Time-varying output coupling complex network state estimation method in low-reliability communication environment

Abstract

The invention discloses a time-varying output coupling complex network state estimation method in a low-reliability communication environment, and belongs to the technical field of distributed state estimation methods. Comprising the following steps: S1, establishing a time-varying output coupling complex network model with random uncertainty probability measurement delay; s2, a periodic communication mechanism is introduced for scheduling; s3, constructing a distributed estimator; s4, deriving one-step prediction # imgabs1 of the i-th node at the s-th moment based on # imgabs0 #; S5, calculating an upper bound xi, s + 1s of one-step prediction error covariance of the i-th node at the s-th moment; s6, deducing a distributed estimator parameter Ki, s + 1 of the ith node at the (s + 1) th moment; s7, deducing state estimation # imgabs2 # S8, solving an estimation error covariance upper bound xi, s + 1s + 1 of the ith node at the (s + 1) th moment; and letting k = k + 1, and returning to S3. According to the method, the problem that the existing state estimation method cannot process complex network state estimation of a low-reliability communication environment and periodic scheduling at the same time is solved, so that the accuracy of the performance of the state estimation algorithm of the problem and the data transmission efficiency are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of distributed state estimation methods, and particularly relates to a distributed state estimation method under a time-varying output-coupled complex network framework in a low-reliability communication environment. Background Art

[0002] In recent years, complex networks have been widely applied in various fields of human production and life, such as social networks, traffic networks, biological neural networks, and power networks. With the popularization of big data technologies (such as Internet of Things sensor data, real-time interactive data of social media, etc.), the amount of information generated by network nodes has shown exponential growth. The problem of low efficiency of traditional centralized state estimation algorithms in massive data throughput and high-dimensional heterogeneous data processing has become increasingly prominent. Against this background, distributed state estimation has become a research hotspot in academia and industry due to its adaptability to big data streams, elastic expansion ability, and potential for edge intelligent computing in the distributed computing architecture. There are mainly two existing distributed state estimation studies, namely the method based on the Kalman filter and the method based on the observer. The first method couples the Kalman filtering theory with the complex network state estimation problem and only uses local node information without the need for a fusion center to perform state estimation. In practical engineering applications, sensor measurements are often affected by uncertain disturbances, and the measured values need to be transmitted through a wireless network, which makes measurement delay an unavoidable problem. Therefore, in-depth research on the distributed state estimation problem of time-varying output-coupled complex networks in a low-reliability communication environment not only has theoretical value but also has important practical significance.

[0003] As the core infrastructure for data transmission, the network communication system not only bears the information interaction function but also is an important guarantee for supporting advanced applications such as remote control and fault diagnosis. In an ideal situation, the communication bandwidth can be regarded as an infinite resource, but the bandwidth resources in the real scenario are extremely limited. When a large amount of data synchronously floods into the shared channel, it is extremely easy to cause network congestion, which in turn leads to a decrease in transmission efficiency and significant delay. Therefore, constructing an efficient communication scheduling mechanism in a low-reliability communication environment has become the key path to improving network performance. The periodic scheduling mechanism allocates communication time slots for each node at preset time intervals, and each node only has one channel access opportunity within a single period. This mechanism has the significant feature of deterministic transmission and can effectively avoid the conflict problem of traditional competitive protocols. In view of the dynamic characteristics in the complex network environment, how to explore its adaptation strategy in the complex network environment based on the characteristics of the periodic scheduling mechanism has important theoretical value and engineering significance for ensuring system real-time performance and data transmission efficiency.

[0004] Existing distributed state estimation algorithms are difficult to handle the state estimation problem of a complex network with time-varying output coupling in a low-reliability communication environment. In view of this situation, it is of practical significance to design a state estimation method for a complex network with time-varying output coupling in a low-reliability communication environment. Summary of the Invention

[0005] The present invention aims to solve the problem that existing distributed state estimation algorithms are difficult to handle the state estimation problem of a complex network with time-varying output coupling in a low-reliability communication environment, resulting in low data transmission efficiency. Furthermore, a state estimation method for a complex network with time-varying output coupling in a low-reliability communication environment is provided.

