A distributed security fusion estimation method under random event attack

Abstract

The application relates to a distributed security fusion estimation method under random event attack and relates to the technical field of safe and reliable operation of a power system. The method comprises the following steps: step a, initializing relevant parameters of the system; step b, acquiring original measurement data of a bottom layer physical device and compressing the original measurement data; step c, calculating an event trigger value; step d, judging whether current time data needs to be transmitted; step e, executing an estimation process by a local estimator; step f, judging whether transmission and a matrix P i y (k) of the diagonal elements; step g, performing state compensation by a fusion center; step h, judging whether information transmission at the current time is finished; and the process is ended after the transmission is finished, otherwise, returning to step b. Through the distributed security fusion estimation method under random event attack, the problem that fusion estimation is inaccurate due to the damage of local estimation caused by random event attack on a communication network is solved, the fusion estimation error can be ensured to be within an allowable range, and the safety of the power system can be ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of safe and reliable operation of power systems, and in particular to a distributed security fusion estimation method under random event attacks. Background Art

[0002] Traditional power systems are gradually evolving into smart grids through the continuous integration of advanced information technology, control methods, and communication technologies, aiming to achieve global optimization of energy, economic, and environmental benefits. This convergence of diverse fields presents significant technical challenges in the wide-area monitoring, planning, and control of smart grid networks. To address these potential challenges, management and control authorities must monitor the operational characteristics of distributed power systems in real time, relying primarily on fundamental and critical state estimation processes. Specifically, this involves wireless network-based information transmission and the fusion of information measured by widely distributed phase measurement units. However, sensor measurements or data flowing through the network can be corrupted by attackers, potentially impacting data monitoring and acquisition systems and even misleading energy management systems. Therefore, secure distributed fusion estimation, which considers cyberattacks, is crucial for ensuring the safe, reliable, and cost-effective operation of power systems.

[0003] Currently, some work has studied the security fusion estimation method under network attacks:

[0004] Literature Zheng X, Zhang H, Wang Z, et al. Stochastic event-based distributed fusion estimation over sensor networks with fading channel [J]. IEEE Transactions on Circuits and Systems I: Regular Papers, 2022, 69(4): 1741-1750. A two-step distributed fusion estimation scheme is proposed in a fading channel environment (equivalent to a denial of service attack). The first step is to obtain a local estimate based on the measurements of the sensor itself and its neighbors, and the second step is to fuse the local estimates of each sensor. The data processing method in this scheme adopts a general matrix weighted fusion method. However, in actual power systems, this scheme may fail because some variables do not have physical meaning.

[0005] A Chinese invention patent, filed on March 29, 2024 and numbered "A Security Fusion Estimation Method for Cyber-Physical Systems Based on a Multi-Rate Sampling Mechanism," describes a technical solution that uses two Bernoulli variables to construct an information security framework encompassing three scenarios: denial of service attacks, false data injection attacks, and no attacks. This ensures the resilience of current security state estimation methods. However, this solution focuses on common denial of service and false data injection attacks. However, with the application of advanced communication technologies and data transmission solutions, power systems are vulnerable to new types of cyberattacks, and there is a lack of analysis of corresponding security strategies.

[0006] At the same time, existing technologies require a large amount of information to be transmitted at every moment to ensure accurate power system estimation, placing a high burden on wireless networks. While some data dimensionality reduction and data quantization methods have been proposed to minimize the amount of data transmitted at each moment, these methods are all lossy data processing solutions.

[0007] In summary, existing security fusion estimation schemes are mostly designed for common types of network attacks and are unable to cope with new types of network attacks caused by the vulnerabilities of event-driven data transmission schemes. Therefore, designing a distributed security fusion estimation method under random event attacks to ensure that the energy management center accurately understands the operating status of each subsystem, thereby facilitating the subsequent stable operation and real-time regulation of the power system, has become an urgent problem in this field. Summary of the Invention

[0008] The technical problem addressed by this invention is to overcome the shortcomings of existing technologies and provide a solution to the problem of inaccurate fused estimation caused by local estimation impairment when a communication network is attacked by a random event. This solution ensures that the fused estimation error remains within an acceptable range. The designed distributed secure fused estimation method under random event attacks can ensure the safety and adjustability of the power system.

