CN108008632A - A kind of method for estimating state and system of the time lag Markov system based on agreement - Google Patents
A kind of method for estimating state and system of the time lag Markov system based on agreement Download PDFInfo
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Abstract
The invention discloses a kind of method for estimating state of the time lag Markov system based on agreement, including：Establish the dynamic model for the nerve network system that time lag and random disturbances are relied on Markov Parameters, sensor nonlinear, mode；Under a given protocol, renewal matrix is established according to the sensor of selected transmission data；According to the renewal matrix and the dynamic model of the nerve network system, the dynamic model of nerve network system under the protocol is established；Estimator is built according to the dynamic model of the nerve network system under the agreement；State estimation error is calculated according to the state vector of the nerve network system under agreement described in the estimated state vector sum of the estimator；Using the state estimation error, estimation augmented system is obtained；Using system stability judgement theorem, according to the gain matrix of the estimation augmented system solution estimator；Bring the gain matrix into the estimator, complete the estimation of the dynamic model of the nerve network system.And system.
Description
Technical field
The present invention relates to field of signal processing, is specifically a kind of state of the time lag Markov system based on agreement and estimates
Count method and system.
Background technology
In decades, due to the outstanding parallel information disposal ability of artificial neural network, adaptive ability and self study energy
Power, has been widely applied to the fields such as brain science, cognitive science and computer science, therefore for the shape of artificial neural network
State estimation problem has had received widespread attention.And noticeable is due to working environment and other influence factors, system
Structure and parameter can occur uncertain change, therefore Markov Parameters are the problems for being subject to everybody to favor in recent years.More
It is worth noting that, in existing nerve network system State Estimation Study, the problem of communication is limited is seldom considered, therefore
Consider the problem of communication is limited emphatically herein, introduce Round-Robin agreements, carry out the sensing of scheduled transmission measurement data
Device.
Current existing method for estimating state cannot consider at the same time limited communication, Markov Parameters, sensor nonlinear,
Mode relies on time lag, random disturbances, and then influences state estimation performance.
The content of the invention
In view of this, the present invention provides a kind of method for estimating state of time lag Markov system based on agreement and is
System, cannot consider that limited communication, Markov Parameters, sensor are non-thread at the same time to solve existing method for estimating state at present
Property, mode rely on time lag, random disturbances, and then influence state estimation performance the problem of.
In a first aspect, the present invention provides a kind of method for estimating state of the time lag Markov system based on agreement, including：
Establish the neutral net system that time lag and random disturbances are relied on Markov Parameters, sensor nonlinear, mode
The dynamic model of system；
Under a given protocol, renewal matrix is established according to the sensor of selected transmission data；
According to the renewal matrix and the dynamic model of the nerve network system, neutral net system under the protocol is established
The dynamic model of system；
Estimator is built according to the dynamic model of the nerve network system under the agreement；
Calculated according to the state vector of the nerve network system under agreement described in the estimated state vector sum of the estimator
State estimation error；
Using the state estimation error, estimation augmented system is obtained；
Using system stability judgement theorem, according to the gain matrix of the estimation augmented system solution estimator；
Bring the gain matrix into the estimator, complete the estimation of the dynamic model of the nerve network system.
Preferably, the given agreement, is Round-Robin agreements；
Under the Round-Robin agreements, renewal matrix is established according to the sensor of selected transmission data.
Preferably, the nerve that time lag and random disturbances are relied on Markov Parameters, sensor nonlinear, mode is established
The K+1 step state vectors of the dynamic model of network system walk state vector, the excitation function with Markov Parameters, tool for K
There is mode to rely on the excitation function of time lag and the linear combination of random disturbances.
Preferably, the nerve that time lag and random disturbances are relied on Markov Parameters, sensor nonlinear, mode is established
The K pacings amount output of the dynamic model of network system walks the linear combination of state vector and sensor nonlinear for K.
Preferably, the excitation function, meets fan-shaped constraints.
Preferably, the K+1 step protocol status vectors of the dynamic model of the nerve network system under the agreement walk augmentation for K
Protocol status vector, the Markov Parameters excitation function with extension dimension, the mode with extension dimension rely on time lag and swash
Encourage function, agreement sensor nonlinear and the linear combination for extending dimension random disturbances；
The K step protocol measure outputs of the dynamic model of nerve network system under the agreement walk augmentation agreement for the K
The linear combination of state vector and the agreement sensor nonlinear.
