Distributed correction method for Beidou satellite navigation system against forwarding attacks

Abstract

The invention belongs to the technical field of distributed correction of navigation systems, and discloses a distributed correction method for a Beidou satellite navigation system for forwarding attacks, comprising S1, homology analysis of forwarding attacks of the Beidou system: a Beidou system simulation positioning program realizes positioning of an unmanned vehicle from satellite information, and analyzes the homology of the attack according to the positioning; S2, system modeling under homology attacks: according to homology signals received from different devices of the same information source, the forwarding attack is regarded as a homology sensor attack, and a system model subjected to the forwarding attack is constructed based on this; S3, design of an observer and selection of a gain matrix: an observer is designed to realize positioning correction of the Beidou system under forwarding attacks; S4, reconstructing system positioning; the invention combines the characteristics of attack homology in a distributed system and the reconstructed state characteristics of a security state observer to realize positioning correction under attacks.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed correction of navigation systems, and in particular to a distributed correction method of a Beidou satellite navigation system for forwarding attacks. Background Art

[0002] Nowadays, the Beidou Satellite Navigation System (BDS) has been widely used in many fields such as aviation, shipping and civil electronics. With the emergence of networked application scenarios such as the Internet of Things and the Internet of Vehicles, the role of the Beidou system in distributed systems has become more and more extensive. However, due to the long signal transmission distance and weak signal encryption, the Beidou system is vulnerable to malicious attacks.

[0003] Attacks on the Beidou system include blocking interference, deception attacks, and forwarding attacks. Blocking interference is to send invalid signals to cover the real signal; deception attacks use malicious devices to simulate satellites to send false malicious signals; forwarding attacks intercept and record the real Beidou system signal, and replay the recorded signal after a delay. They all change the time when the signal arrives at the receiver and change the distance from the satellite calculated by the receiver, thereby causing positioning deviation. Among them, since forwarding attacks do not need to modify the signal content, they are low-cost and have a wide range of applications, making them easier to affect military signals.

[0004] Beidou system forwarding attack detection mostly uses multiple statistical information of the signal when it reaches a single receiver to detect and separate the attack signal. Its detection methods include signal analysis-based methods (mainly relying on the signal's arrival angle, arrival time, arrival frequency, and intensity difference) and data analysis-based methods (represented by the probability density function detection method). However, Beidou system forwarding attacks will show the characteristics of attack homology in distributed multi-device systems, that is, different devices in adjacent ranges will produce the same positioning offset under forwarding attacks.

[0005] With the widespread application of distributed systems, the method of using communication networks to link multiple devices to achieve collaboration has attracted more and more attention; at the same time, a large number of studies have also provided feasible strategies for analyzing and countering network attacks from the perspective of control science. Therefore, this application constructs a Beidou system forwarding attack countermeasure strategy from the perspective of control science and multi-device collaboration, and realizes positioning correction under attack as a feasible method. Summary of the invention

[0006] The present invention aims to provide a distributed correction method for the Beidou satellite navigation system against forwarding attacks, combining the characteristics of attack homology and state reconstruction characteristics of a security state observer in a distributed system to achieve positioning correction under attack.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] The Beidou satellite navigation system distributed correction method for forwarding attacks includes the following steps:

[0009] S1. Homologous analysis of Beidou system forwarding attacks:

[0010] The unmanned vehicle platform is used to sample data, and the actual Beidou system signal is calculated based on the sampled data. The Beidou system signal includes the satellite number, the time of receiving the satellite signal, and the signal-to-noise ratio. The Beidou system simulation positioning program realizes the positioning of the unmanned vehicle from the received satellite information, and analyzes the homology of the attack based on the positioning.

[0011] S2. System modeling under homologous attacks:

[0012] According to the same source signals received by different devices from the same source, the forwarding attack is regarded as a same-source sensor attack, and the system model subjected to the forwarding attack is constructed as follows:

[0013] x i (k+1)=A i x i (k)+B i u i (k)

[0014] y i (k) = C i x i (k)+a(k)

[0015] In the formula, x i (k) is the system state, u i (k) is the system input, y i (k) is the measurement result of agent i being attacked at time k, and a(k) is the same-source attack;

[0016] S3. Observer design and gain matrix selection:

[0017] The observer is designed to realize the positioning correction of BeiDou system under forwarding attack when a real multi-vehicle system uses BeiDou system for positioning.

