A remote estimation sensor scheduling decision method based on threshold structure

Abstract

The present invention designs a remote estimation sensor scheduling decision method based on a threshold structure; considers two modes of sensor transmission of raw data and event trigger mechanism, and limits the two transmission modes to have the same communication rate; under this framework, uses the Kalman filter algorithm to model the information transmission mode of the sensor and the estimation process of the remote state estimator; then, considering the time delay D caused by the data preprocessing method, proposes an estimation performance evaluation index based on the mean square error, and calculates the threshold of the time delay D by constructing a balance model based on the mean square error of the two transmission modes; finally, designs a remote estimation sensor scheduling decision method based on a threshold structure, realizes the reasonable scheduling of the sensor for the above transmission mechanism under different conditions; effectively estimates the real state of the system, and improves the estimation performance of the estimator under the condition of limited transmission energy, which has certain application value in engineering practice.

Description

Technical Field

[0001] The present invention relates to the fields of communication and information-physical system remote estimation technology, and in particular to a remote estimation sensor scheduling decision method based on a threshold structure. Background Art

[0002] Cyber-physical systems consist of computing units, communication units, control units, and the physical processes involved. They are widely used in defense, military, factory production, intelligent transportation, smart grid, and other fields. To realize these applications, wireless sensors are required to measure the state of the steady-state system, and then send the measurement data to the remote state estimator (remotely running the Kalman filter) through the wireless network to remotely estimate the state of the system. The remote end makes decisions based on the estimation of the state of the physical object to realize its application in practical scenarios. Therefore, the problem of remote state estimation in cyber-physical systems has been one of the hot topics of research in recent years.

[0003] Transmission strategies for remote state estimation of cyber-physical systems can be divided into two categories: based on raw data and based on preprocessed data. In traditional remote estimation problems, the estimator estimates the state of the system based on the raw data sent by the sensor. However, this method will affect the estimation performance of the estimator under communication constraints. Therefore, in recent years, more and more studies have been conducted on using data preprocessing mechanisms to improve estimation performance under resource constraints such as limited communication resources and limited energy. Although the existing results show that the remote estimator can obtain better estimation performance by using smart sensors or event triggering mechanisms, in practical applications, additional data preprocessing and related calculations will cause time delays, which will also have a certain impact on the estimation performance of the estimator. However, the existing results do not address the time issues faced by data preprocessing. Therefore, considering the time delay, the existing results cannot improve the estimation performance of the estimator well. In summary, the reasonable scheduling of data preprocessing methods and standard raw data transmission schemes under different conditions is a problem worth studying.

[0004] In the remote estimation problem of traditional cyber physics, the remote estimator estimates the state of the system based on the information sent by the sensor. However, due to resource constraints in practical applications, the above transmission mechanism will affect the estimation performance of the estimator. Although state estimation based on data preprocessing is an important means to improve the estimation performance of the estimator under resource constraints. However, in practical applications, additional data preprocessing and related calculations will cause time delays and will also have a certain impact on the estimation performance. The existing results do not address the time problem faced by data preprocessing. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention designs a remote estimation sensor scheduling decision method based on a threshold structure.

[0006] A remote estimation sensor scheduling decision method based on a threshold structure comprises the following steps:

[0007] Step 1: Model the cyber-physical system as a discrete steady-state system as follows:

[0008] x k+1 =Ax k +w k

[0009] y k =Cx k +v k (1)

[0010] Among them, x k represents the state value of the cyber-physical system at time k, y k represents the output value of the information-physical system, A is the state transfer matrix of the system, and C represents the state conversion matrix; w k and v k is independent and identically distributed Gaussian noise;

[0011] Step 2: After collecting the raw data of the system status, the sensors on the cyber-physical system k In the scenario where the original data is directly sent to the estimator at the far end of the system, the strategy of the raw data transmitted by the sensor is defined as θ1; for strategy θ1, a remote estimation model for the state of the cyber-physical system is established And its corresponding error covariance model At the same time, the value of the model in the steady state is calculated

[0012] After the sensor collects data y k In the future, we need to further calculate through the event trigger mechanism strategy to determine y k Whether to send data to the remote estimator; define the event trigger mechanism strategy as θ2, and calculate the time required for the mechanism to send data to the remote estimator at each moment based on the existing modeling of remote estimation and error covariance of the event trigger mechanism, and establish a new remote estimation model And its corresponding error covariance model