[0006] The technical solution adopted by the present invention is as follows:

[0007] The state estimation method for a complex network with time-varying output coupling in a low-reliability communication environment includes the following steps:

[0008] S1. Establish a time-varying output-coupled complex network model with random uncertain probability measurement delays;

[0009] S2. For the network model constructed in S1, introduce a periodic communication mechanism for scheduling;

[0010] S3. For the time-varying output-coupled complex network model with random uncertain probability measurement delays in S2, construct a distributed estimator;

[0011] S4. Based on the in the distributed estimator, derive the one-step prediction value of the i-th node at the s-th moment

[0012] S5. By solving the matrix difference equation, calculate the upper bound of the one-step prediction error covariance of the i-th node at the s-th moment

[0013] S6. According to the obtained in S5, derive the distributed estimator parameter K of the i-th node at the (s + 1)-th moment by minimizing the trace of the upper bound of the estimation error covariance i,s+1 ;

[0014] S7. According to the K obtained in S6 i,s+1 , derive the state estimation of the i-th node at the (s + 1)-th moment

[0015] S8. According to the K obtained in S6 i,s+1 , solve the upper bound of the estimation error covariance of the i-th node at the (s + 1)-th moment Let k = k + 1, and return to S3.

[0016] The present invention has the following beneficial effects compared with the prior art:

[0017] 1. The present invention simultaneously considers the influence of low-reliability communication environment and periodic scheduling on the performance of the state estimation algorithm, and obtains the least upper bound of the estimation error covariance based on the matrix difference equation.

[0018] 2. The present invention uses a recursive method to estimate the state of a complex network with time-varying output coupling in a low-reliability communication environment. This method has the advantages of being easy to solve and suitable for online implementation. At the same time, with the exponential growth of information traffic today, the disadvantages of centralized state estimation are gradually emerging, while the distributed state estimation method used in the present invention has a lower computational burden.

[0019] 3. The present invention solves the problem that the existing state estimation methods cannot simultaneously handle the complex network state estimation problems under periodic scheduling and low-reliability communication environment, thereby improving the accuracy of the state estimation algorithm performance and the data transmission efficiency for such problems. It can be seen from the simulation diagrams that the state estimation algorithm has good estimation performance, and the logarithm of the mean square error log(MSE i ) is below its upper bound. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is the flowchart of the present invention;

[0021] Figure 2 is the state estimation diagram under periodic scheduling;

[0022] Figure 3 is the actual state trajectory of the system of the first node x 1,s and its state estimation diagram;

[0023] Figure 4 is the actual state trajectory of the system of the second node x 2,s and its state estimation diagram;

[0024] Figure 5 is the actual state trajectory of the system of the third node x 3,s and its state estimation diagram;

[0025] Figure 6 is the logarithm of the mean square error log(MSE i,s ) of three nodes and its upper bound diagram. DETAILED DESCRIPTION OF THE INVENTION

[0026] In order to better understand the purpose, structure and function of the present invention, the following will further describe the present invention in detail with reference to the drawings.

[0027] The present invention provides a method for estimating the state of a complex network with time-varying output coupling in a low-reliability communication environment, as Figure 1As shown, the method includes the following steps:

[0028] Step 1: Establish a time-varying output-coupled complex network model with random uncertain probability measurement delays.

[0029] In this step, the established time-varying output-coupled complex network model with random uncertain probability measurement delays is:

[0030]

[0031] y i,s = η i,s C i,s x i,s +(1 - η i,s )C i,s-τ x i,s-τ + v i,s

[0032] In the formula, represents the system state to be estimated of node i at time s; represents the system state to be estimated of node i at time s - τ; represents the measurement output; τ (τ = 1, 2,...) is the time-delay variable; B i,s , C i,s and C i,s-τ are known appropriate-dimensional matrices; and are zero-mean noises with variances of and Γ and W s = [w il,s N×N respectively represent the internal coupling matrix and the external coupling matrix; f(x i,s ) is a nonlinear function, which is continuously differentiable and has bounded second-order partial derivatives, and satisfies

[0033] ‖f(x i,s )‖ ≤ a1‖x i,s ‖ + a 11

[0034] In the formula, a1 and a 11 are non-negative scalars; ||·|| represents the norm; η i,s is a Bernoulli random variable with an uncertain occurrence probability, in the form of:

[0035]

[0036] In the formula, Prob{η i,s = 1} represents the probability that η i,s takes the value of 1; Prob{η i,s = 0} represents the probability that η​i,s The probability of taking the value 0; is the mathematical expectation; and is a known scalar; the scalar Δη i,s describes the uncertain occurrence probability phenomenon of delay measurement, is bounded, is a known scalar, and η i,s has its variance denoted as σ i,s ; in addition, it is assumed that for all nodes i and all times s, x i,0 , v i,s , η i,s and are mutually independent. Obviously, a time-delay phenomenon occurs when η i,s = 0.

