Weighted state fusion filtering method for coping with noise and one-step random time delay and packet loss

Abstract

The invention relates to the technical field of signal processing, in particular to a weighted state fusion filtering method for coping with noise and one-step random time delay and packet loss, which effectively captures the influence of colored multiplicative noise on the system state by introducing a virtual state vector and constructing a new augmented system model; a weighted state fusion filter is further deduced under a projective theory framework to adapt to the uncertainty of random time delay and data packet loss, and the filtering precision is improved. In addition, through the distributed structure design, effective state fusion can be carried out in a multi-sensor node system. And finally, through a plurality of simulation experiments, the excellent performance of the method in processing complex noise, time lag and packet loss is verified, and the advantages of the filter in precision and robustness are shown.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and in particular to a weighted state fusion filtering method for coping with noise and one-step random time delay and packet loss. Background Art

[0002] In many fields such as modern control systems, wireless sensor system networks, and the Internet of Things, the system state estimation problem is one of the important tasks to ensure the system's operating performance and stability. However, in practical applications, sensor data is often limited by the quality of the communication network. During the transmission process, it is inevitable to encounter time delays, packet loss, and noise pollution. These uncertain factors have a significant impact on state estimation and filtering performance.

[0003] Ideally, filter design usually assumes that the system is subject to additive white noise interference. However, the noise in actual systems often exhibits more complex statistical characteristics. For example, in wireless sensor networks, system noise may appear as multiplicative noise due to uneven sensor sensitivity or fluctuations in environmental conditions. In addition, the spectral density of noise is often no longer a constant (i.e., non-white noise), but varies with frequency, i.e., colored noise. In actual wireless communication networks, data may be lost or delayed due to network congestion, bandwidth limitations, or signal interference. These random time delays and packet loss problems seriously weaken the performance of existing filtering methods. In particular, in distributed state estimation, when each sensor node collects data and performs state estimation independently, packet loss and time delay will lead to information asymmetry between different nodes, affecting the overall estimation accuracy of the fusion filter.

[0004] In recent years, many solutions have been proposed for the problems of noise, time delay and packet loss. For example, the extended Kalman filter (EKF) and robust filter based on H∞ theory have shown certain effects in dealing with random noise and partial time delay. Some studies have combined the Markov chain model to describe the problem of data packet loss and designed filtering algorithms that adapt to uncertain network environments. However, most existing studies focus on systems assuming that the noise is additive white noise, and there are few studies on the treatment of multiplicative noise and colored noise. Multiplicative noise and colored noise are widely present in complex systems (such as industrial automation control systems or large-scale distributed networks). In addition, many methods fail to simultaneously consider the combined impact of random time delay and packet loss on system performance, which limits their scope of application. Summary of the invention

[0005] The purpose of the present invention is to provide a weighted state fusion filtering method for coping with noise and one-step random time delay and packet loss, adapt to the uncertainty of complex noise, random time delay and data packet loss, and improve filtering accuracy.

[0006] To achieve the above object, the present invention provides a weighted state fusion filtering method for dealing with noise and one-step random time delay and packet loss, comprising the following steps:

[0007] Step 1: Introduce a virtual state vector, generate virtual noise, and introduce an augmented state vector to transform the system into a new augmented system;

[0008] Step 2: Based on the projection theory, solve the mutual covariance matrix between the local filter and any two local filter errors, and thus give a distributed fusion filter weighted by the matrix;

[0009] Step 3: Conduct stability analysis and provide simulation results.

[0010] Optionally, the expression and assumptions of the system model are as follows:

[0011] x(t+1)=Φx(t)+Γw(t)

[0012]

[0013] β i (t+1)=h i β i (t)+p i (t)

[0014] v i (t) = D i w(t)+η i (t)

[0015] y i (t) = ξ i (t)z i (t)+(1-ξ i (t))ζ i (t)z i (t-1)+(1-ξ i (t))(1-ζ i (t))y i (t-1)

[0016] Where x(t)∈R n is the estimated state, is the observation received by the sensor, is the observation received by the estimator, w(t)∈R r is the process noise, is the observation noise of the ith sensor and is linearly related to w(t), β i (t) is colored multiplicative noise that is uncorrelated with other random variables, Φ, Γ, H, h i is a known constant matrix of appropriate dimension;