[0018] The method for selecting the gain matrix is:

[0019] A1. Design τ so that The column is full of rank;

[0020] A2. Design an undirected connected graph G;

[0021] A3. Calculate the Laplace matrix L;

[0022] A4. Design ( is the maximum output degree of graph G);

[0023] A5. Design η so that η j >0 and β<1;

[0024] A6. Design N so that 0≤q<1;

[0025] A7; Design M makes And ψ≤1;

[0026] Through steps A1 to A3, the parameters are determined through the system model and the topology matrix; through step A5, the gain matrix of the system is determined; steps A6 and A7 determine the loop steps; thereby analyzing the number of times the observer repeats each step in a single time window;

[0027] S4. Reconstruction system positioning:

[0028] Multiple Beidou system positioning modules are attached to multiple unmanned vehicles in turn, and a communication network between the multiple unmanned vehicles is established; the constructed multi-unmanned vehicle system model and the gain matrix selection algorithm in S3 are used to design and calibrate the observer; the real position of the actual system can be regarded as the system state, the positioning deviation caused by the Beidou system forwarding attack can be regarded as a homologous attack, and the attacked Beidou system positioning can be regarded as the attacked output, and the secure reconstruction feature of the state of the observer in S3 is used to reconstruct the real position of the multi-device system and achieve positioning calibration.

[0029] Furthermore, in S1, the positioning method of the unmanned vehicle is: Beidou system positioning based on pseudorange measurement, and positioning is achieved by calculating the pseudoranges between multiple receivers and satellites; its calculation formula is:

[0030]

[0031] In the formula, x (i) ,y (i) ,z (i) is the coordinate of the i-th satellite; x u ,y u ,z u is the coordinate of the receiver to be measured; τ u is the time deviation between the receiving device and the satellite system; γ is the noise interference in the propagation process; ρ (i) is the pseudorange of the ith satellite, ρ (i) It is the product of signal transmission time and signal speed, and its expression is:

[0032]

[0033] In the formula, is the sending time of the i-th satellite signal; is the reception time of the i-th satellite signal.

[0034] Furthermore, in S1, the method for analyzing the homology of the attack is:

[0035] First, the same forwarding attack is set on the receiver to obtain the positioning offset vector generated by the receiver; then, for the same positioning offset vector, the Euclidean distance, cosine similarity, covariance matrix and variance are considered to prove their homology; finally, the coefficient of variation is used to eliminate the influence of measurement scale and dimension on the experimental results; the expression of the coefficient of variation is:

[0036]

[0037] σ is the standard deviation, μ is the mean, and CV is the coefficient of variation;

[0038] Furthermore, in S1, in order to compare the homology index with the attack homology, the reciprocal of the coefficient of variation CV is called the degree of homology; further considering the coefficient of variation in the longitude and latitude directions, the expression of homology is obtained as follows:

[0039]

[0040] In the formula, θ is the homology degree, CV lon , CV lat is the coefficient of variation of the positioning offset vector in the longitude and latitude components.

[0041] Further, in S3, the observer includes a distributed static dual-loop observer and a distributed online three-loop observer;

[0042] Among them, the distributed static dual-loop observer is used for offline operation; its static dual-loop observer estimates the system state and attack signal simultaneously by combining the average consensus algorithm and residual information, using the distributed average consensus algorithm as its inner loop and nesting the residual update loop outside; the distributed static dual-loop observer uses m as the outer loop mark and n as the inner loop mark; the inner loop guides all estimated values ​​to their average value through average consistency, and the outer loop adjusts the estimated value of each agent through residual information, thereby guiding the overall average value to the true value, and finally each agent's estimate of the attack signal gradually converges to the true value;

[0043] A distributed online three-loop observer is used for online operation by superimposing a time update loop outside the residual update loop, and it is proved that its estimation error converges exponentially with time.

