Time-varying filtering method based on multi-protocol fusion scheduling

Abstract

The invention discloses a time-varying filtering method based on multi-protocol fusion scheduling. The method comprises the following steps: 1, establishing a time-varying interactive network system model based on the action of multi-protocol fusion scheduling; 2, carrying out filter analysis and design on the time-varying interactive network system model, and calculating an upper bound about a prediction error covariance matrix; 3, further optimizing and solving undetermined parameters according to the upper bound of the prediction error covariance; 4, substituting the undetermined parameters into the filter to obtain state estimation at the time of iota + 1 so as to realize real-time estimation of the ith interactive individual; 5, calculating the upper bound of a recursive estimation error covariance matrix according to the undetermined parameters; and 6, repeating the steps 2-5 until the step 4 jumps out of circulation. According to the method, the data transmission frequency is reduced by adopting event response conditions, and the data transmission quantity is controlled by adopting periodic data scheduling, so that redundant data transmission is greatly reduced, the communication burden is relieved, and the data transmission efficiency in the filtering technology is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of state estimation, and relates to a dynamic optimization estimation method for an interactive network system, in particular to a time-varying filtering method based on multi-protocol fusion scheduling. Background Art

[0002] The state estimation strategy of the interactive network system has always been the research focus in the field of networked control, and it is widely applied in fields such as energy networks, social networks, financial networks, and transportation networks. However, due to limited network resources and a large amount of data transmission, signals are prone to conflicts, congestion, and even cause the entire system to collapse during transmission.

[0003] For the interactive network system, the existing theory cannot simultaneously analyze the influence of the periodic scheduling strategy and the event response protocol on the system, nor can it handle the estimation error generated after multi-protocol fusion scheduling, which reduces the robustness and estimation performance of the algorithm. In order to improve the utilization rate of network resources and data transmission efficiency, a multi-protocol fusion scheduling strategy (combining event response and periodic data scheduling) is adopted to allocate data access rights, which can ensure the smooth progress of data transmission. Therefore, in the context of multi-protocol fusion scheduling, designing a new type of time-varying filtering method for the interactive network system has important theoretical and practical significance. Summary of the Invention

[0004] In order to solve the problem that the existing filtering method cannot effectively handle the true error caused by multi-protocol fusion scheduling, resulting in a reduction in the accuracy of the estimation performance, the present invention provides a time-varying filtering method based on multi-protocol fusion scheduling based on a hybrid scheduling protocol. This method uses event response conditions to reduce the data transmission frequency, and uses periodic data scheduling to control the data transmission volume, greatly reducing redundant data transmission, alleviating the communication burden, improving the data transmission efficiency in the filtering technology, and enabling the filter to focus more on processing valid data.

[0005] The object of the present invention is achieved through the following technical solutions:

[0006] A time-varying filtering method based on multi-protocol fusion scheduling includes the following steps:

[0007] Step 1: Establish a time-varying interactive network system model under the action of multi-protocol fusion scheduling:

[0008]

[0009] In the formula, O represents the total number of interactive individuals in the time-varying interactive network system, and are the state characteristics of the i-th interactive individual in the interactive network at the ι-th and ι + 1-th moments respectively; is the state feature of the j-th interacting individual in the interaction network at the ι-th moment; y i,ι is the original measurement value of the i-th interacting individual at the ι-th moment; is the internal interaction weight; γ ij represents the external interaction weight between interacting individuals i and j; is a process noise with a mean of 0 and a variance of Q i,ι ; ν i,ι is a measurement noise with a mean of 0 and a variance of R i,ι ; and are the state transition matrix and the measurement perception matrix respectively;

[0010] Step 2: Conduct filter analysis and design on the time-varying interaction network system model established in Step 1, and calculate the upper bound Λ of the prediction error covariance matrix i,ι+1|ι , and the specific steps are as follows:

[0011] Step 2-1: Select the following event response conditions:

[0012]

[0013] In the formula, represents the measurement output at the ι g-1 moment, ι g-1 represents the event response moment and satisfies ι g-1 < ι, ξ i,ι represents the event response index characterized by and the current moment measurement value y i,ι 's difference, represents the transpose of ξ i,ι , σ i represents the known event response threshold, denoted as the event response measurement at the ι moment, if holds, then otherwise where 0 zero represents an m-dimensional column vector with all elements being 0;

