A safety tobit filtering method based on three-wheel ackerman steering model

Abstract

This invention discloses a secure Tobit filtering method based on a three-wheel Ackerman steering model. The method includes the following steps: 1. Establishing a three-wheel Ackerman steering model with spoofing attacks and censoring measurements; 2. Designing a secure Tobit filter for the three-wheel Ackerman steering model; 3. Calculating the upper bound of the prediction error covariance matrix of the three-wheel Ackerman steering model at time h; 4. Calculating the gain matrix K of the three-wheel Ackerman steering model at time h+1. h+1 5. K h+1 Substitute into step two to obtain the filtering judgment at time h+1. If h+1 < Y, then proceed to step six; step six, through K... h+1 The upper bound of the filter error covariance matrix of the three-wheel Ackerman steering model at time h+1 is calculated, and h = h+1 is set. The process is repeated until h+1 = Y. This invention solves the problem that existing secure Tobit filtering methods cannot simultaneously handle censoring measurements and spoofing injection attacks in nonlinear filtering.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of filtering, and relates to a secure filtering method, in particular to a secure Tobit filtering method for a three-wheel Ackerman steering model with false data injection attacks and missing measurements. BACKGROUND

[0002] The three-wheel Ackerman steering model is usually used to describe the motion characteristics of a vehicle with three wheels and a front wheel turning function. It is an application of the Ackerman steering principle on a three-wheel vehicle. The three-wheel Ackerman steering model is of great significance for improving vehicle design, developing control algorithms and promoting automatic driving technology. How to estimate the parameters based on the three-wheel Ackerman steering model is still a research hotspot.

[0003] Considering that missing measurements caused by sensor measurement saturation often occur in various practical applications, it is of practical significance to study the three-wheel Ackerman steering model with missing measurements. It is noted that in the process of information transmission, an attacker can introduce attack behavior into the system in an unpredictable and covert manner through network components, thereby damaging the performance of the system. Among them, false data injection attacks inject false data into the system to damage the integrity, reliability and trustworthiness of the system, and are therefore considered one of the most important attack behaviors.

[0004] Existing filtering methods cannot solve the secure filtering problem of the three-wheel Ackerman steering model with the above phenomena at the same time. If a traditional filtering scheme is used to estimate the state of the three-wheel Ackerman steering model, the filtering performance will be greatly reduced. SUMMARY

[0005] In order to solve the secure filtering problem of the three-wheel Ackerman steering model with false data injection attacks and missing measurements and other phenomena, the application provides a secure Tobit filtering method based on a three-wheel Ackerman steering model.

[0006] The purpose of the application is achieved by the following technical solutions:

[0007] A secure Tobit filtering method based on a three-wheel Ackerman steering model, comprising the following steps:

[0008] Step one, based on five-dimensional state variables composed of vehicle coordinates, vehicle path angle deviation, linear velocity and steering angle, a three-wheel Ackerman steering model with false data injection attacks and missing measurements is established, and the three-wheel Ackerman steering model with false data injection attacks and missing measurements is:

[0009]

[0010]

[0011]

[0012]