[0044] Furthermore, in S3, to reduce the number of inner loop cycles, two parameters ε and λ2(L) are adjusted; these two parameters correspond to the observer gain and the system topology, respectively; the closer 1-ελ2(L) is to zero, the smaller N is; to reduce the number of intermediate loop cycles, the recursive step size η is adjusted, where the larger β is, the smaller M can be selected; to facilitate parameter design, the gain matrix of the recursive step size is selected as

[0045] The beneficial effects of the technical solution are:

[0046] 1. The distributed correction method for the Beidou satellite navigation system under forwarding attack provided by the present invention provides a feasible and effective solution to the positioning correction problem of the Beidou system under forwarding attack by using the distributed security state estimation method in the control field; and the method can reliably reconstruct the system state when the distributed system is attacked by the same source error data injection, so as to realize the correction of the positioning position;

[0047] 2. The distributed security state observer can maintain reliable performance when all system outputs are attacked. The present invention can correct the positioning when all satellite signals are attacked by forwarding, thus expanding the signal processing detection system based on a single device.

[0048] 3. The present invention can be used in multi-device collaboration fields such as drone formations to achieve effective positioning correction; in the initial application of the Quanser multi-unmanned vehicle platform, it can effectively correct the positioning error of the system; in practical applications, it significantly improves the security of the positioning system and achieves improvements in the positioning performance and anti-interference capability of the Beidou system. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a schematic diagram of the same-source positioning offset caused by the Beidou system forwarding attack on the positioning devices in the area in step S1 in an embodiment of the present invention;

[0050] Figure 2 It is a line graph showing the influence of the attack amplitude of the Beidou system forwarding attack on the homology degree and the change of the attack amplitude in step S1 in the embodiment of the present invention;

[0051] Figure 3 A line graph showing the influence of the number of attacked satellites on the homology degree and the change of the attack amplitude in step S1 in an embodiment of the present invention;

[0052] Figure 4 A line graph of the Monte Carlo experiment results in step S1 in an embodiment of the present invention;

[0053] Figure 5 A distributed safety state estimation diagram of the multi-agent system in step S2 in an embodiment of the present invention;

[0054] Figure 6 A block diagram of the design of an offline dual-loop observer in step S3 in an embodiment of the present invention;

[0055] Figure 7 A block diagram of the design of the online three-ring observer in step S3 in an embodiment of the present invention;

[0056] Figure 8 4 is a curve diagram of the vehicle positioning error using DSSE in step S4 in an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments:

[0058] The Beidou satellite navigation system distributed correction method for forwarding attacks includes the following steps:

[0059] S1. Homologous analysis of Beidou system forwarding attacks:

[0060] This embodiment uses the Quenser unmanned vehicle platform to perform data sampling and obtains the actual Beidou system signal through calculation, which mainly includes: satellite number, time of received satellite signal and signal-to-noise ratio; Beidou system simulation positioning program realizes the positioning of the unmanned vehicle from the received satellite information;

[0061] Among them, the positioning method of the unmanned vehicle is: Beidou system positioning method based on pseudo-range measurement, which realizes positioning by calculating multiple pseudo-ranges (calculating the distance between the receiver and the satellite), and its calculation formula is:

[0062]

[0063] In the formula, x (i) ,y (i) ,z (i) is the coordinate of the ith satellite, x u ,y u ,z u is the coordinate of the receiver to be measured, τ u is the time deviation between the receiving device and the satellite system, γ is the noise interference in the propagation process, and ρ (i) is the pseudorange of the ith satellite, which is equal to the product of the signal transmission time and the signal speed, ρ (i) The expression is:

[0064]

[0065] In the formula, is the sending time of the i-th satellite signal; is the reception time of the i-th satellite signal;

[0066] A receiver can receive data from multiple satellites and use a variety of methods to fit the data of each satellite to obtain reliable positioning; the person who carries out the forwarding attack intercepts, records and replays the real signal, and then lets the receiver track the delayed signal; the malicious attacker carries out the forwarding attack on the i-th satellite in the system, which is essentially to increase This changes the pseudorange, causing equation parameters to change, which in turn affects positioning.