[0014] Step 2-2: Introduce a periodic data scheduling scheme, and its specific design steps are as follows:

[0015] (1) Define the event response measurement as where is the m-th element of the event response measurement ;

[0016] (2) Define the measurement output after the periodic scheduling strategy as where is the m-th element of the periodic scheduling measurement ;

[0017] (3) Give the periodic scheduling formula with the following structure:

[0018]

[0019] In the formula, represents the event response measurement at time ι, and Φ s(ι) is the measurement access matrix at time ι;

[0020] (4) For measurement elements without data transmission permission, adopt the zero-order hold compensator scheme:

[0021]

[0022] In the formula, Φ s(ι)-l represents the measurement access matrix with l-step delay, represents the event response measurement with l-step delay, and m represents the dimension of the original measurement;

[0023] Step 23. Construct the following two-step coupled recursive filter:

[0024]

[0025] In the formula, is the estimated value of the state feature at time ι, is the predicted value of the state feature at time ι, is the estimated value of the state feature at time ι + 1, is the estimated value of the state of the j-th interacting individual, and G i,ι+1 is the undetermined parameter at time ι + 1, and Φ s(ι+1) is the measurement access matrix at time ι + 1, is the true measurement value received by the filter at time ι + 1 after event response and periodic scheduling strategy, is the measurement perception matrix at time ι + 1;

[0026] Step 24. Calculate the upper bound Λ of the prediction error covariance of the i-th interacting individual according to the following formula i,ι+1|ι :

[0027]

[0028] In the formula, θ1 is the first scaling coefficient, and θ1 -1 is the reciprocal of θ1, is the intermediate variable, and Λ i,ι+1|ι is the upper bound of the prediction error covariance of the i-th interacting individual at time ι, and Λ i,ι|ιis the upper bound of the recursive estimation error covariance of the $i$-th interactive individual at time $\iota$. is the matrix transpose, is the matrix transpose; $\Lambda$ j,ι|ι is the upper bound of the recursive estimation error covariance of the $j$-th interactive individual at time $\iota$, $Q$ i,ι is the process noise covariance matrix;

[0029] Step 3: According to the upper bound of the prediction error covariance $\Lambda$ i,ι+1|ι obtained in Step 2, further optimize and solve the undetermined parameter $G$ i,ι+1 :

[0030]

[0031] where $\lambda_1$ and $\lambda_3$ are the first and third correction coefficients respectively, is the transpose of the measurement access matrix $\Phi$ s(ι+1) transpose, is the transpose of the measurement perception matrix at time $\iota + 1$ transpose, $\Lambda$ i,ι+1|ι is the upper bound of the prediction error covariance of the $i$-th interactive individual at time $\iota$, represents the inverse operation of the auxiliary variable $\Omega$ i,ι+1 ;

[0032] Step 4: Substitute the undetermined parameter $G$ i,ι+1 determined in Step 3 into the filter designed in Step 2 to obtain the state estimate at time $\iota + 1$ thus realizing the real-time estimation of the $i$-th interactive individual; at this time, judge whether $\iota + 1$ reaches the total estimation step $N$ of the interactive network. If $\iota + 1 \lt N$, then further execute the next step, otherwise jump out of the loop;

[0033] Step 5: According to the undetermined parameter $G$ i,ι+1 determined in Step 3, calculate the upper bound $\Lambda$ i,ι+1|ι+1 of the recursive estimation error covariance matrix:

[0034]

[0035] where $\Lambda$ i,ι+1|ι+1 is the upper bound of the recursive estimation error covariance of the $i$-th interactive individual at time $\iota + 1$, and are the transposes of the matrices and the matrix $G$ i,ι+1 respectively, and $\lambda_1$, $\lambda_2$, $\lambda_3$ are the first, second, and third correction coefficients respectively, and $\lambda_1$ -1 , are the reciprocals of $\lambda_1$, $\lambda_2$, $\lambda_3$, is the sum of the event response adjustment thresholds of all interacting individuals, Φ s(ι+1)-l represents the measurement access matrix with an l-step delay, is Φ s(ι+1)-l transpose of, Φ s(ι+1) is the measurement access matrix at time ι + 1, is Φ s(ι+1) transpose of, R i,ι+1 represents the measurement noise covariance of i interacting individuals at time ι + 1;

[0036] Step Six: Repeat the above Steps Two to Five until the loop in Step Four breaks out.

