CN109039725A - It is a kind of with the complex network optimal estimating method that couples at random - Google Patents
It is a kind of with the complex network optimal estimating method that couples at random Download PDFInfo
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- H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
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Abstract
It is a kind of with the complex network optimal estimating method that couples at random, the present invention relates to Random Coupling complex network optimal estimating method.The present invention solves standing state estimation method cannot handle the time lag complex network coupled at random with measurement Loss and inaccurate probability of happening simultaneously, cause to estimate that performance accuracy rate is low, and there are loss of transmitted data, transmission failure, switching nodes can not receive in the simultaneous situation of other nodal informations, leads to the problem for estimating that performance accuracy rate is low.Process are as follows: one, the random generation coupling time lag complex network dynamic model of foundation；Two, state estimation is carried out to dynamic model under event-triggered protocols；Three, ∑ is calculatedi,k+1|k；Four, K is calculatedi,k+1；Five, it obtainsJudge whether k+1 reaches M, if k+1 < M, executes six, otherwise terminate；Six, ∑ is calculatedi,k+1|k+1；Another k=k+1 executes two, until meeting k+1=M.The present invention is used for complex network optimal estimating field.
Description
Technical field
The present invention relates to Random Coupling complex network optimal estimating method.
Background technique
The state estimation of complex network, which is that one kind is important in control system, to study a question, in engineering, power grid, social networks
It is widely applied in the signal estimation task in equal fields.
The generation that can frequently result in measurement Loss when network gets congestion, furthermore in practical applications, due to net
Network conversion causes the random generation phenomenon coupled between node.Therefore, design while being suitable for the state of these network inducing phenomenas
Estimation method be very it is necessary to, especially when the probability that couples at random is uncertain situation；
Current existing method for estimating state cannot be handled simultaneously with measurement Loss and inaccurate probability of happening
The time lag complex network coupled at random causes to estimate that performance accuracy rate is low；
There are loss of transmitted data, transmission failure, switching nodes can not receive other sections for existing method for estimating state
When the case where point information, cause to estimate that performance accuracy rate is low.
Summary of the invention
The present invention solves standing state estimation method and cannot handle simultaneously, and there is measurement Loss and inaccuracy to occur
The time lag complex network of probability coupled at random causes to estimate that performance accuracy rate is low, and there are loss of transmitted data, biography
Defeated failure, switching node can not receive in the simultaneous situation of other nodal informations, cause to estimate that performance accuracy rate is low
Problem, and propose a kind of with the complex network optimal estimating method coupled at random.
It is a kind of with the complex network optimal estimating method detailed process that couples at random are as follows:
The complex network can for satellite constitute network, robot constitute network, spacecraft constitute network or
The network that radar is constituted；
Step 1: establishing, there is measurement Loss and the random generation of inaccurate probability of happening to couple time lag complex web
Network dynamic model；
Step 2: there is measurement Loss and inaccurate probability of happening to what step 1 was established under event-triggered protocols
Random generation coupling time lag complex network dynamic model carry out state estimation；
Step 3: calculating the one-step prediction error co-variance matrix upper bound of the state estimation of each node of complex network
∑i,k+1|k；
Step 4: the one-step prediction error co-variance matrix upper bound ∑ obtained according to step 3i,k+1|k, calculate complex network
Each node estimated gain matrix Ki,k+1；
Step 5: by the estimated gain matrix K of each node obtained in step 4i,k+1The state substituted into step 2 is estimated
Formula 8 is counted, obtains i-th of node in the state estimation at+1 moment of kthIt realizes to measurement Loss and not
The random state estimation that coupling time lag complex network occurs of accurate probability of happening.
Judge whether k+1 reaches complex network total duration M, if k+1 < M, thens follow the steps six, if k+1=M, terminate；
Step 6: according to the estimated gain matrix K of each node of complex network calculated in step 4i,k+1, calculate
The evaluated error covariance matrix upper bound ∑ of each node of complex network outi,k+1|k+1；
Another k=k+1 executes step 2, until meeting k+1=M.
