Remote State Estimation Sensor Scheduling Method, Scheduler, and Cyber-Physical System

Abstract

The present invention relates to the field of communication technologies, and in particular to a remote state estimation sensor scheduling method, a scheduler, and a cyber-physical system. The remote state estimation sensor scheduling method of the present invention explores the submodular property of the estimation error covariance matrix at the end time. After analyzing the logarithmic form of the determinant of the covariance inverse matrix, a single-step calculation scheduling method is proposed based on its special submodular property. When the optimization problem satisfies submodularity, the scheduling strategy obtained by solving the single-step optimization problem can be faster and more efficient than solving the original optimization problem, reducing the exponential complexity of solving the original problem in the time dimension to linear, being able to reduce the computational complexity and shorten the computational duration while ensuring the estimation accuracy within a certain range, and providing an effective sensor scheduling method for physical systems that require timely estimation results.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and in particular, to a remote state estimation sensor scheduling method, a scheduler, and a cyber-physical system. Background Art

[0002] In the existing technologies, with the informatization and networking of the new generation of production equipment, the performance of various networked systems in human social production activities is becoming increasingly dependent. A cyber-physical system is a system that tightly connects physical processes, sensors, computing, and control modules through network communication. Typical examples include the Internet of Things, smart grids, and intelligent transportation. It provides technical support for the intelligent upgrading of many important fields related to the national economy. Among them, sensors transmit the measured data to a remote estimator through wireless communication. The remote estimator estimates the state variables in the physical system based on the understanding of the structure and parameters of the system itself and the received measured values. Generally speaking, transmitting data consumes most of the battery energy in the sensors. In a cyber-physical system containing a large number of sensors, for sensors powered by batteries, replacing the battery usually brings high costs and takes a lot of time. Even in some extreme environments such as high temperature and high pressure, the battery replacement operation cannot be performed. In addition to the limited battery energy, the bandwidth limitation of the wireless communication channel also restricts the sensor scheduling method. In the remote state estimation of a cyber-physical system, the design of the sensor scheduling method is one of the research hotspots in recent years.

[0003] The design of the sensor scheduling method can be targeted at different scenarios such as single systems and multi-systems, reliable channels and packet loss channels, etc. Most of the existing scheduling methods use means such as convex optimization to solve optimization problems and construct Markov decision processes, and are designed based on the average estimation error covariance matrix and its trace of the remote estimator. Although a high state estimation accuracy can be obtained under these sensor scheduling methods, as the state dimension, physical system, and the number of sensors increase, the computational complexity also increases exponentially, bringing double pressures of computational resources and timeliness of computational results to practical industrial applications. Considering that in actual production operations, especially for a rapidly changing physical system, the state estimation accuracy only needs to be maintained within an acceptable range, and the timeliness of the results is more important. Therefore, for the case of multi-systems and multi-sensors and relatively complex packet loss channels, how to shorten the calculation time while ensuring a certain estimation accuracy is an urgent problem to be solved. Summary of the Invention

[0004] Therefore, the technical problem to be solved by the present invention is to overcome the problems of large computational amount and long calculation time in the scheduling of multi-systems and multi-sensors under a packet loss channel in the prior art.

[0005] To solve the above technical problems, the present invention provides a remote state estimation sensor scheduling method, including:

[0006] Construct a linear time-invariant state space model for the i-th physical system corresponding to the i-th sensor, where i ∈ 1...N and N is the total number of sensors;

[0007] Model the packet loss channel using the Bernoulli distribution to construct the channel transmission model of the wireless communication network;

[0008] Establish a state estimation equation according to the linear time-invariant state space model and the channel transmission model, and perform state estimation on the i-th physical system according to the state estimation equation to obtain a state estimation value and the corresponding error covariance;

[0009] Establish an optimization objective function for remote state estimation, that is, within a given time window, find a set of scheduling strategies to maximize the weighted value of the expected inverse matrix of the estimation error covariance at the terminal time in the sense of the logarithmic determinant, and adjust the function structure and parameters of the objective function to make it satisfy submodularity;

[0010] For the optimization objective function that satisfies submodularity, solve the scheduling strategy that maximizes the single-step benefit at the current time under the condition of satisfying the communication resource constraint at each moment.