[0013] Step 2.1: Collect the raw data y of the cyber-physical system status from the system sensors kIn the scenario where the data is directly sent to the remote estimator, the strategy of the original data transmitted by the sensor is defined as θ1, and a remote state estimation model of the system state under the original data transmission strategy is established. and its error covariance model Due to the uncertainty of the wireless channel, the original data y k Packet loss occurs, so first define the indicator function γ at the remote estimator end k ∈{0,1} to describe whether the remote estimator receives the data packet y sent by the sensor at each time k k , when the remote estimator receives y k Time k =1, otherwise γ k =0, specifically expressed as follows:

[0014]

[0015] Secondly, define the information set of the remote estimator at time k as follows:

[0016]

[0017] Finally, the minimum mean square error estimate of the cyber-physical system sensor side is calculated under the information set obtained in the above formula: and its corresponding covariance That is, the remote estimation model and the error covariance model:

[0018]

[0019]

[0020] Where E represents mathematical expectation;

[0021] Based on equations 4 and 5, under the transmission strategy θ1, when the data packet sent by the sensor reaches the remote state estimator, the remote state estimator will update its estimated value. Otherwise, the remote state estimator will make a prediction based on the estimated value at the previous moment. Under this mechanism, its state estimation and its error covariance are modeled as follows:

[0022]

[0023]

[0024] in, is the Kalman filter gain; For new breath; The calculation is performed by Kalman filtering as follows:

[0025]

[0026] In order to simplify the formula (8), and For any variable X, the following function is defined:

[0027] h(X)=AXA′+Q (9)

[0028]

[0029] Where Q is the Gaussian noise w k covariance; R is Gaussian noise v k covariance; A′ represents the transpose of matrix A; C′ represents the transpose of matrix C;

[0030] Based on equations (9) and (10), and The abbreviation is as follows:

[0031]

[0032]

[0033] Step 2.2: Build a remote state estimation model based on event-triggered transmission strategy and its error covariance model

[0034] First, define θ2 as an event-triggered transmission strategy. Under this framework, the sensor responsible for collecting system status at the system end needs to generate an independent and identically distributed random variable β at each moment. k Compare it with the exponential function formed by the sensor measurement value to decide whether to send a packet at the current moment, as follows:

[0035]

[0036] Among them, Y is a positive definite matrix that can be designed, ρ k ∈[0,1] is a random variable, β k = 0 means that the sensor does not need to transmit the measured value y to the remote end at time k k , whereas β k =1;y′ k Represents y k The transpose of ; Based on Equation 13, the information set of the remote estimator k at the transmission strategy θ2 is defined as follows:

[0037]

[0038] Assuming that the two transmission strategies transmit data packets in an ideal communication channel with no packet loss, under this framework, the average communication rate is calculated as follows:

[0039]

[0040] in,

[0041]

[0042]

[0043]

[0044] Secondly, the minimum mean square error estimate of the local state of the cyber-physical system is calculated under the information set obtained in Equation 14: and its corresponding covariance as follows:

[0045]

[0046]

[0047] Assuming that the time required for the sensor to calculate whether to transmit data is D ≥ 1, under the information set obtained in Equation 14, the remote state estimation and its error covariance are modeled as follows:

[0048]

[0049]

[0050] Here, h is a composite function that satisfies the following equation for any variable X:

[0051] h 2 (X) = h(h(X))

[0052] Step 3. Obtain the equilibrium relationship model of the two transmission strategies based on error covariance by constructing the objective functions of the two transmission strategies;

[0053] Step 3.1: Assume that the two transmission strategies are compared in a steady-state sense, that is, the error covariance of the two strategies tends to be stable; based on this condition, for a given communication rate λ and time delay length D, for transmission strategies θ1 and θ2, define the following performance indicator function:

[0054]

[0055]

[0056] Among them, Tr represents a matrix operation symbol, indicating the trace of the matrix;

[0057] Step 3.2: Based on Equations 8 and 20, the estimated error covariance of the remote state estimator in the expected sense is as follows:

[0058]

[0059]

[0060] in,

[0061]

[0062]

[0063]

[0064]

[0065] Step 4: For the given communication rate λ in step 2, analyze the performance of the remote state estimation scheduling method of the cyber-physical system from the perspective of time delay D through step 3, and calculate the threshold D * ;

[0066] Step 4.1: For the communication rate λ calculated by Equation 15, the error covariance model of the transmission strategy θ1 in the expected sense is shown in 22, and the steady-state value of the transmission strategy θ1 at the communication rate λ is obtained.