[0067] In order to simulate the forwarding attack, this embodiment replaces the target satellite signal with the old, stored satellite signal to complete a simulated interference attack. At the same time, the satellite affected by the attack is set arbitrarily; then, the real position and attack position of the receiver are calculated using the replaced signal and the unreplaced signal respectively; the position deviation caused by the forwarding attack is calculated;

[0068] like Figure 1 As shown in the figure, a Beidou system satellite carried out a forwarding attack, and the impact of the attack on the positioning of four receivers in the area was obtained, where the coordinate points in the upper and lower boxes correspond to the real coordinates and the coordinates after the attack of the four receivers, respectively, and the arrows are the positioning deviations caused by the malicious attack; the arrows have approximately the same amplitude and direction, that is, the forwarding attack caused homologous positioning deviations on the four receivers.

[0069] After the receiver is subjected to a simulated jamming attack, a set of offset vectors is obtained; as the influencing variables change, the similarity between the offset vectors also gradually changes; Figure 2 As shown in the figure, the positions of the four devices before and after the attack are surrounded by the upper and lower boxes respectively. Obviously, the offset vectors caused by the simulated interference attack are not exactly the same, that is, the factors causing the positioning offset are not only homologous attacks. Specifically, the attacks on each agent are the same, but the performances produced by the attacks are not exactly the same.

[0070] Therefore, the method to evaluate the homology of attack is:

[0071] First, the same forwarding attack is set on the receiver to obtain the positioning offset vector generated by the receiver; then, for the same positioning offset vector, the Euclidean distance, cosine similarity, covariance matrix and variance are considered to illustrate their homology; finally, the coefficient of variation is considered to eliminate the influence of measurement scale and dimension on the experimental results; the expression of the coefficient of variation is:

[0072]

[0073] σ is the standard deviation, μ is the mean, and the coefficient of variation CV decreases as the homology of the attack increases;

[0074] In order to compare the homology index with the attack homology, the inverse of the coefficient of variation is called the degree of homology; considering the coefficient of variation in longitude and latitude, the homology calculation method is obtained as follows:

[0075]

[0076] In the formula, θ is the homology degree, CV lon , CV lat is the coefficient of variation of the positioning offset vector in the longitude and latitude components;

[0077] The coefficient of variation is used because it removes the influence of the measurement scale and class, and the homology index is compared with the attack homology. The inverse of the coefficient of variation is called the degree of homology; the higher the value of Θ, the higher the degree of homology of the attack;

[0078] In addition, this embodiment also explores the changes in homology under different conditions through the experimental idea of ​​controlling variables, and strives to fully consider the impact of these factors on the experiment when implementing attack correction. Data is collected from 30 vehicle-mounted receiving devices and pre-processed. Since some satellites can only be received by a few vehicle-mounted receivers, for the convenience of comparison, only the data of 16 satellites that can be received by all vehicle-mounted receivers are retained. Using the positioning tools and data of 16 satellites, the true positions of 30 vehicle-mounted receivers can be obtained.

[0079] When a malicious attacker conducts a simulated jamming attack, the attack amplitude, i.e., the delay time of the signal, is freely controlled by the attacker. Therefore, the attack amplitude may affect the homology of the attack. Therefore, the experimenters conducted simulated jamming attacks on satellites 1, 3, and 17 respectively. The attack amplitude ranged from 0 to 1000.

[0080] As the attack amplitude increases, the average position deviation increases linearly, proving that the attack has an impact on the position. For example, when the attack amplitude on satellite 17 is 200 or 1000, the homology is θ≈3.9; at the same time, attacks on different satellites result in different homology degrees. For example, the homology degrees of attacks on satellites 1 and 3 are θ≈0.2 and θ≈0.6, respectively.

[0081] Secondly, consider the change in the homology of the number of attacked satellites. Since there are many ways to select the attacked satellites from the 16 satellites, in order to control the variables more clearly and draw conclusions, the experiment is carried out as follows:

[0082] First, the indicators of the 16 satellites received by all vehicle-mounted receivers are randomly sorted into an indicator sequence; then, the first satellite, the first two satellites, and the first three satellites are appropriately attacked until all satellites are attacked. This method can reduce the impact of changes in the number of satellites on the experiment, which is conducive to subsequent large-scale experiments.