[0011] Preferably, the constructing a linear time-invariant state space model for the i-th physical system corresponding to the i-th sensor:

[0012] x i,k+1 = A i x i,k + w i,k

[0013] y i,k = C i x i,k + v i,k

[0014] Wherein, is the process state of the i-th physical system at time k, represents an n-dimensional Euclidean space, x i,k+1 is the process state of the i-th physical system at time k + 1, is the measurement value of the sensor corresponding to the i-th physical system at time k, and are the process matrix and the observation matrix of the system respectively, the process noise w i,k , the observation noise v i,k and the state initial value x i,0 are independent zero-mean Gaussian random variables, and their covariance matrices are Q i≥0, R i >0, Π i,0 >0.

[0015] Preferably, the method for modeling the packet loss channel using the Bernoulli distribution to construct the channel transmission model of the wireless communication network includes:

[0016] Assume that the scheduling policy is where γ i,k = 1 indicates that the scheduler transmits the measurement value y of the physical system i at time k i,k to the remote estimator, and γ i,k = 0 indicates no transmission;

[0017] Considering the packet loss situation existing in the channel itself, use the Bernoulli distribution to model it. When γ i,k = 1, when the indicator variable α i,k = 1, it means that the measurement value y of the physical system i at time k i,k is successfully received by the remote estimator. When the indicator variable α i,k = 0, a packet loss phenomenon occurs.

[0018] Preferably, the method for establishing the state estimation equation according to the linear time-invariant state space model and the channel transmission model, and performing state estimation on the i-th physical system according to the state estimation equation to obtain the state estimation value and the corresponding error covariance includes:

[0019] Define the information set of the remote estimator about system i at time k, which includes all received measurement values up to time k and the indicator variable indicating whether the measurement value is successfully transmitted:

[0020]

[0021] Define the state estimation value as the expected value of the system state x i,k based on the information set and its corresponding error covariance is where represents the mathematical expectation of the random variable;

[0022] Set that when the remote estimator receives the measurement value of the i-th physical system, use the Kalman estimator to perform state estimation to obtain the state estimation value and the corresponding error covariance;

[0023] Set that when the remote estimator does not receive the measurement value of the i-th physical system, use single-step prediction to perform state estimation to obtain the state estimation value and the corresponding error covariance.

[0024] Preferably, when the remote estimator receives the measurement value of the i-th physical system, the Kalman estimator is used for state estimation, and the obtained state estimation value and the corresponding error covariance include:

[0025] When the remote estimator receives the measurement value of the i-th physical system, the Kalman estimator is used for state estimation, and the state estimation value and the error covariance are updated as:

[0026]

[0027]

[0028]

[0029] where K i,k is the Kalman estimation gain for system i at time k.

[0030] Preferably, when the remote estimator does not receive the measurement value of the i-th physical system, single-step prediction is used for state estimation, and the obtained state estimation value and the corresponding error covariance include:

[0031] When the remote estimator does not receive the measurement value of the i-th physical system, single-step prediction is used for state estimation, and the state estimation value and the error covariance are updated as:

[0032]

[0033]

[0034] The optimization objective function for establishing remote state estimation is to find a set of scheduling strategies within a given time window such that the expected value of the inverse matrix of the estimation error covariance at the terminal time is maximized in the sense of the logarithmic determinant:

[0035]

[0036]

[0037] where β i ∈(0, 1] represents the weight factor. The larger β i , the more attention is paid to the estimation performance of the i-th physical system. ||Γ k || 1 ≤d k means that at most d k sensors are allowed to transmit measurement values at time k, and T is the terminal time;

[0038] Set the process noise covariance Q i = 0, the observation matrix C i has full column rank and and such that the objective function satisfies submodularity.