[0013] In the formula, x h =[x h y h η h κ h ζ h ] T T represents the transpose of the matrix; sin(·), cos(·), and tan(·) represent the sine, cosine, and tangent functions of the "·" symbol, respectively; x h y h η h κ h and ζ h Let x represent the original coordinates, path angle deviation, linear velocity, and steering angle of the vehicle at time h in the three-wheeled Ackerman steering model; E represents the distance from the front wheel to the rear axle of the three-wheeled vehicle; Δs is the sampling interval; and x is the distance from the front wheel to the rear axle. b and y b This represents the position of the beacon measured by the sensors installed inside the vehicle; ω h and v h These represent values ​​with zero mean and covariance matrix Q at time h. h >0 and R h Process noise and measurement noise > 0, D h It is a known five-dimensional time-varying matrix; It is the uncensored measurement output (also known as the latent variable) with 5 nodes at time h; It is the censored output vector with 5 nodes at time h, Θ h =diag{θ 1,h ,θ 2,h ,…,θ 5,h}, where diag(·) represents a diagonal matrix whose diagonal elements are "·", and θ i,h (i = 1, 2, ..., 5) is a Bernoulli random variable used to determine whether the i-th node has been censored at time h, and satisfies the following conditions: Prob represents the probability of the event occurring. Let be the uncensored probability of the i-th node at time h, and Ψ(·) be the distribution function of the standard normal distribution. This is a one-step prediction of the state of the three-wheel Ackermann steering model at time h-1. for The i-th element, Let τ be the one-step prediction form of the nonlinear function corresponding to the measurement output based on the three-wheel Ackerman steering model at time h-1. i (i = 1, 2, ..., 5) is The i-th element, Represents the censoring threshold vector. Let R be the measurement noise covariance matrix at time h. h The (i,i)th element, where I is the five-dimensional identity matrix; y h The actual measurement value ξ is generated after a false data injection attack occurs at time h. h It meets the conditions False data, For ξ h transpose, It is a spurious upper bound greater than 0, Γ h =diag{γ 1,h ,γ 2,h ,…,γ 5,h}, γ i,h (i = 1, 2, ..., 5) are Bernoulli random variables used to determine whether an attacker is attacking a sensor node, and satisfy the following conditions: Let be the attack probability of the i-th node at time h;

[0014] Step 2: Design a safety Tobit filter for the three-wheel Ackerman steering model established in Step 1. The designed safety Tobit filter enables state estimation of the three-wheel Ackerman steering model. The specific structure of the safety Tobit filter is as follows:

[0015]

[0016]

[0017] In the formula, This is a one-step prediction of the state at time h for the three-wheel Ackerman steering model. This is the filtered form of the nonlinear function of the state based on the three-wheel Ackerman steering model at time h. The state of the three-wheel Ackerman steering model at time h is filtered. For filtering at time h+1, K h+1 Let y be the gain matrix at time h+1. h+1 The actual measurement value is generated after a false data injection attack occurs at time h+1. It is the probability of the i-th node not being censored at time h+1. This represents the one-step prediction form of the nonlinear function corresponding to the measurement output based on the three-wheel Ackerman steering model at time h. Where φ(·) is the probability density function of the standard normal distribution. for The i-th element, R is the measurement noise covariance matrix at time h+1. h+1 The (i,i)th element express Transpose of;

[0018] Step 3: Calculate the upper bound of the prediction error covariance matrix of the three-wheel Ackerman steering model at time h. The upper bound of the prediction error covariance matrix of the three-wheel Ackerman steering model at time h. The expression is:

[0019]

[0020] In the formula, f(x) is the nonlinear function at time h corresponding to the state based on the three-wheel Ackermann steering model. h ) Filtering at time h Partial derivative at point, Let h be the upper bound of the filter error covariance matrix at time h. as well as Based on f(x) h The known error matrix obtained through Taylor's formula, as well as Represent and D h The transpose of ρ 1,h Describe a known time-varying coefficient and satisfy as well as Represent and ρ 1,h The reverse;

[0021] Step 4: Utilize the results obtained in Step 3 Calculate the gain matrix K of the three-wheel Ackerman steering model at time h+1. h+1 The gain matrix K of the three-wheel Ackerman steering model at time h+1. h+1 The expression is:

[0022]

