Automatic driving safety state estimation method and system based on statistical similarity

Abstract

The invention discloses an automatic driving safety state estimation method and system based on statistical similarity, and the method comprises the steps: firstly constructing a sensor network for sensing the two-dimensional position information and speed information of a moving target: building a system state equation and an observation equation based on the dynamic characteristics of a target vehicle; constructing a local optimization objective function on each distributed node, deducing a local posteriori mean value and covariance update formula, and realizing high-precision state estimation of a two-dimensional target; an alternating direction multiplier method is adopted as a distributed information processing strategy, consistency constraint conditions are introduced, estimation result fusion and global state consistency estimation between nodes are achieved, and vehicle safety state estimation is completed. According to the method, high-precision state estimation and fusion of the two-dimensional target can be realized in a complex environment of non-Gaussian noise and hostile attack, the state estimation precision and the system robustness of the automatic driving vehicle are improved, and the method has a relatively high engineering application value.

Description

Technical Field

[0001] This invention belongs to the technical field of state estimation, and particularly relates to the field of intelligent connected vehicle perception technology. It mainly relates to an autonomous driving safety state estimation method and system based on statistical similarity. Background Technology

[0002] In autonomous driving systems, large-scale sensor networks and miniature intelligent sensor arrays play a crucial role in key tasks such as two-dimensional target trajectory tracking, environmental perception, and onboard signal processing. Distributed estimation technology, by integrating data from multiple sensors such as onboard radar and lidar, enables accurate inference of the state of surrounding targets, and is a core technology for ensuring the safety of autonomous vehicles, achieving high-precision path planning, and collision prevention. Compared to centralized processing methods, distributed estimation can effectively reduce the bandwidth consumption of vehicle network communication, improve the system's robustness to single sensor failures or communication link interruptions, and adapt to the dynamically changing network topology of vehicles and sensor nodes, which is particularly critical for high-speed autonomous driving environments. However, compared to traditional network control systems, large-scale sensor networks are more vulnerable to various security threats and attacks due to their large number of devices and complex structure. Among them, spoofing attacks can introduce non-Gaussian heavy-tailed noise environments, severely damaging the statistical characteristics of observation data, thereby significantly reducing the accuracy of traditional estimation algorithms, and even causing the estimation process to diverge, thus threatening the safe driving and decision-making reliability of vehicles.

[0003] In recent years, research on distributed estimation of large-scale sensor networks under cyberattacks has received widespread attention. Existing studies have proposed a distributed filtering method based on the Cauchy kernel-based maximum correntropy (MCC) criterion [Song H, Ding D, Dong H, et al. Distributed filtering based on Cauchy-kernel-based maximum correntropy subject to randomly occurring cyber-attacks[J]. Automatica, 2022, 135: 110004.]. This method uses the maximum entropy criterion to replace the traditional minimum mean square error criterion, improving the standard Kalman filter and further extending it to distributed system architectures. For the state estimation problem of nonlinear systems, a distributed estimation algorithm based on weighted MCC has been proposed [Song H, Ding D, Dong H, et al. Distributed maximum correntropyfiltering for stochastic nonlinear systems under deception attacks[J]. IEEE Transactions on Cybernetics, 2020, 52(5): 3733-3744.]. This method performs weighted modeling on the basis of the original MCC framework and, combined with fixed-point iterative update rules, derives the iterative update formula for the posterior distribution of the state, thereby improving the system's ability to resist complex factors such as deception attacks, non-Gaussian noise interference, and model nonlinearity to a certain extent.

[0004] Nevertheless, in real-world autonomous driving scenarios, cyberattacks are often dynamic and diverse, potentially occurring asynchronously across different times and state components, with significant variations in attack intensity and impact. In such complex environments, existing methods based on the maximum entropy criterion struggle to achieve optimal estimation accuracy in Gaussian or mixed-interference environments and lack adaptive handling capabilities for multiple interference modes. Therefore, a distributed safety state estimation method that performs well in both Gaussian noise and non-Gaussian attack environments is urgently needed to ensure the safe and efficient operation of autonomous vehicles on complex roads and in harsh environments, and to improve the accuracy and reliability of two-dimensional target state estimation. Summary of the Invention