[0039] Preferably, for the optimized objective function that satisfies submodularity, the solution of the scheduling strategy that maximizes the single-step reward at each moment under the condition of satisfying the communication resource constraint includes:

[0040] Initialize the estimation error covariance P i,0 = Π i,0 , let Γ greedy = (), solve the scheduling strategy that maximizes the single-step reward at each moment under the condition of satisfying the communication resource constraint, and add the solution obtained to the set Γ greedy :

[0041]

[0042] where Γ represents all available scheduling strategies.

[0043] The present invention also provides a remote state estimation sensor scheduler, including:

[0044] A linear time-invariant state space model construction module for constructing a linear time-invariant state space model for the i-th physical system corresponding to the i-th sensor, where i ∈ 1...N and N is the total number of sensors;

[0045] A channel transmission model construction module for modeling the packet loss channel using the Bernoulli distribution and constructing a channel transmission model of the wireless communication network;

[0046] A state estimation calculation module for establishing a state estimation equation according to the linear time-invariant state space model and the channel transmission model, and performing state estimation on the i-th physical system according to the state estimation equation to obtain a state estimation value and a corresponding error covariance;

[0047] An optimization objective construction module for establishing an optimization objective function for remote state estimation, that is, within a given time window, finding a set of scheduling strategies to maximize the weighted value of the expected inverse matrix of the estimation error covariance at the terminal moment in the sense of the logarithmic determinant, and adjusting the function structure and parameters of the objective function to make it satisfy submodularity;

[0048] A scheduling strategy acquisition module for solving the scheduling strategy that maximizes the single-step reward at each moment under the condition of satisfying the communication resource constraint for the optimized objective function that satisfies submodularity.

[0049] The present invention also provides a cyber-physical system including the above-mentioned remote state estimation sensor scheduler.

[0050] The above technical solution of the present invention has the following advantages compared with the prior art:

[0051] For the remote state estimation sensor scheduling method described in the present invention, the submodular property of the estimation error covariance matrix at the end time is exploited. After analyzing the logarithmic form of the determinant of the covariance inverse matrix, a single-step calculation scheduling method is proposed based on its special submodular property. When the optimization problem satisfies submodularity, the scheduling strategy obtained by solving the single-step optimization problem can be faster and more efficient than solving the original optimization problem, reducing the exponential complexity of solving the original problem in the time dimension to linear. It can reduce the computational complexity and shorten the calculation time while ensuring the estimation accuracy within a certain range, providing an effective sensor scheduling method for physical systems that require timely estimation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to make the content of the present invention easier to be clearly understood, the following further details the present invention according to specific embodiments of the present invention in conjunction with the accompanying drawings, where:

[0053] Figure 1 is the implementation flowchart of a remote state estimation sensor scheduling method of the present invention;

[0054] Figure 2 is the estimation performance diagram of different scheduling methods at different terminal times;

[0055] Figure 3 is the estimation performance diagram of different scheduling methods under different numbers of systems;

[0056] Figure 4 is the structural block diagram of a remote state estimation sensor scheduler provided by an embodiment of the present invention;

[0057] Figure 5 is a cyber-physical system provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0058] The core of the present invention is to provide a remote state estimation sensor scheduling method, scheduler and cyber-physical system, which reduce the computational complexity and shorten the calculation time while ensuring the estimation accuracy within a certain range.