[0023] in:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] In the formula, Let ρ be the upper bound of the prediction error covariance matrix at time h. 2,h+1 It is to satisfy The time-varying positive scalar, The nonlinear function g(x) at time h+1 corresponding to the measurement output based on the three-wheel Ackermann steering model. h+1 )exist Partial derivative at point, as well as Based on g(x) h+1 The known error matrix ε is obtained through Taylor's formula. i,h+1 (i = 1, 2, ..., 5) are all weighting coefficients. Let represent the attack probability of the i-th sensor node at time h+1. Represents the intermediate parameter matrix. as well as It is to satisfy positive constants, x h+1 Let represent the state of the three-wheel Ackerman steering model at time h+1, ‖·‖ represent the Euclidean norm, tr{·} represent the trace of the matrix, and "°" represent the Hadamard product between matrices. as well as Representing respectively to as well as To perform a squaring operation as well as Represent ρ 2,h+1 ε 1,h+1 ε 2,h+1 ε 3,h+1 ε 4,h+1 and ε 5,h+1 The reverse, as well as Represent as well as Transpose of;

[0030] Step 5: Use the K calculated in Step 4 h+1 Substitute this into step two to obtain the filter at time h+1. Then, it is judged whether h+1 can reach the total filtering time Y, if h+1 < Y is satisfied, step six is executed, if h+1 = Y is satisfied, the state estimation of the three-round Akman steering model with false data injection attack and missing measurement is stopped;

[0031] Step six, K calculated in step four h+1 The upper bound of the filtering error covariance matrix of the three-round Akman steering model at the h+1 time is calculated h is set as h+1, step two is executed until h+1 = Y is satisfied, the upper bound of the filtering error covariance matrix of the three-round Akman steering model at the h+1 time is The expression of the upper bound of the filtering error covariance matrix of the three-round Akman steering model at the h+1 time is:

[0032]

[0033] Wherein:

[0034]

[0035]

[0036]

[0037]

[0038] In the formula, The upper bound of the filtering error covariance matrix at the h+1 time, Represents the transpose of K h+1 .

[0039] Compared with the prior art, the present application has the following advantages:

[0040] 1、The present application considers the influence of false data injection attack and missing measurement on system performance at the same time, unlike the existing filtering method, the safe Tobit filtering method of the present application can process the phenomenon of missing measurement and false data injection attack, the algorithm has the advantage of being easy to solve online, and solves the nonlinear filtering problem that the existing filtering method cannot process missing measurement and false data injection attack at the same time.

[0041] 2、The application calculates the upper bound of the filtering error covariance matrix by means of matrix theory and stochastic analysis technology. Then, by designing appropriate filter gain, the trace of the upper bound of the filtering error covariance matrix can be ensured to reach the minimum value at each time. This method ensures the minimization of filtering error, and even in the case of false data injection attack and missing measurement, it can still maintain good filtering performance. In the simulation experiment of the application, the filtering error obtained by using the proposed safe Tobit filtering method is reduced by about 40% compared with the filtering error obtained by using the extended Kalman filter method.

[0042] 3、The safe Tobit filtering method based on the three-wheel Ackerman steering model of the application can effectively estimate the state information of the three-wheel Ackerman steering model. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 is the flow chart of the safe Tobit filtering method based on the three-wheel Ackerman steering model proposed by the application.

[0044] Figure 2 is the trajectory of the first component of the actual state of the three-wheel Ackerman steering model at the hth moment and the trajectory of its filtering .

[0045] Figure 3 is the trajectory of the second component of the actual state of the three-wheel Ackerman steering model at the hth moment and the trajectory of its filtering .

[0046] Figure 4 is the trajectory of the third component of the actual state of the three-wheel Ackerman steering model at the hth moment and the trajectory of its filtering .

[0047] Figure 5 is the trajectory of the fourth component of the actual state of the three-wheel Ackerman steering model at the hth moment and the trajectory of its filtering .

[0048] Figure 6 is the trajectory of the fifth component of the actual state of the three-wheel Ackerman steering model at the hth moment and the trajectory of its filtering .

[0049] Figure 7 is the relationship diagram of the logarithm log(MSE) of the mean square error and the logarithm of the trace of the upper bound of the filtering error covariance matrix .