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] 1. The present invention proposes an optimal estimation strategy for a time-varying interaction network system, which simultaneously considers the combined influence of the periodic scheduling strategy and the event response protocol on the state estimation algorithm. Using the idea of the Kalman filtering algorithm, the trace of the recursive estimation error covariance is used as the optimization index, which is a time-varying optimal estimation algorithm. Compared with the existing recursive estimation methods, the present invention takes into account the influence of the periodic scheduling strategy and the event response protocol on the estimation strategy, optimizes the transmitted data with redundant transmission channels, improves the superiority of the estimation strategy, and this method is a recursive algorithm, which has the advantages of not requiring the storage of historical data and being easy to implement.

[0039] 2. The present invention uses the Kalman filtering algorithm under the meaning of the minimum mean square error. By optimizing the performance index in real time, that is, by minimizing the trace of the upper bound of the error covariance at each recursive moment, an explicit expression of the filter estimator parameters is designed, ensuring that the time-varying recursive filtering algorithm is not affected under the simultaneous action of the periodic scheduling strategy and the event response protocol, and improving the accuracy of the filtering algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a flowchart of the time-varying filtering method based on multi-protocol fusion scheduling of the present invention;

[0041] Figure 2 is the state trajectory of the first interacting individual in the interaction network at time ι and the corresponding estimated trajectory is the first element of the first interacting individual in the interaction network;

[0042] Figure 3 is the state trajectory of the first interacting individual in the interaction network at time ι and the corresponding estimated trajectory is the second element of the first interacting individual in the interaction network;

[0043] Figure 4 is the state trajectory of the first interacting individual in the interaction network at time ι and the corresponding estimated trajectory is the third element of the first interacting individual in the interaction network;

[0044] Figure 5 is the state trajectory of the second interacting individual in the interaction network at time ι and the corresponding estimated trajectory is the first element of the second interacting individual in the interaction network;

[0045] Figure 6 is the state trajectory of the second interacting individual in the interaction network at time ι and the corresponding estimated trajectory is the second element of the second interacting individual in the interaction network;

[0046] Figure 7 is the state trajectory of the second interacting individual in the interaction network at time ι and the corresponding estimated trajectory is the third element of the second interacting individual in the interaction network;

[0047] Figure 8 is the state trajectory of the third interacting individual in the interaction network at time ι and the corresponding estimated trajectory is the first element of the third interacting individual in the interaction network;

[0048] Figure 9 is the state trajectory of the third interacting individual in the interaction network at time ι and the corresponding estimated trajectory is the second element of the third interacting individual in the interaction network;

[0049] Figure 10 is the state trajectory of the third interacting individual in the interaction network at time ι and the corresponding estimated trajectory is the third element of the third interacting individual in the interaction network

[0050] Figure 11 is the log mean square error log(MSE) of the interaction network system and its upper bound.

[0051] In the figure: is the state trajectory, is the corresponding estimated trajectory, represents the mean square error, is the upper bound of the mean square error. Detailed implementation method

[0052] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings, but it is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.

[0053] The present invention provides a time-varying filtering method based on multi-protocol fusion scheduling, as Figure 1 shown. The method includes the following steps:

[0054] Step 1: Establish a time-varying interaction network system model under the action of multi-protocol fusion scheduling:

[0055]

[0056] In the formula, O represents the total number of interaction individuals in the time-varying interaction network system, and are the state characteristics of the i-th interaction individual in the interaction network at the ι-th and ι+1-th moments respectively, represents the set of all n-dimensional column vectors; is the state characteristic of the j-th interaction individual in the interaction network at the ι-th moment; is the original measurement value of the i-th interaction individual at the ι-th moment, represents the set of all m-dimensional column vectors; is the internal interaction weight; γ ij represents the external interaction weight between interaction individuals i and j; is a process noise with a mean of 0 and a variance of Q i,ι , is the set of all ρ-dimensional column vectors of the process noise; is a measurement noise with a mean of 0 and a variance of R i,ι , is the set of all ν-dimensional column vectors of the measurement noise; and are the state transition matrix and the measurement perception matrix respectively.