Invention effect:
The present invention proposes a kind of time lag coupled at random with measurement Loss and inaccurate probability of happening
Complex network method for estimating state, while considering the random generation coupling with measurement Loss and inaccurate probability of happening
The influence to state estimation performance is closed, considers having for evaluated error covariance matrix comprehensively using Extended Kalman filter method
Imitate information, compared with existing time lag complex network method for estimating state, time lag complex network method for estimating state of the invention
Processing simultaneously has the random generation coupling phenomenon of measurement Loss and inaccurate probability of happening, has obtained based on expansion card
The time lag complex network method for estimating state of Kalman Filtering method has achieved the purpose that disturbance rejection, and has and be easy to solve and reality
Existing advantage；Solving standing state estimation method cannot be handled simultaneously with measurement Loss and inaccurate probability of happening
The time lag complex network coupled at random causes to estimate that performance accuracy rate is low, improves estimation performance accuracy rate.
The present invention utilizes Extended Kalman filter method, by considering that the effective information of evaluated error covariance matrix obtains
Evaluated error covariance matrix, then guaranteed by designing gain matrix the mark of evaluated error covariance matrix each step all
Minimum value can be obtained.It ensure that the minimum of evaluated error.It realizes in loss of transmitted data, transmission failure and existing coupling
Node can not receive in other nodal informations (random there is a situation where couple) simultaneous situations performance estimation not by shadow
It rings, improves estimation accuracy rate.
Other nodal informations can not be received in loss of transmitted data, transmission failure, switching node by solving existing method
In simultaneous situation, lead to the problem for estimating that performance accuracy rate is low,
Relative error in conjunction with attached drawing obtain situation once all moment of all nodes is 24.82%, the lower institute of situation two
The relative error for having all moment of node is 38.48%.It can be seen that with the increase of activation threshold value, the state estimation performance of network
It gradually decreases.
Detailed description of the invention
Fig. 1 is the method for the invention flow chart；
Fig. 2 a is first node virtual condition track of complex networkThe state estimation rail under two different activation threshold values
MarkComparison diagram,For complex network the 1st node the state variable at kth moment one-component；WhereinIt is system mode track,It is the state estimation track of situation once,It is the shape under situation two
State estimates track；
Fig. 2 b is first node virtual condition track of complex networkThe state estimation rail under two different activation threshold values
MarkComparison diagram,For complex network the 1st node the kth moment state variable second component；
Fig. 3 a is second node virtual condition track of complex networkThe state estimation rail under two different activation threshold values
MarkComparison diagram,One-component of 2nd node of complex network in the state variable at kth moment；
Fig. 3 b is second node virtual condition track of complex networkThe state estimation rail under two different activation threshold values
MarkComparison diagram,Second component of 2nd node of complex network in the state variable at kth moment；
Fig. 4 a is complex network third node virtual condition trackThe state estimation rail under two different activation threshold values
MarkComparison diagram,One-component of 3rd node of complex network in the state variable at kth moment；
Fig. 4 b is complex network third node virtual condition trackThe state estimation rail under two different activation threshold values
MarkComparison diagram,Second component of 3rd node of complex network in the state variable at kth moment；
Fig. 5 a is the mark in the upper bound of the state estimation error co-variance matrix of first node in different measurement losing probabilities
Under trajectory diagram, Σ1,k|kIt is the 1st node in the evaluated error covariance matrix upper bound at kth moment, Σ2,k|kIt is saved for the 2nd
Point is in the evaluated error covariance matrix upper bound at kth moment, Σ3,k|kFor the 3rd node the kth moment evaluated error covariance
The matrix upper bound, trace (Σ1,k|k) it is Σ1,k|kMark, trace (Σ2,k|k) it is Σ2,k|kMark, trace (Σ3,k|k) be
Σ3,k|kMark, step is the number of iterations, and k is the moment；WhereinIt isUnder mark trajectory diagram,
It isUnder mark trajectory diagram,It isUnder mark trajectory diagram,It isUnder
The trajectory diagram of mark；
Fig. 5 b is the mark in the upper bound of the state estimation error co-variance matrix of second node in different measurement losing probabilities
Under trajectory diagram；
Fig. 5 c is the mark in the upper bound of the state estimation error co-variance matrix of third node in different measurement losing probabilities
Under trajectory diagram.
