Method for evaluating state estimation performance based on polling communication protocol under DoS attack

Abstract

The present application relates to the field of information physical system, specifically design a kind of DoS attack based on the evaluation method of state estimation performance of polling communication protocol.The existing system performance research is mainly for the remote state estimation of Markov model.Due to the state estimation when using communication protocol does not conform to Markov model, the existing attack strategy is not suitable for analyzing the state estimation under communication protocol, so there is the defect problem of the research on the evaluation method of remote state estimation performance based on communication protocol under DoS attack in information physical system, provide the state estimation performance evaluation method based on polling communication protocol under DoS attack, this method is based on the design of state estimator under polling communication protocol, according to the open loop and closed loop of actual system two structures, the optimal DoS attack scheduling scheme selected by attacker is analyzed and designed, to evaluate the state estimation performance loss based on polling communication protocol under different DoS attack scheme, provide ideas for scheduling optimization of actual defense strategy.

Description

Technical Field

[0001] This invention relates to the field of cyber-physical systems, specifically to a performance evaluation method for state estimation based on a polling communication protocol under DoS attacks. Background Technology

[0002] Modern industrial control systems are essentially cyber-physical systems. As a type of complex networked system integrating computing, networking, and the physical environment, they are widely present in various infrastructures such as transportation, power grids, and national defense. Therefore, any successful cyberattack can cause enormous damage to critical infrastructure or life and property, and even threaten national security.

[0003] State estimation for networked systems is an effective tool for accurately obtaining the real-time state of a system. It is a method that calculates the unknown state vector of a dynamic process using sensor measurements and state transition equations. However, due to the involvement of networks, information transmission inevitably encounters problems such as latency, packet loss, and limited communication bandwidth, which affect the estimation performance and stability of the system state estimator. Therefore, designing a suitable estimator to obtain accurate networked system states under these challenges is crucial.

[0004] In addition to factors such as limited sensor node resources and network bandwidth, the design of state estimation in cyber-physical systems also involves security issues. Various network attacks have a significant and destructive impact on state estimation in cyber-physical systems. The essence of security issues in state estimation lies in attack and defense. To design an effective defense strategy against attacks, it is essential to understand the consequences of the attacker's actions on state estimation. Malicious network attacks are usually man-made, and the attacker will consider the optimal attack strategy with existing resources to maximize the attack's effectiveness.

[0005] Optimal Denial-of-Service (DoS) attack scheduling refers to the attack strategy employed by a DoS attacker to minimize system performance within a given timeframe. Understanding and mastering the optimal strategies of DoS attackers is crucial for designing effective and targeted defenses, prompting many scholars to explore and design optimal DoS attack strategies.

[0006] To prevent information conflicts and reduce communication burden in large wireless sensor networks, introducing polling communication protocol rules to adjust the transmission order of information from the sensor network to the remote state estimator is a common method. Existing literature considers smart sensor scenarios using Markov chain models, assuming that sensors have local computing capabilities and transmit local state estimates to the remote estimator. However, in complex scenarios, although smart sensors are still used, limitations such as communication protocols prevent the complete transmission of local estimates to the remote estimator. In this case, sensors only measure the system state or transmit the sequences of innovations they have calculated to the remote estimator. In this situation, the filter of the remote estimator cannot always maintain a stable estimate, therefore the state estimation error covariance of the filter no longer remains stable, and the Markov decision process model no longer holds.

[0007] Existing research on system performance mainly focuses on given attack patterns, meaning most attack strategies target remote state estimation based on Markov models. Since state estimation using communication protocols does not conform to Markov models, existing attack strategies are unsuitable for analyzing state estimation under communication protocols. Therefore, methods for evaluating the performance of remote state estimation based on communication protocols under DoS attacks in cyber-physical systems are flawed and cannot effectively provide direction for scheduling and optimizing practical defense strategies. Summary of the Invention

[0008] The purpose of this invention is to address the problem that existing studies on system performance primarily focus on remote state estimation using Markov models. Since state estimation using communication protocols does not conform to Markov models, existing attack strategies are unsuitable for analyzing state estimation under communication protocols. Therefore, this invention addresses the shortcomings of existing methods for evaluating the performance of remote state estimation based on communication protocols under DoS attacks in cyber-physical systems. The invention provides a method for evaluating the performance of state estimation based on polling communication protocols under DoS attacks.

[0009] The technical solution of this application is:

[0010] A performance evaluation method for state estimation based on polling communication protocol under DoS attack: including the following steps:

[0011] S1: Construct a state estimation model for the unmanned system; the state estimation model for the unmanned system is derived from the kinematic model of the unmanned system; the kinematic model of the unmanned system is constructed based on the actual situation of the unmanned system.

[0012] S2: Based on the state estimation model obtained in S1, construct a remote state estimator, which is used to estimate the state of the unmanned system.

[0013] S3: Constructing the optimal DoS attack strategy against remote state estimators * According to the optimal DoS attack strategy γ * Simulate the performance degradation of the remote state estimator when a DoS attacker interferes with a communication network;

[0014] In S3, an optimal DoS attack strategy γ targeting the remote state estimator is constructed. * The specific process is as follows:

[0015] Step 1: Analyze the evolution of the state estimation error of the remote state estimator when the remote state estimator constructed by S2 performs state estimation on the unmanned system;

[0016] Step 2: Assume the attacker can only launch n attacks, where n is a positive integer. Construct M based on the evolution pattern of the state estimation error obtained in Step 1. γ One attack strategy γ; M γ It is a positive integer;

[0017] Step 3: Construct the performance index function J(γ) of the attack strategy γ, and calculate M based on the performance index function J(γ). γ The attack strategy γ is selected as the optimal DoS attack strategy γ based on its performance metrics. * .