[0037] Step 2. For the output of a time-varying output-coupled complex network with random uncertain probability measurement time delay, introduce a periodic communication mechanism for scheduling. The specific steps are as follows:

[0038] Step 2-1. To handle the exponentially growing network transmission information volume, introduce a periodic scheduling as the communication rule to reduce the occurrence of channel congestion, and determine the following periodic scheduling strategy:

[0039]

[0040] where n y represents a cycle period; mod(·) represents the remainder function; φ i,s represents the index of the periodic scheduling strategy of node i at time s.

[0041] Step 2-2. After the transmitted data is processed by the periodic scheduling, obtain the measurement output equation of the i-th node at time s:

[0042]

[0043] where Φ i,s = diag{δ(φ i,s - 1), δ(φ i,s - 2), …, δ(φ i,s - n y )}; diag represents a diagonal matrix; the definition of the function δ(·) is as follows:

[0044]

[0045] Step 2-3. Introduce a zero-order compensator to compensate the scheduled data, and the compensated measurement output equation is as follows:

[0046]

[0047] When s - m < 0, φ i,s-m = m; φ i,s-m represents the index of the periodic scheduling strategy of node i at time s - m; The initial measurement values y of the system at times s = -(n y - 1), …, -1, 0 are i,s = 0;

[0048] In the formula, represents the measured output after compensating node i with a zero - order compensator at time s; represents the measurement output equation of the i - th node at time s; y i,s-m The measured output of node i at time s - m;

[0049] Step 3. For the time - varying output - coupled complex network model with randomly uncertain probability measurement delays in Step 2, construct a distributed estimator:

[0050]

[0051] In the formula represents the estimated output of node l at time s; represents the predicted value of the state of node i at time s - m; represents the estimated value of the state of node i at time s; and represent the predicted value and the estimated value of the state of node i at time s + 1 respectively; represents the measured output of the i - th sensor received by the estimator at time s + 1 in the time - varying output - coupled complex network with randomly uncertain probability measurement delays; And K i,s is the distributed estimator parameter of node i at time s; "Σ" is the summation symbol; represents η i,s+1-m 's nominal mathematical expectation; η i,s+1-m is used to describe the time - delay phenomenon of the i - th node at time s + 1 - m; B i,s , C i,s , C i,s-τ , C i,s+1-m and C i,s+1-τ-m are known proper - dimension matrices.

[0052] Step 4. Based on Derive the one - step prediction of the i - th node at time s

[0053] Step 5. By solving the matrix difference equation, calculate the upper bound of the one - step prediction error covariance of the i - th node at time s

[0054] In this step, the upper bound of the one-step prediction error covariance is calculated as follows:

[0055]

[0056] where,

[0057]

[0058] ζ1 = 1 + ε1 + ε2 + ε3

[0059]

[0060] In the formula, represents the partial derivative symbol; F i,s and E i,s are known matrices; represents the process noise variance of node i at the s-th moment; represents the observation noise variance of node i at the s-th moment; the superscript "-1" represents taking the inverse of the matrix or the reciprocal of the logarithm; the superscript "2" represents taking the square of the logarithm; ε1, ε2, ε3, ε4, ε5, ε6, ε7, ε8, ε9, and ν are known scaling parameters; and ν -1 are the reciprocals of ε1, ε2, ε3, ε4, ε5, ε6, ε7, ε8, ε9, and ν respectively; represents squared; represents squared; represents squared; σ i,s is the variance of η i,s ; Γ T , and represent the transposes of B i,s , A p,s , e j,s|s , C l,s , Γ, and C l,s-τ respectively;

[0061] Step Six: Based on the obtained in Step Five, the distributed estimator parameter K i,s+1 for the i-th node at the (s + 1)-th moment is derived by minimizing the trace of the upper bound of the estimation error covariance

[0062] In this step, the distributed estimator parameter K i,s+1 is calculated as follows:

[0063]

[0064] in,

[0065] ζ5=1+ε 10 +ε 11 +ε 12

[0066]

[0067] In the formula, the superscript "-1" means to invert the matrix or take the reciprocal of the logarithm; the superscript "2" means to square the logarithm; ε 10 , ε 11 , ε 12 , ε 13 , ε 14 , ε 15 , ε 16 , ε 17 and ε 18 is a known scaling parameter; and They are ε 10 , ε 11 , ε 12 , ε 13 , ε 14 , ε 15 , ε 16 , ε 17 and ε 18 The reciprocal of express The square of express The square of express The square of express The square of and Respectively represent C i,s+1 , Φ i,s+1-m , and The transpose of .

[0068] Step 7: According to K obtained in step 6 i,s+1 , derive the state estimate of the i-th node at the s+1th time

[0069] Step 8: According to K obtained in step 6 i,s+1 , solve the upper bound of the estimated error covariance of the i-th node at the s+1th time Let k=k+1 and return to step three.

[0070] In this step, the upper bound of the estimated error covariance is The calculation formula is as follows:

[0071]

[0072] wherein,

[0073]

[0074] ζ5 = 1 + ε 10 + ε 11 + ε 12

[0075]

[0076] wherein, I is the identity matrix; represents squared; represents squared; ε 10 、ε 11 、ε 12 、ε 13 、ε 14 、ε 15 、ε 16 、ε 17 and ε 18 are known scaling parameters; and are respectively the reciprocals of ε 10 、ε 11 、ε 12 、ε 13 、ε 14 、ε 15 、ε 16 、ε 17 and ε 18 ; is the covariance matrix of the measurement noise v i,s+1 of the i-th node in the system under the complex network framework at the (s + 1)-th moment; represents squared; represents squared; represents squared; and respectively represent the transposes of C i,s+1 、Φ i,s+1-m 、 K i,s+1 and ;

[0077] In this step, calculate the of each node to make hold, where P i,s+1|s+1is the estimated error covariance of the \(i\)-th node at the \((s + 1)\)-th moment. Next, by minimizing the trace of, the distributed estimator parameter \(K\) at the \((s + 1)\)-th moment is designed i,s+1 .

[0078] Example:

[0079] In this example, a complex network with three coupled nodes is selected for simulation, and the system parameters are given:

[0080] B 1,s = [-0.4 - sin(0.5s) 0.4 0] T

[0081] B 2,s = [-0.6 -0.8 -0.4] T

[0082] B 3,s = [-0.6 0.5 -0.2] T

[0083]

[0084] In the formula, for each node \(i\) (\(i = 1, 2, 3\)), and sin(·) and cos(·) represent the sine function and cosine function of “·” respectively.

[0085] Other parameters of the system are selected as \(\tau = 2\), \(\varepsilon_1=\varepsilon_2=\varepsilon_9=\varepsilon\) 10 = 1.2, \(\varepsilon_3=\varepsilon_4 = 0.6\), \(\varepsilon_5=\varepsilon_6 = 0.8\), \(\varepsilon_7=\varepsilon_8=\varepsilon\) 17 =\(\varepsilon\) 18 = 1, \(\varepsilon\) 11 =\(\varepsilon\) 12 =\(\varepsilon\) 13 =\(\varepsilon\) 14 =\(\varepsilon\) 15 =\(\varepsilon\) 16 = 1.5, \(\nu = 0.4\), E 1,s = E 3,s = E 3,s = 0.1I3 and F 1,s = F 3,s = F 3,s = 0.1I3. I3 represents the 3-by-3 identity matrix. The random sequences and \(v\) i,s are both zero-mean Gaussian white noise sequences, with variances and I2 represents the 2-by-2 identity matrix.

[0086] The nonlinear function \(f(x\)i,s ) Meet

[0087]

[0088] Wherein And

[0089] log(MSE i,s )(i = 1, 2, 3) represents the logarithm of the mean square error of the i-th sensor node at the s-th moment, where log(·) represents the logarithm of "·", and MSE i,s represents the mean square error of the i-th sensor node at the s-th moment. The present invention uses the mean square error to demonstrate the superiority of the state estimation method, and its calculation formula is:

[0090]

[0091] wherein, L is the number of simulation runs (L = 100 simulation runs in this embodiment), And respectively represent the true state and the estimated state of the l-th run, Is The transpose of.