Specific embodiment
Specific embodiment 1: embodiment is described with reference to Fig. 1, one kind of present embodiment has to be coupled at random
Complex network optimal estimating method detailed process are as follows:
The complex network can for satellite constitute network, robot constitute network, spacecraft constitute network or
The network that radar is constituted；
Step 1: establishing, there is measurement Loss and the random generation of inaccurate probability of happening to couple time lag complex web
Network dynamic model；
Step 2: there is measurement Loss and inaccurate probability of happening to what step 1 was established under event-triggered protocols
Random generation coupling time lag complex network dynamic model carry out state estimation；
Step 3: calculating the one-step prediction error co-variance matrix upper bound of the state estimation of each node of complex network
∑i,k+1|k；
Step 4: the one-step prediction error co-variance matrix upper bound ∑ obtained according to step 3i,k+1|k, calculate complex network
Each node estimated gain matrix Ki,k+1；
Step 5: by the estimated gain matrix K of each node obtained in step 4i,k+1The state substituted into step 2 is estimated
It counts formula (8), obtains i-th of node in the state estimation at+1 moment of kthRealize to have measurement Loss and
The random state estimation that coupling time lag complex network occurs of inaccurate probability of happening.
Judge whether k+1 reaches complex network total duration M, if k+1 < M, thens follow the steps six, if k+1=M, terminate；
Step 6: according to the estimated gain matrix K of each node of complex network calculated in step 4i,k+1, calculate
The evaluated error covariance matrix upper bound ∑ of each node of complex network outi,k+1|k+1；
Another k=k+1 executes step 2, until meeting k+1=M.
Specific embodiment 2: the present embodiment is different from the first embodiment in that: tool is established in the step 1
There is measurement Loss (λi,k) and inaccurate probability of happening (γi,k) random generation couple time lag complex network dynamic analog
Type；
Random generation with measurement Loss and inaccurate probability of happening couples time lag complex network dynamic model
State space form are as follows:
yi,k=λi,kCi,kxi,k+νi,k, i=1,2 ..., N, (2)
In formula,
Respectively i-th of node of complex network is in kth, k+1 and k-d
The state variable at quarter；D is a fixed network time service；For the real number field of the state of complex network dynamic model, n is dimension；
xj,kFor complex network j-th of node the kth moment state variable；For i-th of node the kth moment survey
Amount output；For the real number field of complex network dynamic model output, p is dimension；It is i-th of node at the kth moment
Initial value, k=-d ,-d+1 ..., 0；Γ is known connection matrix；W=[wij]N×NIt is known coupling matrix, wijIt is
The coupled weight of i node and j-th of node；It is mean value be zero variance is Qi,kProcess noise,For complex web
The real number field of network dynamic model process noise, q are dimension；It is mean value be zero variance is Ri,kMeasurement noise；N is multiple
The node number of miscellaneous network；Ai,kFor the sytem matrix at known k moment, Bi,kFor the noise profile matrix at known k moment,
Ci,kFor the calculation matrix at known k moment,For sytem matrix known dimension and relevant to time lag k-d；γi,kWith λi,k
It is the stochastic variable for obeying Bernoulli Jacob's distribution, portrays Random Coupling phenomenon and measurement Loss respectively, and meet following item
Part:
Wherein,
γi,k+1、λi,k+1It is the stochastic variable for obeying Bernoulli Jacob's distribution, portrays Random Coupling phenomenon respectively and lost with measurement
Phenomenon is lost,It is known constant, is the expected probability that at random couples of i-th of node at the k+1 moment；It is
Known constant is measurement losing probability of i-th of node at the k+1 moment；WithValue range be (0,1), Δ
γI, k=1Portray the inaccuracy of probability；Prob { } is probability,For expectation；
It is describedThe inaccuracy of probability is portrayed,It is known to one for the upper bound of probability inaccuracy
Constant, and meet
Other steps and parameter are same as the specific embodiment one.