[0018] Compared with the prior art, this application has the following advantages:

[0019] This invention presents a performance evaluation method for state estimation based on a polling communication protocol under DoS attacks. Based on the design of a state estimator under a polling communication protocol, and considering both open-loop and closed-loop structures of the actual system, this method analyzes and designs the optimal DoS attack scheduling scheme chosen by the attacker. Combining the characteristics of DoS attacks, it analyzes the impact of a single DoS attack on the performance index function, thereby obtaining the optimal DoS defense strategy under multiple DoS attacks. This method evaluates the performance loss of state estimation based on the polling communication protocol under different DoS attack schemes, providing insights for scheduling optimization of practical defense strategies. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the performance evaluation method for state estimation based on polling communication protocol under DoS attack according to the present invention.

[0021] Figure 2 This is a schematic diagram of the estimation results under attack strategy 1 when the remote state estimator of the present invention has an open-loop structure;

[0022] Figure 3 This is a schematic diagram of the estimation results under attack strategy 2 when the remote state estimator of the present invention has an open-loop structure;

[0023] Figure 4 This is a schematic diagram of the estimation results under attack strategy 3 when the remote state estimator of the present invention has an open-loop structure;

[0024] Figure 5 This is a schematic diagram of the estimation results under attack strategy 1 when the remote state estimator of the present invention has a closed-loop structure;

[0025] Figure 6 This is a schematic diagram of the estimation results under attack strategy 2 when the remote state estimator of the present invention has a closed-loop structure;

[0026] Figure 7 This is a schematic diagram of the estimation results under attack strategy 3 when the remote state estimator of the present invention has a closed-loop structure;

[0027] Figure 8 This is a schematic diagram illustrating the relationship between the performance metrics of the DoS attack and the number of attacks in this invention.

[0028] Figure 9 This diagram illustrates the relationship between the performance metrics of the remote state estimator of this invention and the attack probability. Detailed Implementation

[0029] Specific implementation method one: Combining Figure 1 This invention describes a performance evaluation method for state estimation based on a polling communication protocol under a DoS attack. It is crucial to study the optimal scheduling problem of remote state estimation performance under a DoS attack in cyber-physical systems. Existing research mainly focuses on system performance under a given attack pattern. This invention investigates how attackers should design DoS attack strategies to minimize system performance. Specifically, it considers a sensor transmitting its information to a remote estimator via a wireless channel for state estimation. The information transmission is scheduled by a polling communication protocol, where the measurement information from the smart sensor is transmitted through a wireless channel with limited bandwidth.

[0030] Since attackers have limited energy to interfere with the network, the scenario where the attacker decides whether to block the channel at each sampling time is considered. Optimal attack scheduling schemes are constructed for both closed-loop and open-loop systems based on the actual system. Then, the evolution characteristics of the estimation error covariance under different attack schemes are analyzed, thereby determining the optimal attack scheme based on error cost. Finally, the design of the optimal attack scheduling is illustrated through an example.

[0031] A performance evaluation method for state estimation based on polling communication protocol under DoS attack includes the following steps:

[0032] S1: Construct a state estimation model for the unmanned system; the state estimation model of the unmanned system is derived from the kinematic model of the unmanned system; the kinematic model of the unmanned system is constructed according to the actual situation of the unmanned system. The unmanned system includes: physical objects and sensors; the physical objects refer to the controlled unmanned operating objects, including drones, unmanned transport vehicles, autonomous vehicles, etc. The sensors in the unmanned system are used to measure the state information of the physical objects, including the direction of motion, velocity, acceleration, tilt angle, etc., and the measurement information is sent to a remote state estimator through a communication network; the communication network serves as the communication medium between the unmanned system and the remote state estimator, and the communication network adopts a polling communication protocol to adjust the transmission order of information from the sensors to the remote state estimator.

[0033] S2: Based on the state estimation model obtained in S1, construct a remote state estimator, which is used to estimate the state of the unmanned system.

[0034] S3: Constructing the optimal DoS attack strategy against remote state estimators * According to the optimal DoS attack strategy γ * Simulate the performance degradation of the remote state estimator when a DoS attacker interferes with a communication network;

[0035] In S3, an optimal DoS attack strategy γ targeting the remote state estimator is constructed. * The specific process is as follows:

[0036] Step 1: Analyze the evolution of the state estimation error of the remote state estimator when the remote state estimator constructed by S2 performs state estimation on the unmanned system;

[0037] Step 2: Assume the attacker can only launch n attacks, where n is a positive integer. Construct M based on the evolution pattern of the state estimation error obtained in Step 1. γ One attack strategy γ; M γ It is a positive integer;

[0038] Step 3: Construct the performance index function J(γ) of the attack strategy γ, and calculate M based on the performance index function J(γ). γ The attack strategy γ is selected as the optimal DoS attack strategy γ based on its performance metrics. * .