Preferably, described in the K-1 step protocol measure outputs of the dynamic model of the nerve network system under the agreement are used as
The augmented matrix of the K step state vectors of the dynamic model of nerve network system, forms the K step augmentation protocol status vector.
Preferably, using system stability judgement theorem, the estimator is obtained by solving one group of convex optimization problem
Gain matrix.
Preferably, the convex optimization problem is linear matrix inequality condition when making the system reach index ultimate boundness.
Second aspect, the present invention provide a kind of condition estimating system of the time lag Markov system based on agreement, including：
Memory and processor and storage on a memory and the computer program that can run on a processor, the calculating
Machine program is a kind of such as above-mentioned method for estimating state of the time lag Markov system based on agreement, described in the processor execution
Following steps are realized during program：
Establish the neutral net system that time lag and random disturbances are relied on Markov Parameters, sensor nonlinear, mode
The dynamic model of system；
Under a given protocol, renewal matrix is established according to the sensor of selected transmission data；
According to the renewal matrix and the dynamic model of the nerve network system, neutral net system under the protocol is established
The dynamic model of system；
Estimator is built according to the dynamic model of the nerve network system under the agreement；
Calculated according to the state vector of the nerve network system under agreement described in the estimated state vector sum of the estimator
State estimation error；
Using the state estimation error, estimation augmented system is obtained；
Using system stability judgement theorem, according to the gain matrix of the estimation augmented system solution estimator；
Bring the gain matrix into the estimator, complete the estimation of the dynamic model of the nerve network system.
The present invention at least has the advantages that：
The present invention provides a kind of method for estimating state and system of the time lag Markov system based on agreement, considers at the same time
Communication is limited, Markov Parameters, sensor nonlinear, mode rely on time lag, random disturbances are to the shadow of state estimation performance
Ring, stability criterion completely make use of the effective information of time lag, compared to the state estimation side of existing neural network dynamic system
Method, method for estimating state of the invention can handle Markov Parameters, sensor nonlinear, mode at the same time under communication protocol
Time lag, random disturbances are relied on, the gain matrix of estimator is solved according to estimation augmented system, reach the mesh of anti-nonlinear disturbance
, and have the advantages that to be easy to solve with realizing.With solve at present existing method for estimating state cannot consider at the same time communication by
Limit, Markov Parameters, sensor nonlinear, mode rely on time lag, random disturbances, and then influence asking for state estimation performance
Topic.
Brief description of the drawings
By below with reference to description of the attached drawing to the embodiment of the present invention, above-mentioned and other purpose of the invention, feature and
Advantage is apparent, in the accompanying drawings：
Fig. 1 is that a kind of flow of the method for estimating state of the time lag Markov system based on agreement of the embodiment of the present invention is shown
It is intended to；
Fig. 2 is method for estimating state and the system horse of a kind of time lag Markov system based on agreement of the embodiment of the present invention
The evolutionary process schematic diagram of Er Kefu chains；
Fig. 3 is a kind of method for estimating state and system of the time lag Markov system based on agreement of the embodiment of the present invention
Virtual condition track x1(k) and its state estimation trackComparison diagram；
Fig. 4 is a kind of method for estimating state and system of the time lag Markov system based on agreement of the embodiment of the present invention
Virtual condition track x2(k) and its state estimation trackComparison diagram；
Fig. 5 is a kind of method for estimating state and system of the time lag Markov system based on agreement of the embodiment of the present invention
State x1(k) evaluated error track e1(k)；
Fig. 6 is a kind of method for estimating state and system of the time lag Markov system based on agreement of the embodiment of the present invention
State x2(k) evaluated error track e2(k)。
Embodiment
Below based on embodiment, present invention is described, but what deserves to be explained is, the present invention is not limited to these realities
Apply example.Below to the present invention detailed description in, it is detailed to describe some specific detail sections.However, for not detailed
The part described to the greatest extent, those skilled in the art can also understand the present invention completely.
In addition, it should be understood by one skilled in the art that the attached drawing provided simply to illustrate that the purpose of the present invention,
Feature and advantage, attached drawing are not to be actually drawn to scale.
Meanwhile unless the context clearly requires otherwise, the otherwise " comprising " in entire disclosure and claims, "comprising" etc.
Similar word should be construed to the implication included rather than exclusive or exhaustive implication；That is, it is " including but not limited to "
Implication.