[0059] In order to enable those skilled in the art to better understand the solution of the present invention, the following further details the present invention in conjunction with the accompanying drawings and specific embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0060] Please refer toFigure 1 , Figure 1 This is the implementation flowchart of a remote state estimation sensor scheduling method provided by the present invention. The specific operation steps are as follows:

[0061] S101: Construct a linear time-invariant state space model for the i-th physical system corresponding to the i-th sensor, where i ∈ 1...N and N is the total number of sensors:

[0062] x i,k+1 = A i x i,k + w i,k

[0063] y i,k = C i x i,k + v i,k

[0064] The physical systems involved are independent of each other in terms of state. Each physical system can have different state dimensions, system parameters, measurement dimensions, and noise characteristics;

[0065] Among them, is the process state of the i-th physical system at time k, represents an n-dimensional Euclidean space, x i,k+1 is the process state of the i-th physical system at time k + 1, is the measurement value of the sensor corresponding to the i-th physical system at time k, and are the process matrix and the observation matrix of the system respectively. The process noise w i,k , the observation noise v i,k and the state initial value x i,0 are independent zero-mean Gaussian random variables, and their covariance matrices are Q i ≥ 0, R i > 0, Π i,0 > 0. Since the state space model of a linear time-invariant system is usually obtained by linearizing a continuous-time state space model, for a continuous physical system in terms of, when the sampling period is T s the process matrix obtained after its linearization is Obviously A i is non-singular. Therefore, in this embodiment, the physical system for which the process matrix A i is a non-singular matrix.

[0066] S102: Use the Bernoulli distribution to model the packet loss channel and construct the channel transmission model of the wireless communication network;

[0067] The scheduler determines which sensors can transmit measurement values through the wireless channel at the current time instant \(k\). At each time instant, at most \(d\) k sensors are allowed to use the communication channel simultaneously. Assume the scheduling policy is where \(\gamma\) i,k = 1 indicates that the scheduler transmits the measurement value \(y\) of the physical system \(i\) at time instant \(k\) to the remote estimator, and \(\gamma\) i,k = 0 indicates no transmission; the communication resource constraint can be written as \(\|\Gamma\| i,k \leq d k \), which means that at most \(d\) 1 sensors are allowed to transmit measurement values at time instant \(k\). k k

[0068] Considering the packet loss situation existing in the channel itself, it is modeled using the Bernoulli distribution. When \(\gamma\) i,k = 1, when the indicator variable \(\alpha\) i,k = 1, it means that the measurement value \(y\) of the physical system \(i\) at time instant \(k\) is successfully received by the remote estimator. When the indicator variable \(\alpha\) i,k = 0, a packet loss phenomenon occurs. The probability of packet loss is \(\Pr(\alpha i,k = 0)=1 - \alpha i,k \), where \(\alpha\) i is a constant and \(0\lt\alpha i \leq1\). By introducing the indicator variables \(\gamma\) i and \(\alpha\) i,k and \(\alpha\) i,k , the modeling of the packet-loss wireless communication network is thus completed.

[0069] S103: Establish a state estimation equation according to the linear time-invariant state space model and the channel transmission model, and perform state estimation on the \(i\)-th physical system according to the state estimation equation to obtain a state estimation value and the corresponding error covariance;

[0070] Define the information set of the remote estimator about system \(i\) at time instant \(k\) to include all received measurement values up to time instant \(k\) and the indicator variable indicating whether the measurement value is successfully transmitted:

[0071]

[0072] Define the state estimation value as the expected value of the system state \(x\) i,k based on the information set and its corresponding error covariance is where represents the mathematical expectation of a random variable. Define the initial value \(P i,0 =\Pi i,0 ;

[0073] When the remote estimator receives the measurement of the i-th physical system, i.e., γ i,k α i,k = 1, the Kalman estimator is used for state estimation, and the state estimation value and error covariance are updated as follows:

[0074]

[0075]

[0076]

[0077] where K i,k is the Kalman estimation gain for system i at time k. For the convenience of subsequent expression, denote From the non-singularity of the process matrix A i and the positive definiteness of the initial value Π i,0 it can be seen that the inverse matrices in the above Kalman estimator all have solutions.

