Anti-fraud distributed state estimation method

Abstract

The invention discloses an anti-fraud distributed state estimation method, which comprises the following steps: establishing a distributed wireless sensor network topological structure and an observation model, and obtaining a state measurement value of a target to be measured; each node preliminarily estimates the state measurement value of the to-be-measured target by using the local measurement value to obtain the state estimation value of the node, and updates the state estimation values of each node and neighbor nodes thereof by using a multi-node distributed estimation algorithm to obtain the state estimation value of each node at the next moment; fraud detection is carried out on all nodes by using a multivariate statistical confidence domain algorithm, and malicious nodes containing fraud information are discarded; and carrying out iteration on the obtained state estimation value by using a Kalman filtering algorithm to obtain positioning of the to-be-measured target. According to the method, transmission and updating of malicious data in the distributed network are avoided, the robustness of the whole information estimation network is improved, the implementation is simple, and the efficiency is high.

Description

Technical Field

[0001] The present invention relates to the technical field of network communications, and in particular to an anti-fraud distributed state estimation method. Background Art

[0002] The traditional centralized processing mode requires all sensors to transmit their collected data directly to the central node, which is then responsible for performing data analysis and processing. This requires the central node to have a high level of computing and storage resources. However, with the development of distributed sensor networks, sensor nodes are limited by communication bandwidth and energy supply, and it becomes impractical to transmit all data to the central node for centralized processing. Therefore, distributed processing methods have become an effective way to solve this problem. In the distributed state estimation framework, the entire network can comprehensively utilize the observation information of all nodes to obtain a more accurate and reliable system state estimate. In addition, the distributed state estimation method performs data processing locally, effectively reducing the amount of data required for each node, thereby reducing the computational burden of each node.

[0003] However, in practical applications, distributed sensor networks often face various interferences from open environments, including but not limited to data fraud. False data injection is one of the common fraud methods, that is, malicious nodes intentionally inject false information into the measured values ​​during the data collection phase. Due to the frequent data exchange between nodes, this malicious behavior may spread rapidly. Once the erroneous data are passed to other nodes, they may be used as input for subsequent calculations and estimations, thereby destroying the data consistency in the distributed network. Since distributed state estimation relies on the data fusion of all nodes in the network, the propagation of erroneous information may cause the state estimation results of the entire network to deviate from the actual situation, or even converge to completely wrong estimates. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide an anti-fraud distributed state estimation method to solve the problem of malicious fraud or interference signals affecting the information network during the communication process and ensure the validity of the estimation results.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0006] A distributed state estimation method for resisting fraud comprises the following steps:

[0007] S1. Establish a distributed wireless sensor network topology and observation model. Each sensor is a node. Each node measures the position state of the target to be measured to obtain the state measurement value of the target to be measured.

[0008] S2. Each node in step S1 uses local measurement values ​​to make a preliminary estimate of the state measurement value of the target to be measured, and obtains the state estimation value of the node itself. The state estimation value of each node and its neighboring nodes is updated using a multi-node distributed estimation algorithm to obtain the state estimation value of each node at the next moment.

[0009] S3. Based on the state estimation value of each node at the next moment in step S2, all nodes are subjected to fraud detection using the trust region algorithm of multivariate statistics, malicious nodes containing fraud information are obtained, and the nodes are discarded.

[0010] S4. Repeat steps S2-S3 until the number of iterations is reached and a consistent state estimate is finally obtained.

[0011] S5. Use the Kalman filter algorithm to iterate the state estimation value finally obtained in step S4 to obtain the positioning of the target to be measured.

[0012] Furthermore, in step S1, obtaining the state measurement value of the target to be measured includes the following contents:

[0013] The topological structure of a distributed wireless sensor network includes a self-organizing topological graph G and n nodes, where G = (N, E), N represents a node set, N = {1, 2, ..., n}, and E represents an edge set, which is used to represent the connection relationship between nodes. G is undirected.