[0067] Based on Formula 22, given the communication rate λ, the estimated performance of the transmission strategy θ1 is further analyzed as follows:

[0068]

[0069] in:

[0070]

[0071]

[0072] The asymptotic performance of the transmission strategy θ1 is defined as follows:

[0073]

[0074] in Representation function The value at time k;

[0075] Based on Equation 24 and Equation 25, when k→∞, the error covariance of the transmission strategy θ1 in the steady state is as follows:

[0076]

[0077] Step 4.2: For a first given communication rate λ, assume that the time delay caused by the transmission strategy θ2 is D; based on this assumption, the error covariance under the transmission strategy θ2 is modeled as shown in 23;

[0078] Based on Equation 22, for the first given communication rate λ, assuming that the time delay caused by the transmission strategy θ2 is D, its estimated performance is further analyzed as follows:

[0079]

[0080] in, represents the error covariance of the transmission strategy θ2 at time kD.

[0081] Step 4.3: Based on step 4.2, for any time delay step D2>D, since equation 23 is a monotonically increasing function, there exists a D * Make the function values ​​of equation 22 and equation 23 equal;

[0082] Assume that there is a time delay step D2>D, so that the following inequality holds:

[0083]

[0084] From equation 28, equation 23 is a monotonically increasing function, which means that there exists a D * So that the following equation holds:

[0085]

[0086] On this basis, the balance relationship between the two transmission strategies is defined as follows:

[0087]

[0088]

[0089]

[0090] Step 4.4: Based on the monotonicity of the cost function 28 in step 4.2, for a given communication rate λ, calculate the time delay D * Threshold:

[0091] For a given communication rate λ, the threshold based on the time delay D is calculated as follows:

[0092]

[0093] Further rewritten as:

[0094]

[0095] in,

[0096] Define the following inequality:

[0097]

[0098]

[0099] According to formula 33-35, the threshold interval of time delay D is calculated as follows:

[0100]

[0101] in,

[0102]

[0103]

[0104] Step 4.5: Using the threshold calculated in step 4.4, the cyber-physical system remotely estimates the scheduling decisions of the above two data transmission mechanisms under different conditions;

[0105] When D <D, Select strategy θ1 to transmit data to the remote estimator;

[0106] when The strategy θ2 is selected to transmit data to the remote estimator.

[0107] Beneficial technical effects of the present invention:

[0108] The present invention provides a remote state estimation decision algorithm for an information-physical system based on a threshold structure while taking into account the influence of data preprocessing and the time delay caused by it on the estimation performance of the estimator, making the present invention more universal and practical. The method can effectively estimate the true state of the system and can improve the estimation performance of the estimator under the condition of limited transmission energy, and the estimation logic is simple and easy to implement. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] Figure 1 A flow chart of a method for remote estimation and scheduling decision-making of a cyber-physical system based on a threshold structure provided in an embodiment of the present invention;

[0110] Figure 2 A structural block diagram of the original data transmission strategy of the information-physical system provided in the embodiment of the present invention:

[0111] Figure 3 A structural diagram of the information-physical system event-triggered transmission strategy provided by an embodiment of the present invention:

[0112] Figure 4The two transmission strategies provided in the embodiment of the present invention are based on a balance relationship of a threshold structure;

[0113] Figure 5 The performance comparison of the two transmission strategies under certain delay and average communication rate in the embodiment of the present invention is shown in FIG. DETAILED DESCRIPTION

[0114] The present invention will be further described below in conjunction with the accompanying drawings and embodiments;

[0115] Taking the information-physical system as an example, the information-physical system remote state estimation decision algorithm method based on the threshold structure of the present invention is used to obtain the threshold at the equilibrium point, and the transmission scheduling of the system is optimized and analyzed. A remote estimation sensor scheduling decision method based on the threshold structure realizes the reasonable scheduling of the above transmission mechanism by the sensor under different conditions. This method can effectively estimate the real state of the system, and can improve the estimation performance of the estimator under the condition of limited transmission energy. The estimation logic is simple and easy to implement.