Specific embodiment 3: the present embodiment is different from the first and the second embodiment in that: thing in the step 2
There is measurement Loss and when coupling at random of inaccurate probability of happening to what step 1 was established under part triggered protocol
Stagnant complex network dynamic model carries out state estimation；Detailed process are as follows:
Firstly, being directed to i-th of node, following event triggering formula is chosen:
WhereinMeasurement for i-th of node in a upper triggering moment exports,For a corresponding upper triggering moment
Value, δi> 0 is a known adjusting threshold value, and T is transposition；The then next event trigger sequence of i-th of nodeIt is changed by following formula
In generation, generates:
WhereinBe positive set of integers, and inf { } is to remove the limit function；
After event trigger mechanism, the true measurement for passing to filter is
When next event trigger sequence does not reach, true measurement takes always the value of a triggering moment；
For i-th of node of complex network, structural regime estimator:
In formula,
For xi,kIn the one-step prediction (one-step prediction detailed process be formula 7) at k moment,For i-th of node
In the state estimation at+1 moment of kth,State estimation for i-th of node at the kth-d moment, Ki,k+1For i-th of node
In the estimated gain matrix at k+1 moment,State estimation for i-th of node at the kth moment,It is j-th of node
The state estimation at k moment,Measurement for i-th of node at+1 moment of kth exports, Ci,k+1For the survey at known k+1 moment
Moment matrix；It is i-th of node in the expected probability coupled at random at k moment, is known constant.
Other steps and parameter are the same as one or two specific embodiments.
Specific embodiment 4: unlike one of present embodiment and specific embodiment one to three: the step 3
The one-step prediction error co-variance matrix upper bound ∑ of the state estimation of middle each node for calculating complex networki,k+1|k；Specifically
Process are as follows:
On the one-step prediction error co-variance matrix for calculating the state estimation of each node of complex network according to the following formula
Boundary Σi,k+1|k:
In formula, τ1、τ2、τ4、τ5For intermediate variable,
In formula, τ1=1+ ε1+ε2+ε3,
εsFor the weight coefficient greater than zero, s=1,2 ..., 7 (in order to
Make Σi,k+1|kMark it is minimum)；For εsInverse, i=1,2 ..., 7；
wiFor intermediate variable,Σi,k+1|kFor i-th of node the kth moment one-step prediction error covariance
The matrix upper bound, Σi,k|kIt is i-th of node in the evaluated error covariance matrix upper bound at kth moment,Respectively Ai,k,Γ,Bi,k,Transposition；Σi,k-d|k-dIt is i-th of node in kth-d
The evaluated error covariance matrix upper bound at moment, Σj,k|kIt is j-th of node on the evaluated error covariance matrix at kth moment
Boundary.
Other steps and parameter are identical as one of specific embodiment one to three.
Specific embodiment 5: unlike one of present embodiment and specific embodiment one to four: the step 4
The middle one-step prediction error co-variance matrix upper bound ∑ obtained according to step 3i,k+1|k, calculate each node of complex network
Estimated gain matrix Ki,k+1；Detailed process are as follows:
The estimated gain matrix K of each node of complex network is calculated as follows according to (9) formulai,k+1:
In formula,
For intermediate variable,ηlFor the constant greater than zero
(in order to make the Σ in step 6i,k+1|k+1Mark it is minimum), l=1,2,3,4；For ηlIt is inverse,For λi,k+1Variance,Ki,k+1Estimated gain matrix for i-th of node at+1 moment of kth,For Ci,k+1Transposition,
I is unit matrix, Ri,k+1For νi,k+1Variance be.
Other steps and parameter are identical as one of specific embodiment one to four.
Specific embodiment 6: unlike one of present embodiment and specific embodiment one to five: the step 6
The estimated gain matrix K of middle each node according to complex network calculated in step 4i,k+1, calculate the every of complex network
The evaluated error covariance matrix upper bound ∑ of a nodei,k+1|k+1；Detailed process are as follows:
Formula are as follows:
Wherein,
Σi,k+1|k+1It is i-th of node in the evaluated error covariance matrix upper bound at+1 moment of kth,WithRespectivelyWith Ki,k+1Transposition.