In the present invention, MTThe transposition of representing matrix M, M-1The inverse matrix of representing matrix M.Represent Euclidean n-space,Represent the set of all n × m ranks real matrixes.Represent integer set.I and 0 represents unit matrix, zero moment respectively
Battle array.Matrix P>0 represents that P is real symmetric tridiagonal matrices,WithThe mathematic expectaion and y bars of stochastic variable x is represented respectively
The mathematic expectaion of stochastic variable x under part.| | x | | the Euclid norm of representation vector x.diag{A1,A2,…,AnRepresent diagonal
Block is matrix A1,A2,…,AnBlock diagonal matrix, symbol * represents the omission of symmetrical item in symmetrical block matrix.If M is represented
One symmetrical matrix, then λmax(M),λmin(M) maximum and minimal eigenvalue of M is represented respectively.Mod (a, b) represents complementation fortune
Calculate.δ (a) represents a binary function, and as a=0, its value is 1, is otherwise 0.SymbolRepresent Kronecker product computing.If somewhere does not have clear and definite specified matrix dimension in text, assume that its dimension is adapted to the algebraically of matrix to transport
Calculate.
Fig. 1 is that a kind of flow of the method for estimating state of the time lag Markov system based on agreement of the embodiment of the present invention is shown
It is intended to.As shown in Figure 1, a kind of method for estimating state of the time lag Markov system based on agreement, including：Step 101 is established
The dynamic model of the nerve network system of time lag and random disturbances is relied on Markov Parameters, sensor nonlinear, mode；
Step 102 establishes renewal matrix under a given protocol, according to the sensor of selected transmission data；Step 103 according to it is described more
The dynamic model of new matrix and the nerve network system, establishes the dynamic model of nerve network system under the protocol；Step
104 build estimator according to the dynamic model of the nerve network system under the agreement；Step 105 is estimated according to the estimator
The state vector for counting state vector and the nerve network system under the agreement calculates state estimation error；Step 106 utilizes institute
State estimation error is stated, obtains estimation augmented system；Step 107 utilizes system stability judgement theorem, is increased according to the estimation
The gain matrix of estimator described in wide system solution；Step 108 brings the gain matrix into the estimator, completes the god
The estimation of dynamic model through network system.
Further, in Fig. 1, when step 101 is established with Markov Parameters, sensor nonlinear, mode dependence
The stagnant and dynamic model of the nerve network system of random disturbances.Further, in Fig. 1, establish with Markov Parameters, pass
The K+1 step state vectors of dynamic model for the nerve network system that sensor is non-linear, mode relies on time lag and random disturbances are K steps
State vector, the excitation function with Markov Parameters, with mode rely on time lag excitation function and random disturbances line
Property combination.
Further, in Fig. 1, establish and rely on time lag and random with Markov Parameters, sensor nonlinear, mode
The K pacings amount output of the dynamic model of the nerve network system of interference walks linear group of state vector and sensor nonlinear for K
Close.
Further, in Fig. 1, the excitation function, meets fan-shaped constraints.
Specifically, the god that time lag and random disturbances are relied on Markov Parameters, sensor nonlinear, mode is established
Dynamic model through network system, its state space form are：
System primary condition is：
In formula,The state vector of expression system；Represent excitation function, meet fan-shaped
Constraints；For positive definite diagonal matrix,For weights connection matrix,For
Know and be adapted to enclose several matrixes；τ (r (k)) relies on time lag for mode, meets For the measurement of system
Output；For sensor nonlinear, meet fan-shaped constraints；ω (k) is white Gaussian noise, is met:
R (k) is Markov Chain, and transfer probability is Θ=[θij]s×s, wherein θij>=0 and
In order to represent convenient, r (k)=i (i ∈ S) will be expressed as below in we, that is, Z (r (k)) will be indicated as Zi。
Step 102 establishes renewal matrix under a given protocol, according to the sensor of selected transmission data；To update matrix, ζ (k) ∈ { 1,2 ..., m } are quilt
The sensor of selection transmission data.
Step 103 establishes god under the protocol according to the renewal matrix and the dynamic model of the nerve network system
Dynamic model through network system.
Further, in Fig. 1, the given agreement, is Round-Robin agreements；In the Round-Robin agreements
Under, renewal matrix is established according to the sensor of selected transmission data.
Specifically, according to dynamic model in step 101 and the scheduling principle of Round-Robin agreements, establish
The dynamic model of nerve network system under Round-Robin agreements, its spatial model are as follows：
Wherein：
Step 104 builds estimator according to the dynamic model of the nerve network system under the agreement.