[0116] A remote estimation sensor scheduling decision method based on threshold structure, such as Figure 1 As shown, the following steps are included:

[0117] Step 1: Model the cyber-physical system as a discrete steady-state system as follows:

[0118] x k+1 =Ax k +w k

[0119] y k =Cx k +v k (1)

[0120] Among them, x k represents the state value of the cyber-physical system at time k, y k represents the output value of the information-physical system, A is the state transfer matrix of the system, and C represents the state conversion matrix; w k and v k is independent and identically distributed Gaussian noise;

[0121] Step 2: After collecting the raw data of the system status, the sensors on the cyber-physical system k In the scenario where the original data is directly sent to the estimator at the far end of the system, the strategy of the raw data transmitted by the sensor is defined as θ1; for strategy θ1, a remote estimation model for the state of the cyber-physical system is established And its corresponding error covariance model At the same time, the value of the model in the steady state is calculated

[0122] After the sensor collects data y k In the future, we need to use a classic data preprocessing solution, namely the event trigger mechanism strategy, to further calculate and determine y k Whether to send data to the remote estimator; define the event trigger mechanism strategy as θ2, and calculate the time required for the mechanism to send data to the remote estimator at each moment based on the existing modeling of remote estimation and error covariance of the event trigger mechanism, and establish a new remote estimation model And its corresponding error covariance model The estimator is a Kalman filter estimator in this embodiment;

[0123] Step 2.1: Collect the raw data y of the cyber-physical system status from the system sensors k In the scenario where the original data is directly sent to the remote estimator, the strategy of the original data transmitted by the sensor is defined as θ1, as shown in the attached Figure 2 As shown, a remote state estimation model of the system state under the original data transmission strategy is established and its error covariance model Due to the uncertainty of the wireless channel, the original data y k Packet loss occurs, so first define the indicator function γ at the remote estimator end k ∈{0,1} to describe whether the remote estimator receives the data packet y sent by the sensor at each time k k , when the remote estimator receives y k Time k =1, otherwise γ k =0, specifically expressed as follows:

[0124]

[0125] Secondly, define the information set of the remote estimator at time k as follows:

[0126]

[0127] Finally, the minimum mean square error estimate of the cyber-physical system sensor side is calculated under the information set obtained in the above formula: and its corresponding covariance That is, the remote estimation model and the error covariance model:

[0128]

[0129]

[0130] Where E represents mathematical expectation;

[0131] Based on equations 4 and 5, under the transmission strategy θ1, when the data packet sent by the sensor reaches the remote state estimator, the remote state estimator will update its estimated value. Otherwise, the remote state estimator will make a prediction based on the estimated value at the previous moment. Under this mechanism, its state estimation and its error covariance are modeled as follows:

[0132]

[0133]

[0134] in, is the Kalman filter gain; For new breath; The calculation is performed by Kalman filtering as follows:

[0135]

[0136] In order to simplify the formula (8), and For any variable X, the following function is defined:

[0137] h(X)=AXA′+Q (9)

[0138]

[0139] Where Q is the Gaussian noise w k covariance; R is Gaussian noise v k covariance; A′ represents the transpose of matrix A; C′ represents the transpose of matrix C;

[0140] Based on equations (9) and (10), and The abbreviation is as follows:

[0141]

[0142]

[0143] Step 2.2: Build a remote state estimation model based on event-triggered transmission strategy and its error covariance model

[0144] First, define θ2 as an event-triggered transmission strategy, such as Figure 3 As shown in the figure, under this framework, the sensor responsible for collecting the system status needs to generate an independent and identically distributed random variable β at each moment. k Compare it with the exponential function formed by the sensor measurement value to decide whether to send a packet at the current moment, as follows:

[0145]

[0146] Among them, Y is a positive definite matrix that can be designed, ρ k ∈[0,1] is a random variable, β k = 0 means that the sensor does not need to transmit the measured value y to the remote end at time k k , otherwise βk=1; y′ k Represents y k The transpose of ; Based on Equation 13, the information set of the remote estimator k at the transmission strategy θ2 is defined as follows:

[0147]

[0148] Assuming that the two transmission strategies transmit data packets in an ideal communication channel with no packet loss, under this framework, the average communication rate is calculated as follows:

[0149]

[0150] in,

[0151]

[0152]

[0153]

[0154] Secondly, the minimum mean square error estimate of the local state of the cyber-physical system is calculated under the information set obtained in Equation 14: and its corresponding covariance as follows:

[0155]

[0156]

[0157] Assuming that the time required for the sensor to calculate whether to transmit data is D ≥ 1, under the information set obtained in Equation 14, the remote state estimation and its error covariance are modeled as follows:

[0158]

[0159]

[0160] Here, h is a composite function that satisfies the following equation for any variable X:

[0161] h 2 (X) = h(h(X))

[0162] Step 3. Obtain the equilibrium relationship model of the two transmission strategies based on error covariance by constructing the objective functions of the two transmission strategies;

[0163] Step 3.1: Assume that the two transmission strategies are compared in a steady-state sense, that is, the error covariance of the two strategies tends to be stable; based on this condition, for a given communication rate λ and time delay length D, for transmission strategies θ1 and θ2, define the following performance indicator function:

[0164]

[0165]

[0166] Among them, Tr represents a matrix operation symbol, indicating the trace of the matrix;

[0167] Step 3.2: Based on Equations 8 and 20, the estimated error covariance of the remote state estimator in the expected sense is as follows:

[0168]

[0169]

[0170] in,

[0171]

[0172]

[0173]

[0174]

[0175] Step 4: For the given communication rate λ in step 2, analyze the performance of the remote state estimation scheduling algorithm of the cyber-physical system from the perspective of time delay D through step 3, and find the threshold D * ;

[0176] Step 4.1: For the communication rate λ calculated by Equation 15, the error covariance model of the transmission strategy θ1 in the expected sense is shown in 22, and the steady-state value of the transmission strategy θ1 at the communication rate λ is obtained.

[0177] Based on Formula 22, given the communication rate λ, the estimated performance of the transmission strategy θ1 is further analyzed as follows:

[0178]

[0179] in:

[0180]

[0181]

[0182] The asymptotic performance of the transmission strategy θ1 is defined as follows:

[0183]

[0184] in Representation function The value at time k;

[0185] Based on Equation 24 and Equation 25, when k→∞, the error covariance of the transmission strategy θ1 in the steady state is as follows:

[0186]

[0187] Step 4.2: For a first given communication rate λ, assume that the time delay caused by the transmission strategy θ2 is D; based on this assumption, the error covariance under the transmission strategy θ2 is modeled as shown in 23;

[0188] Based on Equation 22, for the first given communication rate λ, assuming that the time delay caused by the transmission strategy θ2 is D, its estimated performance is further analyzed as follows:

[0189]

[0190] in, represents the error covariance of the transmission strategy θ2 at time kD.

[0191] Step 4.3: Based on step 4.2, for any time delay step D2>D, since equation 23 is a monotonically increasing function, there exists a D * Make the function values ​​of equation 22 and equation 23 equal;

[0192] Assume that there is a time delay step D2>D, so that the following inequality holds:

[0193]

[0194] From equation 28, equation 23 is a monotonically increasing function, which means that there exists a D * So that the following equation holds:

[0195]

[0196] On this basis, the balance relationship between the two transmission strategies is defined as follows:

[0197]

[0198]

[0199]

[0200] Step 4.4: Based on the monotonicity of the cost function 28 in step 4.2, for a given communication rate λ, calculate the time delay D * Threshold:

[0201] For a given communication rate λ, the threshold based on the time delay D is calculated as follows:

[0202]

[0203] Further rewritten as:

[0204]

[0205] in,

[0206] Define the following inequality:

[0207]

[0208]

[0209] According to formula 33-35, the threshold interval of time delay D is calculated as follows:

[0210]

[0211] in,

[0212]

[0213]

[0214] Step 4.5: Using the threshold calculated in step 4.4, the cyber-physical system remotely estimates the scheduling decisions of the above two data transmission mechanisms under different conditions;

[0215] When D <D, Select strategy θ1 to transmit data to the remote estimator;

[0216] when The strategy θ2 is selected to transmit data to the remote estimator.