[0039] Those skilled in the art can design a state estimator based on a polling communication protocol, and analyze the optimal DoS attack scheduling scheme chosen by the attacker based on the open-loop and closed-loop structures of the actual system. This will help evaluate the performance loss of state estimation based on the polling communication protocol under different DoS attack schemes and provide ideas for scheduling optimization of actual defense strategies.

[0040] Specific Implementation Method Two: Combining Figure 1 This embodiment describes the state estimation performance evaluation method based on polling communication protocol under DoS attack: The state estimation model of the unmanned system in S1 is as follows:

[0041]

[0042] Where k is time, x k It is the state of an unmanned system, y k This is the sensor measurement output of the unmanned system, where A is the system matrix, C is the observation matrix, and w k It is Gaussian noise with zero mean, w k The covariance is Q > 0, v k It is Gaussian noise with zero mean, v k To measure Gaussian noise, v k For covariances R > 0, w k and v k The systems are independent of each other. Q is the process noise error covariance of the unmanned system, and R is the observation noise error covariance. The initial state of the unmanned system is x0, which follows a Gaussian distribution with zero mean. The covariance of x0 is Σ0>0, and for all k≥0, the initial state x0 of the system is consistent with w. k and v k Irrelevant;

[0043] The state estimation model of the unmanned system includes a closed-loop state estimation model and an open-loop state estimation model.

[0044] When the state estimation model of an unmanned system is a closed-loop structure: the sensors of the unmanned system are intelligent sensors. The intelligent sensors perform prior estimation based on the state information of the unmanned system measured by the intelligent sensors, obtain the updated system measurement output, and transmit the updated system measurement output to the remote state estimator; for example, the intelligent sensors can perform prior estimation based on the measured displacement to obtain the acceleration of the unmanned system, and in this case, the acceleration of the unmanned system is used as the system measurement output; for the closed-loop structure state estimation model: the sensors of the unmanned system are intelligent sensors. The intelligent sensors perform prior estimation based on the state information of the unmanned system measured by the intelligent sensors, obtain the updated system measurement output, and transmit the updated system measurement output to the remote state estimator;

[0045] The state information of unmanned systems measured by intelligent sensors is the same as the state information of unmanned systems measured by sensors (e.g., flow sensors measure flow rate, speed sensors measure speed, and pressure sensors measure pressure).

[0046] The updated system measurement output includes unmanned system status information measured by sensors (e.g., flow sensors measure flow rate, speed sensors measure speed, and pressure sensors measure pressure) as well as unmanned system status information calculated using physical formulas based on the actual environment (e.g., error estimation, uncertainty measurement, confidence level, or reliability indicators).

[0047] When the state estimation model of an unmanned system is an open-loop structure, the sensors of the unmanned system only transmit the state information of the unmanned system measured by the sensors, that is, only transmit the system measurement output to the remote state estimator. For example, when the sensors of the unmanned system are only displacement sensors, the system measurement output is only displacement.

[0048] For the open-loop state estimation model: the sensors of the unmanned system only transmit the unmanned system state information measured by the sensors (e.g., flow sensors measure flow rate, speed sensors measure speed, pressure sensors measure pressure, i.e., the unmanned system state information measured by the sensors), that is, only the system measurement output is transmitted to the remote state estimator. Other steps are the same as any one of the specific implementation methods in Implementation 1.

[0049] Specific implementation method three: Combining Figure 1 This embodiment describes the performance evaluation method for state estimation based on polling communication protocol under DoS attack: The construction of the remote state estimator in step S2 is as follows:

[0050] S2.1: Determine the communication protocol for the remote state estimator;

[0051] S2.2: Based on the structure of the state estimation model obtained in S1, determine the structure of the remote state estimator;

[0052] The communication protocol for the remote state estimator is determined in step S2.1; the specific process is as follows:

[0053] The remote state estimator uses a polling communication protocol; the polling communication process is as follows:

[0054] At time k, the measurement output of the unmanned system's sensors will be... The information is transmitted to the remote state estimator via a communication network using a polling communication protocol. The remote state estimator receives the information and represents it as follows:

[0055] Among them, y i,k This represents the measurement output of the i-th sensor at time k in the unmanned system. For y i,k transpose, The process state estimator receives the received information from the i-th sensor at time k in the unmanned system via the communication network. for The transpose of , i = 1, 2, ..., N, where N is the number of sensors;

[0056] The measurement output of the unmanned system's sensors The elements in the diagram include the measurement outputs of sensors from the unmanned system with transmission permissions and the measurement outputs of sensors from the unmanned system without transmission permissions. For example, at time k, only the first sensor has transmission permissions, so sensors 2 to N do not. At any given time, only one sensor from the unmanned system can access the shared communication channel, which has multiple channels. At each time, the sensor with transmission permissions transmits its measurement information to the remote state estimator via the shared communication channel. The information processing strategies for other sensors without transmission permissions include information preservation strategies and zero-input strategies. Other steps are the same as in Specific Implementation Method Two.

[0057] Specific implementation method four: Combination Figure 1 This embodiment describes the performance evaluation method for state estimation based on a polling communication protocol under a DoS attack: The transmission strategy for the measurement output of the sensors of the unmanned system without transmission permissions to the remote state estimator through the communication network includes an information preservation strategy and a zero-input strategy.