[0057] Step 2: Analyze and design the filter for the time-varying interaction network system model established in Step 1, and calculate the upper bound Λ i,ι+1|ι of the prediction error covariance matrix. The specific steps are as follows:

[0058] Step 2-1: Select the following event response conditions:

[0059]

[0060] In the formula, represents the measurement output at the ι g-1 moment (the most recent response moment), ι g-1 represents the event response moment and satisfies ιg-1 <ι, ξ i,ι Denote the event response index by and the measured value y at the current moment i,ι characterized by the difference Denote ξ i,ι as the transpose of σ i Denote the known event response threshold. For ease of representation, denote as the event response measurement at time ι. If equation (3) holds, then Otherwise where 0 zero denotes an m-dimensional column vector with all elements being 0.

[0061] Step 2: To avoid excessive data accessing the network channel simultaneously and improve the utilization efficiency of the shared network, a periodic data scheduling scheme is introduced. The specific design steps are as follows:

[0062] (1) Define the event response measurement as where and are the first element, the second element, and the m-th element of the event response measurement respectively;

[0063] (2) Define the measured output after the periodic scheduling strategy as where y 2i,ι and are the first element, the second element, and the m-th element of the periodic scheduling measurement respectively;

[0064] (3) Give a periodic scheduling formula with the following structure:

[0065]

[0066] In the formula, denotes the event response measurement at time ι, Φ s(ι) is the measurement access matrix at time ι and satisfies Φ s(ι) = diag{δ(s(ι)-1)I, δ(s(ι)-2)I, …, δ(s(ι-m))I}, where diag{*} is the matrix diagonal function, and the diagonal elements are δ(s(ι)-1)I, δ(s(ι)-2)I, …, δ(s(ι-m))I respectively, δ(·) is the Kronecker function, I is the identity matrix, and s(ι) satisfies s(ι) = mod(ι-1, m)+1, mod(·) is the remainder function.

[0067] (4) For the measurement elements that do not obtain the data transmission permission, adopt the zero-order hold compensator scheme:

[0068]

[0069] In the formula, Φ s(ι)-l represents the measurement access matrix with an l-step delay, represents the event response measurement with an l-step delay, and m represents the dimension of the original measurement.

[0070] Step Two and Three: Construct the following two-step coupled recursive filter:

[0071]

[0072] In the formula, is the estimated value of the state feature at time ι, is the predicted value of the state feature at time ι, is the estimated value of the state feature at time ι + 1, is the state estimate value of the jth interacting individual, G i,ι+1 is the undetermined parameter at time ι + 1, Φ s(ι+1) is the measurement access matrix at time ι + 1, is the true measurement value received by the filter at time ι + 1 after event response and periodic scheduling strategy, is the measurement perception matrix at time ι + 1.

[0073] Step Two and Four: Calculate the upper bound Λ of the prediction error covariance of the ith interacting individual according to the following formula i,ι+1|ι :

[0074]

[0075] In the formula, θ1 is the first scaling coefficient, θ1 -1 is the reciprocal of θ1, is an intermediate variable and satisfies Λ i,ι+1|ι is the upper bound of the prediction error covariance of the ith interacting individual at time ι, Λ i,ι|ι is the upper bound of the recursive estimation error covariance of the ith interacting individual at time ι, is the transpose of the matrix ; is the transpose of the matrix ; Λ j,ι|ι is the upper bound of the recursive estimation error covariance of the jth interacting individual at time ι, Q i,ι is the process noise covariance matrix.

[0076] Step Three: According to the upper bound Λ of the prediction error covariance obtained in Step Two i,ι+1|ι, further optimize the solution of the undetermined parameter G i,ι+1 :

[0077]

[0078] where λ1 and λ3 are the first and third correction coefficients respectively, is the measurement access matrix Φ s(ι+1) transpose, is the transpose of the measurement perception matrix at time ι + 1 Λ i,ι+1|ι is the upper bound of the prediction error covariance of the i-th interacting individual at time ι, represents the inverse operation of the auxiliary variable Ω i,ι+1 Ω i,ι+1 can be expressed by the following formula:

[0079]