[0078] When the remote estimator does not receive the measurement of the i-th physical system, i.e., γ i,k α i,k = 0, single-step prediction is used for state estimation, and the state estimation value and error covariance are updated as follows:

[0079]

[0080]

[0081] The limited communication resources and packet loss of the wireless network itself will both cause the remote estimator to fail to receive the measurements of some physical systems. When the estimator does not receive the measurement of a certain physical system, single-step prediction is used for state estimation; when the estimator receives the measurement of a certain physical system, the Kalman estimator is used for estimation, which greatly improves the estimation performance corresponding to this physical system.

[0082] S104: Establish an optimization objective function for remote state estimation, that is, within a given time window, find a set of scheduling strategies to maximize the weighted value of the expected inverse matrix of the estimation error covariance at the terminal time in the sense of the logarithmic determinant, and adjust the function structure and parameters of the objective function to make it satisfy submodularity;

[0083] For the objective function that satisfies submodularity, the scheduling strategy given when the single-step benefit is the largest can keep its estimation performance within a proportional range of the optimal performance, and compared with the optimal scheduling strategy, the required calculation time and calculation resources are greatly reduced.

[0084] S105: For an optimization objective function that satisfies submodularity, solve the scheduling strategy that maximizes the single-step reward at each moment under the condition of satisfying the communication resource constraint.

[0085] The remote state estimation sensor scheduling method described in the present invention explores the submodular property of the estimation error covariance matrix at the end time. After analyzing the logarithmic form of the determinant of the covariance inverse matrix, a single-step calculation scheduling method is proposed based on its special submodular property. When the optimization problem satisfies submodularity, the scheduling strategy obtained by solving the single-step optimization problem can be faster and more efficient than solving the original optimization problem, reducing the exponential complexity of solving the original problem in the time dimension to linear. It can reduce the computational complexity and shorten the calculation duration while ensuring the estimation accuracy within a certain range, providing an effective sensor scheduling method for physical systems that require timely estimation results.

[0086] Based on the above embodiments, this embodiment further elaborates on steps S104 - S105 in detail:

[0087] Select the estimation error covariance at the terminal time T as the estimation performance measurement index, and define the multi-system remote state estimation sensor scheduling problem as follows:

[0088]

[0089]

[0090] where β i ∈(0, 1] represents the weight factor. The larger β i is, the more attention is paid to the estimation performance of the i-th physical system. In this optimization problem, for a given time window T, it is desired to find a set of scheduling strategies such that the weighted value of the expected value of the inverse matrix of the estimation error covariance at the terminal time is maximized in the sense of the logarithmic determinant. For this optimization problem, when the process noise covariance Q i = 0, the observation matrix C i is full column rank, and and hold, the optimization objective function i.e., the estimation performance, has non-monotonic decreasing property and submodularity. A sequence function is a function that maps a sequence to a real number. The non-monotonic decreasing property of the sequence function f(·) is expressed as for {ζ l} and its subsequence {ζ k}, there is f({ζ k}) ≤ f({ζ l}).

[0091] where, a sequence {ζ k} is another sequence {ζl a subsequence of {ζ}, defined as l ≥ k and the first k elements in the sequence {ζ l} are the same as those in {ζ k}. To illustrate submodularity, define Γ {j} as the scheduling strategy adopted at a certain moment. Then the submodularity of the sequence function f(·) is expressed as for {ζ l} and its subsequence {ζ k}, there is

[0092]

[0093] For the sake of concise expression, define

[0094] The original multi-system remote state estimation sensor scheduling problem needs to solve the scheduling strategy uniformly within the time interval T. However, for an optimization problem satisfying submodularity, for each moment k, under the condition of satisfying the communication resource constraint, the scheduling strategy that maximizes the single-step benefit at the current moment can be calculated separately. The specific process is as follows. First, initialize the estimation error covariance P i,0 = Π i,0 , and let Γ greedy = (). For each moment k = 1:1:T, solve the single-step optimization problem

[0095]

[0096] and add the obtained to the set Γ greedy , and output the scheduling strategy result, that is, Γ greedy . Among them, Γ represents all the available scheduling strategies.