[0005] This invention addresses the problems existing in current technologies by providing a method and system for estimating the safety state of autonomous driving based on statistical similarity. First, a sensor network is constructed to perceive the two-dimensional position and velocity information of moving targets. Based on the dynamic characteristics of the target vehicle, system state equations and observation equations are established. Local optimization objective functions are constructed on each distributed node, and local posterior mean and covariance update formulas are derived to achieve high-precision state estimation of the two-dimensional target. The alternating direction multiplier method is used as a distributed information processing strategy, and consistency constraints are introduced to achieve fusion of estimation results among nodes and global state consistency estimation, thus completing the state estimation for vehicle safety. This invention's method can achieve high-precision state estimation and fusion of two-dimensional targets in complex environments with non-Gaussian noise and malicious attacks, improving the state estimation accuracy and system robustness of autonomous vehicles, and has high engineering application value.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is: an autonomous driving safety state estimation method based on statistical similarity, comprising the following steps:

[0007] S1. Constructing a sensor network: The sensor network consists of multiple sensor nodes and has a specific topology. Each node in the sensor network is used to sense the two-dimensional position and velocity information of the moving target and acquire observation data.

[0008] S2. Establishing System State Equations and Node Observation Equations: The system state equations, based on the dynamic characteristics of the target vehicle, describe the vehicle's state evolution process over continuous time. The observation equations, based on sensor characteristics, establish a mapping relationship between environmental information collected by sensors and vehicle state variables. Through the joint construction of the system state equations and node observation equations, a unified state-space model is provided for subsequent safety state estimation.

[0009] S3. Linearization: The system state equation established in step S2 is discretized and approximated using first-order difference, and the system state equation and nodal observation equation established in step S2 are linearized using first-order Taylor expansion.

[0010] S4. Establish the optimization objective function: Based on multi-dimensional weighted summation, establish a metric function to measure the overall similarity of the system, and use this as the optimization objective to construct an optimization objective function for system security state estimation;

[0011] S5. Solve the objective function to obtain the local state estimate of the target vehicle: By proposing assumptions, simplify the objective function, optimize the cost function, solve for the mean and covariance matrix of the posterior state distribution, and obtain the local state estimate.

[0012] S6. Obtaining Global State Estimation Results: The alternating direction multiplier method is introduced as a distributed information processing strategy to ensure the convergence of global state estimation results and realize the safe state estimation of the vehicle.

[0013] As an improvement of the present invention, the sensor nodes in step S1 include at least a lidar node, a millimeter-wave radar node, a camera node, and an inertial measurement unit node.

[0014] As an improvement of the present invention, in step S2, the system state equation is specifically as follows:

[0015]

[0016] in, For the overall quality of the vehicle, , These represent the vehicle's speed on the two-dimensional horizontal and vertical axes, respectively. , These are the components of the force on the vehicle's front wheels along the horizontal and vertical axes, respectively. , These are the components of the force on the vehicle's rear wheel at the corresponding coordinates. The yaw rate of the vehicle;

[0017] The observation equation is divided into two cases based on the type of node sensor. When the node sensor is a lidar (LiDAR), the observation equation is as follows:

[0018]

[0019] in, and These represent the vehicle's position on the x-coordinate and y-coordinate in the Earth coordinate system, respectively. For the first The output vector of each sensor node;

[0020] When the sensor at this node is a millimeter-wave radar, the specific observation equation is as follows:

[0021] .

[0022] Due to the vehicle's yaw angle and yaw rate In-between satisfaction relationship Let the state vector be The control input is The state-space model composed of the system state equations and nodal measurement equations described above can be expressed in the following form:

[0023]

[0024] in, In order to be in The state vector at time t, To control the input vector, This represents a function that describes the state transition; For the first The output vector of each sensor node For the first The observation function of each sensor node.

[0025] As another improvement of the present invention, the system state equation and nodal observation equation after linearization in step S3 are specifically as follows:

[0026]

[0027] in, In order to be in The state vector at time t, Given the control input vector, Given the system transition matrix, Given the control input matrix, For those with covariance The process noise vector; Indicates the first The actual signal received by each sensor node Given the measurement transition matrix, For a matrix with covariance Measurement noise vector, random variable This indicates that the attacker injected false data. and Two random variables are used to simulate randomly occurring network attacks;

[0028] Under normal circumstances, Modeled as a random vector following a zero-mean Gaussian distribution; random variable and These are independent Bernoulli variables, and their probabilities are as follows:

[0029]

[0030] in, and It is an unknown constant.

[0031] As another improvement of the present invention, the objective optimization function in step S4 is specifically as follows:

[0032]

[0033] in, Let the state vector follow the distribution. The designed statistical similarity measure function, For the state vector in Prior estimates of time, and The nominal prediction error covariance matrix is ​​labeled separately. and the nominal measurement noise covariance matrix of each node The square root matrix.