[0050] Figure 8 is the mean square error of case I (the safety Tobit filtering method proposed in the application) and the mean square error of case II (the extended Kalman filtering method). DETAILED DESCRIPTION

[0051] The technical solutions of the application are further described below with reference to the drawings, but are not limited thereto, and any modifications or equivalent replacements to the technical solutions of the application without departing from the spirit and scope of the technical solutions of the application shall be encompassed in the protection scope of the application.

[0052] The application provides a safety Tobit filtering method based on a three-wheel Ackerman steering model. Firstly, a three-wheel Ackerman steering state model and a three-wheel Ackerman steering measurement model with false data injection attacks and missing measurements are established. h+1 Secondly, an upper bound of a prediction error covariance matrix of the three-wheel Ackerman steering model at the hth moment h+1 and a gain matrix K h at the (h+1)th moment are calculated. h+1 Finally, K h+1 is substituted into the safety Tobit filter, thereby proposing a safety Tobit filtering algorithm with false data injection attacks and missing measurements. Figure 1 As shown in the figure, the method comprises the following steps:

[0053] Step 1: Based on five-dimensional state variables composed of vehicle coordinates, vehicle path angle deviations, linear velocities and steering angles, a three-wheel Ackerman steering model with missing measurements and false data injection attacks is established.

[0054] In this step, the established three-wheel Ackerman steering model with missing measurements and false data injection attacks is as follows:

[0055]

[0056]

[0057] In the formula, x h =[x h y h η h κ h ζ h ] T , T represents the transpose of a matrix; sin(·), cos(·) and tan(·) represent the sine function, cosine function and tangent function of “·” respectively; x h , y h , ηh , κ h and ζ h denote the original coordinates, path angle error, linear velocity and steering angle of the vehicle at the hth time instant for the three-wheeled Ackerman steering model; E represents the distance from the front wheel to the rear axle of the three-wheeled vehicle, Δs is the sampling interval, x b and y b denote the beacon positions measured by the sensors installed in the vehicle; ω h and v h denote the process noise and measurement noise with zero mean and covariance matrices Q h > 0 and R h > 0 at the hth time instant, respectively, and D h is a five-dimensional time-varying matrix known in advance. Y is the unimputed measurement output (also referred to as a latent variable) with 5 nodes at the hth time instant.

[0058] According to the relationship between the known imputation threshold vector and , the imputed measurement equation can be constructed. Specifically, since the actual output value cannot be directly observed due to the imputed measurement, an observable vector is introduced to represent the measurement value after imputation. It is defined that and where col represents a column vector, represents the unimputed measurement output of the ith node at the hth time instant, represents the measurement output of the ith node at the hth time instant after imputation.

[0059] According to the Tobit first-type observation model, the following equation can be obtained:

[0060]

[0061] where τ i (i = 1, 2,..., 5) represents a known constant threshold for .

[0062] A set of independent Bernoulli random variables θ i,h (i = 1, 2,..., 5) determine whether is imputed, which can be represented as follows:

[0063]

[0064] and the probability distribution thereof satisfies the following equation:

[0065]

[0066] where Prob denotes the probability value of an event, represents the un-censored probability of the ith node at the hth time.

[0067] According to some prior statistical information, we can get the approximation of

[0068]

[0069] where Ψ(·) is the distribution function of the standard normal distribution, is a one-step prediction of the state of the three-wheel Ackermann steering model at the (h-1)th time, is the ith element of is a one-step prediction form of the nonlinear function corresponding to the measurement output based on the three-wheel Ackermann steering model at the (h-1)th time, is the measurement noise covariance matrix R h at the hth time.

[0070] After some mathematical processing, we can get:

[0071]

[0072] Define Θ h = diag{θ 1,h , θ 2,h ,..., θ 5,h} and where diag(·) denotes the diagonal matrix whose diagonal elements are "·".

[0073] We can rewrite (7) as:

[0074]

[0075] where I is a five-dimensional identity matrix.