[0217] like Figure 4 It is shown that when the time delay D≤2, the estimated performance of the transmission strategy θ2 is better than the estimated performance of the transmission strategy θ1. When D>2, the estimated performance of the transmission strategy θ1 is better than the estimated performance of the transmission strategy θ2.

[0218] like Figure 5The figure illustrates the performance comparison of the two transmission strategies under a given delay and average communication rate. For example, when the average communication rate λ = 0.15, if D ≤ 1, the estimated performance of the transmission strategy θ2 is better than the estimated performance of the transmission strategy θ1, and if D ≥ 2, the estimated performance of the transmission strategy θ1 is better than the estimated performance of the transmission strategy θ2.

Claims

1. A remote estimation sensor scheduling decision method based on threshold structure, characterized in that: The specific steps include: Step 1: Model the cyber-physical system as a discrete steady-state system; Step 2: After collecting the raw data of the system status, the sensors on the cyber-physical system k In the scenario where the original data is directly sent to the estimator at the far end of the system, the strategy of the original data transmitted by the sensor is defined as θ1. For strategy θ1, a remote estimation model for the state of the cyber-physical system is established. And its corresponding error covariance model At the same time, the value of the model in the steady state is calculated After the sensor collects data y k Later, the event trigger mechanism strategy is used to further calculate and determine y k Whether to send data to the remote estimator, define the event trigger mechanism strategy as θ2, and calculate the time required for the mechanism to send data to the remote estimator at each moment based on the existing modeling of remote estimation and error covariance of the event trigger mechanism, and establish a new remote estimation model And its corresponding error covariance model Get the communication rate λ; Step 3. Obtain a balance relationship model of the two transmission strategies based on error covariance by constructing the objective functions of the two transmission strategies; obtain the time delay D; Step 4: For the given communication rate λ in step 2, analyze the performance of the remote state estimation scheduling method of the cyber-physical system from the perspective of time delay D through step 3, and calculate the threshold D * .

2. According to the threshold structure-based remote estimation sensor scheduling decision method of claim 1, it is characterized in that: Step 1: Model the cyber-physical system as a discrete steady-state system as follows: x k+1 =Ax k +w k y k =Cx k +v k (1) Among them, x k represents the state value of the cyber-physical system at time k, y k represents the output value of the cyber-physical system, A is the state transfer matrix of the system, and C represents the state conversion matrix; w k and v k is independent and identically distributed Gaussian noise.