[0080] where λ1, λ2, and λ3 are the first, second, and third correction coefficients respectively, and λ1 -1 , are the reciprocals of λ1, λ2, and λ3, is the sum of the event response adjustment thresholds of all interacting individuals, and Φ s(ι)-l represents the measurement access matrix with l-step delay, is Φ s(ι+1)-l transpose, R i,ι+1 represents the covariance of the measurement noise of the i-th interacting individual at time ι + 1, and Σ i,ι+1-l can be expressed by the following formula:

[0081]

[0082] where β1 and β2 represent the first and second scaling factors respectively, and β1 -1 , represent the reciprocals of β1 and β2, is the measurement perception matrix of the i-th interacting individual at time ι + 1 - l, is transpose, ξ i,ι+1-l represents the difference between the most recent event response measurement output of the i-th interacting individual and the measurement output of the i-th interacting individual at time ι + 1 - l, is ξ i,ι+1-l transpose, R i,ι+1-l represents the covariance of the measurement noise of the i-th interacting individual at time ι + 1 - l, and the relay variable Θ i,ι+1-l|ι-l can be expressed by the following formula:

[0083]

[0084] where λ4 represents the fourth correction coefficient, is the reciprocal of λ4, Λ i,ι+1-l|ι-l is the upper bound of the prediction error covariance of the i-th interacting individual at time ι-l, represents the predicted value at ι-l, is the transpose of.

[0085] Step Four: Substitute the undetermined parameter G i,ι+1 determined in Step Three into the filter designed in Step Two to obtain the state estimate at time ι+1 thus realizing the real-time estimation of the i-th interacting individual; at this time, judge whether ι+1 reaches the total number of estimation steps N of the interaction network. If ι+1 < N, then further execute the next step, otherwise jump out of the loop.

[0086] Step Five: Calculate the upper bound Λ i,ι+1 of the recursive estimation error covariance matrix according to the undetermined parameter G i,ι+1|ι+1 determined in Step Three:

[0087]

[0088] where Λ i,ι+1|ι+1 is the upper bound of the recursive estimation error covariance of the i-th interacting individual at time ι+1, and are the transposes of the matrices and the matrix G i,ι+1 respectively, and λ1, λ2, and λ3 are the first, second, and third correction coefficients, and λ1 -1 , are the reciprocals of λ1, λ2, and λ3, is the sum of the event response adjustment thresholds of all interacting individuals, Φ s(ι+1)-l represents the measurement access matrix with l-step delay, is the transpose of Φ s(ι+1)-l , Φ s(ι+1) is the measurement access matrix at time ι+1, is the transpose of Φ s(ι+1) , and R i,ι+1 represents the measurement noise covariance of the i interacting individuals at time ι+1;

[0089] Step Six: Repeat the above Steps Two to Five until the loop is exited in Step Four.

[0090] In the present invention, the theories described in Step Two, Step Three, and Step Four are:

[0091] Calculate the upper bound of the estimation error covariance of each interacting individual, that is, find Λ i,ι+1|ι+1 to ensure the inequality Pi,ι+1|ι+1 ≤ Λ i,ι+1|ι+1 holds, where represents the recursive estimation error covariance of the i-th interacting individual at time ι + 1, represents the estimation error of the i-th interacting individual at time ι + 1, represents e i,ι+1|ι+1 transpose, represents mathematical expectation of.

[0092] However, due to the existence of uncertain terms and cross-product terms in the recursive estimation error covariance, it is difficult to obtain the exact value of the recursive estimation error covariance. Therefore, using stochastic analysis methods, matrix theory, and function calculus theory, the specific form of the upper bound of the recursive estimation error covariance is given. In addition, by optimizing the trace of the upper bound Λ i,ι+1|ι+1 the specific expression of the parameter G i,ι+1 is given by solving the optimization problem.

[0093] The following numerical simulation is used to verify the beneficial effects of the present invention:

[0094] The present invention provides a time-varying filtering method based on multi-protocol fusion scheduling for an interactive network model, which can be used to solve problems such as tracking and positioning of multi-target mobile robots. This simulation mainly considers three interacting individuals, i.e., O = 3. The model parameters of the interactive network are as follows:

[0095] The state transition matrices of the three interacting individuals are respectively:

[0096]

[0097] The measurement perception matrices of the three interacting individuals are respectively:

[0098]

[0099] Other simulation parameters and initial values are selected as follows:

[0100] The weight parameters are respectively:

[0101] γ ii = -1.2, γ ij = 0.6 (i ≠ j).