[0014] The expression of the observation model is:

[0015] z i (k) = H i (k)x(k)+v(k)

[0016] Among them, z i (k) represents the observation result of the i-th node at the k-th time, that is, the state measurement value of the target to be measured; H i A(k) represents the observation matrix, which is used to describe how the i-th node extracts the observation value from the environmental state; v(k) represents the observation error or noise, which represents the difference between the observation result and the real environmental state; x(k) represents the state of the real environment of the target to be measured at the kth moment, x(k) = A k x(k-1)+B k w(k), x(k-1) represents the state of the real environment of the target to be measured at the k-1th moment, A k represents the state transfer matrix, B k represents the input matrix, and w(k) represents the environmental error or noise.

[0017] Furthermore, in step S2, obtaining the state estimation value of the node at the next moment includes the following contents:

[0018] According to the communication topology between nodes, a node outputs its own state estimation value to neighboring nodes and receives the state estimation value of neighboring nodes.

[0019] The specific expression of its own state estimation is:

[0020] y i (k) = H i T (k)R i -1 (k)z i (k)

[0021] Among them, y i (k) represents the estimated state value of the i-th node at the k-th time; R i (k) represents the covariance matrix of observation noise; R i -1 (k) represents R i The inverse matrix of (k); H i T (k) indicates H i The transpose of (k).

[0022] The state estimation value of each node is processed using a multi-node distributed estimation algorithm to obtain the state estimation value at the next moment. The specific expression is:

[0023]

[0024] y i (k+1)=y i (k)+β×Δ

[0025] Among them, Δ represents the change in state estimation; j represents the neighboring node of the i-th node, and the neighboring node does not include the node i itself; u j (k) represents the state input of the jth node at the kth time; β represents the gain, which reflects the influence of the neighboring nodes; N represents the node set, y j (k) represents the estimated state value of the jth node at the kth time, y i (k+1) represents the estimated state value of the i-th node at the k+1th time.

[0026] Furthermore, in step S3, the fraud information obtained includes the following contents:

[0027] The state estimation value obtained in step S2 is processed using the trust region algorithm of multivariate statistics. The specific expression is:

[0028]

[0029] Where p represents the dimension of the vector, represents the average value of all node state estimates, F α Represents the critical test value in the F distribution table under the significance level α, numerator degrees of freedom p, and denominator degrees of freedom (np).

[0030] The nodes that satisfy the above processing formula are normal nodes, and their state estimation is used for the next information exchange. The nodes that do not satisfy the above processing formula indicate that the nodes have abnormal state estimation values, that is, malicious nodes. The malicious nodes are discarded before information exchange.

[0031] Furthermore, in step S5, obtaining the location of the target to be measured includes the following:

[0032] The covariance fusion method is used to process the covariance matrix of each node to obtain the fused inverse covariance matrix. The specific expression is:

[0033]

[0034] Among them, S(k) represents the fused inverse covariance matrix.

[0035] Based on the initial position state x0 and initial covariance matrix P0 of the target to be measured at the kth moment, the Kalman filter algorithm is used to process the fused inverse covariance matrix, calculate the weight matrix, and obtain the state of the target to be measured at the kth moment. The specific expression is:

[0036] M(k)=[(nP(k)) -1 +S(k)] -1

[0037]

[0038] Among them, M(k) represents the weight matrix, P(k) represents the error covariance matrix, represents the optimal state of the target to be measured at the kth moment, Represents the prior state of the target to be measured at the kth moment.

[0039] Update the error covariance matrix and the state of the target to be measured to obtain the error covariance matrix at the k+1th moment. Multiply the state value of the target to be measured by the transfer matrix A to obtain the state of the target to be measured at the next moment. The specific expression is:

[0040] P(k+1)=[AM(k)A T +nBQB T ] / n

[0041]

[0042] Among them, P(k+1) represents the error covariance matrix at the k+1th moment, represents the target state to be measured at the k+1th moment, B represents the control input matrix, Q represents the covariance matrix of v(k), A T represents the transpose of A, B T represents the transpose of B.

[0043] The updated P(k+1) and Substitute it into the formula to obtain the state of the target to be measured at the kth moment, predict the state of the target to be measured, update the error covariance matrix and the state of the target to be measured, until the number of iterations is reached, and finally output the position state of the target to be measured.

[0044] Furthermore, the present invention also proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the anti-fraud distributed state estimation method described above when executing the computer program.