[0076] The measurement model of the random false data injection attack is described as:

[0077]

[0078] where y i,h (i = 1, 2,..., 5) is the actual measurement value generated by the ith node at the hth time after suffering from the false data injection attack.

[0079] Let ξ h = col{ξ 1,h , ξ 2,h ,..., ξ 5,h} satisfy ​​false data, is a positive scalar, is ξ h transpose.

[0080] Bernoulli distributed random variables γ i,h (i = 1, 2,..., 5) have the following probability distribution:

[0081]

[0082] where, is the attack probability of the ith node at the hth time.

[0083] Let y h = col{y 1,h , y 2,h ,..., y 5,h}, Γ h = diag{γ 1,h , γ 2,h ,..., γ 5,h} and Therefore, (9) can be transformed into:

[0084]

[0085] Step two, the safety Tobit filter is designed for the three-wheel Ackerman steering model established in step one, and the state estimation of the three-wheel Ackerman steering model is realized through the designed safety Tobit filter equation.

[0086] In this step, the following definitions are introduced for the convenience of subsequent theoretical derivation:

[0087]

[0088]

[0089] where, f(x h ) is a nonlinear function based on the state of the three-wheel Ackerman steering model, and g(x h ) is a nonlinear function based on the measurement of the three-wheel Ackerman steering model.

[0090] Based on the measurable information, the following safety Tobit filter is designed:

[0091]

[0092] In the formula, is one-step prediction of the state of the three-wheel Ackerman steering model at the hth time, is the filtering form of the nonlinear function based on the state of the three-wheel Ackerman steering model at the hth time, is the filtering of the state of the three-wheel Ackermann steering model at the h-th time instant, is the filtering of the h+1-th time instant, K h+1 is the gain matrix of the h+1-th time instant, y h+1 is the actual measurement value generated after suffering from false data injection attack at the h+1-th time instant, is the un-censored probability of the i-th node at the h+1-th time instant, is the one-step prediction form of the non-linear function corresponding to the measurement output based on the three-wheel Ackermann steering model at the h-th time instant, where φ(·) is the probability density function of the standard normal distribution, is the i-th element of is the measurement noise covariance matrix R h+1 of the h+1-th time instant, denotes the transpose of

[0093] Step three, calculating the upper bound of the prediction error covariance matrix of the three-wheel Ackermann steering model at the h-th time instant

[0094]

[0095] In this step, the upper bound of the prediction error covariance matrix of the three-wheel Ackermann steering model at the h-th time instant is calculated as follows:

[0096]

[0097] wherein, is the non-linear function f(x h ) at the h-th time instant corresponding to the state of the three-wheel Ackermann steering model based on the filtering at the h-th time instant, is the upper bound of the filtering error covariance matrix at the h-th time instant, and is the known error matrix obtained by Taylor formula based on f(x h ), and respectively represent and the transpose of D h , ρ 1,h represents a known time-varying coefficient and satisfies and respectively represent and the inverse of ρ 1,h .​

[0098] Step 4: Utilize the results obtained in Step 3 Calculate the gain matrix K of the established three-wheel Ackerman steering model at time h+1. h+1 .

[0099] In this step, the gain matrix K of the three-wheel Ackerman steering model at time h+1 is... h+1 The calculation formula is as follows:

[0100]

[0101] in:

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] In the formula, Let ρ be the upper bound of the prediction error covariance matrix at time h. 2,h+1 It is to satisfy The time-varying positive scalar, The nonlinear function g(x) at time h+1 corresponding to the measurement output based on the three-wheel Ackermann steering model. h+1 )exist Partial derivative at point, as well as Based on g(x) h+1 The known error matrix ε is obtained through Taylor's formula. i,h+1 (i = 1, 2, ..., 5) are all weighting coefficients. Let represent the attack probability of the i-th sensor node at time h+1. Represents the intermediate parameter matrix. as well as It is to satisfy positive constants, x h+1 Let represent the state of the three-wheel Ackerman steering model at time h+1, ‖·‖ represent the Euclidean norm, tr{·} represent the trace of the matrix, and "°" represent the Hadamard product between matrices. as well as Representing respectively to as well as To perform a squaring operation as well as respectively represent the inverse of ρ 2,h+1 , ε 1,h+1 , ε 2,h+1 , ε 3,h+1 , ε 4,h+1 and ε 5,h+1 . and respectively represent the transpose of and .