[0058] When the transmission strategy for the measurement output of sensors in an unmanned system without transmission permissions is a zero-input strategy, the information received by the remote state estimator... The expression is:

[0059]

[0060] Where, Φ s(k) This indicates which sensor communication channel is selected at time k, and is the channel selection indicator function, expressed as Φ. s(k) =diag{δ(s(k)-1)I,..,δ(s(k)-N)I}; s(k)∈{1,2,...,N}, s(k) represents the channel number with transmission permission at time k, s(k) = mod(k+s-2,N)+1, s represents the channel number selected at time k, diag{} represents a diagonal matrix, δ() represents the impulse function, I is the identity matrix, the matrix dimension of I depends on the information transmitted by the sensor, N is the number of sensors, and mod is the modulo function;

[0061] When the transmission strategy for the measurement output of sensors in an unmanned system without transmission permissions is an information preservation strategy, the information received by the remote state estimator... The expression is:

[0062]

[0063] Where l represents the time delay, used to sum the time delays. For example, if a sensor has permissions at times 3s and 9s, and time k is 9s, the time delay is 6. N t Let y be a time variable. k-l This indicates that the sensor of the unmanned system measures the output at kl.

[0064]

[0065] That is, when the remote state estimator receives information through the shared communication channel at each time, only one channel of the shared communication channel has information updates, while the information of other channels remains the information transmitted at the previous time. Other steps are the same as in Specific Implementation Method 3.

[0066] Specific Implementation Method Five: Combining Figure 1 This embodiment describes the performance evaluation method for state estimation based on polling communication protocol under DoS attack: In step S2.2, the structure of the remote state estimator is determined based on the structure of the state estimation model obtained in step S1; the specific process is as follows:

[0067] When the state estimation model of the unmanned system is an open-loop structure, the remote state estimator is also an open-loop structure.

[0068] When the state estimation model of the unmanned system is a closed-loop structure, the remote state estimator is also a closed-loop structure.

[0069] When the state estimation model of the unmanned system is an open-loop structure, that is, the remote state estimator based on the remote state estimator under the query communication protocol selects the open-loop structure remote state estimation algorithm to obtain the open-loop structure remote state estimator.

[0070] For open-loop remote state estimators, state estimation of unmanned systems is performed, i.e., the calculation of the open-loop unmanned system state. and the corresponding covariance ∑ ok ,

[0071] When the state estimation model of the unmanned system is a closed-loop structure, the remote state estimator selects a remote state estimation algorithm with a closed-loop structure to obtain a remote state estimator with a closed-loop structure.

[0072] For open-loop remote state estimators, state estimation of unmanned systems is performed, i.e., calculating the state of closed-loop unmanned systems. and the corresponding covariance ∑ ck The other steps are the same as in Specific Implementation Method Four.

[0073] Specific Implementation Method Six: Combination Figure 1 This embodiment describes the performance evaluation method for state estimation based on polling communication protocol under DoS attacks:

[0074] The specific process by which the remote state estimator in S2 performs state estimation for the unmanned system is as follows:

[0075] When the remote state estimator is an open-loop structure

[0076] The remote state estimator calculates the open-loop state of the unmanned system at time k based on the unmanned system state at time k-1 and the information received by the remote state estimator. and the corresponding covariance ∑ ok The specific process is as follows:

[0077] The initial time is denoted as 0, and the initial state of the unmanned system is x0, which follows a Gaussian distribution with a mean of zero and a covariance of Σ0 > 0. The system iterates from 0 to N. t The open-loop unmanned system state is calculated. and the corresponding covariance ∑ ok The formula is expressed as:

[0078]

[0079] in, Let be the prior minimum mean square error estimate of the state of an open-loop unmanned system over k iterations. Let be the prior error covariance of the open-loop unmanned system in k iterations. Let ∑ be the posterior minimum mean square error estimate of the state of the open-loop unmanned system after k-1 iterations. ok-1 Let K be the posterior error covariance of the open-loop unmanned system obtained from k-1 iterations; ok Let be the gain of the remote state estimator for the open-loop unmanned system after k iterations. Let ∑ be the posterior minimum mean square error estimate of the state of the open-loop unmanned system over k iterations. ok Let R be the posterior error covariance of the open-loop unmanned system over k iterations, ε1 and ε2 be the scaling parameters of the open-loop remote state estimator, and R be the posterior error covariance. · Represented as the equivalent noise covariance matrix, θ k Indicates whether the remote state estimator successfully received the packet at time k:

[0080]

[0081] The prior estimate refers to the state at time k obtained by the remote state estimator based on the state at time k-1 and the state estimation model.

[0082] The posterior refers to the state at time k estimated posteriorly based on the estimated state at time k and the measurement at time k.