[0009] The technical solution adopted by the present invention to solve the technical problem is: a distributed security fusion estimation method under random event attack, characterized by comprising the following steps:

[0010] Step a, system initialization related parameters;

[0011] Step b: All N sensors obtain the original measurement data z of the underlying physical device i (k), and compress the original sensor measurement data into y i (k);

[0012] Step c, calculating the event trigger value;

[0013] Step d, determining whether the current moment data needs to be transmitted, if the current moment data needs to be transmitted, transmitting it and executing step e, if the current moment data does not need to be transmitted, the sensor remains silent and executing step e;

[0014] Step e, the local estimator is based on the currently available information set Perform the estimation process;

[0015] Step f, determine whether to transmit the local estimate and the matrix P i y The diagonal elements of (k) are used to transmit local estimates if necessary. and the matrix P i y (k), then transmit and execute step g. If the local estimate does not need to be transmitted and the matrix P i y (k) diagonal elements, then directly execute step g;

[0016] Step g: The fusion center performs state compensation and performs diagonal matrix weighted fusion to obtain the fusion estimate and the fusion estimation error covariance P f (k);

[0017] Step h, determine whether the information transmission is completed at the current moment. If the transmission is completed, then end it. If the transmission is not completed, return to step b.

[0018] Preferably, in step b, all N sensors acquire the original measurement data z of the underlying physical device. i (k), the corresponding measurement equation is:

[0019] z i (k)=H i x(k)+υ i (k),i=1,2,…,N

[0020] in, Measurement Matrix x(k) represents the state variable at time k, υ i (k) represents the measurement noise at time k.

[0021] Preferably, in step b, the sensor sends the original measurement data Compress to Specifically:

[0022]

[0023] in, R irepresents the measurement noise covariance of the i-th sensor, H i Denotes the measurement matrix of the i-th sensor, there exists a full-rank decomposition transformation such that H i =M i O i , M i and O i are full row rank and full column rank matrices respectively, M i The transposed matrix of , and rank(H i )=r i ≤m i ;

[0024] After equivalent transformation, we get:

[0025]

[0026] in, get The covariance satisfies Represents r i dimensional identity matrix.

[0027] Preferably, in step c, the sensor calculates the event trigger function value according to the following rules:

[0028]

[0029] Among them, η i (k) represents the trigger function value when there is no attack, represents the trigger function value under attack, β i Represents the event trigger parameter, and the information fed back by the estimator satisfies in represents the local prior estimate of the state variable x(k), and Represents the attack signal, generated by the random event attacker, y i (k) represents the compressed original measurement data.

[0030] Preferably, in step d, the event-triggered scheduler based on the sensor calculates the data y at the current moment. i (k) The corresponding decision variable γ i (k) or The calculation rules are:

[0031]

[0032] Among them, the random variable ε i (k) is uniformly distributed in the interval [0,1] and is independent of other variables, η i (k) represents the trigger function value when there is no attack, Indicates the trigger function value under attack;

[0033] When γ i (k) = 1 or Indicates that the current data y needs to be transmitted i (k).