[0092] Effect of the distributed state estimation algorithm:

[0093] Figure 3 、 Figure 4 And Figure 5 Are respectively Figure 3 For node x 1,s 、x 2,s And x 3,s The actual state trajectory of the system and its state estimation diagram; Figure 6 Depicts the logarithm of the mean square error of the three nodes log(MSE i,s ) And its upper bound diagram; The experimental results verify the effectiveness of the method proposed by the present invention.

[0094] In summary, a method for estimating the state of a time-varying output-coupled complex network in a low-reliability communication environment proposed by the present invention can effectively estimate the system state when dealing with periodic scheduling and low-reliability communication environments.

[0095] It will be understood that the present invention is described by way of some embodiments, and those skilled in the art will know that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the present invention. Additionally, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application belong to the scope protected by the present invention.

Claims

1. A method for estimating the state of a complex network with time-varying output coupling in a low-reliability communication environment, characterized by: The following steps are involved: S1. Establish a time-varying output coupled complex network model with random uncertain probabilistic measurement lag; S2. For the network model constructed in S1, a periodic communication mechanism is introduced for scheduling; S3. Construct a distributed estimator for the time-varying output coupled complex network model with random uncertain probabilistic measurement lag in S2; S4. Based on the estimated value of the i-th node in the distributed estimator at the s-th time Derive the one-step prediction value of the i-th node at time s S5. Calculate the upper bound of the one-step prediction error covariance of the i-th node at the s-th time by solving the matrix difference equation S6. According to S5 The distributed estimator parameter K of the i-th node at the s+1th time is derived by minimizing the trace of the upper bound of the estimation error covariance i,s+1 ; S7. According to K obtained in S6 i,s+1 , derive the state estimate of the i-th node at the s+1th time S8. According to K obtained in S6 i,s+1 , solve the upper bound of the estimated error covariance of the i-th node at the s+1th time Let k=k+1 and return to S3.

2. The method for estimating the state of a complex network with time-varying output coupling in a low-reliability communication environment according to claim 1, characterized in that: The model in S1 is: y i,s =the i,s C i,s x i,s +(1-th i,s )C i,s-τ x i,s-τ +v i,s In the formula, represents the system state to be estimated at node i at time s; represents the system state to be estimated at node i at time s-τ; represents the measured output; τ is the time-delay variable; B i,s , C i,s and C i,s-τ is a known suitable-dimensional matrix; is zero mean noise with variances and Γ and W s =[w il,s ] N×N denote the inner coupling matrix and the outer coupling matrix respectively; f(x i,s ) is a nonlinear function that satisfies ‖f(x i,s )‖≤a1‖x i,s ‖+a 11 In the formula, a1 and a 11 is a nonnegative scalar; ||·|| represents the norm; η i,s is a Bernoulli random variable with an uncertain probability of occurrence and has the following form: Among them, Prob{η i,s =1} represents η i,s The probability of taking the value 1; Prob{η i,s =0} represents η i,s The probability of taking the value 0; is the mathematical expectation; and is a known scalar; the scalar Δη i,s Describe the phenomenon of uncertainty in delay measurement, is bounded, is a known scalar, and η i,s The variance is denoted as σ i,s .

3. The method for estimating the state of a complex network with time-varying output coupling in a low-reliability communication environment according to claim 2, characterized in that: The specific steps of S2 are as follows: S21. Determine a periodic scheduling strategy; S22. After the transmitted data is processed by periodic scheduling, the measurement output equation of the i-th node at time s is obtained; S23. Introduce a zero-order compensator to compensate the scheduled data.

4. The method for estimating the state of a complex network with time-varying output coupling in a low-reliability communication environment according to claim 3, characterized in that: The periodic scheduling strategy in S21 is as follows: Where n y represents a cycle; mod(·) represents the remainder function; φ i,s Represents the indicator of the periodic scheduling strategy of node i at time s.