Furthermore, it is possible to prove in the case where other conditions are constant, with probabilityIncrease, evaluated error covariance
Matrix upper bound Σi,k+1|k+1Mark do not increase.Σi,k+1|k+1Bring the step 3 (Σ in replacement formula 9 intoi,k|k)。
Step 3: theory described in step 4 and step 5 are as follows:
Calculate the supremum of the evaluated error covariance matrix of each node.Seek ∑i,k+1|k+1, so that Pi,k+1|k+1≤
∑i,k+1|k+1, whereinEvaluated error covariance matrix for i-th of node at the k+1 moment,For the evaluated error at k+1 moment,For the expectation of element { },ForTurn
It sets.
Since there are indeterminates for evaluated error covariance matrix, its true value can not be acquired.Optimal estimating error
Covariance matrix upper bound ∑i,k+1|k+1Mark, the estimated gain matrix K of i-th of node of k+1 moment can be obtainedi,k+1。
Beneficial effects of the present invention are verified using following embodiment:
Embodiment one:
It is emulated using the method for the invention:
System parameter:
B1,k=[0.8 0.7]T, B2,k=[7.5+0.1sin (2k) 0.55]T, B3,k=[0.65 0.85]T,
C1,k=[1.6 1.8], C2,k=[1.6 1.3], C3,k=[1.65 1.8],
Γ=diag { 0.8,0.8 },
D=3.
Other emulation initial values are chosen as follows:
x1,0=[0.5 1]T, x2,0=[- 1 0.25]T, x3,0=[- 0.5-0.75]T, xi,j=[0.2 0.2]T,
(i=1,2,3, j=-1, -2), Q1,k=0.2, Q2,k=0.15, Q3,k=0.1, R1,k=0.2, R2,k=0.1, R3,k=0.1, ε1
=0.3, εi=0.1 (i=2,3,4), εi=1 (i=5,6,7), η1=0.2, η2=5, η3=1, η4=0.5, Σ1,0|0=2I2,
Σ2,0|0=2.5I2, Σ3,0|0=3I2, Σi,j|j=10I2(i=1,2,3, j=-1, -2, -3).
Situation one (Case I):
δ1=0.1, δ2=0.5, δ3=0.5；
Situation two (Case II):
δ1=5, δ2=5, δ3=5.
State estimator effect:
By Fig. 2 a, Fig. 2 b, Fig. 3 a, Fig. 3 b, Fig. 4 a, Fig. 4 b as it can be seen that existing for having measurement to lose under event trigger mechanism
As and inaccurate probability of happening the time lag complex network coupled at random, the state estimator design method invented can
Effectively estimate dbjective state.
For each node it can be seen from Fig. 5 a, 5b, 5c, with probabilityIncrease, evaluated error covariance square
Battle array upper bound Σi,k+1|k+1Mark successively decrease.
The present invention can also have other various embodiments, without deviating from the spirit and substance of the present invention, this field
Technical staff makes various corresponding changes and modifications in accordance with the present invention, but these corresponding changes and modifications all should belong to
The protection scope of the appended claims of the present invention.
Claims (6)
1. a kind of with the complex network optimal estimating method coupled at random, it is characterised in that: the method detailed process
Are as follows:
Step 1: establishing random generation coupling time lag complex network dynamic model；
Step 2: carrying out shape to the random generation coupling time lag complex network dynamic model that step 1 is established under event-triggered protocols
State estimation；
Step 3: calculating the one-step prediction error co-variance matrix upper bound of the state estimation of each node i of complex network
∑i,k+1|k；
Step 4: the one-step prediction error co-variance matrix upper bound ∑ obtained according to step 3i,k+1|k, calculate the every of complex network
The estimated gain matrix K of a nodei,k+1；
Step 5: by the estimated gain matrix K of each node obtained in step 4i,k+1Step 2 is substituted into, i-th of node is obtained
In the state estimation at+1 moment of kth
Judge whether k+1 reaches complex network total duration M, if k+1 < M, thens follow the steps six, if k+1=M, terminate；
Step 6: according to the estimated gain matrix K of each node of complex network calculated in step 4i,k+1, calculate multiple
The evaluated error covariance matrix upper bound Σ of each node of miscellaneous networki,k+1|k+1；
Another k=k+1 executes step 2, until meeting k+1=M.
