i and target i1 coupled with target i to The true value of each state at time k, F i,k arrive Represents target i and target i1 coupled with target i to The state transfer matrix of each state at time k, G i,k arrive Represents target i and target i1 coupled with target i to The noise driving matrix of each state at time k is, w i,k arrive Represents target i and target i1 coupled with target i to The inherent noise of each state at time k; H ii,k arrive Represents sensor i to target i and target i1 coupled with target i to The mapping matrix of the observation values of each state at time k; The superscript T indicates transpose.

3. The multi-objective Kalman security state estimation method under random deception attack according to claim 2 is characterized in that: For the state x of a single target in a linear system i,k , its dynamic equation is expressed as: x i,k+1 =F i,k x i,k +G i,k w i,k Among them, x i,k ∈R n is the n-dimensional system state vector of target i at time k, R n Indicates the dimension of the R space to which z belongs, F i,k is the system matrix of target i at time k, w i，k It is represented by the Gaussian noise of target i at time k, with a mean of 0 and a variance of Q i,k , G i,k is the input matrix of a single target i, used to describe the process noise w i,k For state x i,k the impact of; The sensor measurement value of target i is coupled with the measurement values of other targets, and the expression is as follows: Where: z i,k ∈R p represents the measurement value of the i-th sensor at time k, is the set of coupled measurement targets associated with the sensor, H i,k is the known measurement matrix, v i,k It has a mean of 0 and a variance of R i,k Gaussian distributed noise random variable; A random deception attack on sensor i at time k will cause the sensor measurement value z to i,k Tampered with Its form is: where γ k The probability of compliance is Bernoulli distribution is the parameter of the Bernoulli distribution, ξ k is satisfied||ξ k A bounded random variable with ||≤δ, where Pr{} represents the probability.

4. The multi-target Kalman security state estimation method under random deception attack according to claim 3 is characterized in that: The method for designing a multi-objective Kalman safety state observer according to the directed graph includes: According to the established directed graph of information interaction between the coupled states of the multi-objective system, the multi-objective Kalman safety state observer is designed as follows: in, is the gain in the i-th Kalman safety state observer at time k; is the gain of the interaction term between the multi-objective state estimator i and the adjacent nodes at time k.

5. The multi-objective Kalman security state estimation method under random deception attack according to claim 4 is characterized in that: The method for updating the parameters related to each observer is: The gain in the i-th Kalman safety state observer at time k Calculate as follows: Among them, P i,k is the augmented error covariance matrix of the state estimate of observer i at time k; is Gaussian noise with mean 0 v i,k The covariance matrix of The gain of the interaction term between the multi-objective state estimator i and the adjacent nodes at time k The calculation method is: Among them, σ i >0,σ i is the gain coefficient, and a suitable value needs to be selected according to the needs of the system; Select the reference value according to the following formula: where ε i is a constant; The calculation method of the observation matrix of the error covariance of the multi-target state estimator i at time k is: in Represents the augmented covariance matrix of target i at time k; if it is the first calculation, its initial value is non-negative.

6. The multi-objective Kalman security state estimation method under random deception attack according to claim 5, characterized in that: The method of outputting the observation value of each target state of the multi-target system is: For the multi-objective safety state estimation system, all updated parameters are substituted into the designed state observer to obtain the estimated value of the target state at the current moment. After each state observer is updated, check whether the multi-objective observer designed for each target has completed an update. If the update of the above state observer is not completed, update the state estimate of the above state observer at time k in sequence according to the constructed directed graph of information interaction between state observer nodes; After the estimated values of the state observer are updated once, the state estimated values of each target at the current moment are output.

7. A multi-target Kalman security state estimation device under random deception attack, characterized in that: including processors and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to execute the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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