[0034] As another improvement of the present invention, the assumptions in step S5 include (1) the posterior probability density function (2) The original cost function is approximated as a Gaussian distribution;

[0035] Simplified cost function Specifically:

[0036]

[0037] in, and It is a state vector The mean and covariance matrix of the posterior distribution. and Representing the system state dimension and nodes respectively The measurement dimensions and This represents the similarity function in statistical similarity measures. and For matrix and The The row vector of a row. and For auxiliary matrix;

[0038] The mean vector of the posterior distribution is obtained by solving:

[0039]

[0040] in, To correct the process noise covariance matrix, Correct the measurement noise covariance matrix for each node;

[0041] Optimal solution of the posterior covariance matrix for:

[0042] .

[0043] As a further improvement of the present invention, step S6 specifically includes the following steps:

[0044] S61: Define the intermediate variables for each node:

[0045] ;

[0046] S62: The alternating direction multiplier method is adopted as a distributed information processing strategy, and a consistency constraint is introduced. The specific optimization objective based on consistency is:

[0047]

[0048] S63: Obtain the closed-form solution of the intermediate variables at each node by minimizing the Lagrange function. In this context, the intermediate variables of each node are obtained solely through local information. and neighbor node information Update to achieve consistency;

[0049] S64: Using intermediate variables after consensus has been reached Instead of a global information set, use a state vector. The posterior distribution is iteratively updated until the global state estimation result converges, thus achieving the safe state estimation of the vehicle.

[0050] As a further improvement of the present invention, in step S63, a Lagrange multiplier is introduced. and By incorporating the constraints into the objective function, the constrained optimization problem is reformulated as an unconstrained optimization problem. Based on the optimization objective function, the consistent iterative equation is solved:

[0051]

[0052] in, Indicates the number of iterations. Represents a node The number of neighbors, the aggregation term of the Lagrange multipliers is defined as Through iteration Each node relies solely on its local information. and information from neighboring nodes The average value of the intermediate variables can then be calculated. .

[0053] To achieve the above objectives, the present invention also adopts the following technical solution: an autonomous driving safety state estimation system based on statistical similarity, comprising at least an information acquisition module, a problem construction module, an estimation value calculation module, and a distributed information processing module.

[0054] The information acquisition module acquires the two-dimensional position and velocity information of the target sensed by the sensors at each node.

[0055] The problem construction module establishes the system state equation and observation equation based on the dynamic characteristics of the target, and constructs an optimization objective function for solving the posterior distribution of the state vector for state estimation by combining multiple statistical similarity measurement functions.

[0056] The solution estimation module: Based on the optimization method, under the given assumptions, simplifies the constructed optimization objective function, derives and solves the iterative update equations for the mean and covariance matrix of the posterior distribution of the state vector;

[0057] The distributed information processing module employs the alternating direction multiplier method for distributed information processing. Under the condition that each local node communicates only with its neighboring nodes, a consistency constraint is introduced to drive the estimation results of all global nodes to remain consistent, thereby achieving global state estimation.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] (1) This invention proposes a novel method and system for estimating the safety status of autonomous vehicles based on multiple statistical similarity measures. It improves and innovates the traditional similarity measurement method. The proposed measure extends the overall vector-level calculation to the method of summing each dimension. Under this framework, the posterior estimation update formula of the state vector based on fixed-point iteration is further derived, which significantly improves the stability and accuracy of the estimation algorithm under non-Gaussian noise and mixed attack conditions.

[0060] (2) In an autonomous driving environment that integrates multi-source sensor information and involves complex traffic scenarios and hybrid network attacks, the system of the present invention can achieve high-precision and robust joint estimation of the dynamic state inside the vehicle, thereby significantly enhancing the safety perception and intelligent decision-making capabilities of the autonomous driving system under conditions of false information injection attacks and denial-of-service attacks. Attached Figure Description

[0061] Figure 1 This is a flowchart of the steps of the method of the present invention;

[0062] Figure 2 This is a schematic diagram of the sensor network topology constructed in step S1 of the method of the present invention;

[0063] Figure 3 This is a schematic diagram of the kinematic model of the vehicle in step S2 of the method of the present invention;

[0064] Figure 4 This is a schematic diagram illustrating the timeline of a successful denial-of-service attack during the testing of this invention.

[0065] Figure 5 This is a time-sharing diagram illustrating the successful execution of a deception attack during the testing of this invention.

[0066] Figure 6 This is a schematic diagram showing the actual two-dimensional position information and algorithm estimation values ​​of the system during the test of this invention;

[0067] Figure 7 This is a schematic diagram of the system estimation error curve during the test of this invention. Detailed Implementation

[0068] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the present invention.