5. The method for estimating the state of a complex network with time-varying output coupling in a low-reliability communication environment according to claim 3, characterized in that: The measurement output equation in S22 is as follows: In the formula, Φ i,s =diag{δ(φ i,s -1),δ(φ i,s -2),…,δ(φ i,s -n y )}; diag represents a diagonal matrix; the function δ(·) is defined as follows:

6. The method for estimating the state of a complex network with time-varying output coupling in a low-reliability communication environment according to claim 3, characterized in that: The measured output equation after compensation in S23 is as follows: When sm<0,φ i,s-m =m;φ i,s-m represents the index of the periodic scheduling strategy of node i at time sm; the system is at s=-(n y -1),…,-1,0, the initial measured value y i,s =0; In the formula, represents the measured output of node i after the zero-order compensator is introduced at time s; represents the measurement output equation of the i-th node at time s; y i,s-m The measured output of node i at time sm.

7. The method for estimating the state of a complex network with time-varying output coupling in a low-reliability communication environment according to claim 3, characterized in that: The distributed estimator is constructed in S3: In the formula Indicates that node l outputs an estimated value at time s; represents the predicted value of the state of node i at time sm; represents the estimated value of the state of node i at time s; and They represent the predicted value and estimated value of the state of node i at time s+1 respectively; represents the measurement output of the i-th sensor received by the estimator at the s+1th time in a time-varying output coupled complex network with random uncertain probability measurement lag; and K i,s is the distributed estimator parameter of node i at time s; "Σ" is the summation symbol; Represents η i,s+1-m The nominal mathematical expectation of ; η i,s+1-m Used to describe the time lag phenomenon of the i-th node at the s+1-mth moment; B i,s , C i,s , C i,s-τ , C i,s+1-m and C i,s+1-τ-m is a known matrix of suitable dimension.

8. The method for estimating the state of a complex network with time-varying output coupling in a low-reliability communication environment according to claim 7, characterized in that: In S5, the upper bound of the one-step prediction error covariance The calculation formula is as follows: in, In the formula, Indicates the symbol for partial derivative; F i,s and E i,s is a known matrix; represents the process noise variance of node i at time s; represents the observation noise variance of node i at time s; the superscript "-1" represents the inversion of the matrix or the reciprocal of the logarithm; the superscript "2" represents the square of the logarithm; ε1, ε2, ε3, ε4, ε5, ε6, ε7, ε8, ε9 and ν are known scaling parameters; and ν -1 are the reciprocals of ε1, ε2, ε3, ε4, ε5, ε6, ε7, ε8, ε9 and ν respectively; express The square of express The square of express The square of i,s is η i,s The variance of Γ T , and Respectively represent B i,s , A p,s 、e j,s|s , C l,s ,Γ, and C l,s-τ The transpose of .

9. The method for estimating the state of a complex network with time-varying output coupling in a low-reliability communication environment according to claim 8, characterized in that: S6, the distributed estimator parameter K i,s+1 The calculation formula is as follows: in, ζ5=1+ε 10 +e 11 +e 12 In the formula, the superscript "-1" means to invert the matrix or take the reciprocal of the logarithm; the superscript "2" means to square the logarithm; ε 10 , ε 11 , ε 12 , ε 13 , ε 14 , ε 15 , ε 16 , ε 17 and ε 18 is a known scaling parameter; and They are ε 10 , ε 11 , ε 12 , ε 13 , ε 14 , ε 15 , ε 16 , ε 17 and ε 18 The reciprocal of express The square of express The square of express The square of express The square of and Respectively represent C i,s+1 , Φ i,s+1-m , and The transpose of .

10. The method for estimating the state of a time-varying output-coupled complex network in a low-reliability communication environment according to claim 9, characterized in that: In S8, the upper bound of the estimated error covariance The calculation formula is as follows: in, ζ5=1+ε 10 +e 11 +e 12 Where I is the identity matrix; express The square of express The square of 10 , ε 11 , ε 12 , ε 13 , ε 14 , ε 15 , ε 16 , ε 17 and ε 18 is a known scaling parameter; and They are ε 10 , ε 11 , ε 12 , ε 13 , ε 14 , ε 15 , ε 16 , ε 17 and ε 18 The reciprocal of is the measurement noise v of the ith node in the system at the s+1th time in the complex network framework i,s+1 The covariance matrix of express The square of express The square of express The square of and Respectively represent C i,s+1 , Φ i,s+1-m , K i,s+1 and The transpose of In S8, the make Established, where P i,s+1|s+1 is the estimated error covariance of the i-th node at the s+1th time; next, by minimizing The trace of the distributed estimator parameter K at the s+1th moment is designed i,s+1 .

Images