[0034] Preferably, in step e, the local estimator is based on the currently available information set Perform the estimation process, specifically:

[0035]

[0036] P i y- (k) = AP i y (k-1)A T +Q

[0037]

[0038] P i y (k)=[IL i (k)C i ]P i y- (k)

[0039] Where A represents the system matrix of the linearized power system, B represents the input matrix of the linearized power system, represents the local estimate of sensor i at time k, P i y (k) represents the estimated error covariance of sensor i at time k, P i y- (k) represents the local prior estimate The error covariance of Q represents the covariance matrix of the system process noise, I represents the identity matrix with the same dimension as the matrix A; u(k-1) represents the input variable at time k-1, P i y (k-1) represents the estimated error covariance of sensor i at time k-1, A T represents the transposed matrix of the system matrix A of the linearized power system, γ i (k) represents data y i (k) corresponding decision variables; intermediate variables where ρ(k)=[β i +1-γ i (k)] / β i ,in, is the measurement matrix C i The transposed matrix of βi Indicates event trigger parameters; available information collection And the local estimation process in the case of random attack will be variable γ i (k) is replaced by

[0040] Preferably, in step f, the index variable λ is updated according to a preset rule i (k), the specific preset rules are as follows:

[0041]

[0042] Among them, γ i (k) is the data y at time k i (k) corresponding decision variables, γ i (k-1) is the data y at the previous moment i (k-1) corresponding decision variables, λ i (0)=0;

[0043] When λ i When (k) = 0, the local estimate is transmitted and the matrix P i y (k) diagonal elements.

[0044] Preferably, in step g, the state compensation scheme adopted by the fusion center is:

[0045] Define vector Λ(k)=[λ1(k),...,λ N (k)] and the variable τ(k) = N - ‖Λ(k)‖0,

[0046] Among them, ‖·‖0 represents the zero norm of the vector;

[0047] Then, assume that the measurement accuracy of sensor 1 is better than that of any other N-1 sensors, and reset that λ1(k)=0 for any k>0, and obtain the information set to be fused as:

[0048]

[0049] The scheme of diagonal matrix weighted fusion is:

[0050]

[0051] Among them, D j =diag[d j1 ,d j2 ,...,d j(5n) ], Indicates the number of synchronous motors in the current power system, represents [1,1,...,1], Denotes the cross covariance matrix P ij The i-th diagonal element of (k);

[0052] Calculate the fusion estimation error covariance P f (k), specifically:

[0053]

[0054] get

[0055] Among them, D i 、D j is the diagonal weight matrix, P ij (k) is the cross covariance matrix.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] Through this distributed secure fusion estimation method under random event attacks, the problem of inaccurate fusion estimation caused by local estimation damage when the communication network is attacked by random events is solved. It can ensure that the fusion estimation error is within the allowable range and ensure the safety and adjustability of the power system.

[0058] This distributed security fusion estimation method under random event attacks proposes a distributed security fusion estimation scheme, which can effectively resist the intrusion of wireless networks under random event attacks, ensure the accuracy of fusion estimation, and significantly improve the robustness of wireless networks when encountering malicious intrusions.

[0059] The state compensation method proposed in this distributed security fusion estimation method under random event attacks can improve the accuracy of fusion estimation.

[0060] This distributed secure fusion estimation method for random event attacks utilizes full-rank decomposition transformation technology, combined with precise setting of estimator index variables, to significantly reduce data transmission within the network. By optimizing communication requirements between sensors and estimators, the wireless network load is reduced, improving overall network efficiency. Combined with full-rank decomposition transformation technology, the system maintains high estimation accuracy while saving significant communication resources, making it suitable for scenarios such as large-scale Internet of Things and smart grids.

[0061] This distributed, secure fusion estimation method for random event attacks achieves a good trade-off between estimation performance and network throughput. By assigning appropriate weights to different data sources, this scheme reduces the negative impact of low-quality data on the overall estimation results. It also optimizes bandwidth consumption during data fusion and improves the system's throughput when dealing with large-scale data streams. The diagonal matrix structure offers high computational efficiency, significantly reducing computational and communication complexity while ensuring estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 Flowchart of the distributed security fusion estimation method under random event attacks.

[0063] Figure 2 Schematic diagram of distributed security fusion estimation of power systems under random event attacks.