[0097] Under this scheduling strategy, the obtained estimation performance target is relatively close to the optimal solution of the original problem, and the value range of its estimation performance can be expressed as

[0098]

[0099] Among them, represents the optimal scheduling strategy of the original multi-system remote state estimation sensor scheduling problem within the time window T. It can be seen that the obtained Γ greedy can achieve at least the performance of the optimal scheduling strategy .

[0100] When the optimization problem satisfies submodularity, the scheduling strategy obtained by solving the single-step optimization problem can be faster and more efficient than solving the original optimization problem, reducing the exponential complexity of solving the original problem in the time dimension to linear, and achieving at least 63.2% of the estimated performance of the optimal solution. This performance range holds for all physical systems and communication channels that meet the conditions. For the multi-system scheduling problem involving 5 physical systems, the estimated performances are compared using the scheduling strategy based on submodular structure proposed in the present invention, the optimal scheduling strategy of the original problem, and the worst scheduling strategy. As Figure 2 shown, for different selections of the time interval T, the scheduling strategy (Greedy Scheduling) proposed in the present invention can obtain performance metrics close to those of the optimal scheduling strategy (Optimal Scheduling), and is far better than the worst scheduling strategy (Worst Scheduling). For different selections of the number of physical systems, as Figure 3 shown, the scheduling strategy (Greedy Scheduling) proposed in the present invention can still achieve performance close to the optimal.

[0101] Please refer to Figure 4 , Figure 4 which is a structural block diagram of a remote state estimation sensor scheduler provided by an embodiment of the present invention; specifically including:

[0102] A linear time-invariant state space model construction module 100, configured to construct a linear time-invariant state space model for the i-th physical system corresponding to the i-th sensor, where i ∈ 1...N and N is the total number of sensors;

[0103] A channel transmission model construction module 200, configured to model the packet loss channel using the Bernoulli distribution and construct a channel transmission model of the wireless communication network;

[0104] A state estimation calculation module 300, configured to establish a state estimation equation according to the linear time-invariant state space model and the channel transmission model, perform state estimation on the i-th physical system according to the state estimation equation, and update the state estimation value and the error covariance;

[0105] An optimization objective construction module 400, configured to establish an optimization objective function for remote state estimation, that is, within a given time window, find a set of scheduling strategies to maximize the weighted value of the expected inverse matrix of the estimation error covariance at the terminal moment in the sense of the logarithmic determinant, and adjust the function structure and parameters of the objective function to make it satisfy submodularity;

[0106] A scheduling strategy acquisition module 500, configured to solve the scheduling strategy that maximizes the single-step benefit at each moment under the condition of satisfying the communication resource constraint for the optimization objective function that satisfies submodularity.

[0107] The remote state estimation sensor scheduler in this embodiment is used to implement the aforementioned remote state estimation sensor scheduling method. Therefore, the specific implementation in the remote state estimation sensor scheduler can be seen in the embodiment part of the remote state estimation sensor scheduling method above. For example, the linear time-invariant state space model construction module 100, the channel transmission model construction module 200, the state estimation calculation module 300, the optimization objective construction module 400, and the scheduling policy acquisition module 500 are respectively used to implement steps S101, S102, S103, S104, and S105 in the above-mentioned remote state estimation sensor scheduling method. Therefore, the specific implementation can refer to the descriptions of the corresponding individual embodiments and will not be elaborated here.

[0108] The present invention also provides a cyber-physical system, as Figure 5 shown, which includes the above-mentioned remote state estimation sensor scheduler. Several sensors respectively measure the corresponding physical systems and transmit the measurement values to the remote estimator through a wireless communication network with packet loss. Due to communication resource limitations, at each moment, the scheduler can only allow a limited number of sensors to perform data transmission. The scheduler schedules the sensors through the method proposed by the present invention.