[0083] When the remote state estimator is a closed-loop structure, it calculates the closed-loop unmanned system state based on the unmanned system state at time k-1 and the information received by the remote state estimator. and the corresponding covariance ∑ ck The specific process is as follows:

[0084] The initial time is denoted as 0, and the initial state of the unmanned system is x0, which follows a Gaussian distribution with a mean of zero and a covariance of Σ0 > 0. The system iterates from 0 to N. t The closed-loop state of the unmanned system is calculated. and the corresponding covariance ∑ ck This can be expressed as a formula:

[0085]

[0086] in, Let be the prior minimum mean square error estimate of the state of the unmanned system in a closed loop with k iterations. Let the prior error covariance of the unmanned system be the k-round iterative closed loop. Let ∑ be the posterior minimum mean square estimation error of the closed-loop unmanned system state obtained from k-1 iterations; ck-1 Let K be the posterior error covariance of the unmanned system obtained in k-1 iterations; ck The gain of the remote state estimator for an unmanned system with a k-round iterative closed loop; Let denot be the posterior minimum mean square error estimate of the state of the unmanned system after k-round iterative closed loop, and let ∑ be the posterior error covariance of the unmanned system after k-round iterative closed loop. ck ε3 is the scaling parameter of the remote state estimator corresponding to the closed-loop unmanned system.

[0087] Specific implementation method seven: Combination Figure 1 This embodiment describes the performance evaluation method for state estimation based on polling communication protocol under DoS attack: Step one analyzes the evolution of state estimation error when the remote state estimator constructed by S2 estimates the state of the unmanned system. The specific process is as follows:

[0088] Construct transformation functions h(X) and g(X), and obtain the evolution law of state estimation error when the remote state estimator performs state estimation on the unmanned system based on the transformation functions h(X) and g(X);

[0089] The state estimation error includes: the open-loop unmanned system posterior error covariance ∑ ok And the posterior error covariance ∑ of the closed-loop unmanned system ck ;

[0090] The transformation functions h(X) and g(X) are constructed as follows:

[0091]

[0092] Where X is the independent variable of the transformation function. To represent a composite function, It is defined as; The update function representing the prior error covariance;

[0093] h(X) represents the posterior estimation error covariance Σ when the remote estimator does not receive a packet at time k. k The measurement update is given by h, which represents the update function of the posterior error covariance, and g(X) represents the posterior estimation error covariance Σ when the remote estimator receives the information packet at time k. k The measurement update, where g represents the posterior error covariance Σ during one iteration. k The update function, The update function representing the prior error covariance;

[0094] When the remote state estimator is an open-loop structure, the update function of the prior error covariance of the remote state estimator. Represented as function Expressed as a formula:

[0095]

[0096] At this point, the posterior error covariance ∑ of the open-loop unmanned system ok The evolution is as follows:

[0097]

[0098] When the remote state estimator is a closed-loop structure, the update function of the prior error covariance of the remote state estimator. express function Expressed as a formula:

[0099]

[0100] At this point, the posterior error covariance ∑ of the closed-loop unmanned system ck The evolution is as follows:

[0101]

[0102] The other steps are the same as in Specific Implementation Method Six.

[0103] Specific implementation method eight: Combination Figure 1This embodiment describes the state estimation performance evaluation method based on a polling communication protocol under a DoS attack: In step two, it is set that the attacker can only launch n attacks, where n is a positive integer. Based on the evolution law of the state estimation error obtained in step one, M is constructed. γ One attack strategy γ; the specific process is as follows:

[0104] Step 21: Assume the attacker can only launch n attacks, where n is a positive integer. Construct the first basic DoS attack strategy based on the evolution of the state estimation error obtained in Step 1. Second basic DoS attack strategy

[0105] Step 22; Based on the two types of basic DoS attack strategies and Linear combination of M γ The attack strategy γ is the same as the other steps in Specific Implementation Method 7.

[0106] Specific Implementation Method Nine: Combining Figure 1 This embodiment describes the state estimation performance evaluation method based on polling communication protocol under DoS attack: In step two, it is set that the attacker can only launch n attacks, where n is a positive integer. Based on the evolution law of state estimation error obtained in step one, a first basic DoS attack strategy is constructed. Second basic DoS attack strategy The specific process is as follows:

[0107] The attack strategy γ is defined as follows: γ k Let γ represent the attacker's decision at time k, k∈{1.,2,...,T}. k Expressed as a formula:

[0108]

[0109] set up and These are two different basic attack strategies.

[0110] in z∈{1,2,...,T-1}, where z is the moment before the decision change;

[0111] First Basic DoS Attack Strategy A DoS attack is applied at every time from time 1 to time n, and no DoS attack is applied from time n+1 to time T. This can be expressed by the formula:

[0112]

[0113] Second Basic DoS Attack Strategy To ensure no DoS attack is applied from time 1 to time n, and to apply a DoS attack from time n+1 to time T, the formula is as follows:

[0114]

[0115] The other steps are the same as in Specific Implementation Method 8.

[0116] Specific Implementation Method Ten: Combining Figures 1 to 3 This embodiment describes the state estimation performance evaluation method based on polling communication protocol under DoS attack: In step three, the performance index function J(γ) of the attack strategy γ includes the maximum error cost function and the average estimation error function.

[0117] When the performance metric function is the average estimation error function, for a given attack strategy γ, the formula for the average estimation error function is:

[0118]

[0119] Where E is the expectation function, and P is the expectation function. k Let be the error function.

[0120] When the performance metric function is the error cost function, for a given attack strategy γ, the formula for maximizing the error cost function is:

[0121] J(γ)=E[P T (γ)] (26)

[0122] Among them, P T Let T be the estimated error function.

[0123] Assuming only the first basic DoS attack strategy Second basic DoS attack strategy hour

[0124] When the performance index function J(γ) maximizes the error cost function and the first judgment condition is met, the first basic DoS attack strategy is... Performance index function With the second basic DoS attack strategy Performance index function The relationship is: The optimal DoS attack strategy is determined as the first basic DoS attack strategy.