[0017] Assumption 1.ξ i (t) and ζ i (t) are independent scalar Bernoulli white noises with values ​​of 0 or 1, respectively, with known probabilities: Prob(ξ i (t) = 1) = α i ,Prob(ξ i (t) = 0) = 1 - α i , Prob(ζ i (t) = 1) = γ i , Prob(ζ i (t) = 1) = 1 - γ i , where α i and γ i is known, and 0≤α i ≤1,0≤γ i ≤1, the symbol Prob(·) is the probability operation operator, ξ i (t) and ζ i (t) is also not correlated with other random sequences;

[0018] The following conclusions are drawn:

[0019]

[0020] Assumption 2. The initial state x(0) and ξ i (t),ζ i (t), w(t), v i (t), β i (t) is unrelated and satisfies: E[x(0)] = μ 0 , E[(x(0)-μ 0 )(x(0)-μ 0 ) Τ ]=P 0 ; and the following statistics:

[0021]

[0022] Among them, Q w , and They are white noise w(t), v i (t), p i (t) and η i The unknown uncertainty variance of (t), Ri is w(t) and v i The cross-covariance of (t), δ ij represents the Kronecker delta function, δ ii =1,δ ij =0(i≠j);

[0023] Assumption 3. β i The initial value of (t)β i The mean of (0) is E[β i (0)]=0, the variance is The other random variables are uncorrelated.

[0024] Optionally, in step 1, a virtual state vector is first introduced Rewrite the colored noise formula as:

[0025]

[0026] in The virtual process noise is calculated as follows:

[0027]

[0028] Then introduce the augmented state vector and rewrite the system into the following form:

[0029]

[0030] in,

[0031]

[0032] And gives the following statistical information:

[0033]

[0034] is the state transfer matrix of the augmented system, is the state of the augmented system, is the process noise transfer matrix of the augmented system, is the process noise of the augmented system, is the observation matrix of the augmented system;

[0035] According to the known conditions, we know and v i (t) are all zero-mean correlated white noises and satisfy certain noise statistics;

[0036] The original distributed fusion system with colored multiplicative noise is transformed into an augmented system with correlated white noise, with the following results:

[0037]

[0038] It can be calculated that: E[ΔΦ i (t)] = E[ΔH i (t)]=0.

[0039] Optionally, after generating a new augmented system in step 1, the second-order moments of the original system and the augmented system need to be solved separately for subsequent calculations. The corresponding second-order moment expression of the original system is as follows:

[0040] A(t+1)=Ε[x(t+1)x Τ (t+1)]=ΦA(t)Φ Τ +ΓQ w Γ Τ

[0041] The second-order moment expression of the augmented system is as follows:

[0042]

[0043] Optionally, in step 2, the local linear filter and predictor of the i-th sensor subsystem of the augmented system are calculated by the following formula:

[0044] For the augmented system, the local linear filter and predictor of the ith sensor subsystem are calculated by the following formula:

[0045]

[0046] The corresponding filtering gain and prediction gain are:

[0047]

[0048] Innovation ε i (t) and the innovation variance They are calculated as:

[0049]

[0050] Filter error variance matrix P i (t|t) and the prediction variance matrix P i (t+1|t) are:

[0051]

[0052] in,

[0053]

[0054] Optionally, the filtering and prediction error cross covariance matrices of the i-th and j-th sensor subsystems of the augmented system are respectively:

[0055]

[0056] By the definition of the augmented state vector System Status x i The local optimal linear filter of (t) is given by Given, and the corresponding filtering error covariance matrix is ​​obtained:

[0057] p ij (t|t)=[I n 000]P ij (t|t)[I n 000] Τ .

[0058] Optionally, during the stability analysis in step 3, a matrix is ​​introduced:

[0059]

[0060] If A i The spectral radius is less than 1, that is, ρ(A i )<1, then with any initial value q i The solution q of the generalized Lyapunov equation (0) i (t) converges to the unique solution of the following generalized steady-state Lyapunov equation

[0061]

[0062] If ρ(A i )<1, is a stable pair, among which, With any initial value P i Solution P of (0|-1)≥0 i (t|t-1) will converge to a unique positive semidefinite solution, resulting in the following algebraic Riccati equation:

[0063]

[0064] Right now And the local steady-state predictor:

[0065]

[0066] Based on the above theorem, with any initial value q ij (0) and ∑ ij The solution q of the generalized Lyapunov equation for (0|-1) ij (t), P ij (t|t-1) converges to the unique solution of the following generalized Lyapunov equation:

[0067]

[0068] And there are:

[0069] The present invention provides a weighted state fusion filtering method for dealing with noise and one-step random time delay and packet loss. By introducing a virtual state vector and constructing a new augmented system model, the influence of colored multiplicative noise on the system state is effectively captured; further, a weighted state fusion filter is derived under the framework of projection theory to adapt to the uncertainty of random time delay and data packet loss, thereby improving the filtering accuracy. In addition, through distributed structure design, effective state fusion can be performed in a multi-sensor node system. Finally, through multiple simulation experiments, the superior performance of the method of the present invention in dealing with complex noise, time delay and packet loss is verified, demonstrating the advantages of the filter in accuracy and robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0071] Figure 1 It is a schematic flow chart of the steps of a weighted state fusion filtering method for coping with noise and one-step random time delay and packet loss of the present invention.

[0072] Figure 2 It is a schematic diagram of the local and fusion filtering results of two state components according to a specific embodiment of the present invention.

[0073] Figure 3 It is a schematic diagram of error variance comparison of local and fusion filters according to a specific embodiment of the present invention.

[0074] Figure 4 It is a schematic diagram of the variation of the filtering error variance according to a specific embodiment of the present invention. DETAILED DESCRIPTION

[0075] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0076] See also Figure 1The present invention provides a weighted state fusion filtering method for dealing with noise and one-step random time delay and packet loss, comprising the following steps:

[0077] S1: Introduce a virtual state vector, generate virtual noise, and introduce an augmented state vector to transform the system into a new augmented system;

[0078] S2: Based on the projection theory, the mutual covariance matrix between the local filter and any two local filter errors is solved, and the distributed fusion filter weighted by the matrix is ​​given;

[0079] S3: Conduct stability analysis and provide simulation results.

[0080] The following is a further explanation of the filter system model and specific implementation steps:

[0081] The expressions and assumptions of the system model are as follows:

[0082] x(t+1)=Φx(t)+Γw(t) (1)

[0083]

[0084] β i (t+1)=h i β i (t)+p i (t) (3)

[0085] v i (t) = D i w(t)+η i (t) (4)

[0086] y i (t) = ξ i (t)z i (t)+(1-ξ i (t))ζ i (t)z i (t-1)+(1-ξ i (t))(1-ζ i (t))y i (t-1) (5)

[0087] Where x(t)∈R n is the estimated state, is the observation received by the sensor, is the observation received by the estimator, w(t)∈R r , is white noise, β i (t) is colored multiplicative noise that is uncorrelated with other random variables, p i(t) and η i (t) is white noise, ξ i (t) and ζ i (t) are independent scalar Bernoulli white noises with values ​​of 0 or 1, respectively, with known probabilities: Prob(ξ i (t) = 1) = α i ,Prob(ξ i (t) = 0) = 1 - α i , Prob(ζ i (t) = 1) = γ i , Prob(ζ i (t) = 1) = 1 - γ i , where α i and γ i is known, and 0≤α i ≤1,0≤γ i ≤1, the symbol Prob(·) is the operation operator, ξ i (t) and ζ i (t) is also not correlated with other random sequences, Φ, Γ, H, h i is a known constant matrix of appropriate dimension;

[0088] Assumption 1. w(t) and v i (t) is linearly related and has a mean of 0, and the variances are Q w and White noise with cross-covariance R(t);

[0089] Assumption 2. The initial state x(0) and ξ i (t),ζ i (t), w(t), v i (t), β i (t) is unrelated and satisfies: E[x(0)] = μ 0 , E[(x(0)-μ 0 )(x(0)-μ 0 ) Τ ]=P 0 ;

[0090] Assumption 3. β i The initial value of (t)β i The mean of (0) is E[β i (0)]=0, the variance is The other random variables are uncorrelated.

[0091] The purpose of the present invention is to seek a distributed fusion filter in the sense of linear minimum variance based on a measurement sequence L(y(1), ...y(t-1)).