3. The remote estimation sensor scheduling decision method based on threshold structure according to claim 2 is characterized in that: Step 2 is as follows: Step 2.1: Collect raw data y of the cyber-physical system status from system sensors k In the scenario where the data is directly sent to the remote estimator, the strategy of the original data transmitted by the sensor is defined as θ1, and a remote state estimation model of the system state under the original data transmission strategy is established. and its error covariance model Due to the uncertainty of the wireless channel, the original data y k Packet loss occurs, so first define the indicator function γ at the remote estimator end k ∈{0,1} to describe whether the remote estimator receives the data packet y sent by the sensor at each time k k , when the remote estimator receives y k Time k =1, otherwise γ k =0, specifically expressed as follows: Secondly, define the information set of the remote estimator at time k as follows: Finally, the minimum mean square error estimate of the sensor side of the cyber-physical system is calculated under the information set obtained in the above formula: and its corresponding covariance That is, the remote estimation model and the error covariance model: Where E represents mathematical expectation; Based on equations (4) and (5), under the transmission strategy θ1, when the data packet sent by the sensor reaches the remote state estimator, the remote state estimator will update its estimated value. Otherwise, the remote state estimator will make a prediction based on the estimated value at the previous moment. Under this mechanism, its state estimation and its error covariance are modeled as follows: in, is the Kalman filter gain; For new breath; The calculation is performed by Kalman filtering as follows: In order to simplify the formula (8), and For any variable X, the following function is defined: h(X)=AXA′+Q (9) Where Q is the Gaussian noise w k covariance; R is Gaussian noise v k covariance; A′ represents the transpose of matrix A; C′ represents the transpose of matrix C; Based on equations (9) and (10), and The abbreviation is as follows: Step 2.2: Build a remote state estimation model based on event-triggered transmission strategy and its error covariance model First, define θ2 as an event-triggered transmission strategy. Under this framework, the sensor responsible for collecting system status at the system end needs to generate an independent and identically distributed random variable β at each moment. k Compare it with the exponential function formed by the sensor measurement value to decide whether to send a packet at the current moment, as follows: Among them, Y is a positive definite matrix that can be designed, ρ k ∈[0,1] is a random variable, β k = 0 means that the sensor does not need to transmit the measured value y to the remote end at time k k , whereas β k =1;y' k Represents y k The transpose of ; Based on formula (13), the information set of the remote estimator k at the transmission strategy θ2 is defined as follows: Assuming that the two transmission strategies transmit data packets in an ideal communication channel with no packet loss, under this framework, the average communication rate is calculated as follows: in, Secondly, the minimum mean square error estimate of the local state of the cyber-physical system is calculated under the information set obtained by equation (14): and its corresponding covariance as follows: Assuming that the time required for the sensor to calculate whether to transmit data is D ≥ 1, under the information set obtained by equation (14), the remote state estimation and its error covariance are modeled as follows: Here, h is a composite function that satisfies the following equation for any variable X: h 2 (X)=h(h(X))。 4. The remote estimation sensor scheduling decision method based on threshold structure according to claim 3 is characterized in that: Step 3 is as follows: Step 3.1: Assume that the two transmission strategies are compared in a steady-state sense, that is, the error covariance of the two strategies tends to be stable; based on this condition, for a given communication rate λ and time delay length D, for transmission strategies θ1 and θ2, define the following performance indicator function: Among them, Tr represents a matrix operation symbol, indicating the trace of the matrix; Step 3.2: Based on equations (8) and (20), the estimation error covariance of the remote state estimator in the expected sense is as follows: in, 5. The remote estimation sensor scheduling decision method based on threshold structure according to claim 4 is characterized in that: Step 4 is as follows: Step 4.1: For the communication rate λ calculated by equation (15), the error covariance model of the transmission strategy θ1 in the expected sense is shown in (22), and the steady-state value of the transmission strategy θ1 at the communication rate λ is obtained. Step 4.2: For the first given communication rate λ, assume that the time delay caused by the transmission strategy θ2 is D; based on this assumption, the error covariance under the transmission strategy θ2 is modeled as shown in (23); Based on formula (22), for the first given communication rate λ, assuming that the time delay caused by the transmission strategy θ2 is D, its estimation performance is further analyzed as follows: in, represents the error covariance of the transmission strategy θ2 at time kD; Step 4.3: Based on step 4.2, for any time delay step D2>D, since equation (23) is a monotonically increasing function, there exists a D * Make the function values ​​of equation (22) and equation (23) equal; Assume that there is a time delay step D2>D, so that the following inequality holds: From equation (28), equation (23) is a monotonically increasing function, which means that there exists a D * So that the following equation holds: On this basis, the balance relationship between the two transmission strategies is defined as follows: Step 4.4: Based on the monotonicity of the cost function (28) in step 4.2, for a given communication rate λ, calculate the time delay D * Threshold: Step 4.5: Using the threshold calculated in step 4.4, the cyber-physical system remotely estimates the scheduling decisions of the above two data transmission mechanisms under different conditions; When D <D, Select strategy θ1 to transmit data to the remote estimator; when The strategy θ2 is selected to transmit data to the remote estimator.

6. The remote estimation sensor scheduling decision method based on threshold structure according to claim 5 is characterized in that: Step 4.1 is as follows: Based on formula (22), given the communication rate λ, the estimated performance of the transmission strategy θ1 is further analyzed as follows: (24) Among them: The asymptotic performance of the transmission strategy θ1 is defined as follows: in Representation function The value at time k; Based on equations (24) and (25), when k→∞, the error covariance of the transmission strategy θ1 in the steady state is as follows:

7. The remote estimation sensor scheduling decision method based on threshold structure according to claim 6 is characterized in that: Step 4.4 is as follows: For a given communication rate λ, the threshold based on the time delay D is calculated as follows: Further rewritten as: in, Define the following inequality: According to formulas (33)-(35), the threshold interval of time delay D is calculated as follows: in,

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