[0102] The initial state values of the three interacting individuals are and the estimated values and predicted values of the interacting individuals at time 0 are respectively and The initial value of the upper bound of the recursive estimation error is Λ i,0|0 = 0.2I3, where I3 is the three-dimensional identity matrix. The covariances of the process noise and measurement noise are Q1,ι = 0.12, Q 2,ι = 0.15, Q 3,ι = 0.22 and R i,ι = 0.01I2, where I2 is a two-dimensional identity matrix.

[0103] Control effect: From Figures 2 to 10 It can be seen that for the time-varying interactive network system with multi-protocol fusion scheduling, the state estimation strategy of the present invention can effectively complete the state estimation task.

Claims

1. A time-varying filtering method based on multi-protocol fusion scheduling, characterized in that The method includes the following steps: Step 1: Establish a time-varying interactive network system model based on multi-protocol fusion scheduling: where O represents the total number of interacting individuals in the time-varying interaction network system, and are the state characteristics of the i-th interacting individual in the interaction network at the ι-th and ι+1-th moments respectively; is the state characteristic of the j-th interacting individual in the interaction network at the ι-th moment; y i,ι is the original measured value of the i-th interacting individual at the ι-th moment; is the internal interaction weight; γ ij represents the diplomatic interaction weight between interactive individuals i and j; is a process noise with a mean of 0 and a variance of Q i,ι ; ν i,ι is a measurement noise with a mean of 0 and a variance of R i,ι ; and are the state transition matrix and the measurement perception matrix, respectively; Step 2: Conduct filter analysis and design on the time-varying interactive network system model established in Step 1, and calculate the upper bound Λ of the prediction error covariance matrix. The specific steps are as follows: i,ι+1|ι , as follows: Step 2-1: Select the following event response conditions: Wherein, represents the measurement output at time ι g-1 where ι g-1 represents the event response time and satisfies ι g-1 <ι, ξ i,ι represents that the event response index is characterized by the difference between and the measured value y at the current time i,ι , represents the transpose of ξ i,ι where σ i represents the known event response threshold, denoted as the event response measurement at time ι. If holds, then otherwise where 0 zero represents an m-dimensional column vector with all elements being 0; Step 2-2: Introduce a periodic data scheduling scheme, and its specific design steps are as follows: (1) Define the event response measurement as where is the m-th element of the event response measurement ; (2) Define the measured output after the periodic scheduling strategy as where is the m-th element of the periodic scheduling measurement ; (3) Give a periodic scheduling formula with the following structure: wherein, represents the event response measurement at time ι, and Φ s(ι) is the measurement access matrix at time ι; (4) For measurement elements that do not obtain data transmission permissions, adopt a zero-order hold compensator scheme: where Φ s(ι)-l represents a measurement access matrix with an l-step delay, represents an event response measurement with an l-step delay, and m represents the dimension of the original measurement; Step 2-3: Construct the following two-step coupled recursive filter: Wherein, is the estimated value of the state feature at time ι, is the predicted value of the state feature at time ι, is the estimated value of the state feature at time ι + 1, is the estimated value of the state of the j-th interacting individual, G i,ι+1 is the undetermined parameter at time ι + 1, Φ s(ι+1) is the measurement access matrix at time ι + 1, is the true measurement value received by the filter at time ι + 1 after the event response and the periodic scheduling strategy, is the measurement perception matrix at time ι + 1; Step 24. Calculate the upper bound Λ of the prediction error covariance of the i-th interaction individual according to the following formula i,ι+1|ι :[[]]END]] Where, θ1 is the first scaling factor, is the reciprocal of θ1, is an intermediate variable, Λ i,ι+1|ι is the upper bound of the prediction error covariance of the i-th interacting individual at time ι, Λ i,ι|ι is the upper bound of the recursive estimation error covariance of the i-th interacting individual at time ι, is the matrix transpose, is the matrix transpose; Λ j,ι|ι is the upper bound of the recursive estimation error covariance of the j-th interacting individual at time ι, Q i,ι is the process noise covariance matrix; Step 3. Further optimize and solve the undetermined parameter G according to the upper bound Λ of the prediction error covariance obtained in Step 2 i,ι+1|ι , i,ι+1 : where λ1 and λ3 are the first and third correction coefficients, respectively, is the measurement access matrix Φ s(ι+1) transpose, is the transpose of the measurement perception matrix at time ι + 1 transpose, Λ i,ι+1|ι is the upper bound of the prediction error covariance of the i-th interacting individual at time ι, represents the inverse operation of the auxiliary variable Ω i,ι+1 inverse operation; Step 4. Substitute the undetermined parameter G determined in Step 3 i,ι+1 into the filter designed in Step 2 to obtain the state estimate at time ι + 1 so as to realize the real-time estimation of the i-th interacting individual; at this time, judge whether ι + 1 reaches the total estimation step length N of the interaction network. If ι + 1 < N, then further execute the next step; otherwise, jump out of the loop; Step 5. Calculate the upper bound Λ of the recursive estimation error covariance matrix based on the undetermined parameter G determined in Step 3 i,ι+1 , i,ι+1|ι+1 as follows: where, Λ i,ι+1|ι+1 is the upper bound of the recursive estimation error covariance of the \(i\)-th interaction individual at time \(\iota + 1\), and are the transposes of the matrix and the matrix \(G\) i,ι+1 respectively, and \(\lambda_1\), \(\lambda_2\), \(\lambda_3\) are the first, second, and third correction coefficients, is the reciprocal of \(\lambda_1\), \(\lambda_2\), \(\lambda_3\), is the sum of the event response adjustment thresholds of all interaction individuals, and \(\varPhi\) s(ι+1)-l represents the measurement access matrix with an \(l\)-step delay, is the transpose of \(\varPhi\) s(ι+1)-l , \(\varPhi\) s(ι+1) is the measurement access matrix at time \(\iota + 1\), is the transpose of \(\varPhi\) s(ι+1) , and \(R\) i,ι+1 represents the measurement noise covariance of the \(i\)-th interaction individual at time \(\iota + 1\);​ Step 6: Repeat steps 2 to 5 above until step 4 jumps out of the loop.