Further, in Fig. 1, the dynamic model of the nerve network system under the agreement K+1 walk protocol status to
Measure and walk augmentation protocol status vector, the Markov Parameters excitation function with extension dimension, the mode with extension dimension for K
Rely on time lag excitation function, agreement sensor nonlinear and the linear combination for extending dimension random disturbances；
The K step protocol measure outputs of the dynamic model of nerve network system under the agreement walk augmentation agreement for the K
The linear combination of state vector and the agreement sensor nonlinear.
Further, in Fig. 1, the K-1 step protocol measures of the dynamic model of the nerve network system under the agreement are defeated
Go out the augmented matrix of the K step state vectors as the dynamic model of the nerve network system, form the K steps augmentation agreement shape
State vector.
Specifically, in step 103 under the protocol have Markov Parameters, sensor nonlinear, mode rely on
The nerve network system of time lag and random disturbances carries out state estimation, its estimator form is：
In formula,ForIn the state estimation at k moment,ForEstimation function,To be non-
Linear functionEstimation function,State estimation gain to be asked.
The state of nerve network system under step 105 agreement according to the estimated state vector sum of the estimator to
Amount calculates state estimation error.According to step 104 to Markov Parameters, sensor nonlinear, mode rely on time lag and
The state estimation of the nonlinear dynamical model of random disturbances, calculates state estimation error：
In formula, e (k) is the evaluated error error at k moment, and e (k+1) is the evaluated error error at k+1 moment.
Step 106 utilizes the state estimation error, obtains estimation augmented system；Specifically, according to the shape of step 105
State evaluated error, obtains state estimation augmented system：
In above formula：
Step 107 utilizes system stability judgement theorem, and the increasing of the estimator is solved according to the estimation augmented system
Beneficial matrix.
Further, in Fig. 1, using system stability judgement theorem, institute is obtained by solving one group of convex optimization problem
State the gain matrix of estimator.
Further, in Fig. 1, the convex optimization problem is that matrix when making the system reach the final Bounded Index of index comes
Obtain the gain matrix of the estimator.
Specifically, using the state estimation augmented system of step 106, with liapunov's theorem of stability and solve
One group of convex optimization problem obtains estimator gain matrix K：
By formula：
According to Lyapunov theorem of stability, matrix when making the system reach the final Bounded Index of index is tried to achieveWithValue, pass through formula：
Calculate state estimation gain matrix.
Matrix concrete form in formula (6)-(8)：
In formula：
For be adapted to digit matrix, γ,0<κ<1 is scalar,
ρ1i,ρ2i,ρ3iFor a series of constants,For known normal matrix.Diag { ... } represents diagonal matrix, ETFor square
The transposition of battle array E, ETXTFor matrix ETWith matrix XTProduct,Represent Kronecker product computing.
Step 108 brings the gain matrix into the estimator, completes the dynamic model of the nerve network system
Estimation.Specifically, estimator gain matrix K step 107 obtained substitutes into the state estimation formula in step 3, realization pair
The nerve network system progress state that time lag and random disturbances are relied on Markov Parameters, sensor nonlinear, mode is estimated
Meter.
Fig. 2 is method for estimating state and the system horse of a kind of time lag Markov system based on agreement of the embodiment of the present invention
The evolutionary process schematic diagram of Er Kefu chains, as seen from the figure, at different moments, the mode residing for system is that saltus step occurs,
After saltus step, the parameter of system can also change therewith.
In addition, the present invention provides a kind of condition estimating system of the time lag Markov system based on agreement, including：
Memory and processor and storage on a memory and the computer program that can run on a processor, the calculating
Machine program is a kind of such as above-mentioned method for estimating state of the time lag Markov system based on agreement, described in the processor execution
Following steps are realized during program：Step 101 establish with Markov Parameters, sensor nonlinear, mode rely on time lag and with
The dynamic model of the nerve network system of machine interference；Step 102 under a given protocol, according to it is selected transmission data sensor
Establish renewal matrix；Step 103 is established under the protocol according to the renewal matrix and the dynamic model of the nerve network system
Nerve network system dynamic model；Step 104 is estimated according to the dynamic model of the nerve network system under agreement structure
Gauge；The state vector of nerve network system under step 105 agreement according to the estimated state vector sum of the estimator
Calculate state estimation error；Step 106 utilizes the state estimation error, obtains estimation augmented system；Step 107 utilizes system
Judgement of stability theorem, the gain matrix of the estimator is solved according to the estimation augmented system；Step 108 is by the gain
Matrix brings the estimator into, completes the estimation of the dynamic model of the nerve network system.Embodiment can refer to Fig. 1
In description.