[0083] like Figure 3 As shown in Figure 3, the homology changes with the number of attacks under three index sequences. The maximum homology points of sequence 1 and sequence 3 appear in 4-5 and 12 attacks respectively. The homology of sequence 2 has two maximum points, 3-7 attacks and 12-13 attacks. When attacking a satellite, the homology and positioning offset may not change. This is because the newly added attacked satellite does not work during positioning due to signal strength or other reasons, and the positioning tool is abnormal. This is also Figure 3 The reason why there are many horizontal segments in the

[0084] Secondly, because the order in which the 16 satellites were attacked was diverse, and the homology changes corresponding to different orders were also different, a Monte Carlo experiment was conducted, 200 index sequences were randomly selected, and the impact of the number of attacks on homology was calculated and analyzed from a statistical perspective; Figure 4 The Monte Carlo experiment results are shown.

[0085] The homology first increases with the number of attacks, and reaches a peak value of about θ ≈ 6.5 when the number of attacks is between 8 and 10. Then, the homology gradually decreases to 0. Therefore, the homology first increases and then decreases with the increase of the number of attacks.

[0086] S2. System modeling under homologous attacks:

[0087] According to the same source signals received by different devices from the same source, the forwarding attack is regarded as a same-source sensor attack, and the system model subjected to the forwarding attack is constructed as follows:

[0088] x i (k+1)=A i x i (k)+B i u i (k)

[0089] y i (k) = C i x i (k)+a(k)

[0090] In the formula, x i (k) is the system state, u i (k) is the system input, y i (k) is the measurement result of agent i being attacked at time k, and a(k) is the same-source attack;

[0091] like Figure 5As shown in the figure, the distributed security state estimation (DSSE) of a multi-agent system is described; the agents modeled in step S1 are in the lower circle and exist in the physical layer; each agent has an observer represented by the upper circle to estimate its state and attack signal; information is shared by observers to create a network layer. At present, the above structure is the basis for DSSE to design strategies for attacks against homologous sensors. According to the design of the observer, the observer can be divided into a multi-periodic structure and a recursive structure.

[0092] S3. Observer design and gain matrix selection:

[0093] The observer is designed to realize the positioning correction of BeiDou system under forwarding attack when a real multi-vehicle system uses BeiDou system for positioning.

[0094] The observers include a distributed static dual-loop observer and a distributed online three-loop observer;

[0095] Among them, the distributed static dual-loop observer is used for offline operation; its static dual-loop observer estimates the system state and attack signal simultaneously by combining the average consensus algorithm and residual information, using the distributed average consensus algorithm as its inner loop and nesting the residual update loop outside;

[0096] like Figure 6 As shown in the figure, the distributed static dual-loop observer has an outer loop marked with m and an inner loop marked with n. The inner loop guides all estimated values ​​to their average value through average consistency, and the outer loop adjusts the estimated value of each agent through residual information, thereby guiding the overall average value to the true value. Finally, each agent's estimate of the attack signal gradually converges to the true value.

[0097] A distributed online three-loop observer is used for online operation by superimposing a time update loop outside the residual update loop, and it is proved that its estimation error converges exponentially with time.

[0098] like Figure 7 As shown in the figure, the composition of the online distributed safe state estimation observer with a three-ring structure; the three loops of the observer are called the outer loop, the middle loop and the inner loop. The green loop, the blue loop and the yellow loop correspond to the outer loop, the middle loop and the inner loop respectively. Among them, k, m, n are the loop indexes of the outer loop, the middle loop and the inner loop respectively; the outer loop is a time loop, k is the number of time loops, which means that in each time step, the outer loop and the inner loops it contains run completely once; m is the number of loops of the residual update loop, and n is the number of loops of the distributed average consistency algorithm. superscript (k,m,n) Used to represent the relevant variables when the outer loop runs for the kth time, the middle loop runs for the mth time, and the inner loop runs for the nth time.