[0108] Step five, using the K h+1 calculated in step four, substitute it into step two to obtain the filtering Then, determine whether h+1 can reach the total filtering time Y, if h+1 < Y is satisfied, the next step is executed, if h+1 = Y is satisfied, the state estimation of the three-round Akman steering model with false data injection attack and missing measurement is stopped.

[0109] Step six, using the K h+1 calculated in step four, calculate the upper bound of the filtering error covariance matrix of the three-round Akman steering model at the h+1 moment Set h = h+1, execute step two until h+1 = Y is satisfied.

[0110] In this step, the expression of the upper bound of the filtering error covariance matrix at the h+1 moment is as follows:

[0111]

[0112] Wherein:

[0113]

[0114]

[0115]

[0116]

[0117] In the formula, P is the upper bound of the filtering error covariance matrix at the h+1 moment, represents the transpose of K h+1 .

[0118] In the present application, the theory described in step three, step four and step five is as follows:

[0119] First, the optimal upper bound of the filtering error covariance matrix is calculated so that wherein is the filtering error covariance matrix at the h+1 moment, is the filtering error at the h+1 moment, is the expectation of “·”, is the transpose of Since the filtering error covariance matrix has an uncertain term, the trace of the upper bound of the filtering error covariance matrix is optimized, and the gain matrix K h+1 at the h+1 moment can be further calculated.

[0120] Embodiment:

[0121] This embodiment takes a three-round Ackerman steering model with false data injection attacks and missing measurements as an example, and simulates as follows by using the method described in the application.

[0122] The error matrix obtained based on the Taylor formula is as follows:

[0123]

[0124]

[0125]

[0126]

[0127] The missing threshold vector is:

[0128]

[0129] The process noise covariance matrix and the measurement noise covariance matrix are:

[0130]

[0131] The time-varying matrix D h is known:

[0132]

[0133] The system-related initial values are:

[0134]

[0135]

[0136] In the formula, and respectively represent the mean of the model state initial value and the initial value of the filtering, and P0 and respectively represent the variance matrix of the initial value and the initial value of the upper bound of the filtering error covariance matrix.

[0137] Other parameters are selected as: weight coefficients are respectively 1,h+1 = 0.004, ε 2,h+1 = 0.7, ε 3,h+1 = 1.89, ε 4,h+1 = 1, ε 5,h+1 = 0.1, are respectively selected as and The sampling interval Δs = 1, the distance from the front wheel to the rear axle of the three-wheeled vehicle E = 5, the beacon position x b = 2 and y b = 5 measured by the sensor installed in the vehicle, the upper bound of the false data The attack probability of the first node at the h+1 time The attack probability of the second node at the h+1 time The attack probability of the third node at the h+1 time The attack probability of the fourth node at the h+1 time The attack probability of the fifth node at the h+1 time

[0138] The proportion of the filter error reduction is defined as: When there are both missing measurements and false data injection attacks, ∑MSE1 represents the sum of all mean square filter errors of the extended Kalman filter method (scenario II) at time h = 1 to h = 200, and ∑MSE represents the sum of all mean square filter errors of the safe Tobit filter method (scenario I) at time h = 1 to h = 200.

[0139] Effect of the safe Tobit filter:

[0140] Figures 2-6 The trajectories of the actual value and the filtered value of the state of the three-wheeled Ackerman steering model with false data injection attacks are given, from Figures 2-6 It can be concluded that for the three-wheeled Ackerman steering model with false data injection attacks and missing measurements, the safe Tobit filter mentioned in the application can effectively estimate the state of the three-wheeled Ackerman steering model.