2. a kind of with the complex network optimal estimating method coupled at random according to claim 1, it is characterised in that:
Random generation coupling time lag complex network dynamic model is established in the step 1；
The random state space form that coupling time lag complex network dynamic model occurs are as follows:
yi,k=λi,kCi,kxi,k+νi,k, i=1,2 ..., N, (2)
In formula,
Respectively i-th of node of complex network is at kth, k+1 and k-d moment
State variable；D is network time service；For the real number field of the state of complex network dynamic model, n is dimension；xj,kFor complexity
State variable of j-th of the node of network at the kth moment；Measurement for i-th of node at the kth moment exports；
For the real number field of complex network dynamic model output, p is dimension；It is initial value of i-th of node at the kth moment, k
=-d ,-d+1 ..., 0；Γ is connection matrix；wijFor the coupled weight of i-th of node and j-th of node；It is equal
Value is that zero variance is Qi,kProcess noise,For the real number field of complex network dynamic model process noise, q is dimension；It is mean value be zero variance is Ri,kMeasurement noise；N is the node number of complex network；Ai,kFor sytem matrix, Bi,k
For noise profile matrix, Ci,kFor the calculation matrix at k moment,For sytem matrix known dimension and relevant to time lag k-d；
γi,kWith λi,kIt is the stochastic variable for obeying Bernoulli Jacob's distribution, portrays Random Coupling phenomenon and measurement Loss respectively, and full
Sufficient the following conditions:
Wherein,
γi,k+1、λi,k+1It is the stochastic variable for obeying Bernoulli Jacob's distribution, portrays Random Coupling phenomenon respectively and measurement loss is existing
As,For i-th of node the k+1 moment the expected probability that couples at random；It is i-th of node at the k+1 moment
Measurement losing probability；WithValue range be (0,1), Δ γI, k=1Portray the inaccuracy of probability；Prob{}
For probability,For expectation.
3. a kind of with the complex network optimal estimating method coupled at random according to claim 2, it is characterised in that:
The random generation coupling time lag complex network dynamic model that step 1 is established is carried out under event-triggered protocols in the step 2
State estimation；Detailed process are as follows:
Firstly, being directed to i-th of node, following event triggering formula is chosen:
WhereinMeasurement for i-th of node in a upper triggering moment exports,For a corresponding upper triggering moment value,
δi> 0 is to adjust threshold value, and T is transposition；The then next event trigger sequence of i-th of nodeIt is generated by following formula iteration:
WhereinBe positive set of integers, and inf { } is to remove the limit function；
After event trigger mechanism, the true measurement for passing to filter is
For i-th of node of complex network, structural regime estimator:
In formula,
For xi,kIn the one-step prediction at k moment,State estimation for i-th of node at+1 moment of kth,State estimation for i-th of node at the kth-d moment, Ki,k+1For i-th of node the k+1 moment estimation gain square
Battle array,State estimation for i-th of node at the kth moment,State estimation for j-th of node at the kth moment,Measurement for i-th of node at+1 moment of kth exports, Ci,k+1For the calculation matrix at k+1 moment；For i-th of node
In the expected probability coupled at random at k moment.
4. a kind of with the complex network optimal estimating method coupled at random according to claim 3, it is characterised in that:
The one-step prediction error co-variance matrix upper bound of the state estimation of each node i of complex network is calculated in the step 3
∑i,k+1|k；Detailed process are as follows:
The one-step prediction error co-variance matrix upper bound of the state estimation of each node of complex network is calculated according to the following formula
Σi,k+1|k:
In formula,
τ1、τ2、τ4、τ5For intermediate variable, wiFor intermediate variable,Σi,k+1|kIt is i-th of node at the kth moment
The one-step prediction error co-variance matrix upper bound, Σi,k|kIt is i-th of node in the evaluated error covariance matrix upper bound at kth moment,ΓT,Respectively Ai,k,Γ,Bi,k,Transposition；Σi,k-d|k-dExist for i-th of node
The evaluated error covariance matrix upper bound at kth-d moment, Σj,k|kFor j-th of node the kth moment evaluated error covariance square
The battle array upper bound.