The present invention is for a kind of method for estimating state and system of the time lag Markov nerve network system based on agreement
Further verification, the lyapunov stability theory described in step 107 is：
Wherein：
In formula,For the Liapunov function at k moment,For the k+1 moment
Liapunov function,ForTransposition,ForTransposition.
Emulated using the method for the invention：(assuming that n=2, m=2, i ∈ { 1,2 })
System parameter settings are as follows：
Excitation function and sensor nonlinear are as follows：
State estimator gain solves：
Formula (6)-(8) are solved, and obtain state estimator gain matrixFor following form：
State estimator effect, illustrates in Fig. 3-Fig. 6.
Fig. 3 is a kind of method for estimating state and system of the time lag Markov system based on agreement of the embodiment of the present invention
Virtual condition track x1(k) and its state estimation trackComparison diagram.Fig. 4 be the embodiment of the present invention it is a kind of based on agreement when
The method for estimating state of stagnant Markov system and the virtual condition track x of system2(k) and its state estimation trackContrast
Figure.As shown in Figure 3 and Figure 4, the state estimation track of system All can be with tracing system state trajectory x1(k), x2
(k), and the final equalization point for all leveling off to system, illustrate that invented state estimator design method is effective.
Fig. 5 is a kind of method for estimating state and system of the time lag Markov system based on agreement of the embodiment of the present invention
State x1(k) evaluated error track e1(k).Fig. 6 is a kind of time lag Markov system based on agreement of the embodiment of the present invention
The state x of method for estimating state and system2(k) evaluated error track e2(k).As shown in Figure 5 and Figure 6, the evaluated error of system
e1(k), e2(k) it is bounded, error fluctuates between [- 2,2], thus furtherly understands proposed method for estimating state
Validity and applicability, it can make system reach the state of ultimate boundness.
By Fig. 3 to Fig. 6 as it can be seen that under communication protocol, for Markov Parameters, sensor nonlinear, mode according to
Rely the nerve network system of time lag and random disturbances pin, the state estimator design method invented can effectively estimate target
State.
The present invention considers that communication is limited, Markov Parameters, sensor nonlinear, mode rely on time lag, random at the same time
The influence to state estimation performance is disturbed, construction Liapunov function completely make use of the effective information of time lag, compared to
The method for estimating state of some neural network dynamic systems, method for estimating state of the invention can be located at the same time under communication protocol
Manage Markov Parameters, sensor nonlinear, mode and rely on time lag, random disturbances, draw dependence linear matrix inequality solution
Method for estimating state, achieve the purpose that anti-nonlinear disturbance, and have the advantages that to be easy to solve with realizing.
Obviously, those skilled in the art should be understood that above-mentioned each unit of the invention or each step can be with general
Computing device realize that they can be concentrated on single computing device, or be distributed in multiple computing devices compositions
On network, alternatively, they can be realized with the program code that computing device can perform, it is thus possible to be stored in
Performed in storage device by computing device, they are either fabricated to each integrated circuit unit respectively or by them
Multiple units or step be fabricated to single integrated circuit unit to realize.In this way, the present invention be not restricted to it is any specific hard
Part and software combine.
Embodiment described above only expresses embodiments of the present invention, its description is more specific and detailed, but can not
Therefore it is interpreted as the limitation to the scope of the claims of the present invention.It should be pointed out that to those skilled in the art,
On the premise of not departing from present inventive concept, some deformations, equal replacement can also be made, improved etc., these belong to the present invention
Protection domain.Therefore, the protection domain of patent of the present invention should be determined by the appended claims.
Claims (10)
- A kind of 1. method for estimating state of the time lag Markov system based on agreement, it is characterised in that including：Establish the nerve network system with Markov Parameters, sensor nonlinear, mode dependence time lag and random disturbances Dynamic model；Under a given protocol, renewal matrix is established according to the sensor of selected transmission data；According to the renewal matrix and the dynamic model of the nerve network system, nerve network system under the protocol is established Dynamic model；Estimator is built according to the dynamic model of the nerve network system under the agreement；State is calculated according to the state vector of the nerve network system under agreement described in the estimated state vector sum of the estimator Evaluated error；Using the state estimation error, estimation augmented system is obtained；Using system stability judgement theorem, according to the gain matrix of the estimation augmented system solution estimator；Bring the gain matrix into the estimator, complete the estimation of the dynamic model of the nerve network system.