[0064] Figure 3 The graph is a comparison of the covariance of the power system fusion estimation errors under different scenarios. DETAILED DESCRIPTION

[0065] Figures 1 to 3 The best embodiment of the present invention is shown below in conjunction with the attached Figures 1 to 3 The present invention is further described.

[0066] like Figure 1 As shown, a distributed security fusion estimation method under random event attack includes the following steps:

[0067] Step 1001, start;

[0068] Start to implement the distributed security fusion estimation method under random event attack, and further combine Figure 2 The diagram below shows a distributed security fusion estimation diagram for a power system under random event attacks. It includes the underlying physical device layer, the middle information and network layer, and the upper fusion center. In the information and network layer, SETM represents the random event-triggered transmission mechanism used by sensors, and FRDT represents the full-rank decomposition transformation of the raw measurement data.

[0069] The physical device layer consists of five synchronous motors and some loads connected via eight buses. N sensors measure the relevant physical parameters and perform full-rank decomposition to compress the measured values. The compressed information is then sent to the local estimator via a wireless network using a random event trigger mechanism. However, the data transmission process may be corrupted by random event attacks (i.e., tampering with the feedback of the prior measurement information). ), causing the local estimation and fusion estimation to deviate seriously from the true value.

[0070] Step 1002, the system initializes relevant parameters;

[0071] Initialization related parameters include: local estimation corresponding to all i sensors and its error covariance P i y (0), fusion estimation and its error covariance P f (0), specifically:

[0072] By selecting the rotor angle Δδ of each synchronous motor i , rotor angular velocity Δω i , q-phase transient voltage ΔE' qi , and the internal state z of the terminal voltage controller 2i ,z 1i As the system state variable, the input of the excitation system is the control input signal Δv i , linearizing the system near its equilibrium point can establish a state-space model for a continuous system. Furthermore, the discrete state-space model can be obtained using the inverse Euler method:

[0073] x(k+1)=Ax(k)+Bu(k)+ω(k)

[0074] Where x(k) represents the state variable at time k, u(k) represents the input variable at time k, ω(k) represents the process noise signal of the system at time k (obeying a Gaussian distribution with zero mean and variance Q ≥ 0), A represents the system matrix of the linearized power system, B represents the input matrix of the linearized power system, and n represents the number of synchronous motors in the system. represents a 5n-dimensional Euclidean space.

[0075] Step 1003: The sensor obtains raw measurement data;

[0076] All N sensors obtain the raw measurement data z of the underlying physical device i (k), the corresponding measurement equation is:

[0077] z i (k)=H i x(k)+υ i (k),i=1,2,…,N

[0078] in, in Indicates m i -dimensional Euclidean space. Measurement matrix Measurement noise υ i (Subject to 0 mean, variance R i >0 Gaussian distribution). Assume (Hi , A) is observable, the initial state variable x(0), the system process noise signal ω(k) at time k and the measurement noise υ at time k i (k) are independent of each other.

[0079] Step 1004, compressing the raw measurement data acquired by the sensor;

[0080] To ease the communication burden, the sensor sends the raw measurement data Compress to Specifically:

[0081]

[0082] in, R i represents the measurement noise covariance of the i-th sensor, H i Denotes the measurement matrix of the i-th sensor, there exists a full-rank decomposition transformation such that H i =M i O i , M i and O i are full row rank and full column rank matrices respectively, M i The transposed matrix of , and rank(H i )=r i ≤m i .

[0083] For the convenience of representation, the following equivalent transformation is given:

[0084]

[0085] Among them, the measurement matrix And it is not difficult to get The covariance satisfies Represents r i dimensional identity matrix.

[0086] Step 1005, calculating the event trigger value;

[0087] The sensor calculates the event trigger function value according to the following rules:

[0088]

[0089] Among them, η i (k) represents the trigger function value when there is no attack, represents the trigger function value under attack, β i Represents the event trigger parameter, and the information fed back by the estimator satisfies in represents the local prior estimate of the state variable x(k), and Represents the attack signal, generated by the random event attacker, y i (k) represents the compressed original measurement data.