2. The time-varying filtering method based on multi-protocol fusion scheduling according to claim 1, characterized in that In the second step, Φ s(ι) = diag{δ(s(ι)-1)I, δ(s(ι)-2)I, …, δ(s(ι-m))I}, where diag{*} is the matrix diagonal function, and the diagonal elements are δ(s(ι)-1)I, δ(s(ι)-2)I, .., δ(s(ι-m))I respectively, δ(·) is the Kronecker function, I is the identity matrix, and s(ι) satisfies s(ι) = mod(ι-1, m)+1, and mod(·) is the modulo function.

3. The time-varying filtering method based on multi-protocol fusion scheduling according to claim 1, characterized in that In the second step (24), 4. The time-varying filtering method based on multi-protocol fusion scheduling according to claim 1, characterized in that In the third step, the auxiliary variable Ω i,ι+1 is represented by the following formula: Wherein, λ1, λ2, and λ3 are the first, second, and third correction coefficients respectively, are the reciprocals of λ1, λ2, and λ3, is the sum of the event response adjustment thresholds of all interacting individuals, Φ s(ι)-l represents the measurement access matrix with an l-step delay, is the transpose of Φ s(ι+1)-l R i,ι+1 represents the covariance of the measurement noise of the i-th interacting individual at the ι+1 moment, Σ i,ι+1-l is represented by the following formula: Wherein, β1 and β2 respectively represent the first and second scaling factors, represent the reciprocals of β1 and β2, is the measurement perception matrix of the i-th interacting individual at time ι + 1 - l, is the transpose of, ξ i,ι+1-l represents the difference between the most recent event response measurement output of the i-th interacting individual and the measurement output of the i-th interacting individual at time ι + 1 - l, is the transpose of ξ i,ι+1-l R i,ι+1-l represents the covariance of the measurement noise of the i-th interacting individual at time ι + 1 - l, Θ i,ι+1-l|ι-l represents the relay variable.

5. The time-varying filtering method based on multi-protocol fusion scheduling according to claim 4, wherein The relay variable Θ i,ι+1-l|ι-l is represented by the following formula: where λ4 represents the fourth correction coefficient, is the reciprocal of λ4, Λ i,ι+1-l|ι-l is the upper bound of the prediction error covariance of the i-th interacting individual at time ι-l, denotes the predicted value at ι-l, is the transpose of.

Images