[0141] Figure 7 The relationship diagram of the filter mean square error MSE of the state x h of the three-wheeled Ackerman steering model and the trace of the upper bound of the filter error covariance matrix is given, and it can be seen that the mean square error MSE is always lower than the trace of the upper bound, thus further verifying the effectiveness of the safe Tobit filtering method.

[0142] When the measurement output is affected by both missing measurements and false data injection attacks,Figure 8 MSE relationship contrast chart of situation I and situation II is given by Figure 8 It can be seen that the overall MSE of situation I is lower than that of situation II, because the missing measurement is properly handled in situation I, while it is not handled in situation II. From the definition of the proportion of the reduction of filtering error, it can be concluded that the filtering error of situation I is reduced by about 40% (i.e. FD=40%) compared to that of situation II, thus it can be illustrated that the feasibility of the safe Tobit filtering method of the present application.

Claims

1. A safe Tobit filtering method based on three-wheel Ackerman steering model, characterized in that The method comprises the following steps: Step one, based on the five-dimensional state variables composed of vehicle coordinates, vehicle path angle deviation, linear velocity and steering angle, a three-wheel Ackerman steering model with false data injection attack and missing measurement is established, and the three-wheel Ackerman steering model with false data injection attack and missing measurement is as follows: In the formula, x h =[x h y h η h κ h ζ h ] T T represents the transpose of the matrix; sin(·), cos(·), and tan(·) represent the sine, cosine, and tangent functions of "·", respectively; x h y h η h κ h and ζ h Let x represent the original coordinates, path angle deviation, linear velocity, and steering angle of the vehicle at time h in the three-wheeled Ackerman steering model; E represents the distance from the front wheel to the rear axle of the three-wheeled vehicle; Δs is the sampling interval; and x is the distance from the front wheel to the rear axle. b and y b This represents the position of the beacon measured by the sensors installed inside the vehicle; ω h and v h These represent values ​​with zero mean and covariance matrix Q at time h. h >0 and R h Process noise and measurement noise > 0, D h It is a known five-dimensional time-varying matrix; It is the uncensored measurement output with 5 nodes at time h; It is the censored output vector with 5 nodes at time h, Θ h =diag{θ 1,h ,θ 2,h ,...,θ 5,h }, where diag(·) represents a diagonal matrix whose diagonal elements are "·", and θ i,h It is a Bernoulli random variable used to determine whether the i-th node has been censored at time h. Represents the censoring threshold vector, where I is a five-dimensional identity matrix; y h The actual measurement value ξ is generated after a false data injection attack occurs at time h. h It meets the conditions False data, For ξ h transpose, It is a spurious upper bound greater than 0, Γ h =diag{γ 1,h ,γ 2,h ,...,γ 5,h }, γ i,h It is a Bernoulli random variable used to determine whether an attacker is attacking a sensor node; i = 1, 2, ..., 5; Step two, the three-wheel Ackerman steering model established in step one is subjected to security Tobit filter design, and state estimation of the three-wheel Ackerman steering model is realized through the designed security Tobit filter, and the specific structure of the security Tobit filter is as follows: wherein is a one-step prediction of the state of the three-wheeled Ackerman steering model at the h-th time instant, is a filtered form of a nonlinear function based on the state of the three-wheeled Ackerman steering model at the h-th time instant, is a filter of the state of the three-wheeled Ackerman steering model at the h-th time instant, is a filter at the h+1-th time instant, K h+1 is a gain matrix at the h+1-th time instant, y h+1 is an actual measurement value resulting from a false data injection attack at the h+1-th time instant, is a non-censored probability of the i-th node at the h+1-th time instant, is a one-step prediction form of a nonlinear function based on the measurement output of the three-wheeled Ackerman steering model at the h-th time instant, where φ(·) is a probability density