[0090] Step 1006, determining whether the current time data needs to be transmitted;

[0091] The event-triggered scheduler based on the sensor calculates the current data y i (k) The corresponding decision variable γ i (k)(or ), the calculation rules are:

[0092]

[0093] Among them, the random variable ε i (k) is uniformly distributed in the interval [0,1] and is independent of other variables, η i (k) represents the trigger function value when there is no attack, Indicates the trigger function value under attack.

[0094] When γ i (k) = 1 or Indicates that the current data y needs to be transmitted i (k), and execute step 1007. Otherwise, execute step 1008.

[0095] Step 1007: Keep silent, i.e., no information is transmitted;

[0096] The sensor remains silent, ie, does not transmit information, and step 1008 is executed.

[0097] Step 1008, the estimator performs an estimation process;

[0098] The local estimator is based on the currently available information set Perform the estimation process, specifically:

[0099]

[0100] P i y- (k) = AP i y (k-1)A T +Q

[0101]

[0102] P i y (k)=[IL i (k)C i]P i y- (k)

[0103] Where A represents the system matrix of the linearized power system, B represents the input matrix of the linearized power system, represents the local estimate of sensor i at time k, P i y (k) represents the estimated error covariance of sensor i at time k, P i y- (k) represents the local prior estimate The error covariance of Q represents the covariance matrix of the system process noise, I represents the identity matrix with the same dimension as the matrix A; u(k-1) represents the input variable at time k-1, P i y (k-1) represents the estimated error covariance of sensor i at time k-1, A T represents the transposed matrix of the system matrix A of the linearized power system, γ i (k) represents data y i (k) corresponding decision variables; intermediate variables where ρ(k)=[β i +1-γ i (k)] / β i ,in, is the measurement matrix C i The transposed matrix of β i Indicates event trigger parameters; available information collection And the local estimation process under random attack only needs to change the variable γ i (k) is replaced by That's it.

[0104] Step 1009: Determine whether transmission is required and P i y diagonal elements of (k);

[0105] Update the index variable λ according to the preset rules i (k), the specific preset rules are as follows:

[0106]

[0107] Among them, γ i (k) is the data y at the current moment (time k) i (k) corresponding decision variables, γ i (k-1) is the data y at the previous moment i (k-1) corresponding decision variables, λ i (0)=0.

[0108] When λ i When (k) = 0, the local estimate is transmitted and the matrix P i y (k) and execute step 1011, otherwise execute step 1010.

[0109] Step 1010: Keep silent, i.e., no information is transmitted;

[0110] The local estimator remains silent, ie, does not transmit information, and executes step 1011.

[0111] Step 1011: The fusion center performs state compensation and performs diagonal matrix weighted fusion to obtain and P f (k);

[0112] The fusion center uses the state compensation and diagonal matrix weighted fusion scheme to fuse the information set and obtain the fusion estimate And calculate the fusion estimation error covariance P f (k) Specifically:

[0113] The state compensation scheme adopted by the Fusion Center is as follows:

[0114] Define vector Λ(k)=[λ1(k),...,λ N (k)] and the variable τ(k) = N - ‖Λ(k)‖0,

[0115] Here, ‖·‖0 represents the zero norm of the vector.

[0116] Then, it is assumed that the measurement accuracy of sensor 1 is better than that of any other N-1 sensors, and it is reset that λ1(k)=0 holds for any k>0.

[0117] Then the information set to be fused is:

[0118]

[0119] The scheme of diagonal matrix weighted fusion is:

[0120]

[0121] Among them, the diagonal weight matrix D j =diag[d j1 ,d j2 ,...,d j(5n) ],

[0122] n represents the number of synchronous motors in the current power system, represents [1,1,...,1], Denotes the cross covariance matrix P ij (k) is the i-th diagonal element, and

[0123]

[0124] Where A represents the system matrix of the linearized power system, A T represents the transposed matrix of the system matrix A of the linearized power system, Q represents the covariance matrix of the system process noise, γ i (k) represents data y i (k) corresponding decision variables, γ j (k) represents data y j (k) corresponds to the decision variable, Denotes the compressed measurement matrix C j Transpose the matrix, Represents the intermediate variable L j The transposed matrix of (k), P ij (k-1) represents the cross-covariance matrix at time k-1.