5. a kind of with the complex network optimal estimating method coupled at random according to claim 4, it is characterised in that:
The one-step prediction error co-variance matrix upper bound ∑ obtained in the step 4 according to step 3i,k+1|k, calculate complex network
The estimated gain matrix K of each nodei,k+1；Detailed process are as follows:
The estimated gain matrix K of each node of complex network is calculated as follows according to (9) formulai,k+1:
In formula,
For intermediate variable,ηlIt is normal greater than zero
Number, l=1,2,3,4；For ηlIt is inverse,For λi,k+1Variance,Ki,k+1It is i-th
Estimated gain matrix of the node at+1 moment of kth,For Ci,k+1Transposition, I be unit matrix, Ri,k+1For νi,k+1Variance
For.
6. a kind of with the complex network optimal estimating method coupled at random according to claim 5, it is characterised in that:
According to the estimated gain matrix K of each node of complex network calculated in step 4 in the step 6i,k+1, calculate multiple
The evaluated error covariance matrix upper bound ∑ of each node of miscellaneous networki,k+1|k+1；Detailed process are as follows:
Formula are as follows:
Wherein, Σi,k+1|k+1It is i-th of node in the evaluated error covariance matrix upper bound at+1 moment of kth,WithRespectivelyWith Ki,k+1Transposition.
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| CN113242063A (en) * | 2021-04-29 | 2021-08-10 | 江南大学 | Large-scale MIMO channel model modeling method based on random coupling |
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| CN115883408A (en) * | 2022-11-28 | 2023-03-31 | 哈尔滨理工大学 | Multi-rate complex network state estimation method based on compensation |
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| CN109088749A (en) * | 2018-07-23 | 2018-12-25 | 哈尔滨理工大学 | The method for estimating state of complex network under a kind of random communication agreement |
| CN109088749B (en) * | 2018-07-23 | 2021-06-29 | 哈尔滨理工大学 | State estimation method of complex network under random communication protocol |
| CN109728795A (en) * | 2018-12-24 | 2019-05-07 | 哈尔滨理工大学 | Time-varying event under unknown probability situation with loss of data triggers filtering method |
| CN109728795B (en) * | 2018-12-24 | 2022-11-18 | 哈尔滨理工大学 | Time-varying event trigger filtering method with data loss under unknown probability condition |
| CN113242063A (en) * | 2021-04-29 | 2021-08-10 | 江南大学 | Large-scale MIMO channel model modeling method based on random coupling |
| CN115883408A (en) * | 2022-11-28 | 2023-03-31 | 哈尔滨理工大学 | Multi-rate complex network state estimation method based on compensation |
| CN115883408B (en) * | 2022-11-28 | 2023-05-30 | 哈尔滨理工大学 | Multi-rate complex network state estimation method based on compensation |
| CN115859030A (en) * | 2022-11-29 | 2023-03-28 | 哈尔滨理工大学 | Two-step state estimation method under complex coupling |
| CN116088303A (en) * | 2022-12-12 | 2023-05-09 | 哈尔滨理工大学 | Uncertain complex dynamic network state time-varying recursion estimation method |
| CN116542541A (en) * | 2023-02-17 | 2023-08-04 | 威海市天罡仪表股份有限公司 | Thermal dynamic estimation method and system for multi-user radiator of next ladder under coding and decoding strategy |
| CN116542541B (en) * | 2023-02-17 | 2024-03-26 | 威海市天罡仪表股份有限公司 | Thermal dynamic estimation method and system for multi-user radiator of next ladder under coding and decoding strategy |
| CN117544956A (en) * | 2023-11-06 | 2024-02-09 | 哈尔滨理工大学 | Multi-mobile robot security positioning method based on network communication |
| CN117544956B (en) * | 2023-11-06 | 2024-04-30 | 哈尔滨理工大学 | Multi-mobile robot safety positioning method based on network communication |
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