[0109] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0110] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of the flows and / or blocks in the flowchart and / or block diagram can also be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0111] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to operate in a particular manner, such that the instructions stored in the computer-readable memory produce a manufacture including instruction means that implement the functions specified in one or more of the flow Figure 1 steps or a plurality of flow steps and / or blocks Figure 1 or a plurality of blocks.

[0112] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable apparatus provide steps for implementing the functions specified in one or more of the flow Figure 1 steps or a plurality of flow steps and / or blocks Figure 1 or a plurality of blocks.

[0113] Obviously, the above embodiments are merely examples for clear illustration and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to exhaustively list all the implementation manners here. And the obvious changes or modifications derived therefrom are still within the protection scope of the present invention.

Claims

1. A remote state estimation sensor scheduling method, characterized in that, it includes: Construct a linear time-invariant state space model for the i-th physical system corresponding to the i-th sensor, where i ∈ 1...N and N is the total number of sensors; Model the packet loss channel using the Bernoulli distribution to construct a channel transmission model for the wireless communication network; Establish a state estimation equation according to the linear time-invariant state space model and the channel transmission model, and perform state estimation on the i-th physical system according to the state estimation equation to obtain a state estimation value and a corresponding error covariance; Establish an optimization objective function for remote state estimation, that is, within a given time window, find a set of scheduling strategies to maximize the weighted value of the expected inverse matrix of the estimation error covariance at the terminal time in the sense of the logarithmic determinant: where, β i ∈(0,1] represents the weight factor, the larger β i is, the more attention is paid to the estimated performance of the i-th physical system, ||Γ k || 1 ≤d k means that at most d k sensors are allowed to transmit measurement values at time k, T is the terminal time; represents the scheduling strategy; represents the mathematical expectation of a random variable; And adjust the function structure and parameters of the objective function to satisfy submodularity, that is, set the process noise covariance Q i = 0, the observation matrix C i to be column full rank, and and such that the objective function satisfies submodularity; where and are the process matrix and the observation matrix of the system respectively; the covariance matrices of the process noise w i,k , the observation noise v i,k and the initial state value x i,0 are Q i ≥ 0, R i > 0, Π i,0 > 0; For the optimization objective function that satisfies submodularity, solve the scheduling strategy that maximizes the single-step benefit at the current time under the condition of satisfying the communication resource constraint at each moment, including: Initialize the estimation error covariance P i,0 = Π i,0 , let Γ greedy = (), solve the scheduling strategy that maximizes the single-step reward at each time instant under the condition of satisfying the communication resource constraint, and add the solution obtained to the set Γ greedy : where Γ represents all available scheduling strategies.

2. The remote state estimation sensor scheduling method according to claim 1, characterized in that, The constructing a linear time-invariant state space model for the i-th physical system corresponding to the i-th sensor: x i,k+1 = A i x i,k + w i,k y i,k = C i x i,k + v i,k where, is the process state of the i-th physical system at time k, represents an n-dimensional Euclidean space, and x i,k+1 is the process state of the i-th physical system at time k + 1, is the measurement value of the sensor corresponding to the i-th physical system at time k, and are the process matrix and the observation matrix of the system respectively. The process noise w i,k , the observation noise v i,k and the initial state value x i,0 are independent zero-mean Gaussian random variables, and their covariance matrices are Q i ≥0, R i > 0, Π i,0 > 0.

3. The remote state estimation sensor scheduling method according to claim 2, characterized in that, The modeling the packet loss channel using the Bernoulli distribution to construct a channel transmission model for the wireless communication network includes: Assume the scheduling policy is where γ i,k = 1 means that the scheduler transmits the measurement value y of the physical system i at time k i,k to the remote estimator, and γ i,k = 0 means no transmission is performed; Considering the packet loss situation existing in the channel itself, it is modeled using the Bernoulli distribution. When γ i,k = 1, when the indicator variable α i,k = 1, it means that the measurement value y i,k of the physical system i at time k is successfully received by the remote estimator. When the indicator variable α i,k = 0, a packet loss phenomenon occurs.