[0125] Calculate the fusion estimation error covariance P f (k), specifically:

[0126]

[0127] get

[0128] Among them, D i 、D j is the diagonal weight matrix, P ij (k) is the cross covariance matrix.

[0129] Step 1012, determine whether the transmission is completed;

[0130] Determine whether the information transmission at the current moment is completed. If it is completed, execute step 1013; if it is not completed, return to step 1002.

[0131] Step 1013, end.

[0132] The following example verifies the effectiveness of the distributed security fusion estimation method under random event attacks:

[0133] Refer to Figure 2 The power system model with 5 synchronous machines and 8 buses is shown in the figure. The sampling time Δt=10 -3 , the covariance of process noise Q = 10 -3 I 25Assume that the output of the discretized state space model is measured by four sensors with different precisions, where The corresponding measurement noises are: 10 -5 I7, 4*10 -4 I7, 6*10 -2 I5, 2*10 -2 I6.

[0134] After full rank decomposition transformation, we get Where i = 1, 2, 3, 4. In addition, the event trigger parameter is set to β1 = 10 -7 ,β2=10 -3 ,β3=10 -1 ,β4=10 -1 .

[0135] After launching a random event attack on some of the feedback confirmation information of the corresponding estimators of the four sensors, the changes in the fusion estimation are analyzed. Figure 3 The solid line, long dashed line, short dashed line, and long and short dashed lines respectively show the change trajectories of the fusion estimation error covariance matrix after 100 Monte Carlo experiments under four different conditions: the method proposed in this invention, with attack and without state compensation, with attack, and without attack. Figure 3 The unit of sampling time of the horizontal axis is seconds, and the interval between two adjacent samplings is 0.02 seconds. Figure 3 It can be observed that the method proposed in the present invention has the smallest performance index, which verifies the effectiveness of the distributed security fusion estimation method proposed in the present invention.

[0136] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other manner. Any person skilled in the art may utilize the above-disclosed technical content to modify or modify the present invention into equivalent embodiments. However, any simple modifications, equivalent variations, and modifications to the above embodiments that do not depart from the technical content of the present invention and are based on the technical essence of the present invention remain within the scope of protection of the present invention.