[0099] The method for selecting the gain matrix is:

[0100] A1. Design τ so that The column is full of rank;

[0101] A2. Design an undirected connected graph G;

[0102] A3. Calculate the Laplace matrix L;

[0103] A4. Design ( is the maximum output degree of graph G);

[0104] A5. Design η so that η j >0 and β<1;

[0105] A6. Design N so that 0≤q<1;

[0106] A7 Design M makes And ψ≤1;

[0107] Through steps A1 to A3, the parameters are determined through the system model and the topology matrix; through step A5, the gain matrix of the system is determined; steps A6 and A7 determine the loop steps; thereby analyzing the number of times the observer repeats each step in a single time window;

[0108] To reduce the number of inner loop cycles, two parameters ε and λ2(L) are adjusted; these two parameters correspond to the observer gain and the system topology respectively; the closer 1-ελ2(L) is to zero, the smaller N is; to reduce the number of middle loop cycles, the recursive step size η is adjusted, where the larger β is, the smaller M can be selected; to facilitate parameter design, the gain matrix of the recursive step size is selected as

[0109] S4. Reconstruction system positioning:

[0110] Attach multiple Beidou system positioning modules to multiple unmanned vehicles in turn, and establish a communication network between multiple unmanned vehicles; use the constructed multi-unmanned vehicle system model and the gain matrix selection algorithm in S3 to design and calibrate the observer; the real position of the actual system can be regarded as the system state, the positioning deviation caused by the Beidou system forwarding attack can be regarded as a homologous attack, and the attacked Beidou system positioning can be regarded as the attacked output. The observer in S3 uses the safe reconstruction feature of the state to reconstruct the real position of the multi-device system and achieve positioning calibration;

[0111] Consider a multi-vehicle system with the following state-space model:

[0112] A1=[0.6531,0.6047;0.3285,0.4984],C1=[1,0]

[0113] A2=[0.7647,0.5918;0.4260,0.2739],C2=[1,0]

[0114] A3=[0.6905,0.1672;0.4273,0.6173],C3=[1,0]

[0115] The two state dimensions represent the longitude and latitude coordinates, respectively, and the system output is the longitude coordinate output by the Beidou system after the forwarding attack. The initial position of the vehicle is set to x10 = [1; 9], x20 = [3; 4], x30 = [5; 10], and the system state from time 1 to time 20 is calculated. By obtaining the calculated state of each vehicle at each time, the Beidou system receiver is placed at the corresponding coordinate position.

[0116] like Figure 8 As shown in Figure 2, the vehicle positioning error using DSSE. The initial observer value is set to the initial attacked position. Therefore, the estimation error at the initial moment can be considered as the positioning offset caused by the attack. The positioning deviation gradually decreases as the observer runs. The initial positioning error is about 200m, but the corrected position is about 20m.