[0069] Example 1

[0070] Methods for estimating the safety state of autonomous vehicles based on multiple statistical similarity measures, such as Figure 1 As shown, the specific steps include the following:

[0071] Step S1: Construct a sensor network consisting of multiple sensor nodes with a specific topology;

[0072] Multiple sensor nodes are deployed on an autonomous vehicle, including at least LiDAR nodes, millimeter-wave radar nodes, camera nodes, and inertial measurement unit nodes. A data transmission topology between the sensor nodes is constructed based on their physical installation locations, data sampling frequencies, and communication bandwidth requirements. For example... Figure 2 As shown, each node is interconnected with neighboring nodes via wireless communication, forming a sensor network with a specific topology. Subsequently, each node independently collects sensing status information within its monitoring range based on its own location, specifically the two-dimensional location information of the target.

[0073] In a sensor network, nodes perceive the two-dimensional position and velocity information of moving targets. The position and velocity state variables involved differ in numerical scale and propagation characteristics. Therefore, when these measurement variables in different dimensions are subjected to mixed attacks such as denial-of-service attacks and spoofing, their impact varies, resulting in each dimension being exposed to varying degrees of non-Gaussian noise. Nodes can collaboratively complete initial data synchronization and exchange according to network protocols, providing the initial observational data foundation for subsequent state estimation and consistency processing.

[0074] Step S2: Based on the sensor characteristics and the dynamic characteristics of the target vehicle, establish the system state equation and the observation equation of each node suitable for the autonomous driving scenario;

[0075] Based on Newton's second law and combined with force equilibrium analysis, such as Figure 3 As shown, a dynamic model of the autonomous vehicle is constructed, and the corresponding system state equations are derived:

[0076]

[0077] in, For the overall quality of the vehicle, , These represent the vehicle's speed on the two-dimensional horizontal and vertical axes, respectively. , These are the components of the force on the vehicle's front wheels along the horizontal and vertical axes, respectively. , These are the components of the force on the vehicle's rear wheel at the corresponding coordinates. Let be the yaw rate of the vehicle.

[0078] Since the vehicle only moves in a plane, we can obtain the following by combining the torque balance equation:

[0079]

[0080] in, and These are the distances from the vehicle's center of gravity to the centers of the front and rear wheels, respectively.

[0081] Based on the vehicle's yaw angle, a coordinate transformation relationship between the vehicle's body coordinate system and the Earth coordinate system can be established:

[0082]

[0083] in, and These represent the vehicle's position on the x-coordinate and y-coordinate in the Earth coordinate system, respectively. This refers to the vehicle's yaw angle.

[0084] The nodal observation equation is divided into two cases based on the type of nodal sensor. In autonomous driving scenarios, when LiDAR is used as the sensor, its measurement model directly outputs the planar position coordinates of the target vehicle in the environmental coordinate system. Therefore, the specific observation equation is as follows:

[0085]

[0086] in, and These represent the vehicle's position on the x-coordinate and y-coordinate in the Earth coordinate system, respectively. For the first The output vector of each sensor node.

[0087] In autonomous driving scenarios, when millimeter-wave radar (Radar) is used as the sensor, its measurement model typically outputs the polar coordinates of the target vehicle relative to the driver vehicle, including radial distance, heading angle, and radial velocity. In this case, the system's measurement model is:

[0088]

[0089] Due to the vehicle's yaw angle and yaw rate In-between satisfaction relationship Let the state vector be The control input is Therefore, the state-space model composed of the system state equations and nodal measurement equations described above can be expressed in the following form:

[0090]

[0091] in, In order to be in The state vector at time t, To control the input vector, This represents a function that describes the state transition; For the first The output vector of each sensor node For the first The observation function of each sensor node.

[0092] Step S3: Discretize the system equations using first-order difference and linearize the constructed system state equations and observation equations using first-order Taylor expansion.

[0093] The state-space model in S2 is approximated by discretization using first-order difference:

[0094]

[0095] in, For discrete-time variables, The sampling period is for The state vector at time t, for The control input vector at time t, This is the measurement vector.

[0096] To better describe the uncertainties faced by autonomous vehicles during actual driving, as well as the noise prevalent in various sensor measurements, process noise and measurement noise are introduced into the system state equation. The processed state-space model is shown below:

[0097]

[0098] in, For those with covariance The process noise vector, For a matrix with covariance The measurement noise vector.