Claims

1. A distributed security fusion estimation method under random event attacks, characterized by: The steps include: Step a, system initialization related parameters; Step b: All N sensors obtain the original measurement data z of the underlying physical device i (k), and compress the original sensor measurement data into y i (k); Step c, calculating the event trigger value; Step d, determining whether the current moment data needs to be transmitted, if the current moment data needs to be transmitted, transmitting it and executing step e, if the current moment data does not need to be transmitted, the sensor remains silent and executing step e; Step e, the local estimator is based on the currently available information set Perform the estimation process; Step f, determine whether to transmit the local estimate and the matrix P i y The diagonal elements of (k) are used to transmit local estimates if necessary. and the matrix P i y (k), then transmit and execute step g. If the local estimate does not need to be transmitted and the matrix P i y (k) diagonal elements, then directly execute step g; Step g: The fusion center performs state compensation and performs diagonal matrix weighted fusion to obtain the fusion estimate and the fusion estimation error covariance P f (k); Step h, determining whether the information transmission is completed at the current moment, if the transmission is completed, then end, if not, return to step b; In step d, the event-triggered scheduler based on the sensor calculates the current data y i (k) The corresponding decision variable γ i (k) or The calculation rules are: Among them, the random variable ε i (k) is uniformly distributed in the interval [0,1] and is independent of other variables, η i (k) represents the trigger function value when there is no attack, Indicates the trigger function value under attack; When γ i (k) = 1 or Indicates that the current data y needs to be transmitted i (k); In step e, the local estimator is based on the currently available information set Perform the estimation process, specifically: Where A represents the system matrix of the linearized power system, B represents the input matrix of the linearized power system, represents the local estimate of sensor i at time k, P i y (k) represents the estimated error covariance of sensor i at time k, P i y- (k) represents the local prior estimate The error covariance of Q represents the covariance matrix of the system process noise, I represents the identity matrix with the same dimension as the matrix A; u(k-1) represents the input variable at time k-1, P i y (k-1) represents the estimated error covariance of sensor i at time k-1, A T represents the transposed matrix of the system matrix A of the linearized power system, γ i (k) represents data y i (k) corresponding decision variables; intermediate variables where ρ(k)=[β i +1-γ i (k)] / β i ,in, is the measurement matrix C i The transposed matrix of β i Indicates event trigger parameters; available information collection And the local estimation process in the case of random attack will be variable γ i (k) is replaced by In step f, the index variable λ is updated according to the preset rules i (k), the specific preset rules are as follows: Among them, γ i (k) is the data y at time k i (k) corresponding decision variables, γ i (k-1) is the data y at the previous moment i (k-1) corresponding decision variables, λ i (0)=0; When λ i When (k) = 0, the local estimate is transmitted and the matrix P i y diagonal elements of (k); In step g, the state compensation scheme adopted by the fusion center is: Define vector Λ(k)=[λ1(k),...,λ N (k)] and the variable τ(k) = N - ‖Λ(k)‖0, Among them, ‖·‖0 represents the zero norm of the vector; Then, assume that the measurement accuracy of sensor 1 is better than that of any other N-1 sensors, and reset that λ1(k)=0 for any k>0, and obtain the information set to be fused as: The scheme of diagonal matrix weighted fusion is: Among them, D j =diag[d j1 ,d j2 ,...,d j(5n) ], n represents the number of synchronous motors in the current power system, represents [1,1,...,1], Denotes the cross covariance matrix P ij The i-th diagonal element of (k); Calculate the fusion estimation error covariance P f (k), specifically: get Among them, D i 、D j is the diagonal weight matrix, P ij (k) is the cross covariance matrix: Among them, γ j (k) represents data y j (k) corresponds to the decision variable, Represents the intermediate variable L j The transposed matrix of (k), P ij (k-1) represents the cross-covariance matrix at time k-1.

2. The distributed security fusion estimation method under random event attacks according to claim 1 is characterized by: In step b, all N sensors acquire the raw measurement data z of the underlying physical device i (k), the corresponding measurement equation is: z i (k)=H i x(k)+υ i (k),i=1,2,…,N in, Measurement Matrix x(k) represents the state variable at time k, υ i (k) represents the measurement noise at time k.

3. The distributed security fusion estimation method under random event attacks according to claim 2 is characterized by: In step b, the sensor sends the raw measurement data Compressed to Specifically: in, R i represents the measurement noise covariance of the i-th sensor, H i Denotes the measurement matrix of the i-th sensor, there exists a full-rank decomposition transformation such that H i =M i O i , M i and O i are full row rank and full column rank matrices respectively, M i The transposed matrix of , and rank(H i )=r i ≤m i ; After equivalent transformation, we get: in, get The covariance satisfies Represents r i -dimensional identity matrix.

4. The distributed security fusion estimation method under random event attacks according to claim 3 is characterized by: In step c, the sensor calculates the event trigger function value according to the following rules: Among them, η i (k) represents the trigger function value when there is no attack, represents the trigger function value under attack, β i Represents the event trigger parameter, and the information fed back by the estimator satisfies in represents the local prior estimate of the state variable x(k), and Represents the attack signal, generated by the random event attacker, y i (k) represents the compressed original measurement data.

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