[0045] Furthermore, the present invention also proposes a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is run by a processor, the anti-fraud distributed state estimation method is executed.

[0046] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0047] The method of the present invention is simple, has low time complexity and high efficiency, and only needs to perform fraud detection during the information transmission between nodes and remove the detected fraud information. The present invention can ensure that normal nodes are not interfered by malicious fraud, avoid the transmission and update of malicious data in the distributed network, thereby ensuring the performance of the original algorithm and improving the robustness of the entire information estimation network. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is an overall implementation flow chart of the present invention.

[0049] Figure 2 It is a schematic diagram of the nodes and communication links of the present invention being defrauded.

[0050] Figure 3 Schematic diagram of the distributed sensor network of the present invention.

[0051] Figure 4 This is the simulation result of the distributed state estimation without anti-fraud in the embodiment of the present invention.

[0052] Figure 5 It is the simulation result of the anti-fraud distributed state estimation in the embodiment of the present invention. DETAILED DESCRIPTION

[0053] 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 solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0054] To achieve the above object, the present invention proposes a distributed state estimation method to resist fraud, such as Figure 1 As shown, the specific steps are as follows:

[0055] S1. Distributed sensor networks often face various interferences from open environments, including but not limited to data fraud. This article is applicable to solving the problem of malicious fraud or interference signals affecting information networks during communication. It mainly deals with three situations: link interference (fraud), node interference (fraud) when transmitting, or node interference (fraud) when receiving signals, such as Figure 2 As shown, the link between node 4 and nodes 1 and 4 in the figure is subject to (interference) fraud.

[0056] like Figure 3 As shown in the figure, a distributed wireless sensor network topology and observation model are established. Each sensor is a node. Each node measures the position state of the target to be measured (human, vehicle, aircraft, etc.) to obtain the state measurement value of the target to be measured. The specific contents are as follows:

[0057] The topological structure of a distributed wireless sensor network includes a self-organizing topological graph G and n nodes, where G = (N, E), N represents a node set, N = {1, 2, ..., n}, and E represents an edge set, which is used to represent the connection relationship between nodes. G is undirected.

[0058] In this embodiment, the distributed wireless sensor network topology includes 5 sensor nodes, that is, n=5, numbered 1 to 5, among which there is a malicious node, namely Figure 3 Node 5 in . In this particular network topology, each node only exchanges data with its neighbor nodes, and the definition of neighbor nodes excludes the node itself. The neighbor nodes of node 1 are nodes 2, 3, 4, and 5. The observation dimension of the target to be measured is 4, which specifically covers the two positions of the target in the spatial coordinate system (x-axis position and y-axis position) and its corresponding velocity components (x-axis velocity and y-axis velocity).

[0059] The expression of the observation model is:

[0060] z i (k) = H i (k)x(k)+v(k)

[0061] Among them, z i(k) represents the observation result of the i-th node at the k-th time, that is, the state measurement value of the target to be measured; H i A(k) represents the observation matrix, which is used to describe how the i-th node extracts the observation value from the environmental state; v(k) represents the observation error or noise, which represents the difference between the observation result and the real environmental state; x(k) represents the state of the real environment of the target to be measured at the kth moment, x(k) = A k x(k-1)+B k w(k), x(k-1) represents the state of the real environment of the target to be measured at the k-1th moment, A k represents the state transfer matrix, B k represents the input matrix, and w(k) represents the environmental error or noise.

[0062] Assume that w(k) and v(k) are both zero-mean Gaussian white noise.

[0063] In this embodiment, H i (k)=[1,0,0,0;0,0,1,0], T=0.1;A k =[1,T,0,0;0,1,0,0;0,0,1,T;0,0,0,1];B k _1=[0,0,0,T 2 / 2;0,0,0,0;0,0,0,T 2 / 2;0,0,0,0]; x(k)=[100;3;100;3].

[0064] S2, each node in step S1 uses the local measurement value to make a preliminary estimate of the state measurement value of the target to be measured, obtains the state estimation value of the node itself, and uses the multi-node distributed estimation algorithm to update the state estimation value of each node and its neighboring nodes to obtain the state estimation value of each node at the next moment; the specific content is:

[0065] According to the communication topology between nodes, a node outputs its own state estimation value to neighboring nodes and receives the state estimation value of neighboring nodes.