4. The remote state estimation sensor scheduling method according to claim 3, characterized in that, The establishing a state estimation equation according to the linear time-invariant state space model and the channel transmission model, and performing state estimation on the i-th physical system according to the state estimation equation to obtain a state estimation value and a corresponding error covariance includes: Define the information set of the remote estimator about system i at time k to include all received measurement values up to time k and an indicator variable indicating whether the measurement value is successfully transmitted; Define the state estimate as the expected value of the system state x based on the information set i,k and its corresponding error covariance is where denotes the mathematical expectation of a random variable; ​ Set that when the remote estimator receives the measurement value of the i-th physical system, use the Kalman estimator for state estimation to obtain a state estimation value and a corresponding error covariance; Set that when the remote estimator does not receive the measurement value of the i-th physical system, use single-step prediction for state estimation to obtain a state estimation value and a corresponding error covariance.

5. The remote state estimation sensor scheduling method according to claim 4, characterized in that, The setting that when the remote estimator receives the measurement value of the i-th physical system, use the Kalman estimator for state estimation to obtain a state estimation value and a corresponding error covariance includes: When the remote estimator receives the measurement value of the i-th physical system, use the Kalman estimator for state estimation, and the state estimation value and error covariance are updated as: where K i,k is the Kalman estimation gain for system i at time k.

6. The remote state estimation sensor scheduling method according to claim 4, characterized in that, The setting that when the remote estimator does not receive the measurement value of the i-th physical system, use single-step prediction for state estimation to obtain a state estimation value and a corresponding error covariance includes: When the remote estimator does not receive the measurement value of the \(i\)-th physical system, single-step prediction is used for state estimation, and the state estimation value and error covariance are updated as follows:

7. A remote state estimation sensor scheduler, characterized in that, it includes: a linear time-invariant state space model construction module for constructing a linear time-invariant state space model for the \(i\)-th physical system corresponding to the \(i\)-th sensor, where \(i\in1...N\) and \(N\) is the total number of sensors; a channel transmission model construction module for modeling the packet loss channel using the Bernoulli distribution and constructing a channel transmission model of the wireless communication network; a state estimation calculation module for establishing a state estimation equation according to the linear time-invariant state space model and the channel transmission model, and performing state estimation on the \(i\)-th physical system according to the state estimation equation to obtain a state estimation value and a corresponding error covariance; an optimization objective construction module for establishing an optimization objective function for remote state estimation, that is, within a given time window, finding a set of scheduling strategies to maximize the weighted value of the expected inverse matrix of the estimation error covariance at the terminal time in the sense of the logarithmic determinant; where, β i ∈(0,1] represents the weight factor, the larger β i is, the more attention is paid to the estimated performance of the \(i\)-th physical system, ||Γ k || 1 ≤d k means that at most \(d\) k sensors are allowed to transmit measurement values at time \(k\), and \(T\) is the terminal time; represents the scheduling policy; represents the mathematical expectation of a random variable; And adjust the function structure and parameters of the objective function to satisfy submodularity, that is, set the process noise covariance Q i = 0, the observation matrix C i has full column rank and and make the objective function satisfy submodularity; where, and are the process matrix and the observation matrix of the system respectively; the covariance matrices of the process noise w i,k , the observation noise v i,k and the initial state value x i,0 are Q i ≥ 0, R i > 0, Π i,0 > 0; a scheduling strategy acquisition module for solving the scheduling strategy that maximizes the single-step reward at the current time under the condition of satisfying the communication resource constraint for each moment for the optimization objective function that satisfies submodularity, including: Initialize the estimation error covariance P ,0 = Π i,0 , let Γ greedy = (), solve the scheduling strategy that maximizes the single-step reward at each time instant under the condition of satisfying the communication resource constraint, and add the solution obtained to the set Γ greedy : where \(\Gamma\) represents all available scheduling strategies.

8. A cyber-physical system, characterized in that, it includes a remote state estimation sensor scheduler as described in claim 7.

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