function of a standard normal distribution, is the i-th element of is a measurement noise covariance matrix R h+1 at the h+1-th time instant, denotes the transpose of ;​ Step three, calculating the upper bound of the prediction error covariance matrix of the three-wheel Ackerman steering model at the hth moment the upper bound of the prediction error covariance matrix of the three-wheel Ackerman steering model at the hth moment The expression is: wherein is a nonlinear function of the state corresponding to the h-th time instant based on the three-wheel Ackerman steering model, h is the partial derivative of the filter at the h-th time instant, is an upper bound of the filter error covariance matrix at the h-th time instant, and is a known error matrix based on f(x h ) by Taylor's formula, and represent the transpose of and D h , respectively, and p 1,h represents a known time-varying coefficient and satisfies and represent the inverse of and p 1,h , respectively; Step four, using the result from step three The gain matrix K of the three-wheel Ackerman steering model at the h+1 time is calculated h+1 The expression of the gain matrix K of the three-wheel Ackerman steering model at the h+1 time is: h+1 The expression of the gain matrix K of the three-wheel Ackerman steering model at the h+1 time is: Wherein: q 1,h+1 = ε 1,h+1 + ε 3,h+1 , In the formula, Let ρ be the upper bound of the prediction error covariance matrix at time h. 2,h+1 It is to satisfy The time-varying positive scalar, The nonlinear function g(x) at time h+1 corresponding to the measurement output based on the three-wheel Ackermann steering model. h+1 )exist Partial derivative at point, as well as Based on g(x) h+1 The known error matrix εi is obtained through Taylor's formula. ,h+1 All are weighting coefficients. Let represent the attack probability of the i-th sensor node at time h+1. Represents the intermediate parameter matrix. as well as It is to satisfy positive constants, x h+1 Let represent the state of the three-wheel Ackerman steering model at time h+1, ‖·‖ represent the Euclidean norm, and tr{·} represent the trace of the matrix. Represents the Hadamard product between matrices. as well as Representing respectively to as well as To perform a squaring operation as well as Represent ρ 2,h+1 ε 1,h+1 ε 2,h+1 ε 3,h+1 ε 4,h+1 and ε 5,h+1 The reverse, as well as Represent as well as Transpose of; Step five, using the K calculated in step four h+1 Substitute it into step two to obtain the h+1 time filtering Then, it is determined whether h+1 can reach the total filtering time Y. If h+1 < Y is satisfied, step six is executed. If h+1 = Y is satisfied, the state estimation of the three-round Ackerman steering model with both the false data injection attack and the missing measurement is stopped. Step six, calculate K by K = P H (H P H + R) -1 h+1 , calculate the upper bound of the filtering error covariance matrix of the three-wheel Ackerman steering model at the h+1 time Set h = h + 1, execute step two until h + 1 = Y, the upper bound of the filtering error covariance matrix of the three-wheel Ackerman steering model at the h+1 time The expression of the upper bound of the filtering error covariance matrix of the three-wheel Ackerman steering model at the h+1 time is: Wherein: q 1,h+1 = ε 1,h+1 + ε 3,h+1 , wherein is an upper bound of the filtering error covariance matrix at time instance h + 1, represents the transpose of K h+1 .

2. The safe Tobit filtering method based on three-wheel Ackerman steering model according to claim 1, characterized in that In step one, θ i,h satisfies Prob represents the probability value of the event occurrence, Ψ(·) is the distribution function of the standard normal distribution, is the one-step prediction of the state of the three-wheel Ackerman steering model at the h-1 moment, is the i-th element of is the i-th element of is the one-step prediction form of the nonlinear function corresponding to the measurement output based on the three-wheel Ackerman steering model at the h-1 moment, τ i is the i-th element of is the i-th element of is the measurement noise covariance matrix R h is the (i, i) element of 3. The safe Tobit filtering method based on three-wheel Ackerman steering model according to claim 1, characterized in that In step one, γ i,h satisfies is the attack probability of the ith node at the hth time.

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