- 2. a kind of method for estimating state of the time lag Markov system based on agreement, its feature exist according to claim 1 In：The given agreement, is Round-Robin agreements；Under the Round-Robin agreements, renewal matrix is established according to the sensor of selected transmission data.
- 3. a kind of method for estimating state of the time lag Markov system based on agreement, its feature exist according to claim 1 In：Establish the nerve network system with Markov Parameters, sensor nonlinear, mode dependence time lag and random disturbances The K+1 step state vectors of dynamic model walk state vector, the excitation function with Markov Parameters for K, are relied on mode The excitation function of time lag and the linear combination of random disturbances.
- 4. a kind of method for estimating state of the time lag Markov system based on agreement, its feature exist according to claim 1 In：Establish the nerve network system with Markov Parameters, sensor nonlinear, mode dependence time lag and random disturbances The K pacings amount output of dynamic model walks the linear combination of state vector and sensor nonlinear for K.
- 5. a kind of method for estimating state of the time lag Markov system based on agreement, its feature exist according to claim 3 In：The excitation function, meets fan-shaped constraints.
- 6. a kind of method for estimating state of the time lag Markov system based on agreement, its feature exist according to claim 1 In：The dynamic model of nerve network system under the agreement K+1 step protocol status vector for K walk augmentation protocol status to Amount, the Markov Parameters excitation function with extension dimension, the mode with extension dimension rely on time lag excitation function, agreement The linear combination of sensor nonlinear and extension dimension random disturbances；The K step protocol measure outputs of the dynamic model of nerve network system under the agreement walk augmentation protocol status for the K The linear combination of agreement sensor nonlinear described in vector sum.
- 7. a kind of method for estimating state of the time lag Markov system based on agreement, its feature exist according to claim 6 In：The K-1 step protocol measure outputs of the dynamic model of nerve network system under the agreement are used as the nerve network system Dynamic model K step state vectors augmented matrix, form K step augmentation protocol status vector.
- 8. a kind of method for estimating state of time lag Markov system based on agreement according to claims 1 to 7, its feature It is：Using system stability judgement theorem, by the gain matrix for solving one group of convex optimization problem acquisition estimator.
- 9. a kind of method for estimating state of the time lag Markov system based on agreement, its feature exist according to claim 8 In：The convex optimization problem is linear matrix inequality condition when making the system reach index ultimate boundness.
- A kind of 10. condition estimating system of the time lag Markov system based on agreement, it is characterised in that including：Memory and processor and storage on a memory and the computer program that can run on a processor, the computer journey Sequence is a kind of method for estimating state of the time lag Markov system based on agreement as described in any one of claim 1~9, described Processor realizes following steps when performing described program：Establish the nerve network system with Markov Parameters, sensor nonlinear, mode dependence time lag and random disturbances Dynamic model；Under a given protocol, renewal matrix is established according to the sensor of selected transmission data；According to the renewal matrix and the dynamic model of the nerve network system, nerve network system under the protocol is established Dynamic model；Estimator is built according to the dynamic model of the nerve network system under the agreement；State is calculated according to the state vector of the nerve network system under agreement described in the estimated state vector sum of the estimator Evaluated error；Using the state estimation error, estimation augmented system is obtained；Using system stability judgement theorem, according to the gain matrix of the estimation augmented system solution estimator；Bring the gain matrix into the estimator, complete the estimation of the dynamic model of the nerve network system.
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Cited By (6)
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| CN108732926A (en) * | 2018-06-05 | 2018-11-02 | 东北石油大学 | Networked system method for estimating state based on insufficient information |
| 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 |
| CN111025914A (en) * | 2019-12-26 | 2020-04-17 | 东北石油大学 | Neural network system remote state estimation method and device based on communication limitation |
| CN111381498A (en) * | 2020-03-09 | 2020-07-07 | 常熟理工学院 | Expectation maximization identification method of multi-sensor based on multi-rate variable time-lag state space model |
| CN111901773A (en) * | 2020-06-23 | 2020-11-06 | 杭州电子科技大学 | Industrial park air quality detection method |
| CN113301673A (en) * | 2021-05-25 | 2021-08-24 | 江南大学 | Distributed filtering method, device, equipment and storage medium for wireless sensor network |
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