[0092] Step S1 includes the following steps:

[0093] (1) β in formula (3) in the original system model i (t) is colored noise, so we first introduce a virtual state vector Rewrite formula (3) into the following form:

[0094]

[0095] Generate virtual process noise:

[0096] Then, we can replace the original system's formula (3) with formula (6), introduce the augmented state vector, and rewrite the system (1)-(6) into the following form:

[0097]

[0098] According to the known conditions, we know and v i (t) are all correlated white noises with zero mean and satisfy certain noise statistical information. In this way, the distributed fusion filtering problem of colored multiplicative noise in the original system is transformed into a distributed fusion filtering problem of an augmented system with correlated white noise, which reduces the computational burden.

[0099] (2) After generating the new augmented system, it is necessary to solve the second-order moments of the original system and the augmented system respectively for subsequent calculations.

[0100] Original system:

[0101] Ε(t+1)=ΦΕ(t)Φ Τ +ΓQ w Γ Τ (9)

[0102] Augmentation System:

[0103]

[0104] In step S2, local linear filters and cross-covariance matrices between any two local filter errors are derived in turn based on the projection theory.

[0105] (1) Local filter

[0106] For the system (7)-(8), the local linear filter and predictor of the i-th sensor subsystem are calculated by the following formulas:

[0107]

[0108] The filtering gain and prediction gain are:

[0109]

[0110] Innovation ε i (t) and the innovation variance They are calculated as:

[0111]

[0112] Filter error variance matrix P i (t|t) and the prediction variance matrix P i (t+1|t) are:

[0113]

[0114] in,

[0115]

[0116] (2) Calculation of the cross-covariance matrix

[0117] In this section, the filter error variance matrix between any two local filter errors will be derived to obtain the fusion weights. For systems (7)-(8), the filter and prediction error cross covariance matrices of the i-th and j-th sensor subsystems are:

[0118]

[0119] By the definition of the augmented state vector System Status x i The local optimal linear filter of (t) is given by Given, and the corresponding filtering error covariance matrix is ​​obtained:

[0120] p ij (t|t)=[I n 000]P ij (t|t)[I n 000] Τ

[0121] (3) Distributed fusion filter weighted by matrix

[0122] Based on the already studied local linear filter Covariance matrix p i (t|t), p ij (t|t), the matrix-weighted distributed fusion filter of the original system (1)-(5) is as follows:

[0123]

[0124] The fusion weight is calculated as: [ω 1 (t),...ωN (t)]=[J Τ Ω -1 (t|t)J] -1 J Τ Ω -1 (t|t)

[0125] The corresponding fusion filter error variance matrix:

[0126] p(t|t)=[J Τ Ω -1 (t|t)J] -1 (27)

[0127] Stability analysis in step S3:

[0128] In all the above steps, the distributed fusion filter is studied. Now we will analyze the fusion filter in the case of 0<α i <1,0<γ i The stability when <1 is a sufficient condition for the convergence of the local filter proposed by the research, and a matrix is ​​introduced:

[0129]

[0130] If A i The spectral radius is less than 1, that is, ρ(A i )<1, then with any initial value q i The solution q of the generalized Lyapunov equation (0) i (t);

[0131] Converges to the unique solution of the following generalized steady-state Lyapunov equation

[0132]

[0133] If ρ(A i )<1, is a stable pair, among which, With any initial value P i Solution P of (0|-1)≥0 i (t|t-1) will converge to a unique positive semidefinite solution, resulting in the following algebraic Riccati equation:

[0134]

[0135] Right now And the local steady-state predictor:

[0136]

[0137] Based on the above theorem, with any initial value qij (0) and ∑ ij The solution q of the generalized Lyapunov equation for (0|-1) ij (t), P ij (t|t-1) converges to the unique solution of the following generalized Lyapunov equation:

[0138]

[0139] And there are:

[0140] The corresponding distributed fusion steady-state filter:

[0141]

[0142] And the weights:

[0143]

[0144] Steady-state fusion variance:

[0145] p s (t|t)=[J Τ Ω -1 (t|t)J] -1

[0146] Based on the above results, it can be concluded that if all local filters are asymptotically stable, then the distributed fusion filter is also asymptotically stable. The corresponding distributed fusion steady-state filter is obtained as:

[0147]

[0148] The optimal weighting matrix is ​​calculated as follows:

[0149] Ω=(p ij ) nN×nN

[0150] Steady-state fusion variance:

[0151] p s =[J Τ Ω -1 J] -1

[0152] in:

[0153] p ij =[I n 000]P ij [I n 000] Τ

[0154] Furthermore, the advantages are described below by combining the old and new systems and simulation experiments:

[0155] 1. Original system model In formula (5), Bernoulli white noise is used to describe one-step random observation delay and packet loss. If ξ i (t) = 1, y i (t) = z i (t) (no delay and packet loss); if ξ i (t) = 0, ζ i (t) = 1, then y i (t) = z i (t-1) (one-step random observation lag); if ξ i (t) = 0, ζ i (t)=0, then y i (t) = y i (t-1)(packet loss), that is, observation z i (t) is lost, but the observation y received by the estimator at time t-1 i (t-1) is used as the compensator at time t. Table 1 explains the one-step random delay and packet loss phenomenon during data transmission.