[0125] When the performance index function J(γ) maximizes the error cost function and the second judgment condition is met, the first basic DoS attack strategy is... Performance index function And the second basic DoS attack strategy Performance index function The relationship is: The optimal DoS attack strategy was determined to be the second basic DoS attack strategy.

[0126]

[0127] The first criterion is: for any X≥0, formula (27) holds;

[0128]

[0129] The second criterion is: for any X≥0, formula (28) holds.

[0130] The other steps are the same as in Specific Implementation Method Nine.

[0131] The performance evaluation method for state estimation based on polling communication protocol under DoS attack in this embodiment is illustrated through simulations using specific implementation methods one through ten.

[0132] like Figures 2 to 9 As shown,

[0133] In the simulation of this invention, the unmanned system is an unmanned vehicle system, and the remote state estimator performs trajectory tracking on the unmanned vehicle system.

[0134] S1: Construct a kinematic model of the autonomous vehicle system and convert it into a state estimation model:

[0135] The XY coordinate system is the world coordinate system. These represent the lateral and longitudinal velocities of the rear axle center of the vehicle in the XY coordinate system, respectively. r It is the vehicle speed along the longitudinal direction of the car body from the center of the rear axle. According to the principle of coordinate transformation, we have:

[0136]

[0137] in, This is the yaw angle of the vehicle. The kinematic constraints for the front and rear axles are:

[0138]

[0139] Where δ f This is the front wheel steering angle. From the above formula, we can obtain:

[0140]

[0141] From the geometric relationship between the front and rear wheels of the cart, the yaw rate of the cart about the center of motion P can be obtained:

[0142]

[0143] Among them l r It is the wheelbase between the front and rear axles of the car, δ f This is the steering angle of the car's front wheels. The steering angle of the car's front wheels can be obtained from the geometric relationships of the car's motion:

[0144] δ f =arctan(l r / R)

[0145] Combining the above equation (25), we can obtain the kinematic model of the car as follows:

[0146]

[0147] Transform the kinematic model of the autonomous vehicle system into a state estimation model:

[0148] In vehicle tracking control, [v] is generally used. r With [v, ω] as the controlled object, the kinematic model is transformed into one with [v, ω] as the controlled object. r [ω] is the state-space expression of the control variable:

[0149]

[0150] The above formula can be further rearranged into the state-space equation form shown below.

[0151]

[0152] Z = CX + DU

[0153] In the formula, X is a state variable. U is the control variable, U = [v] r ,ω] T Then, according to formula (32), the expressions for state matrices A, B, C, and D can be derived as follows:

[0154]

[0155] Discretize it, and let T be:

[0156]

[0157] The results were:

[0158] X(k+1)=A k X(k)+B k U(k)

[0159] in:

[0160] The remote state estimator estimates the state of the autonomous vehicle system, including its lateral and longitudinal velocities and yaw angles.

[0161] Here, the number of attacks, n, is set to 50. Through iteration, three attack strategies for state estimation algorithms employing an information preservation strategy are derived for closed-loop structures, such as... Figures 2 to 4 The effects of the three attack strategies shown are as follows: compared to state estimation without an attack, denial-of-service attacks have a certain negative impact on the state estimation results. To quantitatively analyze the advantages and disadvantages of different attack strategies,

[0162] Using the average estimation error function as the performance index function J(γ), the analysis results are shown in Table 1. It can be seen that continuous attacks starting at a certain moment cause the greatest damage to the state estimation performance, and the attack strategy γ... 50 It is the optimal attack strategy, that is, the optimal attack strategy under multiple DoS attacks.

[0163] Table 1 Attack Strategy Table - CLZOH

[0164]

[0165] Here, the number of attacks, n, is set to 50. Through iteration, three attack strategies are derived for the state estimation algorithm under the information preservation strategy for open-loop structures. Figures 5 to 7 The effects of the three attack strategies shown are as follows: compared to state estimation without an attack, denial-of-service attacks have a certain negative impact on the state estimation results. To quantitatively analyze the advantages and disadvantages of different attack strategies, the average estimation error function is selected as the performance index function J(γ). The results are shown in Table 2. It can be seen that continuous attacks starting at a certain time have the greatest impact on the state estimation performance, and the attack strategy γ is the most detrimental. 50 The optimal attack strategy.

[0166] Table 2 Attack Strategy Table - OLZOH

[0167]

[0168] The optimal attack strategy γ was obtained. 50 Next, we will simulate a DoS attacker reducing the performance of the remote state estimator by interfering with the wireless channel. First, we simulate how the performance index changes with the number of attacks. For easier comparison and analysis, the probability of a successful DoS attack is set to 1 for all attacks. The relationship between the performance index and the number of attacks is shown in Figure 8. The results clearly show that, in the presence of a DoS attack, the performance index function increases significantly with the number of attacks for all three state estimation scenarios, which aligns with our intuitive understanding.

[0169] Then, the performance index was simulated as the probability of a successful DoS attack increased. Using the controlled variable method, the relationship between the performance index and the attack probability was obtained, as shown in Figure 9. The results show that, under the three state estimations, the performance index function increases significantly with the increase of the attack success probability when a DoS attack is present, which is consistent with objective facts.