[0066] The specific expression of its own state estimation is:

[0067] y i (k) = H i T (k)R i -1 (k)z i (k)

[0068] Among them, y i (k) represents the estimated state value of the i-th node at the k-th time; R i(k) represents the covariance matrix of observation noise; R i -1 (k) represents R i The inverse matrix of (k); H i T (k) indicates H i The transpose of (k).

[0069] The state estimation value of each node is processed using a multi-node distributed estimation algorithm to obtain the state estimation value at the next moment. The specific expression is:

[0070]

[0071] y i (k+1)=y i (k)+β×Δ

[0072] Among them, Δ represents the change in state estimation; j represents the neighboring node of the i-th node, and the neighboring node does not include the node i itself; u j (k) represents the state input of the jth node at the kth time; β represents the gain, which reflects the influence of the neighboring nodes; y j (k) represents the estimated state value of the jth node at the kth time, y i (k+1) represents the estimated state value of the i-th node at the k+1th time.

[0073] In this embodiment, R i (k) = [3 2 ,0;0,3 2 ], β=0.1.

[0074] S3, based on the state estimation value of each node at the next moment in step S2, use the trust region algorithm of multivariate statistics to perform fraud detection on all nodes, and obtain fraud information beyond the normal range; discard the malicious nodes containing fraud information; the specific content is:

[0075] The state estimation value obtained in step S2 is processed using the trust region algorithm of multivariate statistics. The specific expression is:

[0076]

[0077] Where p represents the dimension of the vector, represents the average value of all node state estimates, F α Represents the critical test value in the F distribution table under the significance level α, numerator degrees of freedom p, and denominator degrees of freedom (np).

[0078] Nodes that satisfy the above processing formula are normal nodes, and their state estimates are used for the next information exchange. Nodes that do not satisfy the above formula indicate that there are abnormal state estimates, that is, malicious nodes. Malicious nodes are discarded before information exchange.

[0079] In this embodiment, p=2, F α =5.46,α=0.1.

[0080] S4, repeating steps S2-S3 until the number of iterations reaches a maximum of 100 times or all nodes in the network reach a steady state, that is, the difference between the state estimation values ​​of each node is less than 0.1, and finally a consistent state estimation value is obtained;

[0081] S5, using the Kalman filter algorithm to iterate the state estimation value finally obtained in step S4 to obtain the location of the target to be measured; the specific content is:

[0082] The covariance fusion method is used to process the covariance matrix of each node to obtain the fused inverse covariance matrix. The specific expression is:

[0083]

[0084] Among them, S(k) represents the fused inverse covariance matrix.

[0085] Based on the initial position state x0 and initial covariance matrix P0 of the target to be measured at the kth moment, the Kalman filter algorithm is used to process the fused inverse covariance matrix, calculate the weight matrix, and obtain the state of the target to be measured at the kth moment. The specific expression is:

[0086] M(k)=[(nP(k)) -1 +S(k)] -1

[0087]

[0088] Among them, M(k) represents the weight matrix, P(k) represents the error covariance matrix, represents the optimal state of the target to be measured at the kth moment, Represents the prior state of the target to be measured at the kth moment.

[0089] Update the error covariance matrix and the state of the target to be measured to obtain the error covariance matrix at the k+1th moment. Multiply the state value of the target to be measured by the transfer matrix A to obtain the state of the target to be measured at the next moment. The specific expression is:

[0090] P(k+1)=[AM(k)A T +nBQB T ] / n

[0091]

[0092] Among them, P(k+1) represents the error covariance matrix at the k+1th moment, represents the target state to be measured at the k+1th moment, B represents the control input matrix, Q represents the covariance matrix of v(k), A T represents the transpose of A, B T represents the transpose of B.

[0093] The updated P(k+1) and Substitute it into the formula to obtain the state of the target to be measured at the kth moment, predict the state of the target to be measured, update the error covariance matrix and the state of the target to be measured, until the number of iterations (100 moments) is reached, and finally output the position state of the target to be measured.