[0156] Table 1 Data transmission

[0157]

[0158] 2. Simulation experiment

[0159] Consider the following example:

[0160]

[0161] Assuming that the system is measured by three sensors, in the simulation experiment, the initial value is set as:

[0162] h 1 =0.25, h 2 =0.4,h 3 =0.5, D 1 =1,D 2 =0.5, D 3 =1.1,

[0163] α 1 =0.4,α 2 =0.3,α 3 =0.6,γ 1 =0.5,γ 2 =0.3,γ 3 =0.1, Q w =0.5, Q α=1.5,

[0164] The proposed distributed fusion filter is Figure 2 As shown, the local and fusion filtering results of the two state components are given, and the filtering error variance is as follows Figure 3 As shown in Figure 3, the study found that there exists a steady-state fusion filter, and the fusion filter has better accuracy than any local filter. Figure 4 It shows that the fusion variance varies with the acceptance rate (α 1 =α 2 =α 3 ). It is obvious that the proposed fusion filter performs better at a larger receiving rate.

[0165] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0166] (1) The present invention can simultaneously process weighted state fusion filters with colored multiplicative noise and one-step random time delay and packet loss systems. Usually, the research on optimal linear filters is based on white noise. The property of white noise being uncorrelated at different times makes it easier to process the problem, while colored multiplicative noise is more challenging and more practical.

[0167] (2) In order to facilitate the subsequent related calculations of the optimal linear filter, it is first necessary to introduce a virtual state vector to generate virtual process noise. On this basis, the augmented state vector is introduced to generate a new augmented system. In this way, the weighted fusion estimation problem of the original system with colored multiplicative noise is transformed into the weighted fusion estimation problem of the augmented system with correlated white noise, which has a smaller computational burden.

[0168] (3) For multi-sensor systems, local filters are designed, and the cross-covariance matrix between any two local filter errors is derived. Then, the corresponding weighted fusion filter is given based on the linear minimum variance. The proposed algorithm does not need to calculate the virtual state filter and has lower complexity.

[0169] What is disclosed above is only one or more preferred embodiments of the present invention, which certainly cannot be used to limit the scope of rights of the present invention. Ordinary technicians in this field can understand that all or part of the processes of implementing the above embodiments and making equivalent changes according to the claims of the present invention still fall within the scope of the invention.

Claims

1. A weighted state fusion filtering method for dealing with noise and one-step random delay and packet loss, characterized in that: The following steps are involved: Step 1: Introduce a virtual state vector, generate virtual noise, and introduce an augmented state vector to transform the system into a new augmented system; Step 2: Based on the projection theory, solve the mutual covariance matrix between the local filter and any two local filter errors, and thus give a distributed fusion filter weighted by the matrix; Step 3: Conduct stability analysis and provide simulation results.