[0099] Given that the system equations are nonlinear models, this invention employs an extended Kalman filter method based on first-order Taylor expansion to linearize them, thereby obtaining an approximate linear model that can be used for subsequent state estimation, as follows:

[0100]

[0101] in, Given the system transition matrix, Given the control input matrix, The measurement transition matrix is ​​known. The specific calculation form of the matrix in the approximate linear model is shown below:

[0102]

[0103] in, For the state vector in Prior estimates of time, For its in Posterior estimation at time step.

[0104] Due to potential security vulnerabilities in vehicle-mounted sensors, sensor measurements in practical engineering may be simultaneously subjected to a combination of multiple types of network attacks, primarily including False Data Injection (FDI) and Denial-of-Service (DoS) attacks. FDI attacks manifest as additional, typically non-Gaussian or specifically constructed, injection vectors on the observation channel. This invention uses random vectors... To model the injected signal, a random vector is used, which is a random perturbation following a specific distribution, to characterize the error signal injected by the attacker. DoS typically occurs when an attacker prevents legitimate measurements from reaching the receiver by blocking, losing packets, delaying, or forging messages, resulting in missing measurement information or its replacement with spoofed values. To characterize the availability and replacement of measurements, this invention uses Bernoulli variables. Modeling Each sensor at time The availability of measurements, using Bernoulli variables Modeling Each sensor at time Whether spurious value substitution occurred in the measurement. Therefore, based on the above analysis, the available information of the filter can be represented in the following form:

[0105]

[0106] in, Indicates the first The actual signal received by each sensor node, random variable This indicates that the attacker injected fake data. In general, It is modeled as a random vector following a zero-mean Gaussian distribution. Furthermore, two random variables are used to simulate randomly occurring network attacks. and These are independent Bernoulli variables, and their probabilities are as follows:

[0107]

[0108] in, and It is an unknown constant.

[0109] In summary, the system equations and measurement equations obtained after this step, after approximately linearization, are shown below:

[0110]

[0111] Step S4: Based on multi-dimensional weighted summation, establish a function to measure the overall similarity of the system, and use this as the optimization objective to construct an optimization objective function for system security state estimation;

[0112] Because hybrid attacks can be injected into sensor networks, the noise environment faced by the system often exhibits non-Gaussian, heavy-tailed distribution characteristics. In this context, traditional standard Kalman filters based on the minimum mean square error criterion may lead to a significant decrease in state estimation accuracy, or even the risk of filter divergence, when dealing with such interference. Furthermore, hybrid attack types are highly random and complex; their triggering on the time axis is uncertain, and they may exhibit asynchronicity and non-uniformity across different dimensions of the state vector, meaning that the timing and intensity of the attack may differ significantly across state components. To address these challenges, this invention proposes a method and system for estimating the safe state of autonomous driving based on statistical similarity. It constructs a safety state estimation objective function by improving existing statistical similarity metrics, and obtains more accurate autonomous driving safety state estimation results by optimizing and solving the objective function.

[0113] First, the overall statistical similarity measure is extended to a multi-dimensional statistical similarity measure that sums up along each dimension. This allows outliers in each dimension to be handled independently during the estimation process, as follows:

[0114]

[0115] in, The designed statistical similarity measure function, and Indicates two A dimensional random vector, and They are respectively and The Each part. To represent a similar function, the following conditions must be met: (1) exist It is continuously differentiable above; (2) (3) .

[0116] The core design of the proposed state estimation method is to find the optimal posterior probability density distribution by maximizing a cost function based on multiple statistical similarity. Therefore, the objective optimization function based on the aforementioned statistical similarity measure is constructed as follows:

[0117]

[0118] in, Let the state vector follow the distribution. and The nominal prediction error covariance matrix is ​​labeled separately. and the nominal measurement noise covariance matrix of each node The square root matrix, i.e.:

[0119]

[0120] Among them, the prior estimation of the state vector and the nominal prediction error covariance matrix It is given by the following formula:

[0121]

[0122] in, and They are respectively The posterior estimate and posterior covariance matrix at time t.

[0123] Step S5: Solve the objective function to obtain the local state estimate of the target vehicle;

[0124] First, substituting the specific form of the statistical similarity measurement function designed in S4 into the optimization objective function in S4, the simplified form is shown below:

[0125]

[0126] in, and Representing the system state dimension and nodes respectively The measurement dimensions and This represents the similarity function in statistical similarity measures. and For matrix and The The row vector of a row.