[0094] In this embodiment, x0 = [100; 3; 100; 3], P0 = [1,0,0,0; 0,1,0,0; 0,0,1,0; 0,0,0,1], A = [1,T,0,0; 0,1,0,0; 0,0,1,T; 0,0,0,1], B = [1,T,0,0; 0,1,0,0; 0,0,1,T; 0,0,0,1].

[0095] like Figure 4 (a) and Figure 4 As shown in (b), before anti-fraud processing, the filtered values ​​and true values ​​of the target on the x-axis and y-axis positions show good consistency overall, but there is still a certain degree of deviation. This shows that the method without anti-fraud processing needs to be further optimized to improve the accuracy of position information.

[0096] like Figure 5 (a) and Figure 5 As shown in (b), after anti-fraud processing, the filtered values ​​of the target on the x-axis and y-axis positions are highly consistent with the true values, and the two are basically coincident. This shows that the method proposed in the present invention can more accurately approximate the true target state.

[0097] Under the assumption that the proportion of fraudulent sample signals is small, the execution time of the anti-fraud distributed state estimation algorithm is 6.457170 seconds, while the execution time of the distributed state estimation algorithm without anti-fraud is 6.096238 seconds, which shows that the method proposed in the present invention is simple to implement and has low time complexity. Assuming that the error before anti-fraud is d1 and the error after anti-fraud is d2, using the formula Calculations show that the method proposed in the present invention improves performance by 19.67%, indicating that the method can more accurately approximate the true target state and can exhibit higher robustness when processing malicious data and abnormal situations.

[0098] In the current distributed system research, the mechanism for anti-interference (especially fraud) is still insufficient, and the existing solutions often involve complex algorithm design and implementation. The method proposed in the present invention addresses this challenge and effectively improves the resistance of distributed systems to interference and fraud through innovative strategies and algorithm design. This method not only shows superiority in theory, but also shows the characteristics of simplicity and ease in practical applications. Through a streamlined implementation process and low resource consumption, this method can be easily integrated into existing distributed systems, which is conducive to improving the security and stability of the system.

[0099] The embodiment of the present invention further provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. It should be noted that when the processor executes the computer program, the specific steps of the method provided in the embodiment of the present invention are corresponding to the specific steps of the method provided in the embodiment of the present invention, and the processor has the functional modules and beneficial effects corresponding to the execution method. For technical details not described in detail in this embodiment, please refer to the method provided in the embodiment of the present invention.

[0100] The embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program. It should be noted that when the computer program is executed by the processor, it corresponds to the specific steps of the method provided in the embodiment of the present invention, and has the functional modules and beneficial effects corresponding to the execution method. For technical details not described in detail in this embodiment, please refer to the method provided in the embodiment of the present invention.

[0101] 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 distributed state estimation method for anti-fraud, characterized in that: include: S1. Establish a distributed wireless sensor network topology and observation model, where one sensor is one node, and each node measures the position state of the target to be measured to obtain the state measurement value of the target to be measured; S2, each node in step S1 uses the local measurement value to make a preliminary estimate of the state measurement value of the target to be measured, obtains the state estimation value of the node itself, and uses the multi-node distributed estimation algorithm to update the state estimation value of each node to obtain the state estimation value of each node at the next moment; S3, based on the state estimation value of each node at the next moment in step S2, use the trust region algorithm of multivariate statistics to perform fraud detection on all nodes, obtain malicious nodes containing fraud information, and discard the nodes; S4, repeating steps S2-S3 until the set number of iterations is reached, and finally a consistent state estimation value is obtained; S5. Use the Kalman filter algorithm to iterate the state estimation value finally obtained in step S4 to obtain the positioning of the target to be measured.

2. The anti-fraud distributed state estimation method according to claim 1, characterized in that: In step S1, obtaining the state measurement value of the target to be measured includes the following contents: The distributed wireless sensor network topology structure includes a self-organizing topology graph G and n nodes, where G = (N, E), N represents a node set, N = {1, 2, ..., n}, and E represents an edge set. The expression of the observation model is: z i (k)=H i (k)x(k)+v(k) Among them, z i (k) represents the observation result of the i-th node at the k-th time, that is, the state measurement value of the target to be measured; H i A(k) represents the observation matrix; v(k) represents the observation error; x(k) represents the state of the real environment of the target to be measured at the kth moment, x(k) = A k x(k-1)+B k w(k), x(k-1) represents the state of the real environment of the target to be measured at the k-1th moment, A k represents the state transfer matrix, B k represents the input matrix, and w(k) represents the environmental error.