[0117] The above is only an embodiment of the present invention, and the common knowledge such as the known specific technical solutions or characteristics in the solution is not described in detail here. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the technical solution of the present invention, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A distributed correction method for Beidou satellite navigation system against forwarding attacks, characterized in that: The following steps are involved: S1. Homologous analysis of Beidou system forwarding attacks: The unmanned vehicle platform is used to sample data, and the actual Beidou system signal is calculated based on the sampled data. The Beidou system signal includes the satellite number, the time of receiving the satellite signal, and the signal-to-noise ratio; The Beidou system simulation positioning program realizes the positioning of the unmanned vehicle from the received satellite information, and analyzes the homology of the attack based on the positioning; Among them, the method for analyzing the homology of attacks is: First, the same forwarding attack is set on the receiver to obtain the positioning offset vector generated by the receiver; then, for the same positioning offset vector, the Euclidean distance, cosine similarity, covariance matrix and variance are considered to prove their homology; finally, the coefficient of variation is used to eliminate the influence of measurement scale and dimension on the experimental results; the expression of the coefficient of variation is: σ is the standard deviation, μ is the mean, and CV is the coefficient of variation; In order to compare the homology index with the attack homology, the reciprocal of the coefficient of variation CV is called the degree of homology; further considering the coefficient of variation in the longitude and latitude directions, the expression of homology is obtained as follows: In the formula, θ is the homology degree, CV lon , CV lat is the coefficient of variation of the positioning offset vector in the longitude and latitude components; S2. System modeling under homologous attacks: According to the same source signals received by different devices from the same source, the forwarding attack is regarded as a same-source sensor attack, and the system model subjected to the forwarding attack is constructed as follows: x i (k+1)=A i x i (k)+B i u i (k) y i (k)=C i x i (k)+a(k) In the formula, x i (k) is the system state, u i (k) is the system input, y i (k) is the measurement result of agent i being attacked at time k, and a(k) is the same-source attack; S3. Observer design and gain matrix selection: The observer is designed to realize the positioning correction of BeiDou system under forwarding attack when a real multi-vehicle system uses BeiDou system for positioning. The method for selecting the gain matrix is: A1. Design Make The column is full of rank; A2. Design an undirected connected graph G; A3. Calculate the Laplace matrix L; A4. Design is the maximum output degree of graph G; A5. Design η so that η j >0 and β<1; A6. Design N so that 0≤q<1; A7、Design M makes And ψ≤1; Through steps A1 to A3, the parameters are determined through the system model and the topology matrix; through step A5, the gain matrix of the system is determined; steps A6 and A7 determine the loop steps; thereby analyzing the number of times the observer repeats each step in a single time window; S4. Reconstruction system positioning: Multiple Beidou system positioning modules are attached to multiple unmanned vehicles in turn, and a communication network between the multiple unmanned vehicles is established; the constructed multi-unmanned vehicle system model and the gain matrix selection algorithm in S3 are used to design and calibrate the observer; the real position of the actual system can be regarded as the system state, the positioning deviation caused by the Beidou system forwarding attack can be regarded as a homologous attack, and the attacked Beidou system positioning can be regarded as the attacked output, and the secure reconstruction feature of the state of the observer in S3 is used to reconstruct the real position of the multi-device system and achieve positioning calibration.

2. The Beidou satellite navigation system distributed correction method for forwarding attacks according to claim 1, characterized in that: In S1, the positioning method of the unmanned vehicle is: Beidou system positioning based on pseudorange measurement, which achieves positioning by calculating the pseudoranges between multiple receivers and satellites; its calculation formula is: In the formula, x (i) ,y (i) ,z (i) is the coordinate of the i-th satellite; x u ,y u ,z u is the coordinate of the receiver to be measured; is the time deviation between the receiving device and the satellite system; γ is the noise interference in the propagation process; ρ (i) is the pseudorange of the ith satellite, ρ (i) It is the product of signal transmission time and signal speed, and its expression is: In the formula, is the sending time of the i-th satellite signal; is the reception time of the i-th satellite signal.

3. The Beidou satellite navigation system distributed correction method for forwarding attacks according to claim 1, characterized in that: In S3, the observers include a distributed static dual-loop observer and a distributed online three-loop observer; Among them, the distributed static dual-loop observer is used for offline operation; its static dual-loop observer estimates the system state and attack signal simultaneously by combining the average consensus algorithm and residual information, using the distributed average consensus algorithm as its inner loop and nesting the residual update loop outside; the distributed static dual-loop observer uses m as the outer loop mark and n as the inner loop mark; the inner loop guides all estimated values ​​to their average value through average consistency, and the outer loop adjusts the estimated value of each agent through residual information, thereby guiding the overall average value to the true value, and finally each agent's estimate of the attack signal gradually converges to the true value; A distributed online three-loop observer is used for online operation by superimposing a time update loop outside the residual update loop, and it is proved that its estimation error converges exponentially with time.

4. The Beidou satellite navigation system distributed correction method for forwarding attacks according to claim 1, characterized in that: In S3, to reduce the number of inner loop cycles, two parameters ε and λ2(L) are adjusted; these two parameters correspond to the observer gain and the system topology respectively; the closer 1-ελ2(L) is to zero, the smaller N is; to reduce the number of middle loop cycles, the recursive step size η is adjusted, where the larger β is, the smaller M can be selected; to facilitate parameter design, the gain matrix of the recursive step size is selected as

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