[0127] Next, by proposing appropriate assumptions, the objective function is reasonably simplified: since it is difficult to solve the constructed optimization problem, the posterior probability density function cannot be solved. The analytical solution is needed. To solve this problem, two reasonable assumptions are made to simplify the objective cost function.

[0128] Assumption 1: The posterior probability density function Approximately Gaussian distribution:

[0129]

[0130] in, and It is a state vector The mean and covariance matrix of the posterior distribution.

[0131] Assumption 2: Approximate the original cost function as its lower bound:

[0132] By applying the scaling principle of the original cost function using Chinsen's inequality, we can obtain its lower bound:

[0133]

[0134] Therefore, the simplified approximate cost function The format is as follows:

[0135]

[0136] Among them, auxiliary matrix and The calculation method is as follows:

[0137]

[0138] Next, we optimize the cost function and solve for the mean of the posterior distribution of the state.

[0139] Define two auxiliary matrices with diagonal weights:

[0140]

[0141] Based on the maximum point criterion, the Jacobian matrix of the cost function with respect to the mean vector is set to zero. The noise covariance matrix of the correction process and the noise covariance matrix of the corrected measurements at each node are given below:

[0142]

[0143] Therefore, the mean vector of the posterior distribution is obtained by solving:

[0144]

[0145] Next, we optimize the cost function and solve for the covariance matrix of the posterior distribution of the state.

[0146] Since the cost function is negative definite with respect to the Jacobian matrix of the covariance matrix, the approximate cost function... Compared to It is monotonically decreasing. Therefore, the optimal solution for the posterior covariance matrix is... To maximize the cost function, the appropriate value should be selected as follows: The lower bound of the probability density function. Since the covariance matrix of the posterior probability density function is the negative inverse of the Hessian matrix of the least squares cost function in the traditional maximum a posteriori estimation framework, a reasonable assumption is proposed, namely... Not less than the negative inverse of the Hessian matrix, that is:

[0147]

[0148] in, Let be the Hessian matrix of the cost function with respect to the mean vector.

[0149] Therefore, the optimal solution of the posterior covariance matrix for:

[0150]

[0151] Since the local state of a vehicle can be modeled as following a Gaussian distribution, the posterior mean of the Gaussian distribution is used as the estimate of the local state of the vehicle, as shown below:

[0152] .

[0153] Step S6: Introduce the alternating direction multiplier method as a distributed information processing strategy to ensure the convergence of the global state estimation results and achieve reliable estimation of the vehicle's internal state.

[0154] First, define the intermediate variables for each node:

[0155]

[0156] Next, a consistent optimization objective is constructed as follows:

[0157]

[0158] Introducing the Lagrange multiplier and By incorporating the constraints into the objective function, the constrained optimization problem is reformulated as an unconstrained optimization problem.

[0159] Based on the optimization objective function, solve for the consistency iterative equation:

[0160]

[0161] in, Indicates the number of iterations. Represents a node The number of neighbors, the aggregation term of the Lagrange multipliers is defined as Through iteration Each node relies solely on its local information. and information from neighboring nodes The average value of the intermediate variables can then be calculated. .

[0162] To improve communication efficiency, the algorithm can set a smaller number of iterations or terminate the algorithm early, sacrificing some convergence accuracy to achieve lower communication overhead.

[0163] Consensus intermediate variables Divided into two parts: Substituting these two parts into the iterative formula for the posterior mean and variance of the state vector, the specific form is as follows:

[0164]

[0165] Due to the optimal posterior mean vector and the optimal posterior covariance matrix Since they are mutually coupled, this invention uses a fixed-point iterative method to approximate the solution. and Set the maximum number of fixed-point iterations to 0. And set the fixed-point iteration stopping condition:

[0166]

[0167] in, This is the iteration threshold.

[0168] The algorithm terminates when the maximum number of iterations is reached or the iteration stopping condition is met, completing one update process in one time step.

[0169]

[0170] Thus, the target vehicle safety state estimate for the current time step is obtained and used as the initial input for the state update in the next time step.

[0171] Therefore, the posterior estimates of the vehicle's safety state obtained at each time step are arranged in chronological order to form a complete vehicle safety state estimation sequence, achieving continuous and dynamic estimation of the target vehicle's safety state throughout the entire driving process, i.e.:

[0172] .

[0173] Test case

[0174] In this test case, MATLAB R2021a is used to simulate and verify the method proposed in this invention. The estimation accuracy and robustness are evaluated by comparing the state estimate value estimated by the algorithm with the actual state value of the moving target.