[0170] In summary, those skilled in the art can analyze and design the optimal DoS attack strategy chosen by the attacker by designing a state estimator based on the polling communication protocol, according to the open-loop and closed-loop structures of the actual system. They can also evaluate the performance loss of state estimation based on the polling communication protocol under the optimal DoS attack strategy, and provide ideas for scheduling optimization of actual defense strategies.

[0171] The above description is merely of preferred embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention, and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A method for evaluating the performance of state estimation based on a polling communication protocol under a DoS attack, characterized in that, The method includes the following steps: S1: Construct a state estimation model for the unmanned system; in the following form: （1） Where k is time. It is in the state of an unmanned system. It is the sensor measurement output of the unmanned system. For the system matrix, For the observation matrix, It is Gaussian noise with zero mean. The covariance is , It is Gaussian noise with zero mean. The covariance is , and The initial state of the independent, unmanned system is as follows: , It follows a Gaussian distribution with a mean of zero. The covariance is And in all Under these circumstances, the initial state of the system and and Irrelevant; The state estimation model of the unmanned system includes a closed-loop state estimation model and an open-loop state estimation model. S2: Based on the state estimation model obtained in S1, construct a remote state estimator, which is used to estimate the state of the unmanned system. S3: Constructing an optimal DoS attack strategy targeting remote state estimators ; S4: Based on the obtained optimal DoS attack strategy The performance loss value for state estimation based on the polling communication protocol was evaluated. The optimal DoS attack strategy targeting the remote state estimator is constructed in S3. The specific process is as follows: Step 1: Based on the remote state estimator constructed using S2, obtain the evolution law of the state estimation error of the remote state estimator; Step Two: Assume the attacker can only launch n attacks, where n is a positive integer. Construct a system based on the evolution of the state estimation error obtained in Step One. attack strategies ; It is a positive integer; Step 3: Constructing an attack strategy Performance index function According to the performance index function Calculate separately attack strategies Based on performance metrics, the attack strategy with the highest performance metric is selected as the optimal DoS attack strategy. .

2. The performance evaluation method for state estimation based on polling communication protocol under DoS attack as described in claim 1, characterized in that: In step S2, a remote state estimator is constructed based on the state estimation model obtained in S1; the specific process is as follows: S2.1: Determine the communication protocol for the remote state estimator; S2.2: Based on the state estimation model of the unmanned system obtained in S1, determine the structure of the remote state estimator; The communication protocol for the remote state estimator is determined in step S2.1; the specific process is as follows: The remote state estimator uses a polling communication protocol; the polling communication process is as follows: At time k, the measurement output of the unmanned system's sensors will be... The information is transmitted to the remote state estimator via a communication network using a polling communication protocol. The remote state estimator receives the information and represents it as follows: ; in, Representing unmanned systems Time of the first The measurement output of each sensor, for transpose, The remote state estimator receives the corresponding data from the unmanned system via the communication network. Time of the first Information received by each sensor for transpose, , Number of sensors; The measurement output of the unmanned system's sensors The elements include sensor measurement outputs from unmanned systems with transmission permissions and sensor measurement outputs from unmanned systems without transmission permissions.

3. The performance evaluation method for state estimation based on polling communication protocol under DoS attack as described in claim 2, characterized in that: The transmission strategy for the sensor measurement outputs of the unmanned system without transmission permissions to be transmitted to the remote state estimator via the communication network includes an information preservation strategy and a zero-input strategy. When the transmission strategy for the measurement output of sensors in an unmanned system without transmission permissions is a zero-input strategy, the information received by the remote state estimator... The expression is: （2） in, This indicates which sensor communication channel is selected at time k, and is the channel selection indicator function, expressed as: ; , express Channel sequence number that is always authorized to transmit. s represents the channel number selected at time k. Represented as a diagonal matrix, Represents the impulse function. It is the identity matrix. The matrix dimension depends on the information transmitted by the sensor. For the number of sensors, It is the modulo function; When the transmission strategy for the measurement output of sensors in an unmanned system without transmission permissions is an information preservation strategy, the information received by the remote state estimator... The expression is: （3） Where l represents the time delay, used to sum the time delays. For time variables, Indicating the sensors of unmanned systems Time measurement output; The information received by the remote state estimator is represented as follows: , , Number of sensors; The remote state estimator receives the corresponding data from the unmanned system via the communication network. Time of the first Information received by each sensor The value can be: （4）。 4. The performance evaluation method for state estimation based on polling communication protocol under DoS attack as described in claim 3, characterized in that: In step S2.2, based on the state estimation model of the unmanned system obtained in S1, the structure of the remote state estimator is determined; the specific process is as follows: When the state estimation model of the unmanned system is an open-loop structure, the remote state estimator is also an open-loop structure. When the state estimation model of the unmanned system is a closed-loop structure, the remote state estimator is also a closed-loop structure.