3. The anti-fraud distributed state estimation method according to claim 1, characterized in that: In step S2, the state estimation value of the node at the next moment is obtained, including the following contents: According to the communication topology between nodes, a node transmits its own state estimation value to neighbor nodes and receives the state estimation value of neighbor nodes; The specific expression of its own state estimation is: Among them, y i (k) represents the estimated state value of the i-th node at the k-th time; R i (k) represents the covariance matrix of observation noise; Represents R i The inverse matrix of (k); H i (k) represents the observation matrix; Indicates H i (k) is the transpose; The state estimation value of each node is processed using a multi-node distributed estimation algorithm to obtain the state estimation value at the next moment. The specific expression is: and i (k+1)=y i (k)+β×Δ Among them, Δ represents the change in state estimation; j represents the neighboring node of the i-th node, and the neighboring node does not include the node i itself; u j (k) represents the state input of the jth node at the kth time; β represents the gain; N represents the node set; y j (k) represents the estimated state value of the jth node at the kth time; y i (k+1) represents the estimated state value of the i-th node at the k+1th time.

4. The anti-fraud distributed state estimation method according to claim 1, characterized in that: In step S3, the malicious nodes containing fraudulent information include the following: The state estimation value obtained in step S2 is processed using the trust region algorithm of multivariate statistics. The specific expression is: Where n represents the total number of nodes, p represents the dimension of the vector, represents the average value of all node state estimates, F α represents the critical test value in the F distribution table under the significance level α, the numerator degrees of freedom p and the denominator degrees of freedom (np), y i (k) represents the estimated state value of the i-th node at the k-th moment; The node that satisfies the above processing formula is a normal node, and the state estimation value of the node is used for the next information exchange. The node that does not satisfy the above processing formula is a malicious node, and the malicious node is discarded before information exchange.

5. The anti-fraud distributed state estimation method according to claim 1, characterized in that: In step S5, obtaining the location of the target to be measured includes the following: The covariance fusion method is used to process the covariance matrix of each node to obtain the fused inverse covariance matrix. The specific expression is: Among them, S(k) represents the fused inverse covariance matrix; R i -1 (k) represents the inverse matrix of the covariance matrix of the observation noise; H i (k) represents the observation matrix; H i T (k) indicates H i (k) is the transpose; Based on the initial position state x0 and initial covariance matrix P0 of the target to be measured at the kth moment, the Kalman filter algorithm is used to process the fused inverse covariance matrix, calculate the weight matrix, and obtain the state of the target to be measured at the kth moment. The specific expression is: M(k)=[(nP(k)) -1 +S(k)] -1 Among them, M(k) represents the weight matrix, P(k) represents the error covariance matrix, represents the optimal state of the target to be measured at the kth moment, represents the prior state of the target to be tested at the kth moment, n represents the total number of nodes, y j (k) represents the estimated state value of the jth node at the kth moment; Update the error covariance matrix and the state of the target to be measured to obtain the error covariance matrix at the k+1th moment. Multiply the state value of the target to be measured by the transfer matrix A to obtain the state of the target to be measured at the next moment. The specific expression is: P(k+1)=[AM(k)A T +nBQB T ] / n Among them, P(k+1) represents the error covariance matrix at the k+1th moment, represents the target state to be measured at the k+1th moment, B represents the control input matrix, Q represents the covariance matrix of v(k), v(k) represents the observation error or noise, A T represents the transpose of A, B T represents the transpose of B; The updated P(k+1) and Substitute it into the formula to obtain the state of the target to be measured at the kth moment, predict the state of the target to be measured, update the error covariance matrix and the state of the target to be measured, until the number of iterations is reached, and finally output the position state of the target to be measured.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the anti-fraud distributed state estimation method according to any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the anti-fraud distributed state estimation method according to any one of claims 1 to 5 is executed.

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