[0175] In this test case, a sensor network consisting of 10 sensor nodes and 15 edges is used to sense the state of a moving target. Each subsystem has an equal probability of successfully sustaining a denial-of-service attack, set to... The probability of injection-based deception attacks varies depending on the node, as specifically set as follows:

[0176]

[0177] The injected deceptive signal is constructed in the following way:

[0178]

[0179] In addition, attack sequences in different regions and Generated independently by MATLAB R2021a software, its timing characteristics are as follows: Figure 4 and Figure 5 As shown. Among them, Figure 4 and Figure 5 These are discrete point distribution graphs representing the moments when an attack was successfully carried out. The horizontal axis represents the time series index, and the vertical axis represents the state of the attack event. Therefore, each discrete point in the graph corresponds to the moment when an attack was successfully carried out, used to characterize the distribution characteristics of attack behavior in the time dimension.

[0180] The target's true initial state is set to The corresponding estimation error variance is initialized as follows: The initial state estimate for each node is derived from a Gaussian distribution. Independently and randomly generated. Figure 6 The comparison between the estimated trajectory of the vehicle target and its actual trajectory is presented. As can be seen from the figure, the estimated trajectory can fit the actual trajectory well, indicating that the algorithm has good state estimation accuracy and stability in complex environments.

[0181] To evaluate the accuracy of state estimation, this test case uses the root mean square error (RMSE) as a performance metric, which is calculated as follows:

[0182]

[0183] in, and They represent the first Nodes in sub-Monte Carlo simulation The actual state and the estimated state, This represents the total number of Monte Carlo simulations.

[0184] Figure 7 The comparison results of existing algorithms and the estimation method proposed in this invention under the RMSE metric are presented. The blue curve represents the standard Kalman filter algorithm, while the red and green curves represent robust estimation algorithms that model the system state using the Student's t-distribution and a Gaussian-Student's t-mixture distribution, respectively, and combine them with variational Bayesian optimization methods to solve for the state estimates. The results show that the estimation method proposed in this invention converges faster in terms of RMSE, reaching the minimum error value at time 20 and maintaining the lowest level among the compared algorithms in subsequent time intervals. Therefore, the method proposed in this invention is superior.

[0185] The technical features in the embodiments of this invention can be combined arbitrarily according to actual needs. For the sake of brevity, the specification does not exhaustively describe all possible combinations, but as long as there is no conflict between the technical features, their combinations should be considered as covered by the content of this invention.

[0186] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A method for estimating the safety state of autonomous driving based on statistical similarity, characterized in that... Specifically, the steps include the following: S1. Constructing a sensor network: The sensor network consists of multiple sensor nodes and has a specific topology. Each node in the sensor network is used to sense the two-dimensional position and velocity information of the moving target and acquire observation data. S2. Establish system state equations and nodal observation equations: The system state equations, based on the dynamic characteristics of the target vehicle, describe the state evolution process of the vehicle over continuous time; the nodal observation equations, based on sensor characteristics, establish a mapping relationship between the sensor's environmental information and the vehicle's state variables; and a state-space model is constructed by combining the system state equations and nodal observation equations. S3. Linearization: The system state equation established in step S2 is discretized and approximated using first-order difference, and the system state equation and nodal observation equation established in step S2 are linearized using first-order Taylor expansion. S4. Establish the optimization objective function: Based on multi-dimensional weighted summation, establish a metric function to measure the overall similarity of the system, and use this as the optimization objective to construct an optimization objective function for system security state estimation; S5. Solve the objective function to obtain the local state estimate of the target vehicle: By proposing assumptions, simplify the objective function, optimize the cost function, solve for the mean and covariance matrix of the posterior state distribution, and obtain the local state estimate. S6. Obtaining Global State Estimation Results: The alternating direction multiplier method is introduced as a distributed information processing strategy to ensure the convergence of global state estimation results and realize the safe state estimation of the vehicle.

2. The method for estimating the safety status of autonomous driving based on statistical similarity as described in claim 1, characterized in that: The sensor nodes in step S1 include at least a lidar node, a millimeter-wave radar node, a camera node, and an inertial measurement unit node.

3. The autonomous driving safety state estimation method based on statistical similarity as described in claim 2, characterized in that: In step S2, the state-space model jointly constructed by the system state equation and the nodal measurement equation is specifically as follows: ； in, In order to be in The state vector at time t, To control the input vector, This represents a function that describes the state transition; For the first The output vector of each sensor node For the first The observation function of each sensor node.