2. The weighted state fusion filtering method for dealing with noise and one-step random time delay and packet loss as claimed in claim 1, characterized in that: The expressions and assumptions of the system model are as follows: x(t+1)=Φx(t)+Γw(t) β i (t+1)=h i β i (t)+p i (t) v i (t)=D i w(t)+η i (t) y i (t)=ξ i (t)z i (t)+(1-ξ i (t))ζ i (t)z i (t-1)+(1-ξ i (t))(1-ζ i (t))y i (t-1) Where x(t)∈R n is the estimated state, is the observation received by the sensor, is the observation received by the estimator, w(t)∈R r is the process noise, is the observation noise of the ith sensor and is linearly related to w(t), β i (t) is colored multiplicative noise that is uncorrelated with other random variables, Φ, Γ, H, h i is a known constant matrix of appropriate dimension; Assumption 1.ξ i (t) and ζ i (t) are independent scalar Bernoulli white noises with values ​​of 0 or 1, respectively, with known probabilities: Prob(ξ i (t) = 1) = α i ,Prob(ξ i (t) = 0) = 1 - α i , Prob(ζ i (t) = 1) = γ i , Prob(ζ i (t) = 1) = 1 - γ i , where α i and γ i is known, and 0≤α i ≤1,0≤γ i ≤1, the symbol Prob(·) is the probability operation operator, ξ i (t) and ζ i (t) is also not correlated with other random sequences; The following conclusions are drawn: Assumption 2. The initial state x(0) and ξ i (t),ζ i (t), w(t), v i (t), β i (t) is unrelated and satisfies: E[x(0)] = μ0, E[(x(0)-μ0)(x(0)-μ0) Τ ]=P0; and the following statistical information: Among them, Q w , and They are white noise w(t), v i (t), p i (t) and η i The unknown uncertainty variance of (t), R i is w(t) and v i The cross-covariance of (t), δ ij represents the Kronecker delta function, δ ii =1,δ ij =0(i≠j); Assumption 3. β i The initial value of (t)β i The mean of (0) is E[β i (0)]=0, the variance is The other random variables are uncorrelated.

3. The weighted state fusion filtering method for dealing with noise and one-step random time delay and packet loss as claimed in claim 2, characterized in that: In step 1, we first introduce the virtual state vector Rewrite the colored noise formula as: in The virtual process noise is calculated as follows: Then introduce the augmented state vector and rewrite the system into the following form: in, And gives the following statistical information: is the state transfer matrix of the augmented system, is the state of the augmented system, is the process noise transfer matrix of the augmented system, is the process noise of the augmented system, is the observation matrix of the augmented system; According to the known conditions, we know and v i (t) are all zero-mean correlated white noises and satisfy certain noise statistics; The original distributed fusion system with colored multiplicative noise is transformed into an augmented system with correlated white noise, with the following results: It can be calculated that: E[ΔΦ i (t)] = E[ΔH i (t)]=0.

4. The weighted state fusion filtering method for coping with noise and one-step random time delay and packet loss as claimed in claim 3, characterized in that: After generating the new augmented system in step 1, it is necessary to solve the second-order moments of the original system and the augmented system respectively for subsequent calculations. The corresponding second-order moment expressions of the original system are as follows: A(t+1)=E[x(t+1)x Τ (t+1)]=ΦA(t)Φ Τ +GQ w C Τ The second-order moment expression of the augmented system is as follows:

5. The weighted state fusion filtering method for coping with noise and one-step random time delay and packet loss as claimed in claim 4, characterized in that: In step 2, the local linear filter and predictor of the i-th sensor subsystem of the augmented system are calculated by the following formulas: For the augmented system, the local linear filter and predictor of the ith sensor subsystem are calculated by the following formula: The corresponding filtering gain and prediction gain are: Innovation ε i (t) and the innovation variance They are calculated as: Filter error variance matrix P i (t|t) and the prediction variance matrix P i (t+1|t) are: in, 6. The weighted state fusion filtering method for coping with noise and one-step random time delay and packet loss as claimed in claim 5, characterized in that: The cross-covariance matrices of the filtering and prediction errors of the i-th and j-th sensor subsystems of the augmented system are: By the definition of the augmented state vector System Status x i The local optimal linear filter of (t) is given by Given, and the corresponding filtering error covariance matrix is ​​obtained: p ij (t|t)=[I n 000]P ij (t|t)[I n 000] Τ 。 7. The weighted state fusion filtering method for coping with noise and one-step random time delay and packet loss as claimed in claim 6, characterized in that: In the process of stability analysis in step 3, a matrix is ​​introduced: If A i The spectral radius is less than 1, that is, ρ(A i )<1, then with any initial value q i The solution q of the generalized Lyapunov equation (0) i (t) converges to the unique solution of the following generalized steady-state Lyapunov equation If ρ(A i )<1, is a stable pair, among which, With any initial value P i Solution P of (0|-1)≥0 i (t|t-1) will converge to a unique positive semidefinite solution, resulting in the following algebraic Riccati equation: Right now And the local steady-state predictor: Based on the above theorem, with any initial value q ij (0) and ∑ ij The solution q of the generalized Lyapunov equation for (0|-1) ij (t), P ij (t|t-1) converges to the unique solution of the following generalized Lyapunov equation: And there are:

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