5. The performance evaluation method for state estimation based on polling communication protocol under DoS attack as described in claim 4, characterized in that: The specific process by which the remote state estimator in S2 performs state estimation for the unmanned system is as follows: When the remote state estimator is an open-loop structure The remote state estimator calculates the posterior minimum mean square error estimate of the open-loop unmanned system state over k iterations based on the unmanned system state at time k-1 and the information received by the remote state estimator. The posterior error covariance of an open-loop unmanned system with k iterations The specific process is as follows: The initial time is recorded as 0, and the initial state of the unmanned system is: , It follows a Gaussian distribution with a mean of zero. The covariance is Iterative calculation from 0 to... The posterior minimum mean square error estimate of the open-loop unmanned system state after k iterations is calculated. The posterior error covariance of an open-loop unmanned system with k iterations Expressed as a formula: （5） （6） （7） （8） （9） in, Let be the prior minimum mean square error estimate of the state of an open-loop unmanned system over k iterations. Let be the prior error covariance of the open-loop unmanned system in k iterations. Let be the posterior minimum mean square error estimate of the state of the open-loop unmanned system after k-1 iterations. Let be the posterior error covariance of the open-loop unmanned system obtained from k-1 iterations; Let be the gain of the remote state estimator for the open-loop unmanned system after k iterations. Let be the posterior minimum mean square error estimate of the state of the open-loop unmanned system after k iterations. Let be the posterior error covariance of the open-loop unmanned system after k iterations. Scaling parameters for a remote state estimator with an open-loop structure. This is represented as an equivalent noise covariance matrix. Indicates whether the remote state estimator successfully received the packet at time k: （10） When the remote state estimator has a closed-loop structure, it calculates the posterior minimum mean square error estimate of the unmanned system state for k iterations of the closed loop based on the unmanned system state at time k-1 and the information received by the remote state estimator. The posterior error covariance of the unmanned system in k-round iterative closed loop The specific process is as follows: The initial time is recorded as 0, and the initial state of the unmanned system is: , It follows a Gaussian distribution with a mean of zero. The covariance is Iterative calculation from 0 to... The posterior minimum mean square error estimate of the unmanned system state after k iterations of closed loop is calculated. The posterior error covariance of the unmanned system in k-round iterative closed loop This can be expressed as a formula: （11） （12） （13） （14） （15） in, Let be the prior minimum mean square error estimate of the state of the unmanned system in a closed loop with k iterations. Let the prior error covariance of the unmanned system be the k-round iterative closed loop. Let be the posterior minimum mean square estimation error of the closed-loop unmanned system state obtained from k-1 iterations. Let be the covariance of the posterior error of the unmanned system obtained in k-1 iterations. The gain of the remote state estimator for an unmanned system with a k-round iterative closed loop; Let be the posterior minimum mean square error estimate of the state of the unmanned system after k-round iterative closed loop, and let be the posterior error covariance of the unmanned system after k-round iterative closed loop. ; The scaling parameters are for the remote state estimator corresponding to the closed-loop unmanned system.

6. The performance evaluation method for state estimation based on polling communication protocol under DoS attack as described in claim 5, characterized in that: In step one, the remote state estimator built based on S2 is used to obtain the evolution law of the state estimation error of the remote state estimator. The specific process is as follows: Constructing transformation functions and According to the transformation function and The evolution of state estimation error when a remote state estimator performs state estimation on an unmanned system is obtained; The state estimation error includes: the covariance of the posterior error of the unmanned system over k iterations. The posterior error covariance of the unmanned system in k-round iterative closed loop ; The construction transformation function and as follows: h （16） （17） Where X is the independent variable of the transformation function. To represent a composite function, It is defined as; The update function representing the prior error covariance; When the remote state estimator is an open-loop structure, the update function of the prior error covariance of the remote state estimator. Represented as ;function Expressed as a formula: （18） At this point, the posterior error covariance of the open-loop unmanned system The evolution is as follows: （19） When the remote state estimator is a closed-loop structure, the update function of the prior error covariance of the remote state estimator. express ;function Expressed as a formula: （20） At this point, the posterior error covariance of the closed-loop unmanned system The evolution is as follows: （21）。 7. The performance evaluation method for state estimation based on polling communication protocol under DoS attack as described in claim 6, characterized in that: In step two, it is set that the attacker can only launch n attacks, where n is a positive integer. The evolution of the state estimation error obtained in step one is then used to construct... attack strategies The specific process is as follows: Step 21: Assume the attacker can only launch n attacks, where n is a positive integer. Construct the first basic DoS attack strategy based on the evolution of the state estimation error obtained in Step 1. Second basic DoS attack strategy ; Step 22; Based on the two types of basic DoS attack strategies and Linear combination attack strategies .

8. The performance evaluation method for state estimation based on polling communication protocol under DoS attack as described in claim 7, characterized in that: In step two, it is set that the attacker can only launch n attacks, where n is a positive integer. Based on the evolution law of the state estimation error obtained in step one, the first basic DoS attack strategy is constructed. Second basic DoS attack strategy The specific process is as follows: Set attack strategy Represented as , This represents the attacker's decision at time k. , Expressed as a formula: （22） First Basic DoS Attack Strategy A DoS attack is applied at every time from time 1 to time n, and no DoS attack is applied from time n+1 to time T. This can be expressed by the formula: （23） Second Basic DoS Attack Strategy To ensure no DoS attack is applied from time 1 to time n, and to apply a DoS attack from time n+1 to time T, the formula is as follows: （24）。 9. The performance evaluation method for state estimation based on polling communication protocol under DoS attack as described in claim 8, characterized in that: The attack strategy in step three Performance index function To maximize the error cost function or the average estimated error function.

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