4. The autonomous driving safety state estimation method based on statistical similarity as described in claim 3, characterized in that: In step S2, the system state equation is specifically as follows: ； in, For the overall quality of the vehicle, , These represent the vehicle's speed on the two-dimensional horizontal and vertical axes, respectively. , These are the components of the force on the vehicle's front wheels along the horizontal and vertical axes, respectively. , These are the components of the force on the vehicle's rear wheel at the corresponding coordinates. Let be the yaw rate of the vehicle; when the nodal sensor is a lidar, the nodal observation equation is specifically: ； in, and These represent the vehicle's position on the x-coordinate and y-coordinate in the Earth coordinate system, respectively. For the first The output vector of each sensor node; When the node sensor is a millimeter-wave radar, the node observation equation is specifically as follows: 。 5. The autonomous driving safety state estimation method based on statistical similarity as described in claim 4, characterized in that: The system state equations and nodal observation equations after linearization in step S3 are as follows: ； in, In order to be in The state vector at time t, Given the control input vector, Given the system transition matrix, Given the control input matrix, For those with covariance The process noise vector; Indicates the first The actual signal received by each sensor node Given the measurement transition matrix, For a matrix with covariance Measurement noise vector, random variable This indicates that the attacker injected false data. and To simulate random variables that may occur during a network attack; random variable and These are independent Bernoulli variables, and their probabilities are as follows: ； in, and It is an unknown constant.

6. The autonomous driving safety state estimation method based on statistical similarity as described in claim 5, characterized in that: The objective optimization function in step S4 is specifically: ； in, Let the state vector follow the distribution. For statistical similarity measurement functions, For the state vector in Prior estimates of time, and The nominal prediction error covariance matrix is ​​labeled separately. and the nominal measurement noise covariance matrix of each node The square root matrix.

7. The autonomous driving safety state estimation method based on statistical similarity as described in claim 6, characterized in that: The assumptions in step S5 include (1) the posterior probability density function (2) The original cost function is approximated as a Gaussian distribution; Simplified cost function Specifically: ； in, and It is a state vector The mean and covariance matrix of the posterior distribution. and Representing the system state dimension and nodes respectively The measurement dimensions and This represents the similarity function in statistical similarity measures. and For matrix and The The row vector of a row. and For auxiliary matrix; The mean vector of the posterior distribution is obtained by solving: ； in, To correct the process noise covariance matrix, Correct the measurement noise covariance matrix for each node; Optimal solution of the posterior covariance matrix for: 。 8. The autonomous driving safety state estimation method based on statistical similarity as described in claim 7, characterized in that: Step S6 specifically includes the following steps: S61: Define the intermediate variables for each node: ； S62: The alternating direction multiplier method is adopted as a distributed information processing strategy, and a consistency constraint is introduced. The specific optimization objective based on consistency is: ； S63: Obtain the closed-form solution of the intermediate variables at each node by minimizing the Lagrange function. In this context, the intermediate variables of each node are obtained solely through local information. and neighbor node information Update to achieve consistency; S64: Using intermediate variables after consensus has been reached Instead of a global information set, use a state vector. The posterior distribution is iteratively updated until the global state estimation result converges, thus achieving the safe state estimation of the vehicle.

9. The autonomous driving safety state estimation method based on statistical similarity as described in claim 8, characterized in that: In step S63, the Lagrange multiplier is introduced. and By incorporating the constraints into the objective function, the constrained optimization problem is reformulated as an unconstrained optimization problem. Based on the optimization objective function, the consistent iterative equation is solved: ； in, Indicates the number of iterations. Represents a node The number of neighbors, the aggregation term of the Lagrange multipliers is defined as Through iteration Each node relies solely on its local information. and information from neighboring nodes The average value of the intermediate variables can then be calculated. .

10. An autonomous driving safety state estimation system based on statistical similarity, characterized in that: It includes at least an information acquisition module, a problem construction module, a solution estimation module, and a distributed information processing module. The information acquisition module acquires the two-dimensional position and velocity information of the target sensed by the sensors at each node. The problem construction module establishes the system state equation and observation equation based on the dynamic characteristics of the target, and constructs an optimization objective function for solving the posterior distribution of the state vector for state estimation by combining multiple statistical similarity measurement functions. The solution estimation module: Based on the optimization method, under the given assumptions, simplifies the constructed optimization objective function, derives and solves the iterative update equations for the mean and covariance matrix of the posterior distribution of the state vector; The distributed information processing module employs the alternating direction multiplier method for distributed information processing. Under the condition that each local node communicates only with its neighboring nodes, a consistency constraint is introduced to drive the estimation results of all global nodes to remain consistent, thereby achieving global state estimation.

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